dataesr/scientific-paragraphs-categorization huggingface dataset:
Data graph acquisition We have created a new dataset containing information from both DBpedia and Eurostat. From both sources we have extracted data of type: dbo:Settlement, dbo:City, and dbo:Town. Note that in the DBpedia ontology 16 the classes dbo:City and dbo:Town are subclasses of the class dbo:Settlement. Therefore, we use the term settlement to refer to all of them. We also notice that certain big cities such as Montpelier are annotated in DBpedia with their superclass dbo:Settlement rather than the more precise annotation dbo:City. Eurostat data has been transformed into RDF and related with their WikidataID then associated to DBpedia using the owl:sameAs relation. Eurostat and DBpedia datasets have been merged obtaining 5841 triples corresponding to 869 instances with 16 properties.
Results for the nested and inferences scenarios In this section we present the results obtained using QAVAN in the DBpedia-Eurostat dataset. We expose in detail our findings and we answer the proposed research questions. Table  11  presents the results of QAVAN on DBpedia Eurostat considering three different scenarios, i. e. , the default one, one using Nested ANRs and finally one using both Nested ANRs & Inferences, over three different queries (𝑞 1 , 𝑞 2 and 𝑞 3 ). QAVAN allowed us to represent the above mentioned mathematical formulas in form of ANRs for the class dbo:Settlement. However, relying on the scenario that each formula was or not activated, later we explain in detail the ANRs activated by scenario. Note that in all scenario the execution time was less than 2 s for all the tests showing that QAVAN is also efficient for such datasets.
Our evaluation for the two approaches exhibited similar execution time although QAVAN performs a partial materialisation before answering the query. In this experiment, we notice that PerfectRefEQ provides more results that QAVAN. Note that in PerfectRefEQ if a property participating in a formula (i. e. , calculable property) exists in both datasets and has different values for the same instance, two different answers are going to be created. For example, for the resource dbr:Montpellier, having the properties dbp:urbanPop=449187 and eurostat:populationTotal=364723, PerfectRe-fEQ returns two answers for the population density of this resource. This is not the case for our approach since we set priorities in the input dataset based on their quality. For the moment this step is performed manually for QAVAN but an automatic strategy can be deployed in the future.
Discussion of QAVAN extension evaluations on DBpedia and eurostat datasets In this second evaluation, in addition to the processing time, we were also interested to evaluate the number of results obtained when the nested and inference features are activated. This evaluation demonstrates that our approach is generic and it may apply for well-known KG. Moreover, we show that, since we follow W3C recommendations, extending the approach with new features is straightforward. In particular, the implementation of the nested feature was facilitated by having the mathematical formulas in a LOD format, whilst the inference feature was facilitated by enabling ontological reasoning in the query-answering engine. Each of the research questions formulate on Section 5. 3. 3 are discussed next. Answer to RQ1.
Introduction Clustering is a popular and valuable data mining technique aimed at revealing a hidden structure within a dataset. The revealed structure is commonly expressed as a collection of homogeneous subsets called clusters. According to Mirkin and Muchnick  [23] , there are three major approaches to determine a cluster as based on definition, direct algorithm and optimality criterion. The present paper is mainly concerned with some definition-based clusters, namely clusters defined as being convex in the sense of an interval function. An interval function I on a dataset S is a symmetric function that maps each ordered pair (x, y) ∈ S × S to a subset I(x, y) of S, containing x and y. The subset I(x, y) is called the I-interval of extremities x and y. A subset A of S is said to be convex in the sense of the interval function I, or I-convex, if it contains each I-interval whose extremities belong to A.
e. the collection of the whole dataset and its singletons) only by a few small non trivial clusters (cf. [13] ). It results that in the context of an applied data analysis, the interest per se of the Apresjan hierarchy is often limited. By showing that the set of D-convex subsets coincide with the collection of Apresjan clusters, the next proposition gives the semantics of D-convex subsets. Proposition 12. For all dissimilarity δ on S and all nonempty subset C of S, the following statements are equivalent. (i) C is an Apresjan cluster of δ. (ii) C is D δ -convex. (iii) δ(x, y) < δ(x, z) for all (x, y, z) ∈ C × C × (S ∖ C). PROOF. (i) ⇔ (ii). Let C be a nonempty subset of S and δ a dissimilarity defined on S. First, assume that C is an Apresjan cluster of δ, and consider two elements x, y of C.
D ) instead of notations D SL (δ) (resp. D (δ)). Figure  7  displays the curves of ∆(ρ ) and ∆(δ ) when varies. We observe that ∆(ρ 10 ) < 0. 05, which indicates that D 10 is a faithful simplification of dendrogram D SL. In order to display clearly the differences between D SL and its simplified dendrogram D 10 , we restrict our comparison between a (non trivial) subdendrogram of D SL (cf. Figure  8 (a) ) and its corresponding part in D 10 (cf. However, the Apresjan hierarchy of an ultrametric dissimilarity coincides with its single link hierarchy (cf. Proposition 29), so that it may contain clusters of arbitrary sizes. By an argument of continuity, the Apresjan hierarchy of a dissimilarity δ whose distortion ∆(δ) is small, may also contain clusters of arbitrary size. If the distortion ∆(δ) is not small, our experimentations have confirmed that Apresjan clusters of such datasets are, in general and as expected, small sized.
This assertion outlines guidelines for identifying single-linkage clusters whose size is large enough, and which are both compact and isolated in the sense of a more or less strengthening of the single-linkage criterion. By way of example, there are forty-seven non trivial Apresjan clusters for the Iris flower dataset: forty-one are of size 2, five of size 3 and one of size 4, which is consistent with the assertion that Apresjan clusters of an arbitrary dissimilarity are generally small-sized. Regarding clusters of interest to data analysts, it is well known that applying a standard partitionning method to the Iris dataset leads usually to identify clearly two clusters: the cluster of Setosa iris, say A, and the cluster that gathers Virginica and Versicolor irises, say B. Computations show that A and B are single-linkage clusters such that: λ(A) = 2 with A = 50 and λ(B) = 4 with B = 100.
With respect to the guidelines roughly defined above for identifying relevant single-linkage clusters, these numerical results and the graph presented in Figure  9  are consistent with the common knowledge that clusters A and B are the most pertinent single-link clusters of the Iris dataset. However, additional theoretical and empirical insights are clearly required to make these guidelines both more precise and reliable. Recall that δ = δ +1 if ≥ r(δ), so that this inequality is obvious for ≥ r(δ) -1, and therefore the conjecture holds true when r(δ) ∈ {1, 2}. This conjecture suggests a general property of dissimilarities, whose formulation is rather simple, but whose study is not straightforward for r(δ) ≥ 3. As a consequence, the conjecture seems beyond the scope of this paper. While the idea of an unifying framework based on abstract convexity in order to characterize several multilevel clustering models has been discussed before (cf.
Given its simple and accurate description of natural synchronization phenomena, the Kuramoto model has also inspired the design of distributed communication protocols in engineering applications where the coupling function among different agents can be arbitrarily assigned to achieve synchronization, as in the bio-inspired synchronization of moving particles in  (Sepulchre et al. (2007) ), the synchronized acquisition of oceanographic data from Autonomous Underwater Vehicles  (Baldoni et al. (2007) ), in clock synchronization  (Kiss (2018) ), in mobile sensors networks modeled as particles with coupled oscillator dynamics  (Paley et al. (2007) ), in monotone coupled oscillators  (Mauroy and Sepulchre (2012) ) or in other engineering applications surveyed in  (Dörfler and Bullo (2014) ). While the sinusoidal coupling of Kuramoto models provides a powerful tool to obtain synchronization in coupled networks of oscillators, it also introduces some undesirable properties for engineering applications.
These methods estimate the financial risk associated with the operation costs. Only when the expected cost does not exceed the confidence level α, V a R can be used to assess risk. C V a R is a better mechanism because it allows a more robust solution when the scenario costs exceed α. In this situation the value of α considered was 95%, a typical value for this parameter  [5]. The value of V a R α is calculated through the cumulative probability distribution function, after knowing the value of the expected cost ( f exC ), which is calculated through a weighted sum of the total scenario costs ( f totC s ) and the scenario probability (π s ). With this information, C V a R α can be calculated as follows: C V a R α ( f totC s ) = V a R α ( f totC s ) + 1 1-α ∑ s∈N x π s × ( f totC s - f exC -V a R α ( f totC s )) (3) where the parameter N x is represented by the scenarios where the cost exceeds that of the expected cost in addition to the V a R α given by: f totC s ≥ f exC + V a R α ( f totC s ) ∀s ∈ N x (4) where: V a R α ( f totC s ) = z -scor e(α) × std( f totC s ) (5) zscor e is computed in MATLAB with α equal to 95% using the norminv() function.
Evolutionary algorithms Multiple state-of-the-art EAs are used in this problem together with DE, namely: Hybrid-Adaptive Differential Evolution (HyDE) and the three first EAs classified in this years' competition, namely Restart-assisted Selfadaptive DE (ReSaDE), Ring Cellular Encode-Decode UMDA (RCEDUMDA)  [23]  and Chaotic Levy Hybrid RCEDUMDA (CLHC2RCEDUMDA) based on  [24]. These following algorithms are proposed so we can compare with CUMDANCauchy, the algorithm utilized in  [4].
RCEDUMDA A cellular estimation of distribution algorithm is known as RCEDUMDA (Algorithm 4)  [24]. In this algorithm, a varied but encouraging sampling of the search space is the initial population that contains one of the solutions initialized with the variable's lower limits. It divides the global population into several tiny sub-populations using a ring structure. Additionally, it divides the continuous data into categorical variables (codes) during each neighborhood's reproductive cycle using an encoding technique, reducing the search space. Then the encoded solution is estimated and scaled (steps 12 and 13), and a new solution is generated. After this process, a decode needs to occur to transform the categorical variables into continuous variables, and this solution is inserted in an aux Pop, which then replaces the current (Pop).
Fitness evaluation The risk-based scheduling methodology's optimization approach seeks to reduce the OF cost in Eq. (  6 ). The database comprising all 15 created scenarios, including the extreme events generated as previously detailed in Section 2. 3, is loaded to begin the fitness function evaluation done by each EA. The value of the risk-aversioncontrolling variable (β) is likewise set. Then, for each scenario, variable bounds are updated according to the scenario data because load consumption and renewable generation are scenario-dependent, and if not corrected, costs wrongly associated with variable bound violations (B s ) are added to the f totC s. The total costs of each scenario are also calculated according to the mathematical formulation in Eq. (7). The expected price, V a R, and C V a R (Eqs.
Acknowledgments The authors acknowledge the support provided by the  Thematic Network   723RT0150  " Red para la   integración a gran escala de energías renovables en sistemas eléctricos (RIBIERSE-CYTED) " financed by the call for  Thematic Networks of the CYTED (Ibero American Program of Science and Technology for Development)  for 2022. José Almeida  is supported by  FCT  with Ph. D. Grant  2022. 09590. BD. João Soares  is also supported by the grant  CEECIND/00420/2022. The authors acknowledge the work facilities and equipment provided by GECAD research center ( UIDB/00760/2020  and  UIDP/00760/2020 ). Bruno Francois  acknowledges  Ecole Centrale Lille  to support this research and provide the necessary facilities. He also acknowledges the funds from  Centrale Lille  for supporting the invited professor visiting stay of  João Soares  in November 2022 and June-July 2023.
One interesting implication of such analysis would be the case in which only one of the qubits in an ebit is lost, and what happens if the loss is not communicated before other swapping operations are undertaken, i. e. the error propagates along the swapping route. All these considerations would require a more refined physical model, which would in turn imply revisions to our mathematical framework, but should not be excessively difficult to include in the numerical part of our discussion: the simulator code was written from the ground up in order to provide a simpler and more agile contribution, but it was designed with particular attention to keeping a layered and modular structure that should be reasonably adaptable to well-established quantum network simulation packages such as NetSquid  [47]  or QuISP  [48].
We acknowledge funding by the  French  state through the  Programme d'Investissements d'Avenir  managed by the  Agence Nationale de la Recherche  (project  ANR-21-CMAQ-0001 ) and by the  European Union 's  Horizon 2020 research and innovation program  under Grant Agreement No. 820445  and project name " Quantum Internet Alliance ". This work extends [1], which was presented at the  IEEE International Conference of Quantum Computing  and Engineering 2022.
Eyemovement recordings A virtual drum consisting of gratings with a frequency of 0. 16 cycles per degree (cpd) was displayed on 4 monitors (Dell U2412B) around the setup and drifted during the entire recording at 1Hz. The vestibular stimulus was delivered by the rotation platform in clockwise (CW) and counterclockwise (CCW) directions at 40 °/s. Images were recorded using an ELP-USBFHD01M web camera at 30 Hz. The pupil outlines were detected as illustrated in Figure  4b  using DeepLabCut  [14]. Briefly, 8 points were detected on the edge of the pupil (red circles), onto which an ellipse was fitted (cyan line). The pupil position was defined as the centre of the ellipse (red square). Data were acquired and analysed using custom-written Python scripts.
HD cell recordings We followed the recording method from  [15]. We made post-subicular recordings (AP: -4. 25 mm; ML: -1 to -2. 5 mm; DV 1. 25 to 1. 75 mm from pia) from 2 adult male mice for at least five full bidirectional rotations in passive and at least 1 (but typically 3-4) full cycles in active rotation. Extracellular recordings were made using a tetrode-arranged silicone probe (A8x1-tet-2mm-200-121, Neuronexus), connected to a digitizing headstage (RHD2132, Intan technologies) via an adaptor (Adpt. A32-Omnetics32, Neuronexus). Voltage signals were filtered (0. 1 -7. 5 kHz) and digitized at 24414 Hz using an LR10 interface and SynapseLite software (Tucker-Davies Technologies, TDT). Data were extracted using the TDT python SDK, spikes were detected and clustered using klusta  [16]  and further analysed using custom-written Python scripts.
Implementation We provide full documentation, including assembly instructions, design choices and characterization of the components and the platform, as well as software requirements and code at https://ranczlab. github. io/RPM/. In brief, the movement of the spherical treadmill is read out by optical sensors and fed through the rotary joint to connect to a microcontroller (PJRC Teensy ® 3. 5). In addition, the microcontroller receives information from a homing sensor and a rotary encoder (Figure  1a ). The microcontroller, in turn, controls the platform movement through the motor controller (Figure  1b ), and outputs the position of the spherical treadmill and the platform for recording. Other signals recorded on the platform, e. g. from cameras, or signals to the platform to control additional devices, can also be fed through the rotary joint (Figure  1c ).
A. Example: Neural Aesthete on small-sized Random Graphs We provide a qualitative proof-of-concept example for the aforementioned Neural Aesthete for edge-crossing in Figure  1. We built an artificial dataset composed of 100K entries to train the Neural Aesthete. Each entry of the dataset is formed by an input-target couple (x, ŷ). The input pattern x corresponds to the Neural Aesthete arcs input positions 2 as defined in Section III, whose node coordinates are randomly picked inside the interval [0, 1]. The corresponding target ŷ is defined as in Eq. 4. 2 Which are defined as x := [eu, ev] = [p i , p j , p h , p k ], given two arcs eu = (p i , p j ) and ev = (p h , p k ). We balanced the dataset composition in order to have a comparable number of samples between the two classes (cross/nocross).
We trained a Neural Aesthete implemented as a Multi-Layer Perceptron (MLP) with two hidden layers of 100 nodes each and ReLu activation functions, minimizing the crossentropy loss function with respect to the targets and leveraging the Adam optimizer  [56]. We tested the generalization capabilities of the learned model on a test dataset composed of 50K entries, achieving an accuracy of 97%. Hence, the learned model constitutes the Neural Aesthete for the task of edge crossing. Given an unseen input composed of a couple of arcs, the learned model outputs a probability distribution representing a degree of intersection. Following the common pipeline of Graph Drawing methods with Gradient Descent, the Neural Aesthete output represent a differentiable function that provides an admissible descent direction for the problem parameters P.
To test the capability of the proposed solution, we leverage an artificial dataset of random graphs with a limited number of nodes (N ∈  [20, 40] ). We generated Erdős-Rényi graphs with the method presented in  [57]  for efficiently creating sparse 3  random networks, implemented in NetworkX  [58]. We selected the connected component of the generated graph having the biggest size (max node number). Figure  1  reports a qualitative example of the proposed method in three graphs from the aforementioned dataset. To generate the graph layout, we carried on an optimization process on mini-batches of 10 arc-couples for an amount of 2K iterations (gradient steps). The first column depicts the starting random positions of the nodes; second column reports the graph layout obtained with an in-house implementation of the Stress function (see Eq.
C. Experimental setup We test the capabilities of the proposed framework comparing the performances of three commonly used GNN models (see Table  I ). In the following, we describe the learning tasks and the datasets employed for testing the different models. In Sections IV-D, IV-E and IV-F, instead, we will give qualitative and quantitative evaluations for each learning problem, showing the generality of our approach. Given the fact that the outputs of GND are node coordinates, we can impose on such predictions heterogeneous loss functions that can be optimized via BackPropagation. In the proposed experiments, we test the GND performances on the loss functions defined as the following: (i) distance with respect to ground truth node coordinates belonging to certain layouts, produced by Graph Drawing packages (Section IV-D); (ii) aesthetic loss functions (e.
g. Stress) (Section IV-E); (iii) loss functions provided by Neural Aesthetes (Section IV-F). We assume to work with solely the graph topology, hence the node are not characterized by additional features. We employed two different graph drawing datasets with different peculiarities. We chose to address small-size graphs (≤ 100 nodes) to assure the graph layout readability since prior works highlighted node-link layouts are more suitable to small-size graphs  [15] ,  [64]. The former one is the ROME dataset  5  , a Graph Drawing benchmarking dataset containing 11534 undirected graphs with heterogeneous structures and connection patterns. We preprocessed the dataset removing three disconnected graphs. Each graph contains a number of nodes between 10 and 100. Some samples of the dataset are reported in the first column of Figures  3  and 4 , drawn with different layouts (see the following).
We built a second dataset, which we refer to as SPARSE, with the same technique described in Section III-A. We generated 10K Erdős-Rényi graphs following the method presented in  [57]  for efficient sparse random networks and implemented in NetworkX  [58]. We randomly picked the probability of edge creation in the interval (0. 01, 0. 05) and the number of nodes from 20 to 100. To improve the sparsity and readability, we discarded all the created graphs having both more than 60 nodes and more than 120 edges. Afterwards, we selected the connected component of the generated graph having the biggest size (max node number). We report in Figure  2  a visual description of the datasets composition. In order to carry out the training process and afterwards evaluate the obtained performances, we split each of the datasets into three sets, (i.
The GAT model is composed by four attention heads. The variable in the GIN aggregation process is set to 0, as suggested in  [22]. We leverage the PyTorch implementation of the models provided by the Deep Graph Library (DGL) 7. We searched for the best hyper-parameters selecting the models with the lowest validation error obtained during training, in the following grid of values: size of node hidden states x i in {10, 25, 50}; learning rate η in {10 -4 , 10 -3 , 10 -2 }; the number of GNN layers in {2, 3, 5}; PE dimension k in {5, 8} (20 is added to the grid in the case of the SPARSE dataset, given its greater node number lowerbound); drop-out rate in {0. 0, 0. 1}. We considered 100 epochs of training with an early stopping strategy given by a patience on the validation loss of 20 epochs. For each epoch, we sampled non-overlapping mini-batches composed by β graphs, until all the training data were considered.
We searched for the best mini-batch size β in {32, 64, 128}. In Figures  3  and 4 , we report a qualitative evaluation obtained by the best performing models for each different GNN architecture on three randomly picked graphs from the test set of each dataset. Figure  3  shows the aforementioned evaluation in the case of the KAMADA-KAWAI layout supervision, both for the ROME dataset (first four columns, where the first one depicts the Ground Truth (GT)) and for the SPARSE dataset. Figure  4  shows the same analysis in the case of the SPECTRAL layouts. The results show the good performances of the Graph Neural Drawer framework in generating two heterogeneous 7 https://www. dgl. ai/ The Graph Attention Network achieves the best performances in all the settings. We believe that the attention mechanism plays a crucial role in the task of distinguishing the right propagation patterns, alongside the fact that the multi-head attention mechanism provides a bigger number of learnable parameters with respect to the competitors.