dataesr/scientific-paragraphs-categorization huggingface dataset:
Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where the dynamics of the underlying phenomenon can be described by a linear operator, based on the Koopman operator theory. However, despite being able to provide reliable long-term predictions for some dynamical systems in ideal situations, the methods proposed so far have limitations, such as requiring to discretize intrinsically continuous dynamical systems, leading to data loss, especially when handling incomplete or sparsely sampled data. Here, we propose a new deep Koopman framework that represents dynamics in an intrinsically continuous way, leading to better performance on limited training data, as exemplified on several datasets arising from dynamical systems.
While one can easily design an ideal synthetic dataset with regular high-frequency data (i. e. observations sampled at a high rate), this is not always the case for natural data. For example, optical satellite image time series are generally acquired every several days, and some of the images can be partially or totally unexploitable when the ground is covered by clouds, resulting in spatially and temporally irregularly sampled data  [5]. Therefore, there is a growing need to be able to handle low-frequency or even irregularly-sampled time series data. Models handling intrinsically continuous dynamics This work was supported by Agence Nationale de la Recherche under grant ANR-21-CE48-0005 LEMONADE. can naturally answer this issue, contrary to recent approaches that need to re-sample irregular data on a fixed discrete grid  [6, 7].
The discrete setting In this setting, we use the same assumptions and notations as in equation (1). Our dataset is composed of m discrete trajectories of T regularly sampled points. Given the m initial conditions xi,0 corresponding to each trajectory with index 1 ≤ i ≤ m, one can write: ∀ 1 ≤ i ≤ m, ∀ 0 ≤ t ≤ T, xi,t = F t (xi,0). (3) The key to being able to represent the data with a finite-dimensional linear operator is to find a Koopman invariant subspace  [15]  (KIS), i. e. a set J of measurement functions such that ∀g ∈ J, K(g) ∈ J. While there exists trivial KIS, for example with observable functions corresponding to constant values, we need to find one that contains enough information to reconstruct the observation state x. Our chosen architecture is composed of 3 trainable components: (1) a deep encoder network φ : R n → R d , (2) the corresponding decoder network ψ : R d → R n and (3) a square matrix K ∈ R d×d.
For the fluid flow dynamics, we use the exact same data as in  [17] , with time series of length 121. This time, we did not keep any of the training data for validation since we did not observe any overfitting in our experiments. Our evaluation criterion for the pendulum and fluid datasets is the mean squared error, averaged over all time steps from all of the testing trajectories. We chose this metric since, as one can see on figure  2 , the prediction error follows a complex pattern which does not always increase with time. Thus, the error measured only at one given time step is not representative of the accuracy of a prediction. We compare our method against the state-of-the art  [17] , which we refer to as DeepKoopman, and against an ablated version of our work where we remove the orthogonality loss  (7) , i.
e. set β1 = β2 = 0 in loss functions L1 (8) and L2 (9), making the method similar to  [19]. We evaluate two settings: the first one is a typical high-frequency regular sampling setting, which was used in  [17]. The second one has an increased data sampling period: from 0. 01s to 0. 2s for the   pendulum, and from 0. 02s to 0. 4s for the fluid flow. This reduced frequency results in an important gap between consecutive sampled points, giving an incomplete view of the dynamical systems. We evaluate the trained models in the original high frequency in order to assess their ability to learn a continuous evolution from lowfrequency data. For our method, we compute a continuous operator D from the learned matrix K to eventually provide high-frequency predictions, as described in section 3. 2. For the method from  [17] , since it cannot be used to make predictions at a different frequency from the one it has been trained on, we will simply perform a linear interpolation between the points predicted at the low training frequency.
Methods: We performed a systematic literature search to extract cases of TTC after adult cardiac surgery (from 1990 to 2021). Additionally, we extracted all cases of TTC in a prospective single-center cohort database of 10,000+ patients (from 2007 to 2019). We then combined all cases in a single cohort to describe its clinical features. Results: From 694 screened articles, we retained 71 individual cases published in 20 distinct articles (19 cases reports and 1 case-series). We combined these to 10 cases extracted from our cohort [among 10,682 patients (0. 09%)]. Overall, we included 81 cases. Patients were aged 68 ± 10 years-old and 64/81 (79%) were women. Surgery procedures included mitral valve and/or tricuspid valve surgery in 70/81, 86%. TTC was diagnosed in the first days after surgery [median 4 (1-4) days].
Methods In a single-centre cohort study, we retrospectively screened patients who underwent cardiac surgery with cardiopulmonary bypass from January 2007 to March 2019 using a prospectively collected database, including 35 perioperative data. The cohort study was approved by our local institutional review board committee. Data are part of the REGISTRY for the improvement of Postoperative OutcomeS in Cardiac and Thoracic Surgery (RIPOSTE) database (NCT03209674). Since this study was observational, the need for written consent was waived according to French Law (Law 88-1138 relative to Biomedical Research of  December 20, 1988 , modified on  August 9, 2004). Lack of patients' opposition to the use of data was systematically sought for. Patients who had previously had TTC were not involved in setting the research question or the outcome measures.
Material and Methods First, following Guérémy and Marre  [19]  and Moeyersons et al. [20] , a large scale geomorphological map of the Jacotines landslide (1/10,000) was produced to delimit surface morphology and to localize springs. The internal structure of the landslide was then investigated using geophysical methods. On the one hand seismic refraction tomography data (profiles 1, 2 and 3 on Figure  3 ) can provide structural information  [21] [22] [23] [24]. On the other hand electrical resistivity tomography data (profile 3, dipole-dipole and Wenner-Schlumberger methods) can provide information on water content  [25] [26] [27] [28] [29] [30] [31] [32] [33] [34]. The two methods are also complementary since the seismic data are more reliable in depth while the electrical data give more accurate results near the surface  [23].
The size of these volumes depends on the main frequency of the seismic signal-taken here as 40 Hz-so that the quasi-Newton inversion scheme is stabilized and converge toward the global minimum of the cost function. To optimize the convergence process, we maximized the likelihood function defined as: L = exp -∑ N tc-to σ  is the number of considered wavepaths, tc and to are calculate and observed propagating time respectively, s is the time picking a priori uncertainty-taken here as 0. 01 s. In order to avoid overfitting, as well as underfitting, we decided to stop the iterative process when L reach 0. 9. To invert apparent resistivities, we used the Res2dinv software (version 3. 59)  [38]  based on a least squares/quasi-Newton inversion approach also able to damp the convergence process in order to avoid local minimum solutions.
s. l. and the N is the number of considered wavepaths, tc and to are calculate and observed propagating time respectively, s is the time picking a priori uncertainty-taken here as 0. 01 s. In order to avoid overfitting, as well as underfitting, we decided to stop the iterative process when L reach 0. 9. To invert apparent resistivities, we used the Res2dinv software (version 3. 59)  [38]  based on a least squares/quasi-Newton inversion approach also able to damp the convergence process in order to avoid local minimum solutions. Data fusion based on fuzzy subsets theory was realized to interpret jointly seismic (Vp) and electrical (ρ) tomograms in regard to physical behaviors and physical properties of the materials  [39]. In the fusion process, the definition of belonging functions is determinant because they link the values of the geophysical parameters (Vp, rho) to the possibility that a specific geotechnical behavior occurs.
Here, instead of a detailed 'How To', I provide an overview of the principal ways to represent relational datasets in animal societies, pointing towards more detailed resources for less-used approaches and offering guidance on when different approaches are most valuable. Even for the same dataset it is possible to represent interaction or association data in different ways, meaning decisions about the best approach to use should depend first and foremost on the research questions of interest  (Carter et al. 2015)  and second on any limitations inherent to the dataset analysed. I hope to provide a resource that can be valuable for researchers designing animal social network projects and analyses (e. g. for pre-registered studies or funding applications) as well as for those faced with previously collected data with particular limitations or constraints.
Edges represent some form of interaction or association between the nodes. Examples in animal social behaviour include specific behavioural interactions (e. g. grooming, aggressive interactions), close contact (e. g. as recorded using proximity loggers) or co-occurrence of individuals within a group or at a particular location. Sometimes edges will represent more abstract indications of the social relationship between individuals based on one or more of these data sources. In typical network approaches all nodes will represent the same "type" of entity (e. g. you wouldn't mix individuals and locations) and edges only connect pairs of nodes (or dyads). However, alternative network representations also discussed below relax these restrictions. For example, bipartite networks can be used to represent networks with interactions only between two types of node  (Larremore et al.
2021b). In addition, for some animal network datasets including both the frequency and duration or strength of interactions could provide valuable additional information. In this case it is necessary to analyse a weighted multigraph (Fig. 1c ). For example, when testing hypotheses in grooming networks it may be that the length of individual grooming bouts and frequency of grooming bouts provide independent information about the social relationship between two individuals. Taking this approach can open up new research questions about the relative importance of frequent versus long duration social interactions in group social structure and stability. It may also be important, for example, when studying social contagions if the likelihood of transmission depends on the duration of interactions (e.
g. for less infective pathogens or for social learning of more complex behaviours). When using multigraphs in this way it will be important to control for variation in sampling effort (e. g. the number of times individuals were observed) if this varies among individuals when conducting subsequent statistical analyses. Using multigraphs can also create challenges when representing networks visually (especially with many edges between nodes) and is more computationally intensive than using weighted networks, so using them should be reserved for contexts in which maintaining the independence of the frequency and duration of interactions provides valuable additional information on social relationships and their ecological and evolutionary consequences as outlined above. The R package igraph  (Csardi & Nepusz 2006)  facilitates storing and representing weighted multigraphs.
1  in  (Facchetti et al. 2011)). The presence of unbalanced triads (e. g. the triad described in the previous sentence) in a signed network could be used to predict network dynamics or changes in group composition. There may be interest in investigating the relative importance of structural imbalances involving different combinations of positive and negative ties. Similarly, the commonly-used stochastic block model has been extended to signed networks with the aim of identifying clusters or communities characterized by positive interactions with each other but negative ties with other clusters  (Jiang 2015). This offers a very natural way to characterize complex social structures such as those dominated by matrilines or where alliances govern access to mates or reproductive opportunities. Analysis of signed networks in R can be conducted using the R package signnet  (Schoch 2020) , an extension of igraph for signed networks.
Bipartite (two-mode) networks Bipartite (or two-mode) networks connect two different types of node, with connections between the same type of node not possible  (Larremore et al. 2014 ) (Fig. 3 ). They have been commonly used to study ecological networks such as plant-pollinator  (Dupont et al. 2014; Miele et al. 2020)  or host-pathogen  (Valverde et al. 2020; Albery et al. 2021)  networks. However, one of the classic social network datasets -the Davis' Southern women networkillustrates the potential values of bipartite networks in behavioural ecology. The Southern women network links a set of 18 women to the parties or events that they attended  (Davis et al. 1941; Opsahl 2013). This is equivalent to group-based methods of animal social network construction  (Franks et al. 2010; Farine & Whitehead 2015).
These datasets can be naturally represented as a bipartite network linking individuals to particular groups or aggregations (see Case Study: Alternative network representations of animal groups). Frequently, this network is then collapsed into a weighted network using the gambit of the group assumption (see Case Study: Alternative network representations of animal groups). Other datasets such as mating networks  (Fisher et al. 2016; McDonald & Pizzari 2016)  or those connecting individuals to locations they have visited (e. g. refuges, watering holes, foraging locations) are also a natural fit to bipartite representations (e. g. (Sah et al. 2016)). By representing these networks as bipartite rather than collapsing them to be conventional (unipartite) social networks, key structural information is maintained that would otherwise be lost.
This can be very helpful in addressing particular questions. For example, in the case of group-based networks, questions related to choices of group membership for individuals or in breaking down gregariousness into a tendency to be in more and/or larger groups. A wealth of tools is available to analyse bipartite networks, although predominantly tailored to other fields. For example, as well as (generalised) linear model approaches, exponential random graph models have been extended to incorporate bipartite dependency assumptions  (Wang et al. 2013 ) and the R package bipartite  (Dormann et al. 2008)  provides capability calculating a range of measures and fitting some more specialist models (albeit with the analysis of ecological rather than social networks in mind). It is important to note that issues with biased sampling (and potentially also identification errors) that apply to dyadic network representations will also apply to the statistical analysis of some bipartite networks, requiring careful consideration during statistical model design.
Here we provide a case study (Supplementary Materials) in which three research teams study the same social system. Because they are asking different questions using the dataset they elect to use different network approaches to represent their dataset. Research Team 1 are interested in whether individual social relationships are assorted by different phenotypic traits. Because the goal of their study is to infer potential social relationships in the population (with the assumption that individuals with strong social relationships will be found together more often in groups) using a dyadic network representation distils relevant information conveniently and provides an effective way to answer their question. However, in other contexts the weighted (dyadic) network represents a simplification that loses some information about the system.
Ego networks Ego networks represent only individuals (nodes) that a single focal individual associates, interacts or shares a social relationship with, along with the social connections between these neighbours (Fig. 5 ). If desired ego networks can be weighted, signed, multiplex, dynamic etc. in the same way as population or group-level networks  (Liu et al. 2018; Rezaeipanah et al. 2020; Wang et al. 2020). The package egor  (Krenz et al. 2022)  provides tools for ego network representation, visualisation and analysis in R. While ego networks are commonly used in sociological research, this has not extended to animal behaviour. Ego network analyses and measures typically focus on how embedded an individual is within its network neighbourhood or the extent to which it acts as a bridge between different neighbourhoods  (Butts 2008c).
General recommendations for choosing between approaches With such diverse approaches available and many applicable to the same datasets, choosing the best representation is not always easy. However, there are a few general rules that can help: • The research question should always be central to driving the choice of network analyses applied, and this extends beyond how edges are defined  (Carter et al. 2015; Farine & Whitehead 2015)  to broader considerations around network representations. For example, higher-order networks provide valuable additional information when researchers are interested in the ecological or evolutionary effects of larger (nondyadic) interactions, i. e. non-dyadic effects. • Sampling constraints are important when selecting representations to use. More complex approaches such as multilayer and dynamic network analyses are more data hungry and require more time-intensive sampling.
Network Representations Case Study Matthew Silk In this case study I will use association-based (gambit of the group) data to illustrate the value of using different network representations to ask different research questions. I will first simulate a data set of observations of individuals in groups, in which group membership is determined by an underlying social network that depends on various phenotypic traits. I will then set up three research teams, each with different questions, that will analyse this data set in different ways. Team 1 will use weighted dyadic networks to test whether individual social relationships are assorted by different phenotypic traits Team 2 will use bipartite networks to: a) quantify whether differences in individual gregariousness are better explained by the number of groups they occur in or the average size of groups that they occur in; and b) ask if different social groups are nested (i.
library(igraph) library(boot) library(genNetDem) library(asnipe) library(assortnet) library(bipartite) library(vegan) library(ergm) library(latentnet) library(sbm) The next step is to provide additional functions that are needed to simulate the data. The functions here are adapted from the genNetDem R package (https://github. com/NETDEM-project/genNetDem). I will not show this code chunk in the output. I can then simulate the data set. First, the individuals and their traits.
Acknowledgements This project has received funding from the  European Union 's  Horizon 2020 research and innovation programme  under the  Marie Sklodowska Curie  grant agreement No. 101023948. I'd like to thank  Josh Firth , two anonymous reviewers and the editor for constructive comments on the first submission of the paper. I'd also like to thank  Julian Evans  and  Nina Fefferman  for their thoughts on a draft of this paper along with the many other colleagues I have discussed social network analyses with especially  Noa-Pinter Wollman ,  Liz Hobson  and  David Fisher  who have all discussed ideas with me directly related to this paper.
These data were collected through 19 semi-structured individual interviews, three focus groups and three months of participant observation during an immersive field mission. We developed a systemic approach by combining data on biophysical and social dimensions of the landscape. Our analysis shows that in the absence of continued anthropic interventions, both savannahs and swamps dominated by herbaceous vegetation will experience closure by encroaching woody vegetation, leading to eventual biodiversity loss. Our methodology based on an SES approach to landscapes could improve the conservation programs developed by Ramsar site managers. Designing actions at the local scale, rather than applying one set of actions to the entire protected area, allows the integration of human perceptions, practices and expectations, a challenge that is more than essential in the context of global change.
Data collection and analyses To study the landscape through a socio-ecological approach, both qualitative and quantitative data are necessary. These data were collected during an immersive mission of three months between June and September 2022, following a first exploratory mission of 15 days in April 2022. This immersive field mission allowed collection of qualitative and quantitative data about local livelihoods and perceptions of landscapes, through field observations and exchanges with local populations. Geographical and botanical data concerning the structure and dynamics of the landscape were collected during field visits using a GPS device. All local names collected in the Myéné language are written in [square brackets]. Finally, note that the following subsections are presented in the chronological order of their implementation in the field, highlighting an approach through local knowledge, using ethnographic methods, before conducting analyses of remotely sensed data.
Qualitative data on livelihoods and landscape perceptions Different qualitative methodologies from the social sciences were used to collect local knowledge about inhabitants' perceptions of the landscape, the exploitation of natural resources, and more generally the livelihoods of local populations. Thus, focus groups, semi-structured interviews and participatory observation constitute the panel of qualitative methods used in this study. All surveys were conducted in French and did not require an interpreter, as the entire population is French-speaking. First of all, work with three focus groups was conducted, the first comprising the inhabitants of N'Tyatanga and Amendje, the second comprising the inhabitants of Ompomona, and the last the inhabitants of Azo II and Bordeaux. Each of these focus groups included approximately ten people, including men and women of all ages, all engaged in the human activities practiced locally, namely agriculture, fishing, hunting and gathering or logging.
Quantitative data on land use After determining, through focus groups, the different classes of land units that comprise the landscape according to local perceptions, a questionnaire was conducted with 66 men and women living in the area. They were asked to name the activities that they personally carried out in each class, and to rate the value of the class for the corresponding activity between 0 and 5. In a second step, they were asked to give two global scores to the land-unit classes, one for the socio-economic value and the other for the socio-cultural value, both scores being also between 0 and 5. This questionnaire allows quantifying the importance of the different classes for human activities and practices, and determining the land uses within the local landscape.