dataesr/scientific-paragraphs-categorization huggingface dataset:
In general, the SPECTRAL layout is easier to be learned by the models. This can be due to the fact that the Laplacian PE represent an optimal feature for this task, given the common spectral approach. Even from a qualitative perspective generated layouts are almost identical to the Ground Truth. Vice versa, the KAMADA-KAWAI layout represents an harder task to be learned from ground-truth positions, especially in the case of the SPARSE dataset. As pointed out in  [52] , Laplacian-based PE have still some limitations given by natural symmetries such as the arbitrary sign of eigenvectors, that several recent works are trying to solve  [49].
For this 8 We used the following average Stress definition to avoid potential numerical issues: experiment, we use the stress value obtained on the validation split as the metric to select the best performing model. We report in Figure  5  and 6 some qualitative examples of the graph layouts produced by the best selected GNN models on test samples (the same graphs selected for Figure  3 ) of the two datasets, following the aforementioned setting. Noticeably, all three models succeed in producing a layout that adheres to the typical characteristics of graphs obtained via Stress STRESS(P ) = 1 D i<j w ij ||p i -p j || -d ij 2 where D is the number of considered node couples. minimization. 9 Also in this case, it is easy to see from a qualitative analysis that the GAT model is the best performing one.
The peculiar characteristics of the SPARSE dataset (sparse connection patterns, causing many symmetries and isomorphic nodes) entail a hardship in minimizing the stress loss function in some of the reported examples. A quantitative comparison is reported in Table  III , with the stress values obtained by the best models for each competitor and dataset, both at training time and test time, averaged over three runs initialized with different seeds. Once again, GAT performs the best. The metrics obtained by the GIN model highlight an overfit of the training data, given the selected grid parameters. Summing up, the experimental campaign showed the generalization capabilities of the proposed framework even in the task of minimizing common aesthetic criteria imposed on the GNNs node-wise predictions, such as the stress function, on unseen graphs.
Given such predicted node positions and the input graph adjacency matrix, the Neural Aesthete (which was trained beforehand as explained in Section III-A) processes couples of arcs and output their degree-of-intersection. The overall loss function can then be composed by the contribution given by each of the considered arc-couples, as in Eq. 5. In order to provide a qualitative proof-of-concept of our claims, we built a synthetic dataset, which we refer to as SMALLSPARSE, composed of 1000 graphs, with the same procedure as for the SPARSE dataset described in Section IV-C. It only differs for the graph size, ranging in the interval  [10, 30]  with the purpose of facilitating the task of edgecrossing avoidance. We split the dataset in training, validation, test partitions with ratio (75%, 10%, 15%) and early stop the learning on the validation loss with a patience of 20 epochs.
STATISTIC SIMILARITY (DEFINED IN EQ. 12) ON THE TEST SPLIT OF THE ROME AND SPARSE DATASET. WE COMPARE THREE GNN MODELS WITH TWO GRAPH LAYOUTS GENERATION, KAMADA-KAWAI AND SPECTRAL. WE REPORT THE AVERAGE VALUED AND ITS STANDARD DEVIATION OVER THREE RUNS WITH DIFFERENT WEIGHTS INITIALIZATION. In order to give a more comprehensive analysis, we report in Table II a quantitative comparison among the global Procrustes Statistic similarity values obtained on the test set by the best models, for both datasets. We report the average score and its standard deviation over three runs with different seeds for the weights random number generator.
Recent tools addressing memory safety of C programs at runtime, such as Valgrind and MemCheck  [36, 42] , DrMemory  [10]  or AddressSanitizer  [41] , have become very popular and successful in detecting bugs when the program is running. However, their soundness is usually not formally established, and often does not hold, since most of them rely on very eicient but possibly unsound heuristics  [49] , such as redzoning  [41]. While for a reported bug, it can be possibleÐat least, in theoryÐto carefully analyze the execution and check whether an error is correctly reported, the soundness of the łno-bugž verdict cannot be checked. For runtime assertion checking, soundness becomes a major concern. Often applied in complement to sound static veriication techniques, RAC is used to check the absence of failures on parts of annotated code which were not (yet) proved  [33].
The contributions of the paper include: • a formalization of all major steps of a runtime assertion checker for a representative imperative language with assertions; • a deinition of an observation memory model, suitable for a modular deinition and veriication of program transformations injecting non-interfering code for observing and monitoring block-level memory properties; • a formalization  2  and proof of consistency of the proposed axiomatic deinitions of the execution and the observation memory models and their key properties in Coq; • a proof of soundness of a runtime veriier for block-level memory properties. Outline. Section 2 gives an overview of the work and a motivating example. Section 3 deines the source language, including an assertion statement and a language of predicates, and its semantics.
It makes our results applicable to various implementations, as soon as they satisfy this speciication. The memory model of our source language is an adaptation of the irst version of CompCert's  [29]  memory model  [30]. The block structure of this model its the concept of block in E-ACSL speciications. Moreover, the CompCert model was designed in the context of a C compiler, and our language can be seen as a subset of C. In this model, at every moment of program execution, the program memory (state) consists of a set of memory blocks. Each block has a size and a unique identiier. A byte in the memory is identiied by the block it belongs to   and an ofset being the index of this byte in the block. The set of memory states is denoted by mem, and block denotes the set of block identiiers. The predicate ⊨ deines the validity of a block in a given memory, while the function length gives its size.
The signatures of all memory operations are given in Fig. 6. We assume we always have suicient memory, so allocation cannot fail, while all other operations may fail. That is why they return a value of type option t, which adds a speciic value for a failing operation. The returned value is in case of a failure, and ⌊⌋ where has type t in case of success. The initial memory of CompCert was not speciied for many cases that cannot occur within the operational semantics of CompCert languages. This is not the case here: we want to express a relationship between the execution memory and the observation memory. The observation memory stores information that is more detailed that what is needed in CompCert. Therefore our execution memory is less abstract and its behaviour is speciied in more cases than the CompCert memory model.
In the last case, the value can be Undef (e. g. unintialized), so in some of the evaluation rules below, an additional check of the form ≠ Undef will be used to eliminate this case. In order to exclude any risk of inconsistency in the axioms of the execution memory model, we formalize them and prove their consistency with respect to a simple implementation using the Coq proof assistant  [7]. We implement the signatures of Fig. 6  and the axioms of Fig. 7  in a module type (see ile ExecutionMemoryModel. v in our Coq formalization). To check the consistency we implement a module that respects this module type by giving deinitions for the functions and proving the axioms as lemmas (see ile ExecutionMemoryImplementation. v). As mentioned above, Axiom  (10)  and the case returning Undef in Axiom (  9 ) do not actually occur during the execution of our programs with the considered operational semantics because of well-typedness and wellalignedness of memory accesses.
Operational Semantics The semantics of our source language is a big-step semantics adapted from CompCert's semantics  [9]. We use an error-free blocking semantics: the evaluation cannot proceed in case of an error. We have ive evaluation relations, all captured by the following schema: context ⊨ mode syntactic object ⇓ result. In the source language, an (evaluation) context = (, ) is a pair consisting of an environement and a memory state. When there is no risk of ambiguity, parentheses in (, ) will be omitted. An axiomatic deinition of memory states and operations was given in Section 3. 4. An environement is a partial injective mapping : → block which maps variable names to block identiiers. It is used to identify in which memory block the value of a given variable can be found. More precisely, for a variable name , if there exists a block containing , then is deined for and we write () = ⌊⌋.
Finally, Axioms (  36 ),  (37)  state that all blocks are invalid and all locations are non-initialized in ∅. As for the execution memory model, in order to exclude any risk of inconsistency in the axioms of the observation memory model, we formalize them and prove their consistency with respect to a simple implementation in our Coq development in the same way as for the execution memory model. We deine a module type for signatures and axioms and provide another module satisfying this module type to implement the functions and to demonstrate that they satisfy the axioms.
This language is arguably a much larger language than ours. However, the observation memory model introduced in this paper is representative of spatial memory errors occurring in C (without inline assembly code): we only need to know the memory efects done by each C statement or expression in order to decide how to instrument the code. Our programming language also includes a dedicated let construct to model global and local variables, and this choice simpliies our formalization. Support for local blocks and global and local variables instead of this construct is easy to implement in practice. Additionally, we also rely on a memory model broadly inspired by CompCert  [30]  to model the execution memory of our C-like language. Our memory models support badly typed and badly aligned accesses, even if our current source and target languages do not include them.
The C ++ standardization committee considered contracts for C ++ 20, although this new feature has been inally deferred to a later standard. In Eifel, assertions are Boolean expressions written in the programming language. In Ada 2012, it is also the case, but the language has been extended with quantiied expressions to allow bounded universal and existential quantiication. These new expressions have been inspired by Spark, a well-deined subset of Ada, extended to express contracts for static and dynamic veriication. Zhang et al. [51]  study veriied runtime checking in the context of Spark: the checks to be performed are however not explicitly stated as assertions in the source language, but are implicit (e. g. division by zero). The authors provide a formalization and proof using the Coq proof assistant  [7].
Findler et al. [15, 16]  study runtime checking in the context of object-oriented language such as Java, focusing in evaluating contracts' pre-and postconditions in presence of method calls and inheritance. They prove the soundness of their approach. Cheon  [12]  formalizes RAC of JML, but provides no proof of soundness, while Lehner  [28]  formalizes the semantics of a large subset of JML and proves in Coq an algorithm that checks assignable clauses at runtime. Such clauses are memory properties that do not require memory observation. As our work focuses on memory observation, it is related but complementary to these works. Indeed, in the context of Java and Ada, even runtime checks for out-of-bounds accesses are related to arithmetic inequalities. In the case of C, however, as the bounds of an array are not attached to the array itself, out-of-bound accesses correspond to invalid accesses to the memory, and are therefore handled in ACSL by the predicate \valid.
Engagement is the process by which participants establish, maintain, and end their perceived connection. Automatic engagement inference is one of the tasks required to develop successful human-centered HMI applications. Engagement is a multi-faceted multimodal construct requiring high accuracy in interpretating contextual, verbal and non-verbal cues, making the development of an intelligent automated engagement inference system challenging. Existing surveys concentrate on specific application settings, and a comprehensive survey covering the different engagement facets, definition and inference across various contexts is lacking. Moreover, despite the importance of context-aware modeling, the literature lacks a systematic context-aware overview on the topic. This paper presents a comprehensive survey on previous work in engagement for HMI, entailing interdisciplinary definition, engagement components, publicly available datasets, ground truth assessment, and commonly used features and methods, serving as a guide for the development of future HMI interfaces with reliable context-aware engagement inference capability.
Personal Factors Personal factors such as the user's gender, culture, age, ethnicity, personality, or if the user has a certain pathology were underlined in the literature as intrinsic factors affecting the engagement state of an individual  [79]. From the system's perspective, specifically in embodied HMI, the system's personal factors (e. g. gender, personality) were also found to directly affect the user's engagement state. Other personal factors such as age and ethnicity are not explored in the literature of engagement inference. This might be related to the fact that most studies in engagement restrict their studies to specific age groups (e. g. adults or children), and it is rare to find studies with datasets that include different age groups or different ethnicities. Gender. The effect of gender on user's engagement was discussed in some studies  [78] ,  [80].
Data Acquisition Usually data is collected using unimodal or multimodal sensors such as microphones, cameras, 3D sensors (e. g. Kinect c ), and physiological sensors. However, the choice of modalities depends on the context of application. Collected samples are then given ground truth labels reflecting the perceived or reported engagement state of the user. Engagement ground truth assessment largely depends on the context in which the engagement is being measured. Compared to emotion data annotation where categorical and dimensional scales are commonly used to assess emotions ground truth  [96] , there are no common scales used to collect engagement ground truth. Whether to treat engagement as a process, a discrete or a continuous value, or to concentrate on a specific component of the construct (e.
g. behavioural vs. cognitive engagement) is highly dependent on the interaction context and end-goal. Moreover, there is no agreement on the optimal time scale for engagement annotation, e. g. frame-level or segment-level (cf. Section 4. 2). Indeed, in the literature, there is no unified strategy for user engagement state annotation. In the following, we give an overview of the publicly available engagement datasets (Section 3. 1. 1) as well as common annotation strategies to obtain ground truth data (Section 3. 1. 2). We finalise with reviewing the problem formulation for engagement and the definition of categories that commonly appear in the stateof-the-art (Section 3. 1. 3).
Publicly Available Datasets Since engagement is a context-dependent construct and a relatively recent subject in human-machine interaction, there are only a few publicly available datasets in the literature, which provide engagement annotations. These datasets are given in Table  2  and are introduced based on the interaction mode below. HHI. The Remote Collaborative and Affective Interactions (RECOLA) database  [97]  provides engagement labels in addition to set of affective and social behaviour annotations including arousal, valence, agreement, dominance, performance, and rapport in a mediated interaction context. The participants in this corpus were recorded remotely in dyads during a video conference while completing a collaborative task (the survival task). In addition to video, the corpus includes audio and physiological data (ECG and EDA).
Engagement annotations in this corpus are performed for each interaction session with a discrete Likert scale of (1 -7). Another HHI dataset is the NOvice eXpert Interaction (NoXi) multi-lingual dataset  [98]. NoXi features natural screen-mediated dyadic human interactions between a novice and an expert. The context of the dataset is social and educative, where it features spontaneous social human-human interactions as well as information exchange where the participant playing the role of the expert transfers their knowledge to the novice participant on a specific topic of their expertise. The dataset provides audio-visual data, in addition to discrete engagement annotations. Relevant non-verbal social signals to engagement such as gestures, smiles, turn-taking, and dialogue acts are also included in the dataset.
HCI. Existing datasets in HCI are mostly recorded in the context of online learning. For instance, the DAiSEE dataset  [99]  includes learner's videos captured while they were watching a video tutorial, with a webcam mounted on a computer. It was collected in unconstrained conditions at different locations with varying illumination settings. Learner's engagement level as well as relevant emotions (bored, confused, and frustrated) annotations on a scale of (0 -3) are provided for each video. Similarly, "inthe-wild" dataset  [70]  for engagement assessment includes student's videos collected via Skype in an unconstrained environment. Engagement levels were annotated using crowdsourcing in terms of 4 classes, including disengaged, barely, normally, and highly engaged. Finally, the HBCU dataset  [41]  includes student's engagement level annotations assessed via crowdsourcing on data captured as the participants were engaged in a cognitive skill training study.
HRI. The Multimodal Human-Human-Robot Interactions (MHHRI) Dataset  [102]  was introduced for studying the relationship between personality and engagement simultaneously in dyadic HHI and triadic HRI. The context of the dataset is purely social revolving around personal questions asked by the interaction entities to each other. The dataset was recorded using biosensors, Kinect depth sensors in addition to first-person vision cameras attached to the participants heads. The engagement state of the users was assessed with a post-study questionnaire asking the participants about their perceived enjoyment of the interaction. In a later study  [103] , labels from external annotators were obtained for this dataset using crowdsourcing. Another HRI dataset, the User Engagement in spontaneous HRI (UE-HRI) dataset  [106] , was presented to study spontaneous social interactions between humans and a robot.
The dataset includes 54 dyadic HRI interactions with the robot Pepper situated in a public space, collected over a period of 56 days. The dataset was recorded using two 2D cameras, a 3D depth sensor, 4 directional microphones, sonar, and laser sensors. Recorded streams include face, speech, gesture, and dialog features. Engagement labels were obtained by external annotators. In an educative HRI context, the Productive Engagement in HRI (PE-HRI) dataset  [104]  is a multimodal dataset that allows studying engagement in collaborative robotmediated educational contexts. The dataset includes productive engagement scores which are computed via a linear combination of the most discriminatory features  [109]. Additionally, the dataset consists of multimodal team level behaviours and learning outcomes (34 teams of two children).
An important advantage of rule-based engagement inference approaches is explainability, an important aspect to take into account to avoid potential unwanted bias towards certain protected social groups (e. g. gender or race). Other advantages include the simplicity and rapidity of implementation, and the non-necessity of large training datasets. On the other hand, such advantages come at the cost of ignoring important complex patterns that can be automatically discovered from data by machine learning models, compromising the accuracy of rule-based methods.
CONCLUSION In this paper, we presented a context-aware survey on engagement in human-machine interaction across various modes of interaction (HHI, HCI, HRI, and HAI). We reviewed more than 200 papers and we introduced widely used engagement definitions, available datasets, widely used features, and machine learning approaches. Engagement is a key component of social intelligence. We believe our survey will be a helpful guide for researchers working or planning to work on the problem of engagement inference, and aiming to equip machines with social intelligence. The most important conclusion from this research is that engagement is a context-dependent construct. The fact that the construct was defined and modelled differently across various application and interaction scenarios, confirms this statement.
ACKNOWLEDGEMENTS Funding: H. Salam is supported in part by the  NYUAD Center for Artificial Intelligence and Robotics , funded by  Tamkeen  under the  NYUAD Research Institute  Award  CG010. O. Celiktutan is supported by the  LISI -Learning to Imitate Nonverbal Communication Dynamics for Human-Robot Social Interaction  project, funded by the  EPSRC  (Grant Ref. :  EP/V010875/1 ). H. Gunes is funded by the  EPSRC/UKRI  under grant ref. EP/R030782/1 -ARoEQ:  Adaptive Robotic Emotional Intelligence  for Well-being. M. Chetouani 's work has received funding from  European Union 's  Horizon 2020 ICT-48 research and innovation actions  under grant agreements No  952026  ( HumanE-AI-Net ) and No  765955  ( AN-IMATAS ). Open Access: For open access purposes, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising.
Oxo-components were considered only for nomenclature. Clinopyroxene is recalculated at 4 cations and 6 O, feldspar at 4 O, and biotite at 11 O. The apatite formula is recalculated according to  Ketcham (2015). Results of mineral-chemical analyses are shown in Tables  2  and 3. The dataset is attached as Supplementary File S2. Crystallization temperature (± 45 • C) and pressure (± 0. 5 GPa) for  igneous clinopyroxene was estimated by using the single-phase thermobarometer of  Putirka (2008). Crystallization temperature (± 30 • C) for igneous amphibole was estimated applying the single-phase thermometer of  Putirka (2016). Estimates on igneous amphibole crystallization pressure were avoided since amphibole barometers are less accurate than clinopyroxene barometers (see Putirka, 2016 for a discussion).
BCR-2G glass was included in the analytical run as a quality control sample. The raw data was processed using GLITTER software  (Van Achterbergh et al. , 2001). The results are in Supplementary File S3. Biotite 40 Ar/ 39 Ar geochronology was performed at Géoazur, Université Cote d'Azur with an ARGUS VI mass spectrometer from Thermo-Fischer. A sample from Nembra was crushed and a 300-500 μm size fraction was cleaned in ultrasonic bath. Igneous biotite grains without evidence of alteration and inclusions were handpicked under a binocular microscope and packaged in aluminum foils and irradiated for 97 h in the McMaster Nuclear Reactor together with Fish Canyon sanidine grains as flux monitor (28. 030 ± 0. 056 Ma,  Jourdan and Renne, 2007). Raw data from each step and blank were processed, and ages were calculated using Ar -Ar CALC software  (Koppers, 2002).