dataesr/scientific-paragraphs-categorization huggingface dataset:
We obtained four factors explaining 64% of the total variance of the dataset (see Fig. 3 , Ext data Fig 2 and methods sect. 5. 3), which synthesise a degree of association between the criteria, i. e. each factor corresponds to a family of assessment criteria that tend to appear in the same policy document. Strikingly, these four factors broadly agree with the conceptualisation of assessment criteria policies that we had previously reached by consensus ex-ante (methods section 4. 3) Each criterion aligns with at least one of the four factors (listed in order of prominence), which can be interpreted as follows: (F1) "candidate quality": overall candidate quality, mainly assessed using qualitative criteria and encompassing a wide range of skills and competencies, and particularly including various service roles to the profession or community as well as mentoring, teaching, administration, commercialisation, and consultancy; (F2) "cumulative output": a researcher's cumulative output, especially in terms of publications (irrespective of quality), and length of service; (F3) "impact metrics": several metrics, mostly focusing on publications with regard to productivity, citations, order and role of authors, and journal impact factors, but also including patents, awards, and the ability to attract external funding; (F4) "career development": the development of the candidate's career, including experience abroad, identi able contributions to publications, patents, professional titles, awards, presentations, service to the profession, as well as pro ciency in relevant languages.
Theoretical background According to Moreland, a team includes at least 3 individuals sharing knowledge, activities and so on  [62]. Unlike dyads, team interactions are more complex since they include oneto-one and one-to-many interactions. As a consequence, this Fig. 1  An overview of our approach. From the multimodal dataset WoNoWa (see Sect. 4), we extract nonverbal multimodal features: audio, movement and spatial arrangement of teams. The choice of these features is mainly inspired by those previously found to be relevant for estimating the team's emergent states related to TMS. We compute team features and team scores from the extracted team member's features and self-assessed TMS (see Sect. 5). Finally, we analyse the role of team features in modelling and predicting TMS by running multiple linear regression analyses (see  Sect.
The WoNoWa dataset WoNoWa (W ho kNows W hat) is a multimodal (audio and video) dataset of interactions within 15 teams, performing several activities  [11]. The dataset includes automatically extracted features and manual annotations of team members' nonverbal behaviours, as well as self-assessment measures of TMS. WoNoWa was designed to address the 3 phases of TMS, i. e. , Encoding, Storage and Retrieval (see Sect. 2). In the Encoding phase, the team was given a list with 3 fields of expertise and each member could choose the preferred one. These fields were: Logistical, Mathematical and Manual expertise. In the Storage phase, each team member watched a brief tutorial about the chosen field of expertise. We focus, here, on the interactions related to the Retrieval phase. During this phase, the team members were together in the Interaction Area shown in Fig.
Head position features Team members' head position and rotation were tracked through a marker-based approach. Each team member wore a cap with an ArUco marker  [29]  attached on the top. Three additional reference markers were positioned on the floor in a way that they were visible by both cameras and remained constant throughout the experiment (see M1, M2 and M3 in Fig. 2 ). These markers were used as references to compute the position of the members' head markers in the room. Since each camera performed a separate head tracking, they had to be merged before using them. The processing was carried out via a Python script using the OpenCV library  [15]. We applied linear interpolation and average smoothing in case of missing frames. For each video frame and team member, the following data were extracted: the 3D head position (meters) HP = (HP x , HP y , HP z ) and the 3D head rotation (radians) HR = (HR x , HR y , HR z ).
Head velocity and quantity of motion entropy As detailed in  [79] , Sample Entropy (SampEn) is a non-linear entropy extraction technique that was developed to quantify behaviour regularity by taking into account the "recent" movement history. Higher values of SampEn are associated with the higher disorder, while smaller values indicate regularity. We used SampEn to estimate the degree of regularity of a team member's HV and QoM, that we consider as an approximation of team coordination (one of the components of TMS, see Sect. 2). We adopted the SampEn Matlab implementation described in  [56]  with parameters: Embedding Dimension m = 3, Tolerance r = 0. 2. SampEn was computed on moving time windows of 15 s with 3 s overlap. Figure  3  illustrates the movement feature extraction by providing a high-level representation of the process, and by highlighting the main data and features computed at each step.
This result could also be linked to the difficulty for the team members to self-assess Coordination, which could be easier estimated by external observers. In the future, we will consider collecting additional annotations of TMS given by external observers. Our work faces the following limitations. First, the WoNoWa dataset contains a relatively small number of observations, compared to the set of features available. This often occurs when dealing with human behaviour analysis. We show, however, that the 3 dimensions of TMS can be effectively detected as a linear combination of multimodal features. Using simple models such as multiple linear regressions also allowed for interpreting the role of each feature. Second, the generalisability of our findings may be limited to tasks similar to the ones realised in the WoNoWa dataset (i.
Here the tangent vector in Riemannian geometry is analogous to the usual gradient in Euclidean geometry, and a tangent vector value of size zero implies a stationary point, like the typical Fermat condition. To make more quantitative statements, we conduct a simulation study where we implement coordinate descent with sub-problems (  8 ) and (10) solved using the optim function in R, where we use the Broyden-Fletcher-Goldfarb-Shanno algorithm in the case of (  8 ) and the Dekker-Brent algorithm in the case of (10) (see  Quarteroni et al. , 2010, Chs. 6 and 7). Sub-problems (  9 ) and (  11 ) are solved using the manifold. optim function from the ManifoldOptim package  (Martin et al. 2020 ) in R, implementing the Riemannian symmetric rank one trust region method of  Huang et al. (2015). In our study, we simulate n ∈ {50, 100, 200, 500, 1000} observations X 1 ,.
Second, a Wishart prior is placed on Ω: Ω ∼ W(ν Ω , S Ω ), where ν Ω ∈ (d -1, ∞) and S Ω is symmetric and positive definite, and can be fixed or can be given hyperpriors. And finally, uniform priors are placed on ρ and ν: ρ ∼ U(0, 1), ν ∼ U(S d-1 ). Note that in the presence of prior information, more informative priors than the ones presented here could be considered in order to encode such prior knowledge. Finally, the data generating process for observations X 1 ,. , X n is the MED: X 1 ,. , X n | µ, Ω, ρ, ν, φ iid ∼ MED µ, Ω -1 , Ω -1/2 ν, ρ , where φ represents potential hyperparameters described above. We have implemented the model in the Stan probabilistic programming language  (Carpenter et al. , 2017) , which uses Hamiltonian Monte Carlo. See Appendix B. 2 for implementation details.
The MEDdist R package We describe an R package termed MEDdist 2 containing the MLE and Bayesian procedures introduced above. Density, distribution function, quantile function and random generation for the MED are also documented. • fitmed: estimates the parameters µ, Σ, ρ and ν from a sample (input) using the MLE procedure of Section 5. 1. The starting parameters µ (0) , Σ (0) , ρ (0) and ν (0) may be chosen as inputs, as well as the maximum number of iterations maxiter. • dmed: returns the value of the p. d. f. of the MED with parameters µ, Σ, ρ and ν (inputs) at point x ∈ R d (input) using Equation (2). • pmed: returns the value of the c. d. f. (only in dimension d = 1) of the MED with parameters µ, Σ, ρ and ν (inputs) at point x ∈ R (input). • qmed: returns the quantiles (only in dimension d = 1) of the MED with parameters µ, Σ, ρ and ν (inputs) of level τ ∈ (0, 1) (input).
In this section, we estimate geometric expectiles in the Bayesian framework described in Section 5. 2. We adopt the bivariate simulation experiments of  Herrmann et al. (2018). More specifically, we consider four bivariate random variables X (1) ,. , X (4) (See Table  6  in the Appendix for a description of the data distributions). We are interested in geometric expectiles e ρ,ν(ϕ),I d (X (i) ), where ρ = 0. 98 and the whole spectrum ν(ϕ) = (cos(ϕ), sin(ϕ)) with ϕ ∈ [0, 2π) is considered. According to the Bayesian model of Section 5. 2, estimation of such expectiles is carried out by simply setting the parameters (ρ, ν, Σ) to fixed desired values (0. 98, ν(ϕ), I d ) (i. e. no prior is set) and by estimating the expectile through parameter µ. We sampled n = 1, 000 observations for each of the four distribution settings.
For each value of ϕ in the grid {ϕ ℓ = 2π(ℓ -1)/100, ℓ = 1,. , 100}, we used Stan (code described in Appendix B. 2) with 2, 000 HMC iterations after a 1, 000-iteration burn-in. Stan provides a R value of 1 for all of the chains, thus not indicating convergence issues. Expectiles were estimated by the posterior mean. For each value of ϕ, credible bands could be computed as those regions containing a prespecified proportion of iterations from the HMC chain (see, for instance, Section 7. 2). We have followed a different approach in order to better visualize the credible regions as bands around the estimated expectiles. More specifically, we used multivariate quantiles (in the sense of  Chaudhuri, 1996)  of orders 2. 5% and 97. 5%, to get pointwise credible bounds for each value of ϕ ℓ , and then connected them with a curve visible as blue dashed lines on Figure  4.
Bayesian estimation of the mode of a distribution We take advantage of the property that the MED mode coincides with its location parameter µ (Proposition 3 (i)) to propose a procedure for estimating the mode of a distribution. Consider the four distribution settings of the previous section. For each of them, we generated n observations, n ∈ {100; 500; 1, 000}. We used the Bayesian model of Section 5. 2 implemented in Stan (code described in Appendix B. 2) with 2, 000 HMC iterations after a 1, 000-iteration burnin. Stan provides a R value of 1 for all of the chains, thus non indicating any convergence issue. As a competitor to the MED, we used a multivariate Gaussian distribution as a fitting distribution. The Gaussian distribution can be simply obtained from the MED by fixing the ρ parameter to 0, see Proposition 2 (i) (this automatically makes the ν parameter deprecated).
Discriminant analysis We propose a discriminant analysis on real data, by considering the Banknote authentication data set, available at this url 3. The data of size n = 1, 372 contain four covariates (X 1 = variance, X 2 = skewness, X 3 = kurtosis and X 4 = entropy of wavelet transformed banknote images), and a binary variable indicating whether the banknote is genuine (0) or forged (1). As illustrated in Figure  6 , the genuine (blue) vs forged (red) balance in the data set is 56% vs 44%. We randomly split the data set into a training sample of size n = 1, 000 and a testing sample of size 372, and repeat 100 times the experiment. For each experiment, we fit the genuine and forged classes of banknotes with a Gaussian, Skew normal (SN ) distribution (Azzalini and Cap-  Covariates (X 1 ,. , X 4 ) in blue (genuine) and in red (forged) as bivariate scatterplots.
project, learning about funding sources and how to tailor proposals to meet those source requirements, and working through an essential checklist of preexpedition planning and operations. The Master Class covered leading an expedition at sea, at-sea operations, and ship-board etiquette, and the strengths and challenges of telepresence. It also included post-expedition training on data management strategies and report preparation and outputs. Throughout the Master Class, Fellows also discussed education and outreach, international ocean law and policy, and the importance and challenges of team science. Fellows further learned about how to develop concepts respectfully with regard to geographic and cultural considerations of their intended study sites. An assessment of initial outcomes from the first iteration of the COBRA Master Class reinforces the need for such training and shows great promise with one-quarter of the Fellows having submitted a research proposal to national funding agencies within six months of the end of the class.
One of the express goals of COBRA is to train future generations in inclusive ocean exploration, policy, research, and data accessibility. To that end, in 2022, COBRA launched its inaugural COBRA Fellowship and accompanying Master Class, which trained 12 early career Fellows in deep-sea expedition leadership (and will do so annually for five years). The goal was to equip Fellows with the skills and tools to successfully design, propose, and execute deep-sea oceanographic field research, with a collaborative, just, equitable, diverse, and inclusive approach. This 13-week virtual class included weekly synchronous, online sessions for two hours, followed by asynchronous interaction throughout the week. The "master class" concept was designed to be a class taught by masters in the field, for the upcoming generation of masters in the field.
COBRA aims to increase representation of diverse genders, races and ethnicities, and nations in deep-sea research, with a metric of offering programs that have more demographic diversity than the demographics of recent ocean science graduates in the U. S. (National Center for Science and Engineering Statistics (NCSES), 2022). If provided, demographic data was summarized and reported to the evaluation committee in aggregate, without personally identifying applicants. To avoid conflicts of interest, demographic data was only made available to the COBRA Director and Managing Director, who were not part of the evaluation committee. All eligible, qualified applicants (determined by the evaluation committee) were then entered into a lottery pool that was subjected to a random lottery process, re-sampling from the qualified population as needed to achieve a diverse demographic based on gender identity, race and/or ethnicity, country of citizenship, and country of residence.
Fellows then added three objectives to challenge them to think about them in further detail regarding specific hypotheses, samples and analysis required to answer their questions, expected importance, and expertise required to accomplish their objectives. Fellows worked in teams to identify data repositories where they could find information about their areas of interest that may already exist. In addition to the science, Fellows also drafted education, public outreach, and/or communication approaches for their expedition. Fellows completed a table based on the US Department of State's Application for Consent to Conduct Marine Scientific Research table for their area of interest, or another area if theirs was not in another country's jurisdiction. Finally, Fellows were asked to prepare a 3-slide/3-minute overview about their Dream Cruise Project or prepare a presentation on any aspect of the class, which would be delivered to the COBRA instructors and Fellows during the final week.
Class/schedule/modules/topics The Master Class met synchronously and virtually weekly, with asynchronous materials provided in advance and with follow-up. To promote asynchronous communications, a Slack channel was devoted to the course. The combination of virtual synchronous and asynchronous delivery was a major factor in successfully engaging a geographically dispersed cohort. In addition, to deliver the Master Class materials, we made use of the open-source publishing platform PubPub to create a course website (https://cobra. pubpub. org/). Class materials from 13 weeks of instruction were made available to Fellows approximately one week prior to the relevant class. Fellows' Dream Cruise Project work remains private for their intellectual use and development.
Week 6: telepresence For Week 6, which was focused on Telepresence, the goals were to understand: (1) what telepresence is and (2) the strengths, opportunities, weaknesses and challenges of telepresence with regards to science and outreach. A COBRA instructor and guest lecturer discussed telepresence technology and its power, goals, strengths, and weaknesses. Fellows also participated in a live telepresence interaction with scientists aboard EV Nautilus, which supports the ROV Hercules. This opportunity enabled Fellows to participate in real-time data streams and use the scientist ashore portal to get a glimpse of the shipboard experience  (Wagner, 2023).
Week 8: introduction to deep data In Week 8, we focused on Introduction to Deep Data, and the goals were to: (1) familiarize Fellows with existing data repositories, (2) enhance data discoverability by learning to find desired publiclyavailable data types and datasets for regions of interest, and (3) determine feasibility of at-home data use and what requires prosoftware. This class focused on discoverability and use of existing data. COBRA instructors reviewed data repositories, types of data repositories, and how to extract and display data. The class focused on GeoMapApp as a case study of one innovative open-access data repository linked to a data manipulation and display application. In preparation for this class, Fellows researched one or more locations to identify and access data including bathymetric data, but also searched for data types and datasets most relevant to their 'Dream Cruise' projects.
Week 9: data management plan to cruise report Week 9 focused on Data Management Plans to Cruise Reports and built upon lectures and work introduced in Week 8. Goals for this week were to: (1) learn about data management plan (DMP) goals, components, and formats for metadata, digital data, sample data, and engineering plans; (2) understand various data storage challenges and strategies; (3) create a data management plan for the Fellows' Dream Cruise; (4) learn about goals for expedition reports, components, and formats; and (5) create an expedition report outline for Fellows' proposed Dream Cruise. COBRA instructors explored the details of DMPs and expedition reports. They reviewed the necessary components of DMPs, as well as a range of styles and resources to help create them. In the first half of this class, Fellows worked in breakout groups to begin drafting their own DMPs.
Public access to course resources In addition to supporting the Fellows and the class, the COBRA PubPub site (https://cobra. pubpub. org/) was also intended to be a public resource for deep-sea expedition leadership and planning. All class plans, readings, videos, etc. , are publicly available. In the 82 weeks between the creation of the PubPub site (Feb 17 2022) and the page proofs submission for this manuscript (September 17 2023), 1256 users from 69 countries and territories have accessed 22,902 page views on the site (Figure  3 ).
Acknowledgments COBRA is grateful to many Subject Matter Experts who contributed expertise to the 2022 Master Class, including:  Kasey Cantwell ,  Gabriella David ,  Allan Doyle ,  Barbara Endemaño Walker ,  Dijanna Figueroa ,  Peter Girguis ,  Brian Kennedy ,  Lisa Levin ,  Catalina Martinez ,  Leonard Pace ,  Lu Wang ,  Amanda Williams , and  Karen Young. We are grateful to the deep-sea community for collectively training all of us and providing the inspiration to formally launch this Master Class in expeditionary leadership. The  National Science Foundation  does not assume responsibility for the findings or the interpretations. Survey data collected is exempt from US federal requirements for human subject research according to the  NIH Office of Extramural Research , especially as the subjects are co-authors on this manuscript.
This extends the result in  [48]  where local solutions for any initial data and global solutions for small initial data have been obtained in H s ˆHs with s ą 1. A similar result adapted to Besov spaces was obtained in  [49]. More recently, ill-posedness for the two-dimensional shallow water equations in critical Besov spaces has been shown in  [45]. Existence of global weak solutions and convergence to the strong solution of the viscous quasi-geostrophic equation, on the two-dimensional torus is shown in  [6]. In  [7]  the authors construct a sequence of smooth approximate solutions for the shalow water model obtained in  [6]. The approximated system is proven to be globally well-posed, with height bounded away from zero. Global existence of weak solutions is then obtained using the stability arguments from  [6].
[22]  This allows determining a faradaic efficiency (FE) for hydrogen production and to calculate the turnover numbers (TON dye ) achieved by the different dye-sensitized photocathodes. The data are summarized in Table  2  (full set of data in Table  S1 , Supporting Information). As expected from the steady-state photocurrent measurements discussed above, NiO|pRK1 is the most effective photocathode, producing 1. 9 μmol cm À2 of hydrogen with a Faradaic efficiency of 66%; 145 TON dye are achieved by pRK1 during the course of the 6 h experiments, which is almost double compared to P1. Notably, these performances are much better than those previously recorded with a related dye-sensitized photocathode in the presence of the cobaloxime catalyst [Co(dmgBF 2 ) 2 (OH 2 ) 2 ] in solution. [45]  Control experiments recorded either on a blank NiO film or in the absence of 1(BF 4 ) 2 in the electrolyte produced only traces of H 2 compared to NiO|P1 and NiO|pRK1.
Acknowledgements C. B. and A. M. contributed equally to this work. This work was supported by the  French National Research Agency  ( Labex ARCANE ,  CBH-EUR -GS ,  ANR-17-EURE-0003 ) and the CEA through the  DRF-Impulsion program. A. M. acknowledges  CEA  for funding through a  CFR  Ph. D. grant. R. D. acknowledges the  European Research Council (ERC)  for funding. This work was partially funded under the  European Union 's  Horizon 2020 Research and Innovation Program  (grant agreement no. 832606 ; project PISCO). The authors thank  Dr. P. Maldivi  for her help with the DFT calculations. The authors thank  Dr. C. Aumaitre  for helpful discussions.
In addition, we look at investor reactions to the varying intensity of the current pandemic. Our dataset allows us to differentiate between the pandemic effects of various sizes, in terms of volatility. The investigation covers a 12month period, from 1 January 2020 to 1 January 2021, using daily data. In this work, we use relevant Markov switching techniques in order to investigate the aforementioned questions in a high and low volatility state, respectively. More precisely, we allow the data to be characterized by two states, namely a high-mean state, which represents the market expectation of more volatile returns, and a low-mean state, which represents low volatility expectations  (Burdekin and Tao, 2021). The aforementioned situation is modeled by estimating a two-state dynamic Markov-Switching Regression (MSR), with a state-dependent intercept term to capture the dynamics of the series, across unobserved regimes.