dataesr/scientific-paragraphs-categorization huggingface dataset:
Experimental Results In order to test our formulated models (Model 1 and Model 2), we consider the benchmark of  [29]  for "VRPTW-TD-2MS" and the benchmark of  [20]  for Vehicle Routing Problem with Time Window and Synchronization constraint "VRPTWSyn" to generate new instances, based on the same rules provided by the latter, for VRPPTW-TD-2MS and VRPBTW-TD-2MS problems. The below generated instances are clustered according to visits and vehicles number (in our data instance, we use 60 visits and 12 vehicles). We use Cplex 12. 5 coupled with C++ language to solve Model 1 and Model 2. Note that the addition of the second objective function makes the problem more complex than the traditional one. All combinations of time windows and weights objective functions, i. e. 9 test problems, are presented in these tables.
Hydrodynamical simulations with radiative transfer We model the 21 cm forest during inhomogeneous reionisation using a sub-set of the high resolution cosmological hydrodynamical simulations drawn from the Sherwood-Relics simulation programme (see  Gaikwad et al. 2020 , for an initial application of these models). The Sherwood-Relics simulations were performed with a modified version of the P-GADGET-3 code -which is itself an updated version of the GADGET-2 code described in  (Springel 2005)  -and uses the same initial conditions as the earlier Sherwood simulation suite  (Bolton et al. 2017). In this work we adopt a flat ΛCDM cosmology with Ω Λ = 0. 692, Ω m = 0. 308, Ω b = 0. 0482,  8 = 0. 829,  s = 0. 961, ℎ = 0. 678, consistent with Planck  Collaboration et al. (2014) , and a primordial helium fraction by mass of  p = 0.
managed by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility. The equipment was funded by BEIS capital funding via STFC capital grants ST/P002293/1 and ST/R002371/1, Durham University and STFC operations grant ST/R000832/1. DiRAC is part of the National e-Infrastructure. This work has made use of matplotlib  (Hunter 2007) , astropy (Astropy Collaboration et al. 2013), numpy  (Harris et al. 2020 ) and scipy  (Virtanen et al. 2020). TŠ is supported by the University of Nottingham Vice Chancellor's Scholarship for Research Excellence (EU). JSB acknowledges the support of a Royal Society University Research Fellowship. JSB and NH are also supported by STFC consolidated grant ST/T000171/1. MGH acknowledges support from the UKRI STFC (grant numbers ST/N000927/1 and ST/S000623/1).
ACKNOWLEDGEMENTS We thank  Benedetta Ciardi ,  Margherita Molaro , and  Shikhar Mittal  for helpful discussions. We also thank an anonymous referee for their insightful comments. The simulations used in this work were performed using the Joliot Curie supercomputer at the  Tré Grand Centre de Calcul (TGCC)  and the  Cambridge Service for Data Driven Discovery  ( CSD3 ), part of which is operated by the  University of Cambridge Research Computing  on behalf of the  STFC DiRAC HPC Facility  (www. dirac. ac. uk). We acknowledge the  Partnership for Advanced Computing in Europe (PRACE)  for awarding us time on Joliot Curie in the 16th call. The DiRAC component of CSD3 was funded by  BEIS  capital funding via STFC capital grants  ST/P002307/1  and  ST/R002452/1  and  STFC  operations grant  ST/R00689X/1.
Understanding facial signals in humans and other species is crucial for understanding the evolution, complexity, and function of the face as a communication tool. The Facial Action Coding System (FACS) enables researchers to measure facial movements accurately, but we currently lack tools to reliably analyse data and efficiently communicate results. Network analysis can provide a way to use the information encoded in FACS datasets: by treating individual AUs (the smallest units of facial movements) as nodes in a network and their co-occurrence as connections, we can analyse and visualise differences in the use of combinations of AUs in different conditions. Here, we present 'NetFACS', a statistical package that uses occurrence probabilities and resampling methods to answer questions about the use of AUs, AU combinations, and the facial communication system as a whole in humans and non-human animals.
g. ,  Abramson et al. , 2020; Aviezer et al. , 2008) ; at the same time, different signals can have the same function  (Isac & Reiss, 2008). The strong focus on few stereotypical facial signals has prevented us from understanding whether the same is true for facial signals. With the development of automated FACS-coding(e. g. ,  Lewinski et al. , 2014) , large datasets of diverse facial signals will become increasingly important, but the development of coding software has outpaced the development of appropriate statistical tools to interpret resulting data. Most studies try to establish how much the use of each AU differs across conditions, such as different social contexts or internal experience of participants. However, currently, many different approaches are in circulation, reducing reproducibility, and FACS datasets have some features that make traditional statistical models unsuitable for this task.
FACS data mix spatial and temporal combinations of AUs, with temporal information influencing comprehension  (Krumhuber et al. , 2013) ; different signals are also strung together in sequences, often combined with speech or gestures  (Kessous et al. , 2010). At a basic level, for each data point in FACS coding (either a static description, or a time point in a dynamic analysis), AUs are either present or absent (or categorical if intensity measures are provided). When testing whether the mean use of an AU across data points differs between conditions, many analyses of FACS data are based on analysis of variance (e. g. ,  Harris & Alvarado, 2005). When testing which AUs occur together in specific contexts, researchers often use dimension reduction techniques such as principal component analysis or factor analysis (e.
g. ,  Stratou et al. , 2017). As FACS data are inherently binomial (AUs are either there or not), categorical (if coded using intensity measures), or proportional (proportion of events in which AU is active), they violate distributional assumptions of these methods. Additionally, the use of different AUs does not have to follow the same distributionfor example, if only a subset of individuals in a population use some AUs while others do not, or an AU is occasionally combined with another to change meaning, the distribution of that AU in the population would be bimodal. FACS datasets contain dependencies between units and events on different levels: for example, participants often provide multiple videos. Muscle movements throughout a video are not independent from each other. Participants often share many characteristics (e.
, 2011; Ferrer i Cancho et al. , 2004; Liu & Xu, 2011). For example, the 'Netlang' software package  (Barceló-Coblijn et al. , 2017)  creates networks of words in a corpus while controlling for their syntactic relations. Networks have also been applied to temporal information in animal vocalisations  (Kershenbaum et al. , 2016) , elucidating transitions between call types in songbirds  (Deslandes et al. , 2014; Hedley, 2016; Sasahara et al. , 2012; Weiss et al. , 2014)  and humpback whales  (Allen et al. , 2019). The musculature underlying facial movements has been described in terms of networks of muscles  (Esteve-Altava et al. , 2015). Dynamic Bayesian networks of AU co-occurrence probabilities have been used to improve correct automated identification of AU intensity from video data  (Li et al.
, 2002). Fundamentally, these approaches rely on the creation of appropriate null models to address the question at hand, enabling researchers to account for the underlying data structure, autocorrelation, and potentially important control variables  (Farine & Whitehead, 2015). In this article, we set out to present the potential power of using network analysis to understand and visualise detailed facial signal data. To demonstrate the fundamentals of the method to a wide audience, we use a simple dataset of stereotypical static signals, while the true potential for network analysis in this context lies in applying it to 'natural' datasets of non-posed facial signals with temporal information. For many researchers working with facial signal data, networks are not part of the toolset they apply regularly.
We have therefore developed the R package 'NetFACS' (https://github. com/ NetFACS/NetFACS) that facilitates the application of the methods described in this article. We will use network measures to address questions on different levels: (a) How specific are AUs to certain stereotypical signals (unit level)? (b) Which AUs are conditional on each other (dyad level)? (c) Can we reconstruct the stereotypical facial signals for each context through dyadic networks, and how do networks in different contexts compare (signal level)? (d) Can we identify clusters of AUs without knowledge of the underlying contexts (system level)? Ultimately, the goal of NetFACS is to create a standardised way to analyse facial signals to determine how the face as a communication system compares to other systems in humans and other species.
Dataset For this study, we used the peak frames of 327 FACS-coded videos assigned to one of seven conditions (anger: 45 images, contempt: 18, disgust: 59, fear: 25, happy: 69, sadness: 28, surprise: 83) in the Extended Cohn-Kanade Database  (Kanade et al. , 2000; Lucey et al. , 2010). Videos included only one facial signal, produced based on instructions from an experimenter, and were specifically designed as a baseline dataset for automated facial expression detection  (Kanade et al. , 2000). Images represented a subset of posed facial expressions judged to fit the stereotypical expressions for those conditions (e. g. , AU6+12 for a 'happy' face). Thus, the dataset is designed to reduce variability within conditions and increase variability between conditions, making the specificity of AUs unnaturally high; however, this suits our purpose of presenting the method in a clear-cut example.
In the following, we will talk about the emotion labels that were assigned to each video as experimental 'conditions', to make clear that while here we use the labels as an example, researchers could also compare other conditions with each other, e. g. , participant gender. There is no sequential information available in this database, and we omit information about intensity of AU activity as NetFACS is currently designed to work on presence/absence information only. Data including intensity measures can easily be adapted to represent presence/absence. Data were organised so that each image (subsequently 'event') is one row, and each AU is a column that is either present (1) or absent (0). As no 'neutral' condition is available, all analyses compare the data for each of the conditions against all the other conditions.
Probability All networks in NetFACS are built based on the probability of AU occurrence and co-occurrence of multiple AUs. This builds on previous work using a probabilistic representation of AU co-occurrence  (Li et al. , 2015). Co-occurrence of communicative units is an important feature in language learning: repeated coupling of units enables infants to learn word composition and syntactic rules  (Isac & Reiss, 2008). When analysing units of facial communication (either AUs, combinations of AUs, or whole signals), we are interested in the unconditional probability that they occur and co-occur with each other. The unconditional probability for FACS-like data represents the number of events in which an AU or combination was active, given the total number of events: so, if an AU is active in 5% of all events, its unconditional probability is 0.
NetFACS package The NetFACS package for R allows users to explore their FACS-like data and test specific hypotheses based on occurrence and co-occurrence probabilities and resampling methods. The package represents the different probabilities of AUs or combinations in the form of undirected (unconditional probability) and directed (conditional probability) networks. Networks can be weighted-the connection between two nodes represents their observed probabilities. Alternatively, networks can be unweighted, only representing connections between two AUs as 'present' if they occur more frequently than expected given a null model  (Newman, 2010). Networks can represent the connections between two AUs, or the connection between AUs and conditions in the form of bipartite networks. To test hypotheses using networks, it is essential to construct meaningful null models against which to compare observed data  (Farine, 2017).
We want to know how much more or less likely the use of an AU or combinations of AUs is than expected, but we have to first define what we expect. Our expectations depend on the question: If we have one large dataset and want to know which AU combinations form predictable units, our expectations are set by the basic probability of each AU to occur on its own. If we compare two conditions (e. g. , angry and happy faces), our expectations for the angry faces are set by what would be expected in the happy faces. In NetFACS, if all events are part of the same condition, expected probability distributions are calculated using prenetwork permutations  (Farine, 2017) : the existing data are shuffled with certain restrictions, to simulate 'random' data that still follow some of the underlying rules of the dataset.
First, the package extracts the conditional and unconditional probabilities of all possible combinations of AUs in the observed data. To establish whether single AUs occur more or less frequently than expected, the number of AUs in each event (e. g. , photo, video frame) is held constant, but which AU occurred is randomised. Thus, if a facial signal contained five AUs before randomisation, it will also do so after randomisation. To establish whether combinations of AUs occur more or less frequently than expected, NetFACS shuffles which AUs occur in each event while keeping the probability of each AU across all events, as well as the number of AUs observed in each event, constant. This randomisation procedure is repeated 1000 times, or any value set by the user. Probabilities for all AU combinations for each randomisation are stored, creating the likely probability space for each combination in the population.
The resulting null probability distributions for AU combinations represent the expected data given that AUs were not combined into predictable facial signals. The observed probabilities for the test dataset are compared with the distribution of expected probabilities by calculating a p-value (proportion of expected probabilities that are more extreme than the observed value) and effect size (the difference between the observed and average expected value). If we want to compare two conditions (e. g. , old and young participants, or happy and neutral participants), NetFACS uses bootstraps  (Carsey & Harden, 2014; Julle-Danière et al. , 2020). We use one of the conditions to create the expected distribution for all AUs and their combinations using a bootstrapping procedure  (Carsey & Harden, 2014) : events from the 'null' condition are repeatedly selected randomly with replacement  (Efron & Tibshirani, 1993).
Probabilities for all combinations are stored, and the procedure is repeated 1000 times (more iterations allow for more stringent tests). As above, the resulting distribution of expected probabilities under the null condition is compared against the observed value in the test condition, and a p-value is calculated representing the proportion of expected values that was more extreme than the observed value. By using bootstraps to create null distributions of probabilities for each AU and combination, we do not presuppose normally distributed data  (Carsey & Harden, 2014). This bootstrap approach does not make any statements about some unknown population that the data might have been drawn from: it directly compares two empirical distributions. Note that the interpretability of results depends on how well the test and null datasets represent the conditions from which they were drawn: if the probabilities are based on small datasets, the interpretation has to consider this.
The more variation there is in the null dataset or the fewer data points we have available, the broader the probability space will be-the expected value becomes more uncertain. Thus, especially for rare elements and noisy data, the resampling approach will potentially favour false negative over false positive values in small datasets. If individuals provide multiple data points, or videos are analysed, NetFACS allows users to perform the random selection of the bootstrap on the level of the video or individual, so that the null distribution accounts for inter-individual differences and autocorrelation within videos  (Harden, 2011). For example, it is possible that only some subjects use specific muscles, in which case the probabilities under the null condition will not be normally distributed.
g. , their valence). If AUs are specific to and common in one condition, they are likely part of a standardised facial signal of this condition. If they are context specific and rare in that condition, their occurrence might indicate a change in meaning, for example if they signal sender uncertainty. The AU might also be very rare and their occurrence in this specific condition might be accidental, or it might have been miscoded. Alternatively, there could be interindividual differences, and only a subset of individuals displays the AU. To create the network, we compared the dataset of each condition against all other data points using bootstraps. Thus, to determine whether 'angry' faces show specific features at the AU level, we compared the probabilities of AUs occurring in 'angry' faces to the null model that AU probabilities across all conditions were the same.
Each event was considered independent, i. e. , not taken from the same individual or part of a sequence. No information on other variables, such as gender or place of origin, was available in the database we used. Edges between an AU and a condition were assigned if the conditional probability of the AU occurring in this condition was significant at p < 0. 01, i. e. , the observed probability was higher than in 990 out of 1000 bootstraps of the null condition. We represent two distinct graphs for easier comprehension, one quantifying the conditional probability of the AU given the condition ('Occurrence Probability') and another quantifying the conditional probability of the condition to the AU ('Context Specificity'). To test whether distinct 'clusters' of nodes existed in the network (signifying groups of AUs and conditions that have strong connections with each other but weak connections to the outside  (Girvan & Newman, 2002 )), we used the 'cluster_fast_greedy' community detection algorithm  (Clauset et al.
Method To understand the connections between AUs, we tested their conditional probabilities to occur together. Conditional probabilities were defined by the probability that one AU occurs, given that another one is also present. We explored three possibilities: two AUs can show low conditional probabilities in both directions, in which case they were likely unconnected in the dataset. They can show high conditional probabilities both ways, in which case they formed a functional unit in this condition, with each AU always occurring when the other was present. This connection could indicate that, at least in this condition, they should be treated as one unit rather than two separate units. The third alternative was that conditional probabilities were asymmetrical: if one AU was more common than the other, it is possible that the rare AU always appeared when the more common AU was present, but the same was not true vice versa.
These dyads would allow us to identify units that potentially modify meaning, and the cases with and without combinations of the two AUs could be analysed in more detail. For example, in facial signal research, it has long been assumed that adding AU6 (cheek raiser) to AU12 (lip corner puller) modifies the meaning of a smile  (Martin et al. , 2017; Rychlowska et al. , 2017). In that case, when analysing a large number of smiles, we would see a high conditional probability of AU12 occurring when AU6 is present, but not vice versa. Here, we presented the directed weighted network of conditional probabilities of AUs for two conditions in the dataset, 'sadness' and 'surprise', to exemplify the information that can be obtained by this approach. The weights of each edge represent the conditional probability going each way.
Strongly stereotyped facial signals will consist of tight clusters of strongly interconnected AUs associated with high computed transitivity (if A → B and A → C, then B → C), while more variable signals should show fewer closed triads and weak connections between larger numbers of AU. Here, we represented the signal for each condition as an unweighted, undirected network, based on the comparison with all other data points using bootstraps. Thus, a link between two nodes indicates that the two AUs were significantly more likely to co-occur in this condition than across the other conditions. Besides displaying the graphs, we report the network-level centrality measures of density and transitivity (see Glossary for definitions). Density is the ratio of actually existing edges in a network of all possible edges  (Newman, 2010) ; networks with high density have connections between most nodes, indicating either that each facial signal in this condition contains more AUs than in other conditions, or that the AUs are connected more variably.
Results Figure  4  represents the networks for each condition, with significant connections between AUs used as edges and AUs that occurred significantly more often than expected as larger points. Connections between AUs were significant if they occurred at a higher probability in this condition than would be expected across the other conditions. Small points were nodes that occurred in the condition, but not significantly more than expected. The graphs showed that in this dataset, each of the conditions consisted of a core of AUs that were common and strongly linked to each other, corresponding to the known facial signals  (Ekman & Oster, 1979 ): 'happy', for example, consisted of AU6+12, 'sadness' of AU1 + 4 + 15 + 17, and so on. However, this way of plotting the data also revealed that even in this posed dataset, there was variation within facial signals, and a number of rare AU accompanied at least a subset of signals in each category.
This was especially clear in 'fear', which consisted of a core of AU1 + 2 + 4 + 5 + 20, but was often accompanied by  AU10, 14, 16, 17, and 26. That all of these different combinations were still recognised as the same condition when the dataset was compiled indicates that facial signals are relatively robust to variation in AU activity. Besides plotting connections using graphs, we can represent information about the network structure using different centrality measures. Here, we exemplified this by using the density of the graph (number of edges compared to number of possible edges) and the transitivity (ratio of closed triads; Table  1 ). 'Happy' faces (0. 04) and 'contemptuous' faces (0. 03) were the least dense, indicating that they employed only a very small number of possible combinations of AUs, which is also visible in Fig.