dataesr/scientific-paragraphs-categorization huggingface dataset:
In the absence of such policies it is possible that even greater levels of superspreading could be expected. For example, findings from Shenzhen (China)  13  estimated roughly comparable levels of SARS-CoV-2 overdispersion using contact tracing data (k = 0. 58, 95% CI, 0. 35-1. 18), but a study from Singapore 14 reported k = 0. 11 (95% CI, 0. 05-0. 25). Other studies utilizing global cluster size datasets have estimated similarly high potential for SARS-CoV-2 superspreading (k = 0. 10, 95% CI, 0. 05-0. 20), which together suggest that as few as 10% of cases could account for 80% of all SARS-CoV-2 transmission  15. However, such extreme degrees of overdispersion can be advantageous to disease control efforts if interventions can effectively target the core high-risk groups or settings responsible for the majority of transmission  16, 17.
Interestingly, our dataset did not contain any instances of nosocomial transmission, which has been observed for SARS-CoV-2  26, 27. It should be noted, however, that hospital infection control in Hong Kong substantially strengthened following the 2002-2003 SARS epidemic. Seroprevalence studies among frontline healthcare workers in Hong Kong will be able to confirm the effectiveness of infection control and whether any unrecognized nosocomial transmission has occurred. Future studies could also incorporate SARS-CoV-2 genetic sequence data to assist in uncovering hidden chains of transmission within the city (including within hospitals) and to discretize clusters more accurately. Overall, there is substantial heterogeneity in the transmissibility of SARS-CoV-2 infection and therefore potential for superspreading with COVID-19.
Characterization of clusters and chains of SARS-CoV-2 transmission. Using case line lists and contact tracing data collected in Microsoft Excel by the Centre for Health Protection (CHP) of the Department of Health in Hong Kong, we characterized clusters of SARS-CoV-2 infections and chains of transmission within clusters up to 7 May 2020. All cases of SARS-CoV-2 infection were laboratory-confirmed via nasopharyngeal swab and PCR with reverse transcription (RT-PCR). In Hong Kong, all contacts of a confirmed case are traced and sent to mandatory government quarantine facilities for 14 days if negative at identification, or admitted to hospital if testing positive, regardless of symptom presentation. A close contact was defined as someone with prolonged face-to-face interaction with a confirmed case (with or without prior symptoms) in excess of 2 h if both persons were wearing a mask or 15 min without mask usage.
Clusters of solely imported cases were characterized as overseas-acquired clusters if all cases were determined to have acquired SARS-CoV-2 infection overseas as before. Cases not linked to any cluster were categorized as sporadic local cases or sporadic imported cases if infection was acquired locally or overseas, respectively. For cases within local and imported clusters (excludes overseas clusters), probable infector-infectee transmission pairs and chains of transmission within clusters were determined from reported contact histories data provided by the CHP. Within clusters, the case with the earliest onset date was considered the source of subsequent cases where contact was confirmed within the primary cluster setting. Subsequent transmission generations and clusters settings (secondary, tertiary, quaternary and so on) were traced back to the primary cluster case based on the reported contact histories only and did not rely on symptom onset dates, meaning that instances of asymptomatic or pre-symptomatic transmission were possible from cases intermediate to the chain of transmission.
We modeled the relationship between the delay in days from symptom onset to confirmation and the number of secondary cases per infector by linear regression as a proxy for individual duration of potential infectiousness in the community (n = 98 infectors, including one travel-related infector but excluding two asymptomatic infectors whose delay could not be calculated). The mean delay from symptom onset to confirmation of 269 symptomatic cases within local clusters was also assessed by linear regression by cluster size with (10 discrete cluster sizes) and without (eight discrete cluster sizes) excluding the largest two clusters. Serial interval and observed offspring distribution. We calculated serial intervals as the difference between the symptom onset dates of each infector-infectee pair, excluding asymptomatic cases, and fitted normal, lognormal, gamma and Weibull distributions using the R package 'fitdistrplus' by maximum-likelihood, excluding seven non-positive intervals for the latter three distributions.
Superspreading and individual variance of SARS-CoV-2 transmission. Following the approach described by Lloyd Smith et al. , estimates of the effective reproductive number (R) were determined from the mean of the negative binomial distribution fit to the observed offspring distribution, and the degree of transmission heterogeneity from the corresponding dispersion parameter k (ref. 28 ). This was performed for all resolved pairs within clusters, including later generation pairs where prior transmission chains could not be determined from epidemiological data alone, which were excluded from the primary analysis. Owing to potential biases affecting the observed offspring distributions resulting from these exclusions, we performed a sensitivity analysis by generated two additional offspring distributions based on presumed but unconfirmed transmission scenarios (described in the results) where evidence was indicative but insufficient to fully resolve all pairs within clusters in the primary analysis.
Acknowledgements We thank the  Department of Health of the Food and Health Bureau of the Government of Hong Kong  for conducting the outbreak investigation and providing the data for the analysis. This project was supported by the  Health and Medical Research Fund, Food and Health Bureau, Government of the Hong Kong Special Administrative Region (SAR ; grant no. COVID190118 ) and the  Theme-based Research Scheme  (project no. T11-712/19-N ) of the  Research Grants Council  of the  Hong Kong SAR Government.
Acknowledgement The work of  G. Hu  is supported by the  NSFC  grant (No. 11671028 ) and  NSAF  grant (No. U1530401 ). The work of  Y. Kian  is supported by the  French National Research Agency ANR  (project  MultiOnde ) grant  ANR-17-CE40-0029. The authors would like to thank  Yikan Liu  for his remarks that allow to improve Theorem 3. The second author would like to thank the  Beijing Computational Science Research Center , where part of this article was written, for its kind hospitality.
Finally, step (f) consists in the actual measurement of the velocity profile by means of the reconstruction method  [13]. All the operations described below were implemented by means of Matlab ® software (The MathWorks Inc. , Natick, MA, USA) and were systematically applied to all the recorded images. The way step (a) is performed was thoroughly described in the previous section. The next steps of the procedure are discussed below in detail. Micromachines 2020, 11, x 11 of 32 flow conditions is of great help for the validation of MTV velocity reconstructions. As the Knudsen number at the test section increased, the ratio of the slip velocity to the average velocity was expected to raise from 2. 5% to 10%.
Finally, step (f) consists in the actual measurement of the velocity profile by means of the reconstruction method  [13]. All the operations described below were implemented by means of Matlab ® software (The MathWorks Inc. , Natick, MA, USA) and were systematically applied to all the recorded images. The way step (a) is performed was thoroughly described in the previous section. The next steps of the procedure are discussed below in detail. (b) Wall detection: the strategy employed in this work for the identification of the channel walls was based on the investigation of the light emission provided by the top and bottom Suprasil ® windows. The fluorescence of the silica is short-lived but very strong in the first few nanoseconds after the laser excitation. By recording the light emission of the silica with no tracer vapor inside the channel, the spots of maximum intensity on the windows correspond to the locations of entrance and exit of the laser beam, and, therefore, they represent the position on the image of the intersection between the tagged line and the channel walls.
As it has been done in previous works  [12, 14, 20] , the Gaussian fitting applied to each horizontal line of pixels at any position  =   is 𝑓(𝑥) = 𝑎 2 √2𝜋𝑎 3 𝑒 - (𝑥-𝑎 4 ) 2 2𝑎 3 + 𝑎 1 , (1) where the fitting parameters  1 ,  2 ,  3 , and  4 represent, respectively, the offset, the amplitude, the variance, and the peak position. Thus,  4, corresponds to the displacement  , at each discrete location. Figure  11   (f) Velocity reconstruction: the final step is the application of the velocity reconstruction algorithm to the set of displacement data  , determined in step (e). The reconstruction method of Frezzotti et al. [13]  provides the velocity profile that makes the numerical displacement   () fit at best the displacement dataset  ,. The numerical solving of the diffusion-advection equation requires providing the channel height  and the diffusion coefficient  characterizing the tracer diffusion through the background gas.
The reconstruction method is sensitive to both parameters. For a given velocity profile () and a given diffusion coefficient , the displacement profile   () at a certain time  has a thickness, defined as Δ = max   () -min   (), that is proportional to  2  [13]. The value of the wall distance  used in defining the mathematical domain needs, therefore, to be as accurate as possible in order to have a correct velocity reconstruction. As discussed in step (b), the localization of the channel walls on the image cannot be done with the highest accuracy and is (f) Velocity reconstruction: the final step is the application of the velocity reconstruction algorithm to the set of displacement data s x,j determined in step (e). The reconstruction method of Frezzotti et al. [13]  provides the velocity profile that makes the numerical displacement s x (y) fit at best the displacement dataset s x,j.
5 × 10 -6 m 3 and it has been accurately calculated by measuring its weight when filled with water. By considering that at the initial and final thermodynamic states the air is at ambient temperature, the volume of the reservoir is calculated from p v V + p atm V = p eq V + V. (3) This experiment has been repeated several times for a statistical characterization of the measurement uncertainty. The volume of the upstream reservoir has been measured to be V = 0. 176 m 3 with a relative uncertainty of 0. 08%. The evaluation of the derivative dp 1 dt is carried out by fitting the pressure data p 1 (t) with a proper analytical function. The most suitable fitting function for the pressure relaxation characterizing the type of experimental setup employed in this work is a series of N exponential functions: p 1 = N i=1 a i e -t/τ i.
Experimental Results The presentation of the experimental data was organized in the following manner. Section 6. 1 reported MTV measurements of argon flows in non-rarefied conditions and at pressures between 30 and 6 kPa. Section 6. 2 presented MTV data of helium flow in rarefied conditions and at pressures between 1. 6 kPa 900 Pa. In Section 6. 3, the comparison between MTV and CV data was analyzed for the cases presented in Sections 6. 1 and 6. 2. The kinetic diameter for the acetone molecule used for all the calculations was d = 470 pm, as reported in Van der Perre et al. [24] , which is also similar to the values reported in other recent works  [25, 26]. Moreover, since the investigated gas flow can be considered as isothermal, the mean free path of the mixture was estimated by modeling molecular interactions through hard sphere potentials.
6. 1. 2. Experiments at Low Pressure (p m = 6. 5 kPa) Argon-acetone mixture flows were also investigated by MTV at lower pressures, in order to verify the reconstruction method in non-rarefied conditions but with higher molecular diffusion. The images of Figure  15  illustrate MTV acquisitions carried out at an average pressure of 6. 5 kPa and at ∆t = 20, 30, 40, and 50 µs. All thermodynamic characteristics of the observed experimental flow are reported in Table  2. As for the case at higher pressure, the thermodynamic properties associated to each image were not exactly the same but, again, quite similar. Since the gas pressure was 4 times lower than the case presented previously, the Knudsen number was 4 times higher. Figure  16a ,b reports, respectively, the displacement data with the corresponding numerical displacement profiles and the reconstructed velocity profiles.
Comparison between MTV and CV Data In this section, MTV and CV techniques were cross-validated by comparison of the measured average velocity at the test section. Since the average velocity u CV is derived from the mass flow rate data through analytical formulas, the following data comparison represents also a validation of the theoretical models of the pressure distribution along the channel length of Arkilic et al. [22]  and the velocity distribution across the channel section of Ebert and Sparrow  [19]. In order to make the data comparison more meaningful, the results were also provided with estimated uncertainty values. The uncertainty ranges reported in Table  6 , Table  7 , and Table  8  correspond to ± 2 standard deviations, with an associated confidence interval of 95%. For the CV measurements, the uncertainty on u CV was determined by the uncertainty on the average velocity u CV,2D over the cross-section.
Although the local velocity results provided by the reconstruction method depend on the accuracy of the height H and the diffusion coefficient D used in the algorithm, the average velocity u MTV only depends on the measured mean displacement s x and the delay ∆t. This explained why, even though the MTV velocity profiles might be inaccurate, the reconstruction method always provided profiles with an average velocity that is identical to an average velocity computed simply as u MTV = s x ∆t. (8) As for Equation (  7 ), s x and ∆t are assumed to be statistically uncorrelated. The mean displacement s x was calculated from the displacement profiles s x (y) provided by the reconstruction method. For most of the experimental measurements presented in Sections 6. 1 and 6. 2, the fluctuations of the displacement data point s x,j around the numerical solution s x (y) were relatively limited; therefore the computation of s x from the displacement data practically provided the same results.
Experiments in Helium-acetone Flows As for the case of argon-acetone flow, even though the reconstructed velocity was inaccurate, the average velocity was well extracted from the displacement data and was always approximately the same, regardless of the delay considered. Tables  8  and 9  compared the values of u MTV with those of u CV. Since the helium-acetone flow was characterized by much higher mean molecular displacements, the relative standard deviation on u MTV given by the CCD resolution was at most 1. 7%, for the data at 1. 6 kPa, and 2. 4%, for the data at 920 Pa. The highest values of s x were recorded for the helium flow at 1. 6 kPa, where it varied from 0. 89 mm at ∆t = 20 µs to 2. 15 mm at ∆t = 50 µs, which was more than 4 times the displacement imaged in the argon-acetone flows.
For the case at 920 Pa, the molecular slip at the wall represented between 85% and 90% of the mean molecular displacement. This might explain why the difference between CV and MTV measurements were higher than for the case at 1. 6 kPa, where the molecular slip at the wall contributed to the mean displacement at about 75%. However, the 4 values of u MTV were measured by repeating the experiment 4 different times, and the MTV velocity measured at different delays varied around the average value of 2% for the data at 1. 6 kPa and 4. 5% for the data at 920 Pa. These variations were of the same order of magnitude of the estimated variations due to fluctuations of the thermodynamic conditions characterizing the 20 averaged images (Section 6. 2). As it can be noted from Tables  8  and 9 , the value of u MTV was always higher than that of u CV , and their relative deviation was on average about 6.
2% for the flow at 1. 6 kPa and 11. 6% for the flow at 920 Pa. This suggests the existence of a constant biasing error affecting the measurements. While MTV measurements are only based on the optical tracking of the gas displacement, the calculation of the CV average velocity makes use of the measured dimensions of the channel cross-section. At working pressures of the order of 1 kPa, the distance between the Suprasil ® windows might be slightly reduced by the higher external pressure. Therefore, the bias between CV and MTV average velocities was probably partly due to the uncertainty on the value of H. The idea that the compression of the channel height should be higher at lower pressures was reflected by the higher differences between CV and MTV data obtained for the case at 920 Pa. Variations of 6.
2% for the flow at 1. 6 kPa and 11. 6% for the flow at 920 Pa. This suggests the existence of a constant biasing error affecting the measurements. While MTV measurements are only based on the optical tracking of the gas displacement, the calculation of the CV average velocity makes use of the measured dimensions of the channel cross-section. At working pressures of the order of 1 kPa, the distance between the Suprasil® windows might be slightly reduced by the higher external pressure. Therefore, the bias between CV and MTV average velocities was probably partly due to the uncertainty on the value of. The idea that the compression of the channel height should be higher at lower pressures was reflected by the higher differences between CV and MTV data obtained for the case at 920 Pa. Variations of 6.
3% from the average velocity measured by the CV technique. For the flow at 920 Pa,  ̅′  = 27. 28 m/s, which was smaller than the average of the reconstructed velocity profiles by 10% but differed only by 2. 2% from the CV value. The MTV velocity that resulted from the linear fitting was likely more accurate than the average velocities measured from each MTV image individually, since more displacement data were used at once. This final result suggests the idea that the reconstruction algorithm might provide more accurate velocity profiles if properly modified to allow processing all the displacement data at different delays simultaneously.
Discussions and Conclusions This work demonstrated a successful application of the MTV technique to low-pressure gas flows in a millimetric channel. To the best of our knowledge, the images of Figures  17  and 18  are the A linear interpolation of these data provided a second measurement for the average velocity. For the case at 1. 6 kPa, this second measurement was u MTV = 42. 2 m/s, which differed by about 4% from the average of the reconstructed velocity profiles, and only 2. 3% from the average velocity measured by the CV technique. For the flow at 920 Pa, u MTV = 27. 28 m/s, which was smaller than the average of the reconstructed velocity profiles by 10% but differed only by 2. 2% from the CV value. The MTV velocity that resulted from the linear fitting was likely more accurate than the average velocities measured from each MTV image individually, since more displacement data were used at once.
Discussions and Conclusions This work demonstrated a successful application of the MTV technique to low-pressure gas flows in a millimetric channel. To the best of our knowledge, the images of Figures  17  and 18  are the first flow visualizations ever reported of a gas flow in the slip regime and in a confined domain. MTV data were reported for gas flows with Knudsen numbers as high as Kn = 0. 014. For the case of helium-acetone flow, a slip velocity at the wall of about 2 m/s is expected when a Maxwell boundary condition is used, which indicates that rarefaction has significant effects at the wall in the investigated flow conditions. As shown in Figures 14a, 16a and 18a,b, MTV could provide, even at pressures as low as 920 Pa, accurate data on the gas displacement, which was very well fitted by the numerical prediction of the 1D advection-diffusion equation.
In particular, the MTV data here reported gave clear experimental evidences of the strong effects produced by the Taylor dispersion on the molecular displacement, which was, up to now, only theoretically and numerically predicted  [13, 15]. The comparison with the CV technique demonstrated also the good accuracy of the MTV technique in providing average displacement and average velocity measurements in rarefied gas flows. Some estimations of the uncertainties on the measured velocities were provided. A better quantification of the errors on the MTV average velocity would require the collection of more experimental data, thus allowing a more complete statistical analysis of the fluctuations on the signal generated by the molecular diffusion, the phosphorescence emission, and the intensified CCD itself.
Further investigation is necessary to understand whether the available MTV dataset is not large enough or the post-processing method needs to be improved (or both). Preliminary analysis revealed a significant sensitivity of the reconstructed velocity profile to the parameters H and D. Future efforts aim to better characterize the sensitivity of the post-processing algorithm and to improve the accuracy on the measurements of the channel height and of the diffusion coefficient. An important challenge related to the latter intent is given by the fact that the diffusion coefficient D strongly depends on the value used for the acetone molecular diameter d. In this work, the value d = 470 pm provided by Van der Perre et al. [24]  was considered because this result is supported by several other authors  [25, 26].
In  [11, 12]  used the CP decomposition into image compression and classification. Marcella Astrid et al used the CP decomposition into Convolutional Neural Networks (CNNs) to solve the image classification tasks  [13]. Bauckhage introduced discriminant analysis to higher order data(i. e. color images) for classification  [14]. For hyperspectral and multispectral images (i. e. multi-source heterogeneous data), kinds of methods exploits the Bayesian framework  [15] [16] [17]  to fuse such images. Rodrigo and Jeremy proposed a Bayesian framework to define flexible coupling models for joint tensor decompositions of multiple datasets  [18, 19]. They cast the problem of data fusion as the analysis of latent variable. And the latent models between data are coupled through subsets of their variables, where the coupling refers to the relationship between these variables subset.
That is, there is a coupling relationship between the factor matrix after the tensor decomposition. In this paper, we hope to use the coupling relation between images to solve the problem, improving the accuracy and interpretability of the latent variables related to the other data set from the information of one data set through joint tensor decomposition algorithm. In application, data analysis from different data sources needs to be handled the heterogeneous datasets (i. e. a matrix or a high-order tensor)  [20, 21]. Recently, matrix factorization and tensor-based factorization have been successfully applied to multi-frame data restoration  [22] [23] [24] [25] , recognition  [26, 27] , unmixing  [28]  and data fusion  [18] , etc. For the data analysis of some coupled matrices and tensors, corresponding coupled matrix and tensor factorization-optimization algorithm (i.