Lucas Jarnac
email: lucas.jarnac@orange.com

Miguel Couceiro
email: miguel.couceiro@loria.fr

Relevant Entity Selection: Knowledge Graph Bootstrapping via Zero-Shot Analogical Pruning

Keywords: Computing methodologies → Knowledge representation and reasoning, Artificial intelligence, • Information systems → Clustering and classification, World Wide Web knowledge graph, construction, analogical inference, zero-shot learning, graph embedding

Knowledge Graph Construction (KGC) can be seen as an iterative process starting from a high quality nucleus that is refined by knowledge extraction approaches in a virtuous loop. Such a nucleus can be obtained from knowledge existing in an open KG like Wikidata. However, due to the size of such generic KGs, integrating them as a whole may entail irrelevant content and scalability issues. We propose an analogy-based approach that starts from seed entities of interest in a generic KG, and keeps or prunes their neighboring entities. We evaluate our approach on Wikidata through two manually labeled datasets that contain either domain-homogeneous or -heterogeneous seed entities. We empirically show that our analogybased approach outperforms LSTM, Random Forest, SVM, and MLP, with a drastically lower number of parameters. We also evaluate its generalization potential in a transfer learning setting. These results advocate for the further integration of analogy-based inference in tasks related to the KG lifecycle.

INTRODUCTION

Knowledge graphs (KGs) are "graphs of data intended to accumulate and convey knowledge of the real world, whose nodes represent entities of interest and whose edges represent relations between these entities" [START_REF] Hogan | Knowledge Graphs[END_REF]. More formally, KGs are directed and labeled multigraphs (E, R, T ), where E is the set of entities, R is the set of relations, and T is the set of triples ⟨ℎ, 𝑟, 𝑡⟩ ∈ E × R × E, where 𝑟 qualifies the relation holding between ℎ and 𝑡. An example of such a triple could be ⟨BarackObama, instanceOf, Person⟩. KGs have proven useful in many academic and industrial applications, including search enhancement, question-answering, recommender systems, and eXplainable Artificial Intelligence [START_REF] Hogan | Knowledge Graphs[END_REF][START_REF] Noy | Industry-scale knowledge graphs: lessons and challenges[END_REF][START_REF] Tiddi | Knowledge graphs as tools for explainable machine learning: A survey[END_REF].

Building and completing a KG can be achieved with knowledge extraction approaches from structured or unstructured data (e.g., tables, texts) [START_REF] Sequeda | Designing and Building Enterprise Knowledge Graphs[END_REF][START_REF] Weikum | Machine Knowledge: Creation and Curation of Comprehensive Knowledge Bases[END_REF]. This forms a virtuous loop in which the KG is both a supporting structure that provides entities and relations of interest to detect in data and the target structure to refine and complete. However, the cold start problem appears when the initial KG is empty, which motivates the need to build first a high quality nucleus [START_REF] Weikum | Machine Knowledge: Creation and Curation of Comprehensive Knowledge Bases[END_REF]. Such a nucleus could be manually bootstrapped by experts, but this process is time-consuming. Some authors thus propose to focus on premium sources of entities and categories to automatically constitute the nucleus [START_REF] Weikum | Machine Knowledge: Creation and Curation of Comprehensive Knowledge Bases[END_REF]. In this view, several works consider Wikidata [START_REF] Vrandecic | Wikidata: a free collaborative knowledgebase[END_REF], a large and generic KG collaboratively built to support Wikipedia, as a premium source [START_REF] Jarnac | Wikidata to Bootstrap an Enterprise Knowledge Graph: How to Stay on Topic?[END_REF][START_REF] Shbita | Understanding Customer Requirements -An Enterprise Knowledge Graph Approach[END_REF]. However, the sheer size of Wikidata entails a need to restrict Wikidata knowledge to be integrated into the KG nucleus to avoid irrelevant knowledge and scalability issues. As Wikidata contains more than 100 million entities 1 , authors adopt a distillation [START_REF] Shbita | Understanding Customer Requirements -An Enterprise Knowledge Graph Approach[END_REF] or a pruning [START_REF] Jarnac | Wikidata to Bootstrap an Enterprise Knowledge Graph: How to Stay on Topic?[END_REF] process, in which seed entities 2 of interest are identified in Wikidata and only parts of their neighborhood are included in the KG nucleus (see Figure 1). The selection of the neighboring entities leverages the ontology hierarchy, either only upward [START_REF] Shbita | Understanding Customer Requirements -An Enterprise Knowledge Graph Approach[END_REF], or both upward and downward [START_REF] Jarnac | Wikidata to Bootstrap an Enterprise Knowledge Graph: How to Stay on Topic?[END_REF]. The latter brings much more entities, which makes it more prone to gathering irrelevant knowledge in the KG nucleus.

For instance, the downward neighbors of Microsoft SharePoint include Content Management System, a relevant entity to keep, and Dating App, an irrelevant one to prune. Jarnac and Monnin [START_REF] Jarnac | Wikidata to Bootstrap an Enterprise Knowledge Graph: How to Stay on Topic?[END_REF] thus use several pruning thresholds based on node degrees and distances in the embedding space but highlight the difficulty to set global thresholds when applied to heterogeneous entities with different distributions of degrees and distances. Additionally, to the best of our knowledge, there is no publicly available benchmark dataset to evaluate such approaches.

In our work, we propose to tackle the limitations of fixed thresholds by training classifiers to select (or keep) relevant neighboring entities and prune irrelevant ones in a KG bootstrapping process. Specifically, we propose an analogy-based zero-shot approach. Analogies are quadruples of the form Paris : France :: Berlin : Germany, which can be read "Paris is to France as Berlin is to Germany", that simultaneously capture similarities and dissimilarities between objects [START_REF] Miclet | Analogical Dissimilarity: Definition, Algorithms and Two Experiments in Machine Learning[END_REF][START_REF] Mitchell | Abstraction and analogy-making in artificial intelligence[END_REF]. Analogical reasoning is a remarkable capability of the human mind, that has recently obtained impressive results on NLP tasks when applied on character and word embeddings [START_REF] Lim | Solving Word Analogies: A Machine Learning Perspective[END_REF][START_REF] Marquer | A Deep Learning Approach to Solving Morphological Analogies[END_REF][START_REF] Sultan | Life is a Circus and We are the Clowns: Automatically Finding Analogies Situations and Processes[END_REF]. Such a reasoning has also been proposed for KGs [START_REF] Ilievski | Does Wikidata Support Analogical Reasoning?[END_REF][START_REF] Liu | Analogical Inference for Multi-relational Embeddings[END_REF][START_REF] Monnin | Interactions Between Knowledge Graph-Related Tasks and Analogical Reasoning: A Discussion[END_REF][START_REF] Portisch | Knowledge graph embedding for data mining vs. knowledge graph embedding for link prediction -two sides of the same coin?[END_REF][START_REF] Yao | Analogical Inference Enhanced Knowledge Graph Embedding[END_REF], using KG embeddings, i.e., vector representations of KG entities and relations that preserve as much as possible the properties of the graph [START_REF] Cai | A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications[END_REF].

In our approach, we combine analogical reasoning and graph embedding to keep or prune neighboring entities. Our intuition is that the analogy-based model will be able to capture relative similarities and dissimilarities between seed entities and their neighbors to keep or to prune, and thus avoid the caveats of fixed thresholds that have difficulty generalizing to heterogeneous entities. Furthermore, our approach is zero-shot: the model learns to detect relative similarities and dissimilarities on a set of seed entities and their neighbors and can extrapolate to unseen seed entities and their neighbors. We experiment our approach on the Wikidata KG and two annotated datasets of seed entities and their neighbors to keep or prune, and that we make available for the benefit of the community. We empirically compare the behavior of our approach with several classifiers (e.g., Random Forest, LSTM) and symbolic approaches (e.g., depth pruning, threshold pruning [START_REF] Jarnac | Wikidata to Bootstrap an Enterprise Knowledge Graph: How to Stay on Topic?[END_REF]). We also assess the performance of the different approaches based on evaluation metrics and number of parameters. Moreover, we test the generalization of this analogy-based approach on a transfer learning setting.

The main contributions of the paper are:

• We propose an analogy-based zero-shot approach to select relevant entities in the neighborhood of seed entities. This approach only needs training examples of entities to keep or prune for some seed entities and can extrapolate to new seed entities without selection / pruning examples for them. • We present a comparative study of our analogy-based approach to other methodologies with respect to different performance metrics, the number of parameters to be trained and the generality of the models considered. • We provide two annotated datasets of seed entities and relevant or irrelevant neighbors in Wikidata to start constituting publicly available benchmarks for the community.

The remainder of this article is structured as follows. We briefly survey related work about KG bootstrapping and analogy-based inference in Section 2, and we detail our analogy-based zero-shot approach to select relevant entities to bootstrap a KG in Section 3. We experiment with Wikidata and two datasets in Section 4 and we discuss our results in Section 5. Finally, Section 6 summarizes our work and outlines future research work.

RELATED WORK

Our work positions within approaches focusing on bootstrapping KGs, especially by pruning to limit the scope of the built KG. We review some prominent works of this line of research in Subsection 2.1. Additionally, we rely on analogical reasoning which has recently achieved significant performance on NLP-related tasks, and has been identified as a promising research direction for KGrelated tasks as outlined in Subsection 2.2.

KG Bootstrapping and Pruning

The construction of ontologies and KGs usually entails the possibility of their reuse for other purposes. That is why, it is common to leverage existing ontologies and KGs to bootstrap others [START_REF] Fernández-López | METHONTOLOGY: from ontological art towards ontological engineering[END_REF][START_REF] Swartout | Toward distributed use of large-scale ontologies[END_REF], since they can be seen as premium sources [START_REF] Weikum | Machine Knowledge: Creation and Curation of Comprehensive Knowledge Bases[END_REF]. To illustrate, YAGO3 combines the taxonomy of WordNet and the categories of Wikipedia pages [START_REF] Mahdisoltani | YAGO3: A Knowledge Base from Multilingual Wikipedias[END_REF], Knowledge Vault integrates the FreeBase KG [START_REF] Dong | Knowledge vault: a web-scale approach to probabilistic knowledge fusion[END_REF], and PGxLOD first integrates several biomedical KGs to then interconnect and enrich them [START_REF] Monnin | PGxO and PGxLOD: a reconciliation of pharmacogenomic knowledge of various provenances, enabling further comparison[END_REF].

Due to the size and generic aspect of some KGs and ontologies, some authors resort to pruning to construct domain-specific KGs from them. One of the early examples is the work of Swartout et al. in 1996 [START_REF] Swartout | Toward distributed use of large-scale ontologies[END_REF] where they propose to build a domain-specific ontology starting from a large and generic ontology, SENSUS, of 50,000+ concepts. To do so, they start with seed concepts from the domain of interest that are manually linked to SENSUS. They then include all super-concepts up to the root. They also discuss that some subtrees bring additional concepts of interest. They manually identify them with the rationale that if some nodes of a subtree have been identified relevant, then the other nodes of the subtree may be relevant too. However, such a manual process is time-consuming. Furthermore, incorporating subtrees of large ontologies may come at the expense of incorporating irrelevant knowledge, which is difficult to manually assess. To face such issues, automatic distillation or pruning approaches can be considered. The distillation process can be guided by documents from the domain of interest. For instance, Babayeva et al. develop a domain ontology for Cyber Defence exercises by collecting concepts from an existing ontology and documents on this topic [START_REF] Babayeva | Building an Ontology for Cyber Defence Exercises[END_REF]. Shbita et al. [START_REF] Shbita | Understanding Customer Requirements -An Enterprise Knowledge Graph Approach[END_REF] build a KG about customer requirements starting from client verbatim and Wikidata. Specifically, they detect entities in text, link them to Wikidata, and integrate their direct classes and all their super-classes.

Regarding pruning approaches, they can be classified into two categories: aggressive pruning based on topology of the graph and soft pruning that requires human input to define the relevant taxonomic concepts. In [START_REF] Faralli | Efficient Pruning of Large Knowledge Graphs[END_REF], Faralli et al. introduce the CrumbTrail algorithm that prunes a directed noisy knowledge graph with the aim of obtaining an acyclic subgraph that contains all previously selected seed nodes. Using this CrumbTrail algorithm, Bordea et al. propose to build domain-specific taxonomies from the KG of Wikipedia categories. After a user has selected leaf nodes and a root node, the algorithm is applied on the KG to build the directed and acyclic graph that will form the taxonomy. They provide three datasets but they are not directly applicable to our task. Indeed, they have specific concerns w.r.t. to taxonomy building (e.g., upward extension from leaves to root, acyclic aspect) while we mainly focus on gathering terms of interest w.r.t. a domain without such concerns. Additionally, we consider that seed nodes may not be leaves and propose to perform a downward expansion (see Subsection 3.1). This is a more difficult pruning task since not all subclasses of a class of interest may be relevant. In this view, Jarnac and Monnin [START_REF] Jarnac | Wikidata to Bootstrap an Enterprise Knowledge Graph: How to Stay on Topic?[END_REF] bootstrap an enterprise KG by expanding a set of business terms semi-manually aligned to Wikidata entities along their ontology hierarchy. According to the authors, the distance in the embedding space appears to be a good indicator of topic similarity or drift. Thus, to limit the expansion, they propose an automatic approach relying on node degree and distance thresholds. However, such thresholds are globally fixed for all seed entities, which may lead to varying performance when these entities belong to heterogeneous domains.

Analogy-Based Inference in KGs

Analogy-based inference is a basic process in human cognition [START_REF] Chollet | On the Measure of Intelligence[END_REF][START_REF] Mitchell | Abstraction and analogy-making in artificial intelligence[END_REF] that is tightly related to abstraction, adaptation and creativity. Analogy-based inference can be viewed as transferring knowledge from a source domain to a different, but somewhat similar, target domain by leveraging simultaneously on similarities and dissimilarities. Most of the literature in analogy-based inference is built on the notion of analogical proportions, i.e., statements of the form "𝐴 is to 𝐵 as 𝐶 is to 𝐷" represented as 𝐴 : 𝐵 :: 𝐶 : 𝐷 [START_REF] Miclet | Analogical Dissimilarity: Definition, Algorithms and Two Experiments in Machine Learning[END_REF], and relies on two main tasks, namely, analogy detection that involves deciding whether a quadruple (𝐴, 𝐵, 𝐶, 𝐷) constitutes a valid analogy 𝐴 : 𝐵 :: 𝐶 : 𝐷, and analogy solving that consists in finding the possible elements 𝑋 that make 𝐴 : 𝐵 :: 𝐶 : 𝑋 a valid analogy.

When the underlying objects 𝐴, 𝐵, 𝐶 and 𝐷 are represented as vectors 𝑒 𝐴 , 𝑒 𝐵 , 𝑒 𝐶 and 𝑒 𝐷 , respectively, in some vector space R 𝑛 , analogical proportions can be thought of in geometric terms as the parallelogram rule 𝑒 𝐷 -𝑒 𝐶 = 𝑒 𝐵 -𝑒 𝐴 . For instance, the underlying elements 𝐴, 𝐵, 𝐶 and 𝐷 of the analogical proportion could be words [START_REF] Peter | The Latent Relation Mapping Engine: Algorithm and Experiments[END_REF], and 𝑒 𝐴 , 𝑒 𝐵 , 𝑒 𝐶 and 𝑒 𝐷 their vectorial representations [START_REF] Mikolov | Efficient Estimation of Word Representations in Vector Space[END_REF][START_REF] Mikolov | Distributed Representations of Words and Phrases and their Compositionality[END_REF] or larger chunks of text such as sentences [START_REF] Stergos | Analogies Between Sentences: Theoretical Aspects -Preliminary Experiments[END_REF][START_REF] Stergos | Theoretical Study and Empirical Investigation of Sentence Analogies[END_REF][START_REF] Zhu | Sentence Analogies: Linguistic Regularities in Sentence Embeddings[END_REF]. Analogybased inference has been used to solve hard reasoning tasks and has shown its potential with competitive results in several machine learning tasks such as classification, decision making and recommendation [START_REF] Couceiro | Galois theory for analogical classifiers[END_REF][START_REF] Ahmadi | Learning to Rank Based on Analogical Reasoning[END_REF][START_REF] Ahmadi | Analogical Embedding for Analogy-Based Learning to Rank[END_REF][START_REF] Hug | Analogical proportion-based methods for recommendation -First investigations[END_REF], in data augmentation through analogical extrapolation for model learning, especially in environments with few labeled examples [START_REF] Couceiro | Analogypreserving functions: A way to extend Boolean samples[END_REF][START_REF] Couceiro | Behavior of Analogical Inference w.r.t. Boolean Functions[END_REF]. Moreover, it has been successfully applied in classical natural language processing (NLP) tasks such as machine translation [START_REF] Langlais | Improvements in Analogical Learning: Application to Translating Multi-Terms of the Medical Domain[END_REF], several semantic [START_REF] Lim | Solving Word Analogies: A Machine Learning Perspective[END_REF][START_REF] Lim | Classifying and completing word analogies by machine learning[END_REF] and morphological tasks [START_REF] Alsaidi | A Neural Approach for Detecting Morphological Analogies[END_REF][START_REF] Marquer | A Deep Learning Approach to Solving Morphological Analogies[END_REF][START_REF] Murena | Solving Analogies on Words based on Minimal Complexity Transformation[END_REF], as well as in (visual) question answering [START_REF] Sadeghi | Visalogy: Answering Visual Analogy Questions[END_REF], solving puzzles and scholastic aptitude tests [START_REF] Peyre | Detecting Unseen Visual Relations Using Analogies[END_REF], and target sense verification [START_REF] Zervakis | An Analogy based Approach for Solving Target Sense Verification[END_REF].

Analogy-based inference can also be used to address and tackle tasks related to the KG lifecycle such as semantic table interpretation or knowledge matching [START_REF] Monnin | Interactions Between Knowledge Graph-Related Tasks and Analogical Reasoning: A Discussion[END_REF]. A few works already exist in this line of research and rely on graph embedding, similarly to NLP approaches relying on character or word embeddings. For example, Liu et al. [START_REF] Liu | Analogical Inference for Multi-relational Embeddings[END_REF] tackles the task of link prediction, i.e., completing triples (ℎ, 𝑟, ?), and study whether KG embedding models respect the parallelogram rule of analogical inference. They show that modeling analogical structures in KG embedding models brings additional performance. Similarly, Yao et al. [START_REF] Yao | Analogical Inference Enhanced Knowledge Graph Embedding[END_REF] propose a model based on analogy functions to enhance a KG embedding model for link prediction. Alternatively, Portisch et al. [START_REF] Portisch | Knowledge graph embedding for data mining vs. knowledge graph embedding for link prediction -two sides of the same coin?[END_REF] evaluate whether KG embedding models for link prediction or data mining can be used for analogy detection. In a similar fashion, we propose to leverage KG embeddings in an analogy detection task, where analogies serve to detect relevant or irrelevant entities w.r.t. seed entities of interest.

P31 P279 P279 P279 P279 P279 P279 P279 P279 P279 P279 P279 P279 P279 P279 P31 P279 P279 P279 P279 P279 P279 P279 P31 P279 P279 P279 P279 P279 P279 P279 P279 P279 (a) (b) (c)

ANALOGY-BASED ZERO-SHOT SELECTION OF RELEVANT ENTITIES

We consider that we have at our disposal a set of seed entities of interest. Such entities can be identified (semi-)manually by experts and/or via an automatic extraction of entities from texts in the domains of interest [START_REF] Jarnac | Wikidata to Bootstrap an Enterprise Knowledge Graph: How to Stay on Topic?[END_REF][START_REF] Shbita | Understanding Customer Requirements -An Enterprise Knowledge Graph Approach[END_REF][START_REF] Swartout | Toward distributed use of large-scale ontologies[END_REF]. These seed entities are aligned with a generic KG, e.g., Wikidata, and we retrieve their neighboring entities of interest along the ontology hierarchy. We first describe how we traverse the ontology hierarchy (Subsection 3.1), and then how we keep relevant entities and prune irrelevant ones during this traversal using an analogy-based model (Subsection 3.2).

Expansion Along the Ontology Hierarchy

We retrieve the neighboring entities of seed entities of interest along the ontology hierarchy as illustrated in Figure 2, which distinguishes two directions for the expansion.

In the upward expansion (Figure 2b), we retrieve from a seed entity , its first-level classes following P31 ("instance of") and P279 ("subclass of") edges, i.e., we retrieve the classes that the entity directly instantiates, or those that directly subsume it. Then, we retrieve all their superclasses by following P279 edges up to the root of the hierarchy in a breadth-first search expansion.

In the downward expansion (Figure 2c), we retrieve from a seed entity , its first-level classes by following P31, P279, and reversed P279 edges, i.e., we retrieve the classes that the entity directly instantiates, those that directly subsume it, or those that it directly subsumes. We then retrieve all their subclasses following reversed P279 edges up to the leaves, in a breadth-first search expansion.

Selection of Relevant Entities

In this subsection, we focus on the problem of keeping relevant and pruning irrelevant entities when traversed during the expansion described in Subsection 3.1.

Formalization.

We formalize the problem as follows: given a seed entity 𝑒 𝑠 and an entity 𝑒 𝑟 reached during the graph expansion from 𝑒 𝑠 , our goal is to decide whether to keep or to prune 𝑒 𝑟 . If 𝑒 𝑟 is kept, then its neighbors are explored as described in Subsection 3.1. Otherwise, its neighbors are not explored.

We propose an analogy-based zero-shot classifier model A such that:

A (𝑒 𝑠 , 𝑒 𝑟 ) = 1 if 𝑒 𝑟 should be kept 0 if 𝑒 𝑟 should be pruned (1)
Recall that analogies are statements of the form "A is to B as C is to D" represented as A : B :: C : D [START_REF] Marquer | A Deep Learning Approach to Solving Morphological Analogies[END_REF]. In our case, we use analogies of the form 𝑒 1 𝑠 : 𝑒 2) is a valid analogy and we know the decision for the pair (𝑒 1 𝑠 , 𝑒 1 𝑟 ), then we can extrapolate the decision for the pair (𝑒 2 𝑠 , 𝑒 2 𝑟 ). To illustrate, if the analogy Hadoop : Big Data :: SharePoint : Content Management System is valid and we know that Big Data should be kept, then Content Management System should also be kept.

We propose three different configurations for our analogy-based classifier, that consider different valid and invalid analogies. To ease notation, we note k a keeping decision for a pair, and p a pruning decision for a pair. The three configurations are as follows:

Configuration 𝑠 , 𝑒 2 𝑟 ), depending on the known decision for the pair (𝑒 1 𝑠 , 𝑒 1 𝑟 ). The same rationale can be applied on invalid analogies. For example, with C 1 , invalid analogies lead to a pruning decision for the pair (𝑒 2 𝑠 , 𝑒 2 𝑟 ). On the contrary, with C 3 , invalid analogies lead to decide for the pair (𝑒 2 𝑠 , 𝑒 2 𝑟 ) the opposite decision of the pair (𝑒 1 𝑠 , 𝑒 1 𝑟 ). In addition to configurations, we propose to consider or not paths in the graph within the analogy-based model. To illustrate, consider the analogy in Equation ( 2) and the two following expansion paths that generated it:

𝑒 1 𝑠 - → 𝑒 3 𝑟 - → 𝑒 1 𝑟 𝑒 2 𝑠 - → 𝑒 4 𝑟 - → 𝑒 5 𝑟 - → 𝑒 2

𝑟

Our first formalization in Equation ( 2) only considers seed entities and reached entities, on which a decision is known or a decision is to be made by the model. We also propose to consider the paths leading to the reached entities. In this view, the analogy in Equation ( 2) becomes as follows:

𝑒 1 𝑠 : (𝑒 3 𝑟 , 𝑒 1 𝑟 ) :: 𝑒 2 𝑠 : (𝑒 4 𝑟 , 𝑒 5 𝑟 , 𝑒 2 𝑟 ). (3)
3.2.2 Model. We adopt the supervised machine learning model proposed by Lim et al. [START_REF] Lim | Solving Word Analogies: A Machine Learning Perspective[END_REF]. This model is presented in Figure 3 and relies on convolutional neural networks (CNNs). It takes as input the vector embeddings of each constituent of a quadruple. In our case, for a quadruple without paths (i.e., Equation ( 2)), we simply concatenate the embeddings of the entities (i.e., 𝑒 ) and use zero-padding in order to respect the model's fixed input dimension. We experimented with three zero-padding methods: before zeros are added before the sequence (e.g., before 𝑒 1 𝑠 and before 𝑒 2 𝑠 ) between zeros are added between the embedding of the seed entity and the embeddings of the entities in the path (e.g., between 𝑒 1 𝑠 and 𝑒 3 𝑟 , and between 𝑒 2 𝑠 and 𝑒 4 𝑟 ) after zeros are added after the embeddings of the entities in the path (e.g., after 𝑒 1 𝑟 and after 𝑒 2 𝑟 ) The model has two convolution layers, followed by a flattening operation and one fully connected layer. The first convolution layer is composed of 𝑛 1 filters. Each filter has a kernel size of 1 × sequence length and a ReLU activation function. Filters are initialized with a He normal initializer and applied with a stride of (1, sequence length). The second convolution layer is composed of 𝑛 2 filters. Each filter has a kernel size of 2 × 2 and a ReLU activation function. Filters are initialized with a He normal initializer and applied with a stride of (2, 2). The last layer is a fully connected layer with one output and a sigmoid activation function to obtain a binary classification score in [0, 1]. We also add dropout after each convolution layer.

This model is well-suited to the task at hand. Indeed, the first convolution layer allows to compute dissimilarities for each pair of entities, while the second convolution layer compares these dissimilarities between the first and the second pairs forming the quadruple to classify as a valid or invalid analogy.

Training.

We consider that we have at our disposal pairs (𝑒 1 𝑠 , 𝑒 1 𝑟 ) whose keeping or pruning decision is known (e.g., annotations by experts).

To train our model, for each annotated pair (𝑒 1 𝑠 , 𝑒 1 𝑟 ), and for each form of valid and invalid analogies of the considered configuration, we build 𝑀 analogies by sampling 𝑀 other adequate labeled pairs. To illustrate, in configuration C 1 , invalid analogies are of the form 𝑘 :: 𝑝. Thus, for a pair (𝑒 1 𝑠 , 𝑒 1 𝑟 ) whose decision is keep, we build 𝑀 invalid analogies by selecting 𝑀 other pairs whose decision is prune. These 𝑀 pairs are selected by ascending order of proximity of seed entities in the embedding space. We then train our model by minimizing the binary cross-entropy loss and taking into account possible unbalancing between valid and invalid analogies.

Inference. At inference, on an unknown pair (𝑒 2

𝑠 , 𝑒 2 𝑟 ): (1) We select 𝑁 pairs (𝑒 1 𝑠 , 𝑒 1 𝑟 ) whose decision is known to be keeping and 𝑁 pairs (𝑒 1 𝑠 , 𝑒 1 𝑟 ) whose decision is known to be pruning. Specifically, for each type of decision, we order known pairs by ascending proximity of 𝑒 1 𝑠 and 𝑒 2 𝑠 in the embedding space and select the 𝑁 first.

(2) We generate 2𝑁 quadruples with selected known pairs on the left and the unknown pair (𝑒 2 𝑠 , 𝑒 2 𝑟 ) on the right3 . (3) For each of these quadruples, our model predicts whether it is a valid or invalid analogy, which constitutes a keeping or pruning prediction, depending on the chosen configuration (see Subsubsection 3.2.1). ( 4) We compute the average of the scores output by the model (in [0, 1]) on each of the 2𝑁 quadruples as follows:

• For C 1 : we interpret the score as a vote for keeping • For C 2 : we interpret the score as a vote for keeping

• For C 3 : (i) if the known pair (𝑒 1 𝑠 , 𝑒 1
𝑟 ) has a keeping decision, the score is considered as a vote for keeping; (ii) if the known pair (𝑒 1 𝑠 , 𝑒 1 𝑟 ) has a pruning decision, the score is considered as a vote for pruning. Indeed, in this case, a score close to 1 corresponds to a valid analogy of the form 𝑝 :: 𝑝. A score close to 0 corresponds to an invalid analogy of the form 𝑝 :: 𝑘. Thus, we use 1 -𝑠𝑐𝑜𝑟𝑒 as a vote for keeping.

(5) If the averaged keeping score is above a fixed threshold, we keep 𝑒 2 𝑟 . Otherwise we prune it. It should be noted that, at inference, our model extrapolates on pairs in which 𝑒 2 𝑠 , and potentially 𝑒 2 𝑟 were not seen in training. This makes our approach fundamentally zero-shot.

EXPERIMENTS

We evaluate our analogy-based model on the Wikidata knowledge graph [START_REF] Vrandecic | Wikidata: a free collaborative knowledgebase[END_REF] and two datasets containing seed entities and labeled keeping and pruning decisions for their neighboring entities. In particular, we compare the latter with baseline models such as Multi-Layer Perceptron (MLP), Long Short Term Memory (LSTM), Support Vector Machine (SVM), Random Forest, depth pruning, and threshold pruning [START_REF] Jarnac | Wikidata to Bootstrap an Enterprise Knowledge Graph: How to Stay on Topic?[END_REF]. We also evaluate our model in a transfer learning setting.

Since our approach requires KG embeddings, we experiment with the pre-trained embeddings of Wikidata available in PyTorch-BigGraph [START_REF] Lerer | Pytorch-BigGraph: A Large Scale Graph Embedding System[END_REF] 4 . These embeddings were learned for more than 78,000,000 entities of the 2019-03-06 version of Wikidata. For building, training, and evaluating our models we used TensorFlow's Keras API and scikit-learn [START_REF] Pedregosa | Scikit-learn: Machine Learning in Python[END_REF]. Datasets5 and code6 of our experiments are publicly available.

Datasets

To the best of our knowledge, there is no publicly available benchmark dataset for the present task. This motivated us to build and publicly release the two datasets whose characteristics are detailed in Table 1. Specifically, we gathered two sets of seed entities: 455 seed entities from the Computer Science / Information Technology domain for Dataset 1 (e.g., entities related to telecommunications, network, or programming languages), and 105 seed entities from more heterogeneous domains for Dataset 2 (e.g., entities related to food, music, sport, or science). Table 1 shows the number of nodes reached with an unconstrained (i.e., without pruning) upward and downward expansion as described in Section 3.1 for both datasets. It can be noticed that the number of reached nodes upward is drastically lower than the number of reached nodes downward. This motivated us to solely focus on pruning during the downward expansion.

To obtain labeled keeping and pruning decisions for downward nodes for both datasets without having to label the whole neighborhood, we adopted the following process. We performed a downward expansion with the pruning approach proposed by Jarnac and Monnin [START_REF] Jarnac | Wikidata to Bootstrap an Enterprise Knowledge Graph: How to Stay on Topic?[END_REF] with thresholds based on node degrees and distance in the embedding space. To configure these thresholds, we set 𝛼 = 1.5, 𝛾 = 20, 𝛽 = 1.3 following [START_REF] Jarnac | Wikidata to Bootstrap an Enterprise Knowledge Graph: How to Stay on Topic?[END_REF]. Accordingly to their proposal, we also consider two different embeddings for entities: (i) Embedding E 1 in which the embedding of an entity is its vector in the considered pre-trained embeddings, and (ii) Embedding E 2 in which the embedding of an entity is the centroid of the embeddings of its instances. If an entity does not have instances, its pre-trained embedding vector is used instead. Then, we manually labeled keeping and pruning decisions output by this approach on the two sets of seed entities. Note that, since we use pre-trained embeddings from 2019 and a Wikidata dump from 2022, some entities do not have embeddings. To deal with this problem, we filtered both datasets to ensure that all seed and reached entities have an embedding vector.

Experimental Setup

We now describe our experimental protocol.

Cross validation.

We applied a 5-fold cross validation. We split the seed entities of each dataset into 5 sets S 𝑖 , 𝑖 ∈ {1, 2, 3, 4, 5}, where each set contains the same number of seed entities. Each set S 𝑖 is successively used for testing, while S (𝑖 -1) is used for validation, and the remaining sets are used for training. To prevent over-fitting, we implement an early-stopping method based on the validation loss. We set the patience to 5 for models trained with 50 epochs, and to 20 for models trained with 200 epochs.

Such a splitting on seed entities at testing, guarantees that we evaluate the ability of the model to generalize on unseen seed entities. Additionally, some entities reached from these unseen seed entities are not seen during training either, as highlighted in Table 2. Such an experimental setup thus assesses the model's capability to learn a relative similarity or dissimilarity between seed entities and reached entities, and to extrapolate it on unseen seed and reached entities. This extrapolation roots our zero-shot approach.

It can be noticed in

Models

We compare our proposed analogy-based model to the following baseline models: MLP, LSTM, Random Forest, SVM, depth pruning, and threshold pruning [START_REF] Jarnac | Wikidata to Bootstrap an Enterprise Knowledge Graph: How to Stay on Topic?[END_REF]. We call analogy the model that does not considers paths (Equation ( 2)), and path analogy the model that consider paths (Equation ( 3)).

Note that the dimension of the pre-trained embeddings of Wikidata is 200. Some parameters are used by several models and are detailed below: Batch size We set the batch size do 32. Optimizer We use the Adam optimizer. Embedding We consider the embeddings E 1 and E 2 , as proposed in [START_REF] Jarnac | Wikidata to Bootstrap an Enterprise Knowledge Graph: How to Stay on Topic?[END_REF] and explained in Subsection 4.1. Concatenation Consider a pair (𝑒 𝑠 , 𝑒 𝑟 ) formed by a seed entity and an entity reached. To decide whether to keep or prune 𝑒 𝑟 , some models can take as input the horizontal concatenation of the embeddings of 𝑒 𝑠 and 𝑒 𝑟 (called horizontal) or their difference (called translation). Zero padding We consider three zero-padding methods: before, between, and after, as detailed in Subsubsection 3. For all models except analogy-based models, we explored all combinations of different parameter values. Given the important parameter space, for analogy-based models we first fixed the embedding to E 1 , and the configuration to C 1 on Dataset 2 in order to find the three best numbers of filters, the two best path lengths, the best zero padding method, and the best dropout rate. We then experimented with this reduced parameter space on Dataset 1 and Dataset 2.

Evaluation Metrics

Figure 4 illustrates the expansion along the ontology hierarchy from a seed entity ( ) with a pruning model. In such a setting, we only evaluate the model on nodes that are associated with a gold decision, i.e., nodes depicted by are not considered. In this view, it should be noted that it is possible for the model to leave nodes with gold decisions unexplored due to erroneous pruning decisions are entities unexplored by the model due to pruning decisions but that have a gold decision; represent unlabeled entities that are not considered in the evaluation. higher in the hierarchy (i.e., nodes depicted by ). To take into account these various cases in our evaluation, we use the following metrics:

Precision = K K + P Recall = K K + K + K Accuracy = K + P K + P + K + P + K + P F1 = 2 × Precision × Recall
Precision + Recall This corresponds to a binary classification in which the keeping decision is the positive class and the pruning decision is the negative class.

Results

We introduce our results in this section following the two setups described in Section 4. We further discuss them in Section 5. 3 the performance of the different models on the task of keeping relevant entities and pruning irrelevant ones on Dataset 1 and Dataset 2. Figure 5 depicts these results with error plots to better assess the variability or stability of each model. Note that we present the results of the reference Threshold whose decisions were labeled to build the datasets. However, we do not use them to draw comparisons and conclusions because of the bias that would constitute using such results in both the dataset building and evaluation processes.

Cross validation. We present in Table

For each model, Table 3 and Figure 5 only present the best results in terms of F1-score (primary criterion) and accuracy (secondary criterion) that were obtained when exploring the parameter space. The best parameters were the following: 4.5.2 Transfer learning. For our transfer learning setting, we used the best parameters found during the cross-validation on Dataset 1. We trained each model on 80% of Dataset 1, using 20% as validation for early-stopping. We then tested the trained models on Dataset 2. Results are presented in Table 4. Regarding classifier performance, the LSTM and path analogy models are the best performing models, which outlines the importance of paths leading to entities to decide on their relevance. Figure 5 indicates that the LSTM and path analogy models are the more stable, with the path analogy model being particularly stable on Dataset 1 for the precision metric. On this dataset, the path analogy model obtains the best results in precision and accuracy whereas the LSTM has the best F1-score and recall. However, it should be noted that scores are close. On Dataset 2, the path analogy model outperforms the LSTM by about 3 points in precision, 2 points in F1-score, and 4 points in accuracy, while obtaining a similar recall. Recall that Dataset 1 is based on a set of homogeneous seed entities from the Computer Science / Information Technology domain whereas Dataset 2 mixes heterogenous domains such as food, sport, and science. Dataset for models to correctly learn similarity and dissimilarity between reached entities and seed entities. Additionally, such an homogeneity may also entail a fuzzy keeping/pruning boundary. To illustrate, starting from a network protocol of a specific layer of the OSI model, a protocol from another OSI layer was manually labeled with a pruning decision. Such a very fine-grained decision may be difficult to capture by models. To better reflect the performance of each model, we also provide their number of trainable parameters in Table 5. It is then striking that the path analogy model obtains close or better performance than the LSTM with 150 to 800 times fewer parameters. This global evaluation, taking into account the performance measured with traditional metrics as well as the number of trainable parameters, shows the superiority of our proposed analogy-based model. Table 4 shows the performance of the compared models on the transfer learning setting. Again, it appears that the LSTM and pathanalogy models are the two best performing models. While the LSTM obtains a better precision, the path-analogy model outperforms on recall, F1-score, and accuracy by 4 to 9 points. To better assess the generalization capability of these two models, we provide in Table 6 the breakdown of results from Table 3 depending on whether the reached entities when testing were seen or unseen during training. As can be expected, both models perform less on unseen entities. We notice that their scores are similar on Dataset 1 whereas the path analogy model outperforms the LSTM on both unseen and seen entities in Dataset 2. Recall that Dataset 2 contains much more unseen entities in testing that Dataset 1 (Table 2). These results thus demonstrate the higher generalization capability of our proposed analogy-based model. We posit that the formalization of Table 6: Performance of the LSTM and path analogy models depending on whether entities reached when testing where seen or unseen in training. P stands for average precision, R stands for average recall, F1 stands for average F1-score, and ACC stands for average accuracy. Best results for each category (i.e., seen or unseen) are in bold.

Analogy Embedding E 1 , (𝑛 1 , 𝑛 2 ) = (16, 8

DISCUSSION

analogical quadruples and the use of a CNN lead the model to learn to compute and compare relative similarities and dissimilarities between the two pairs in a quadruple. In turn, this leads to better extrapolation capabilities to decide on an unseen pair when compared to a seen pair within an analogical quadruple. Consequently, we think analogy-based model are well-suited for such zero-shot settings.

To extend our approach, we could envision to test our model in a few-shot setting by having some labeled decisions to train on for seed entities considered in testing. In a real-world use-case scenario, this would correspond to asking experts to label a few neighbors of each seed entity before performing the expansion along the ontology hierarchy. This could be of interest to further test the extrapolation capability of our analogy-based model. However, we believe that in a real-world scenario, experts would rather label as many neighbors as possible of some seed entities and expect the model to extrapolate on new seed entities, hence our focus on the zero-shot setting. As aforementioned, some pruning decisions are motivated by errors in the ontology hierarchy of Wikidata, which is known to contain to be potentially noisy [START_REF] Shenoy | A study of the quality of Wikidata[END_REF] 7 . Another extension of our approach thus consists in applying it to ontology maintenance.

Regarding our model, we leverage KG embeddings pre-trained with a translational model. However, there exist several types of KG embedding models, such as translational, complex, Gaussian or Graph Neural Network-based ones [START_REF] Ji | A Survey on Knowledge Graphs: Representation, Acquisition, and Applications[END_REF]. It would thus be interesting to evaluate which types of embedding models are better suited to serve an analogy-based model. Additionally, instead of using frozen KG embeddings previously learned on a specific task, we could envision learning simultaneously the graph embeddings and the CNN layers, similarly to what was done in [START_REF] Marquer | A Deep Learning Approach to Solving Morphological Analogies[END_REF] with character and word embeddings. Finally, it is noteworthy that our work does not rely on Large Language Models (LLMs) such as BERT [START_REF] Devlin | BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding[END_REF]. This purposely allows us to assess if the structure of the graph provides enough information to learn useful embeddings for selecting relevant entities. Future research directions could involve enriching our approach with LLMs, while raising additional issues to face such as noisy labels or homonyms. To illustrate, the entity "role" can be a part played by a performer8 or an identity of an item in relation to another specified item 9 .

CONCLUSION

In this paper, we considered the task of bootstrapping a knowledge graph (KG) by selecting relevant entities in the neighborhood of seed entities of interest in a generic KG. We proposed an analogybased model to keep or prune neighors of seed entities in a zero-shot setting and two labeled datasets to evaluate models on this task. Compared with standard classifiers, our model outperformed while presenting a drastically lower number of parameters. Additionally, it showed better extrapolation capabilities in zero-shot and transfer learning settings. Such results advocate for the further study of analogy-based models in tasks related to the KG lifecycle or requiring extrapolation capabilities, which we will address in future work.

Figure 1 :

 1 Figure 1: Outline of the bootstrapping of a knowledge graph from Wikidata.

Figure 2 :

 2 Figure 2: Expansion from a seed entity along the ontology hierarchy. P31 stands for "instance of" and P279 stands for "subclass of". (a) depicts the full ontology hierarchy, (b) depicts classes reached in the upward expansion, and (c) depicts classes reached in the downward expansion.

  C 1 Valid analogies are of the form 𝑘 :: 𝑘. Invalid analogies are of the form 𝑘 :: 𝑝. Configuration C 2 Valid analogies are of the form 𝑘 :: 𝑘. Invalid analogies are of the form 𝑘 :: 𝑝 and 𝑝 :: 𝑝. Configuration C 3 Valid analogies are of the form 𝑘 :: 𝑘 and 𝑝 :: 𝑝. Invalid analogies are of the form 𝑝 :: 𝑘 and 𝑘 :: 𝑝 It is worth noting that depending on the chosen configuration, the aforementioned analogical inference is adapted. For example, with C 1 and C 2 , valid analogies only allow to extrapolate keeping decisions. On the contrary, with C 3 , valid analogies can conclude on keeping or pruning the pair (𝑒 2

Figure 3 :

 3 Figure 3: The analogy-based classifier model with two convolution layers and one fully connected layer from [23].

Figure 4 :

 4 Figure 4: Example of an evaluation setting for a pruning model. Gold decisions are represented by the letters K (for keep) and P (for prune). represents the seed entity; are entities kept by the model; are entities pruned by the model;are entities unexplored by the model due to pruning decisions but that have a gold decision; represent unlabeled entities that are not considered in the evaluation.

2 Figure 5 :

 25 Figure 5: Error plot depicting the precision (P), recall (R), F1-score (F1), and accuracy (A) of each model on Dataset 1 and Dataset 2.

  𝑠 and 𝑒 2 𝑠 are two seed entities, 𝑒 1 𝑟 is reached during the expansion from 𝑒 1 𝑠 , and 𝑒 2 𝑟 is reached during the expansion from 𝑒 2 𝑠 . Using analogical inference, if Equation (

1 𝑟 :: 𝑒 2 𝑠 : 𝑒 2 𝑟 (2) where 𝑒 1

  1 𝑠 , 𝑒 1 𝑟 , 𝑒 2 𝑠 , 𝑒 2 𝑟 ). For a quadruple with paths (i.e., Equation (3)), we concatenate the embeddings of the entities (i.e., 𝑒 1 𝑠 , 𝑒 3 𝑟 , 𝑒 1 𝑟 , 𝑒 2 𝑠 , 𝑒 4 𝑟 , 𝑒 5 𝑟 , 𝑒 2 𝑟

Table 1 :

 1 Table 2 that test seed entities in Dataset 1 lead to more entities that were seen in training than in Dataset 2 (51-61% instead of 10-21%). This is a direct consequence of the Dataset # Seed entities # Nodes up # Nodes down # P decisions Depths P # K decisions Depths K Statistics of Dataset 1 and Dataset 2 before and after filering to only retain entities with embeddings. K stands for Keeping and P stands for Pruning.

	Dataset 1	w/o filtering w/ filtering		455 439	1,507 1,469	2,593,609 2,593,575	3,464 2,910	⟦1, 4⟧ ⟦1, 4⟧	1,769 1,619	⟦1, 4⟧ ⟦1, 4⟧
	Dataset 2	w/o filtering w/ filtering		105 104	1,159 1,152	1,247,385 1,247,383	388 314	⟦1, 2⟧ ⟦1, 2⟧	594 577	⟦1, 3⟧ ⟦1, 3⟧
	Dataset	Fold 1 Fold 2 Fold 3 Fold 4 Fold 5
	Dataset 1	56.51	59.61	51.72	55.76	61.19
	Dataset 2	20.50	21.49	12.36	17.04	10.05

Table 2 :

 2 Percentage of entities reached when testing and already seen when training, for each fold and dataset. homogeneity of seed entities in Dataset 1. Since all seed entities are from the Computer Science / Information Technology domain, the entities traversed during the expansion from each seed entity may overlap. On the contrary, Dataset 2 involves heterogeneous seed entities from different domains, leading to different entities being traversed when expanding from each seed entity.

4.2.2 Transfer learning.

We also tested our model in a transfer learning setting. We trained our model on labeled decisions of Dataset 1 and tested it by traversing the neighborhood of seed entities in Dataset 2.

  2.2. Learning rate We test with learning rates ∈ {0.0001, 0.001, 0.01}. Dropout rate We test with dropout rates ∈ {0, 0.3, 0.5}. Path length We consider paths of length ∈ {3, 4, 5}. Analogy configuration We consider the three configurations for valid and invalid analogies C 1 , C 2 , C 3 presented in Subsubsection 3.2.1. Number of filters We test with (𝑛 1 , 𝑛 2 ) ∈ {(2, 1), (4, 2), (8, 4), (16, 8), (32, 16), (64, 32), (128, 64), (256, 128)}. The parameters used by the different considered models are given below, where we also describe specific parameters that are only applicable to one model. Batch size, optimizer, embedding, learning rate, dropout rate, analogy configuration, number of filters, 𝑀 ∈ {5, 10, 15, 20, 50, 100}, 𝑁 = 20. Path analogy (PA) Batch size, optimizer, embedding, learning rate, dropout rate, zero padding, path length, analogy configuration, number of filters, 𝑀 ∈ {5, 10, 15, 20, 50, 100}, and 𝑁 = 20. Embedding, 𝛼 ∈ {1.0, 1.1, . . . , 2.0}, 𝛾 = 20, 𝛽 ∈ {1.0, 1.1 . . . , 2.0}, and absolute degree = 200. Note that for models with a non-zero dropout rate, we use Monte Carlo Dropout.

	Analogy (A) SVM Embedding, concatenation, and unlimited number of
	iterations.
	Random Forest (RF) Embedding, concatenation, and num-
	ber of estimators ∈ {10, 50, 100, 150, 200, 250, 300, 400, 500}.
	MLP Batch size, optimizer, embedding, concatenation, learn-
	ing rate, dropout rate, and hidden layers ∈ {(100), (100, 50),
	(100, 50, 25), (200), (200, 100), (200, 100, 50), (200, 100, 50, 25)}.
	LSTM Batch size, optimizer, embedding, learning rate, zero
	padding, path length, and number of units ∈ {50, 100, 150}.
	Depth pruning (D) Depth threshold ∈ ⟦1, 20⟧.
	Threshold pruning (T)

Table 3

 3 ± 7.10 56.66 ± 2.25 66.57 ± 3.09 68.85 ± 15.59 100.00 ± 0.00 80.50 ± 11.39 68.93 ± 15.

	highlights that depth in the ontology hierarchy cannot be
	used to keep relevant entities and prune irrelevant ones. Here, with
	a depth of 3-4, we obtain a perfect recall but a low precision. Using
	greater thresholds does not change results while lower ones would
	reduce the recall in favor of the precision. This was expected, es-
	pecially in a collaborative and generic knowledge graph such as
	Wikidata, since different communities may have different granu-
	lar representations of knowledge. To tackle this issue, one would
	need to specify different depth thresholds depending on the seed
	entity domains. Additionally, not all subclasses of an interesting

Table 3 :

 3 Pruning evaluation results on Dataset 1 and Dataset 2, with the parameters leading to the best results for each model. P stands for average precision, R stands for average recall, F1 stands for average F1-score, and ACC stands for average accuracy. The best results are in bold and we underline the second best result. Also, we decided to present the reference threshold results used in the construction of both datasets.

	Model		Dataset 1 → 2
		P	R	F1	ACC
	Random Forest 83.09 20.40 32.75 33.06
	SVM	64.62 57.04 60.59 43.97
	MLP	69.90 51.99 59.63 48.26
	LSTM	92.83 74.73 82.80 80.04
	Analogy	74.95 64.26 69.19 59.86
	Path analogy	91.49 83.39 87.25 84.33

Table 4 :

 4 Transfer results obtained by training on Dataset 1 and testing on Dataset 2. P stands for average precision, R stands for average recall, F1 stands for average F1-score, and ACC stands for average accuracy. The best results are in bold and the second best are underlined.

	class may be of interest w.r.t. a seed entity, especially in case of
	errors in the ontology hierarchy (e.g., erroneous subclass edges,
	misinterpretation of the subclass semantics by users, introduction
	of cycles). Such results motivate the use of classifiers to learn a
	relative similarity and dissimilarity between reached entities and
	seed entities, based on labeled examples given by a user (e.g., an
	expert, the KG owner).

Table 5 :

 5 1 may thus provide less diversity Number of trainable parameters for each model.

	Model	Dataset 1 Dataset 2
	LSTM	210,751	210,751
	MLP	105,401	65,401
	Analogy	1,369	1,369
	Path analogy	1,401	251

  .90 ± 5.97 69.69 ± 7.90 71.33 ± 4.73 78.06 ± 6.15 75.44 ± 8.99 94.21 ± 2.99 83.33 ± 4.72 76.35 ± 6.37 Seen entities 84.63 ± 6.80 80.95 ± 5.51 82.32 ± 1.29 87.55 ± 1.83 94.62 ± 1.71 95.51 ± 3.99 95.02 ± 2.14 91.71 ± 3.39 analogy Unseen entities 73.82 ± 3.62 69.44 ± 6.09 71.36 ± 3.64 78.20 ± 4.78 78.84 ± 8.34 94.46 ± 2.83 85.67 ± 5.01 80.49 ± 5.97 Seen entities 85.20 ± 2.10 78.25 ± 5.20 81.47 ± 3.01 87.41 ± 2.05 96.07 ± 2.47 94.90 ± 5.45 95.44 ± 3.82 93.15 ± 4.98

			Dataset 1				Dataset 2
		P	R	F1	ACC	P	R	F1	ACC
	LSTM	Unseen entities 73

https://www.wikidata.org/wiki/Wikidata:Statistics

Note that entities in Wikidata are identified by QIDs.

It is noteworthy that for configuration C 1 , the 𝑁 pairs (𝑒 1 𝑠 , 𝑒 1 𝑟 ) whose decision is pruning are not used, leading to only 𝑁 quadruples being generated.

https://torchbiggraph.readthedocs.io/en/latest/pretrained_embeddings.html

https://doi.org/10.5281/zenodo.8091584

https://github.com/Orange-OpenSource/analogical-pruning

See also https://commons.wikimedia.org/wiki/File:WikidataCon_2021_-_Overview_ of_ontology_issues.pdf.

https://www.wikidata.org/wiki/Q1707847

https://www.wikidata.org/wiki/Q4897819

ACKNOWLEDGMENTS

This work is supported by the AT2TA project (https://at2ta.loria.fr/) funded by the French National Research Agency ("Agence Nationale de la Recherche" -ANR) under grant ANR-22-CE23-0023.


N Keeley

R S Mackintosh

C Beck

Breakup Coupling Effects on Near-Barrier 6 Li, 7 Be and 8 B + 58 Ni Elastic Scattering Compared

New data for near-barrier 6 Li, 7 Be and 8 B + 58 Ni elastic scattering enable a comparison of breakup coupling effects for these loosely-bound projectiles. Coupled Discretised Continuum Channels (CDCC) calculations suggest that the large total reaction cross sections for 8 B + 58 Ni are dominated by breakup at near-barrier energies, unlike 6 Li and 7 Be where breakup makes a small contribution. In spite of this, the CDCC calculations show a small coupling influence due to breakup for 8 B, in contrast to the situation for 6 Li and 7 Be. An examination of the S matrices gives a clue to this counter-intuitive behaviour.

INTRODUCTION

Recent data [1] for near-barrier 6 Li, 7 Be and 8 B + 58 Ni elastic scattering allow some interesting comparisons for these weakly-bound nuclei. Optical model fits find much larger total reaction cross sections (σ R ) for 8 B than for 6 Li or 7 Be, even when "reduced" [2]; while the reduced σ R for other weakly-bound projectiles lie on a universal curve, those for 8 B and 6 He are significantly larger [1]. The low 8 B → 7 Be + p breakup threshold (0.1375 MeV) suggests a dominant contribution to the direct part of σ R . This is not automatic: for 6 He with an α + 2n breakup threshold of 0.973 MeV, 1n-and 2n-stripping are the main contributors to σ R at near-barrier energies. However, the weakly-bound proton in 8 B experiences Coulomb barrier and charge polarisation effects tending to suppress transfer.

CDCC calculations [3] find that breakup does dominate the direct component of σ R for 8 B: as the cross sections are large -of the order of 100 mb or more -one might expect an equally important coupling effect on the elastic scattering angular distribution. However, this is not the case [3]. We thus have an apparent paradox: 6 Li, with a relatively small breakup cross section, exhibits an important breakup coupling effect on the elastic scattering (see e.g. [4]) whereas 8 B, with a large breakup cross section, shows only a modest coupling effect. A comparison of S matrices obtained from CDCC calculations for 6 Li, 7 Be and 8 B + 58 Ni provides a clue to this behaviour. Preliminary dynamic polarisation potentials (DPPs) are also presented.

CALCULATIONS

Calculations were performed with the code FRESCO [5]: only a brief outline is given here. The 6 Li, 7 Be and 8 B nuclei were modelled as α + d, α + 3 He and 7 Be + p clusters, respectively. The 7 Be core was treated as inert but its non-zero spin was retained. Interaction potentials were obtained by Watanabe-type folding of global optical potentials, with a 6 Li potential as surrogate for 7 Be, the well-depths being adjusted to give the best fit to the data. The 6 Li and 7 Be calculations were similar to those in [4] and [6], but with finer continuum binning for 7 Be. The 8 B calculations included couplings to the L = 0, 1, 2 and 3 continuum and the 0.774 MeV 1 + and 2.32 MeV 3 + resonances. Good fits to all the data were obtained. Due to lack of space we show only results for the same values of E c.m. -V B for each system, where V B is the nominal Coulomb barrier, taking as our "benchmark" the 8 B data at E lab = 29.26 MeV. This procedure yields values of E lab = 19.04 and 24.12 MeV for 6 Li and 7 Be + 58 Ni, respectively. In this way effects due to differences in projectile charge should be minimised.

Results are presented in Fig. 1: the coupling effect is much stronger for 6 Li and 7 Be, with 6 Li → α + d and 7 Be → α + 3 He breakup thresholds of 1.47 and 1.59 MeV, respectively, an order of magnitude larger than the 8 B → 7 Be + p threshold. The 6 Li → α + d process has the additional peculiarity that it cannot proceed via dipole breakup. If we include population of the bound 1/2 -state in 7 Be (considering breakup as an inelastic excitation) the total breakup cross sections for both 6 Li and 7 Be are about a factor of three smaller than for 8 B. To obtain a clue to this apparent paradox, we show in Fig. 2 the modulus and argument of the J-weighted S matrices [7] obtained from full and no-coupling calculations. The coupling effect on |S| is almost negligible for 8 B and largest for 6 Li, but qualitatively similar for all three nuclei: a decrease of |S| at small L and an increase at large L. By contrast, for arg(S) the coupling effect is greatest for 8 B, smallest for 7 Be and intermediate for 6 Li.

DISCUSSION

For protons and other light particles, changes in |S| correspond to changes in the imaginary part of the potential, while changes in arg(S) correspond to changes in the real part. While this simple picture is not so clear-cut in the presence of strong absorption (as here) it provides a useful guide. Thus, the coupling effect on |S| suggests reduced absorption at small L, switching to increased absorption at large L. The effect on arg(S) suggests repulsion at small L and attraction at large L. These effects are qualitatively similar for all three nuclei. The fact that the coupling effect on both the elastic scattering and |S| is so small for 8 B suggests that, paradoxical as it may seem for a coupling producing such a large cross section, its effective imaginary potential is small.

DPPs may be obtained by inversion of the S matrix, see e.g. [8]. In Fig. 3 we show the results of such a procedure for 8 B and 7 Be. Those for 7 Be are preliminary; we expect the final DPPs to be somewhat smoother. While the DPPs are qualitatively similar, short-range repulsion and long-range attraction combined with surface absorption (this behaviour seems to be universal, see e.g. [9]), the details are very different. The small imaginary DPP for 8 B is particularly striking, confirming the conclusions inferred from the S matrices. The surface repulsion for 8 B is also much smaller than for 7 Be, although for radii larger than about 9 fm it is significantly larger than for 7 Be, having a longer, more repulsive tail. Our results show that a large cross section is no guarantee of a large coupling effect. The S matrices and DPPs shed some light on this, but it remains to be explained at a more fundamental level.

Figure 1 .

 1 Figure 1. CDCC calculations for 8 B, 7 Be and 6 Li + 58 Ni at E lab = 29.26, 24.12 and 19.04 MeV. Solid and dashed curves denote full and no-coupling results, respectively.

Figure 2 .

 2 Figure 2. |S| and arg(S) from CDCC calculations for 8 B, 7 Be and 6 Li + 58 Ni at E lab = 29.26, 24.12 and 19.04 MeV. Solid and dashed curves denote full and no-coupling results, respectively.

Figure 3 .

 3 Figure 3. DPPs from CDCC calculations for 8 B (solid curves) and 7 Be (dotted curves).


domain: chim spi

text:
David Tilve-Martinez

Wilfrid Neri

Dylan Horaud

Nicolas Vukadinovic

Benoit Berton

Arnaud Desmedt

Jinkai Yuan

Philippe Poulin
email: philippe.poulin@crpp.cnrs.fr

David Tilve-Martínez

Wilfred Neri

W Neri

ased T ransparent R esins F or A ccurate 3D P rinting of C onductive M aterials

Keywords: 3D printing, nanocomposites, graphene oxide, conductivity

établissements d'enseignement et de recherche français ou étrangers,

Introduction

Digital Light Processing (DLP) [1] is an additive manufacturing technology generally limited to transparent photocurable resins. Transparency is required to ensure fast and spatially accurate photopolymerization upon UV irradiation. Unfortunately, the requirement of transparency makes the processing of electrically conductive resins difficult. Manufacturing conductive materials would broaden the spectrum of applications of the DLP [2][3][4] by allowing the fabrication of 3D objects with sensing, actuating, or communicating functionalities.

The addition of electrically conductive filler in a polymer matrix is a common strategy to make an initially insulating polymer conductive [5][6][7][8] . Classical conductive fillers include metal or carbon micro-or nano-particles. The particles must be sufficiently concentrated to form a connected and conductive network. Their volume fraction must be above the so-called percolation threshold to achieve a sufficiently high conductivity [9] . A high percolation threshold is associated with a substantial loss of transparency because conductive particles absorb and scatter UV light.

In this context, anisotropic particles such as rod-like or plate-like particles have been used in the last years to make 3D printable resins. Anisotropic particles are used because they display a percolation threshold lower than spherical or quasi-spherical particles [9][10][11] . Multi-Walled Carbon Nanotubes (MWCNTs) for example have been used in recent work [12][13][14][15] . However, the formulations contain aggregates that can settle in the long term, and make 3D printing more difficult. Besides, above the percolation threshold, the quality of 3D printing decreases because of scattering and defects. Graphene Nano-Platelets (GNP) [16] , [17] have also been tested but with lower conductivity or greater percolation threshold compared to nanotubes. Dried reduced graphene oxide (rGO) has also been used as conductive fillers for DLP applications [18] . However, GO layers tend to stack and aggregate irreversibly upon drying [19][20][21][22][23] .

GO powders in water have also been added to low molecular weight water-soluble poly (ethylene glycol)diacrylate (PEGDA) resins for 3D printing applications [24] . This approach is interesting because GO absorbs much less UV than rGO [5,6] . However, the method is limited to water-miscible PEGDA resins which unfortunately do not sustain high-temperature treatments for efficient reduction of GO. The obtained materials remain therefore poorly conductive with conductivities on the order of 10 -7 S m -1 .

In the present work, we use GO monolayers as precursor particles. In contrast to previous studies, GO is used during 3D printing in its neat oxidized state and never dried during all processes. Neat and undried GO monolayers enjoy several advantages. They display a low percolation threshold because of their plate-like shape and giant aspect ratio [25] . Their UV absorption is lower than that of other conductive particles generally used for making conductive composites, including rGO [5,6] . Neat GO is insulating but can be easily made conductive by an in-situ thermal or chemical reduction after 3D printing [19] if dispersed in a robust resin that can sustain the reduction treatments. In this work, we use acrylic resins that can be heated up to 300°C, ensuring an efficient reduction of GO. We take advantage of the solubility of GO monolayers in ethanol, and of the miscibility of ethanol and acrylic resins to transfer GO atomic monolayers from water to the resin (Figure 1). For this, we initially prepared a concentrated GO liquid crystal ethanol solution by a phase transfer method. This GO liquid crystal solution is mixed with a resin that can withstand high temperatures. The formulation is then 3D printed by DLP. It is thermally treated to reduce the GO, and finally obtain a conductive 3D-printed nanocomposite. The use of undried GO materials allows accurate and fast printing. The low percolation threshold (0.05% wt) and the efficient reduction of GO lead to materials with enhanced electrical conductivity, with conductivities on the order of 10 -2 S m -1 , largely above those of related materials [18,24] . We also qualitatively show that the present method allows much better resolution when compared to 3D printing using rGO or nanotube materials.

Results and Discussion

Formulation and 3D printing of GO composites

Manufacturing of a conductive GO-based composite by DLP requires the formulation of a stable and homogeneous dispersion in the acrylic matrix in order to have a material sufficiently transparent to UV light at 405 nm. As shown in Figure 2, GO is a weak UV-visible absorber. It is therefore well appropriate for DLP. In contrast, as most conductive fillers, rGO obtained after reduction is a much stronger UV absorber, less appropriate for DLP in spite of being electrically conductive . Besides, directly adding rGO to the resin and using a tip sonication results in a poor dispersion with irreversible aggregates formed during reduction. As can be seen in Figure 3 (a), the aggregate size spans from a few microns to 50 microns. Instead, a homogeneous liquid crystal solution of GO atomic monolayers forms in ethanol (Figure 3b). This concentrated solution is added to the acrylic resin by taking advantage of the high solubility of ethanol in the resin. This results in a homogeneous and stable dispersion of the GO monolayers inside the matrix (Figure 3 c,d). The absence of aggregation is revealed in the optical micrographs by the absence of large black particles. Dispersion rheology is particularly useful to optimize 3D printing. A viscosity of 3 to 5 Pa•s at a shear rate of 10 s -1 is considered as an upper limit for the DLP of ceramics [26][27][28] . This condition is necessary to facilitate the coating and self-leveling of the resin. It avoids also the formation of bubbles that could lead to printing failure. The neat resin used in this work has a Newtonian behavior. But a strong shear-thinning behavior is observed as soon as GO is added to the resin (Figure 4). The viscosity increases with the fraction of GO. The viscosity at 10 s -1 is 3.94 Pa•s for a filler concentration of 0.35% wt . This viscosity is lower than 5 Pa•s estimated as an upper limit for ceramic materials [28] . The viscosity of the 0.45% wt GO formulation is 9.38 Pa•s which slightly overcomes this limit. But this viscosity level remains on the same order of magnitude, meaning that our present materials still remain 3D printable. The efficiency of photopolymerization can be evaluated by the so-called Jacobs model [42] . In this model, Cd, the depth of polymerization, is plotted as a function of E0 (mJ cm - 2 ) the irradiation energy, and the data are fitted according to Equation (1).

𝐶 𝑑 = 𝐷 𝑝 𝑙𝑛 ( 𝐸 0 𝐸 𝑐 ⁄ ) (1)
Ec (mJ cm -2 ) is a characteristic energy associated with the crosslinking of the polymer.

Dp (µm) is the so-called penetration depth. This semi-logarithmic working curve results from the Beer-Lambert relation. It allows the printing parameters to be optimized, and the printing limitations of the DLP technique to be determined.

Commercial DLP resins are highly transparent at 405 nm to allow for efficient photoinduced cross-linking reactions. The addition of fillers can affect the process because of light scattering and absorption [26,27] . GO sheets can also induce free radical trapping of acrylic chains by reacting with the sp 2 carbons of GO [29,30] . This effect also limits the cross-linking mechanisms. The influence of the above phenomena on DLP can be quantified by the determination of the Jacobs working curves. Figure 5 shows how the presence of fillers in the matrix limits the penetration depth of light (Dp). Dp decreases clearly with increasing the weight fraction of GO in the resin. Nevertheless, printing remains easily doable thanks to the weak UV absorption and limited scattering of neat GO monolayers. Determination of the Jacobs curves provides key information to set optimal printing parameters, as indicated in the next section. ). Cd is the depth of polymerization. E0 is the irradiation energy.

DLP of GO and rGO composites

Knowing all these details, we are able to optimize the time of exposure depending on the GO loading in our formulation. Figure 6 shows a CAD model of a complex cellular structure which has been 3D printed using 0.15% wt of GO and 0.15% wt MWCNTs respectively.

According to the Jacobs equation (1), 1.5 mJ cm -2 (equivalent to 4.5 s) must be irradiated to 3D print a 50 µm layer for a 0.15% wt MWCNTs formulation (Figure 2S). In our case, if we irradiate 1.5 mJ cm -2 for a 0.15% wt GO formulation the layer thickness 3D printed is 150 µm.

As can be seen, the structure 3D printed with GO is flawless and has a remarkable resolution because of its transparency. By contrast, the structure printed with carbon nanotubes at the same concentration display several defects, in the finest areas that require greater precision [31] .

The optical micrograph of the carbon nanotube dispersions (Figure 3S)) shows aggregates bigger than 50 μm. Even setting an exposure time of 2.3 mJ cm -2 (equivalent to 10 s) still leads to defects and failures in the process. Those come from the strong UV absorption of nanotubes and from their difficult dispersion with aggregates that can be as large as the printing layers. UV transparent GO formulations at the monoatomic level can be printed faster with better resolution. For other characterizations, 2x2x2 mm 3 cubes were printed. Figure 7 shows how the color of the resin changes with the addition and reduction of GO particles. Thermogravimetric analysis (Figure S1) under a flow of oxygen shows that the resin sustains temperatures up to 300 ºC with a weight loss of only 4%. This high resistance to temperature allows the GO to be effectively reduced by thermal annealing. After treatment at 200 ºC, the object turns actually to a dark black color. The maximum GO weight fraction of printed composites was 0.55%. At this high weight fraction, and already above 0.45% wt, the printing quality decreases.

At 0.45% wt of GO, our formulations meet the rheological limits of 3D printing found empirically for ceramic composites. Moreover, the Jacobs working curves show a clear decrease in the 3D printing depth, associated to a more difficult printing. The as-printed composite materials display a lower stiffness and greater strain at break than as-printed neat resins. This behavior is likely due to the presence of ethanol in the composite resin during 3D printing. Ethanol can indeed limit the degree of cross-linking. The Young's modulus of the neat cross-linked resin is 10.8 ± 0.9 GPa. This modulus is reduced by half with the addition of only 5% wt ethanol in the same conditions of UV irradiation. Young's modulus increases after the reduction treatment of GO. This increase is more likely due to an improved curing of the resin upon thermal treatment, rather than to an increase in the stiffness and reinforcement efficiency of the rGO particles. Because even without GO additives, the neat resin also presents a significant improvement in Young's modulus after the thermal treatments.

Electrical properties

Printed composites are found to be conductive after the in-situ reduction treatment of GO. The conductivity of the samples as a function of the weight fraction of GO is shown in Figure 9. The data are fitted using the following percolation scaling equation:

𝜎 = 𝜎 0 (𝜌 -𝜌 𝑐 ) 𝑡 ( 2
)
where 0 is a scaling factor (S/m), ρ is the weight fraction of filler (wt %), ρc is the percolation threshold (wt %) and t is a critical exponent. We observe that the nanocomposite becomes conductive with the reduction of GO.

Factors deduced from the fitting with Equation ( 2) are given in Table 1. The conductivity shows a typical percolation behavior. The critical exponent t of the two fits is close to 2, as expected for percolation systems in three dimensions [32] .

The GO was first reduced at 200°C for two hours. The percolation threshold deduced from the fits of the conductivity data is found to be 0.15% wt. This is lower than previous studies on conductive GO and rGO-based composites [18,24] and actually comparable to the percolation threshold of composites loaded with MWCNTs [12][13][14]17] . The maximum conductivity achieved at 0.55% wt of GO is 9.93•10 -3 S m -1 . This value is higher than those found by Qian et al. [18] and Chiappone et al. [24] However, it is slightly smaller than the values obtained for MWCNT-based composites. From a more general point of view, the percolation threshold of overlapping ellipsoids is expected to scale with the aspect ratio of the particles with a prefactor actually close to 1 [33] . This scaling is in agreement with the so-called excluded volume model.

Here, considering the graphene sheets as oblate ellipsoids with large aspect ratio one could expect that 𝜌 𝑐 ~𝑙 𝐷 , where l and D are the thickness and diameter of the graphene sheets. Taking reasonable values for D=1m and l=0.4nm, the excluded volume would predict a percolation threshold of about 0.04% vol, which would correspond to a weight fraction of nearly 0.02% wt assuming a density of 2g cm -3 for GO materials. This expected value is somewhat lower than that experimentally observed. Nevertheless, actual graphene sheets do not overlap in reality. It has been shown that the excluded volume model is not applicable to 2D non-penetrable particles, while it remains suitable for 1D objects [25,34] . In the case of 2D particles, correlation of orientations lead to an increase of the actual percolation threshold. After a second thermal annealing at 300 ºC for two hours. We see a decrease in the percolation threshold (0.05% wt), and an increase in the electrical conductivity (Figure 9). This behavior is likely due to two factors: a further reduction of the GO sheets due to the increase in temperature, and to an improvement of the rGO inter-layer electrical contacts. Indeed, the matrix can potentially relax at high temperatures so that rGO can approach each other more closely in response to van der Waals interactions. Even minute changes in the interparticle spacing can result in significant decreases in the contact resistances between neighboring particles, electron-tunneling being the main mechanism of conduction in the present composites.

Changes in the tunneling distance and electrical connectivity criteria can result in variations of the percolation threshold [35,36] .

Conclusion

We have developed a new strategy for making 3D conductive composites by DLP.

Monolayer GO-acrylic resin mixtures were formulated. Monolayer GO liquid crystal was used without any drying stage during all processes to achieve UV-transparent resins. The Jacobs working curves and viscoelastic properties of the formulations have been studied to validate their 3D printability. The weak UV absorption and scattering of GO make the present formulations much more suitable for DLP than other conductive formulations. Taking advantage of the high-temperature resistance of the acrylic resin, we are able to efficiently reduce in-situ GO into rGO. This efficient reduction allowed highly conductive materials to be 3D printed. The present method can be useful in future potential applications for which electrical conductivity is needed, from antistatic materials [5][6][7][8] to sensors and soft robotics [37] through microwave absorption [38][39][40] .

Experimental Section

Materials:

Aqueous GO solutions at 0.4% wt and 2.5% wt were purchased from Graphenea (Spain).

According to the datasheet, the 2.5% wt solution contains GO flakes with a lateral size of 6-33 μm. The 0.4% wt solution contains GO flakes with a particle size of >10 μm. Bile salts were purchased from Fluka. Acrylic-based photocurable commercial resin Industrial Blend (IB) was purchased from FunToDo. Ethanol (EtOH) and isopropanol (IPA) purchased from Carlo Ebra Reagents were used as received.

Formulation:

Ethanol is added to the 2.5% wt GO solution to dilute the GO materials down to 0.4% wt. This solution is sonicated (Branson digital sonifier 450) in order to homogenize the suspension and disrupt possible aggregates with a sonication tip (tapped exponential horn 13 mm) for 30 minutes, amplitude set to 25% with pulses of 0.5 s on, and 0.2 s off. The resulting solution is centrifuged at 30,000 g for 30 minutes in an ultracentrifuge (Beckman coulter). From this, a concentrated slurry at 2.40% wt of GO monolayers (measured by dry extract) in an ethanol-rich solution (85% wt) is obtained. Ethanol, in contrast to pure water, is soluble in the IB resin. It can thus serve as an intermediate solvent to disperse GO monolayers in the resin without any drying step. For this, the slurry is directly mixed with the resin using a light-opaque container. The mixture is homogenized by sonication with a tip (microtip 3.2 mm) for 30 minutes, an amplitude set at 30%, and pulses of 0.5s on and 0.2s off.

GO solutions for UV-vis characterizations are prepared as follows. A 0.4%wt GO aqueous solution is diluted down to 0.005% wt by adding distilled water. The added water contains 0.35% wt of bile salt surfactants. These compounds are expected to stabilize the GO flakes in water as they become hydrophobic upon reduction. Thermal reduction of GO, to yield rGO, is done by pouring 20 mL of the solution into an autoclave and heating it for 1h at 90 ºC.

The color of the sample turns dark black during the reduction reaction. Bile salt surfactants are found to be particularly efficient at stabilizing rGO in water [41] . The solution is indeed found to remain stable without any aggregation or sedimentation of the rGO particles.

The rGO powder was prepared by thermal reduction of GO. As before, we heat up to 90 ºC for 1h the 0.4% wt GO aqueous solution in the autoclave. After that, we evaporate the water by heating it at the same temperature without the cover. Then, the powder was recuperated and added to the resin. The mixture is homogenized by sonication with a tip (microtip 3.2 mm) for 30 minutes, an amplitude set at 30%, and pulses of 0.5s on and 0.2s off.

The MWCNTs powder is directly added to resin and dispersed by tip sonication. For that, a Branson digital sonifier 450 is used in order to homogenize the suspension and disrupt the CNT aggregates with a sonication tip tapped exponential horn 13 mm for 1 hour, amplitude set to 45% with pulses of 0.5 s on, and 0.2 s off. Finally, to remove the bubbles formed during the sonication, the formulation is put under vacuum for 2 hours.

3D printing:

The IB/GO formulation is poured into the tank of the DLP 3D printer Phrozen Sonic Mini 4k. This printer operates with UV irradiation at a wavelength of 405 nm.

A printing layer thickness of 25 µm is selected along with an irradiation time of 10s. As explained further, these values have been chosen after characterizations of the so-called Jacob's curves. Once printed, the IB/GO composite is soaked in an IPA bath for 15 minutes to remove the non-reticulated resin. It is then placed in a UV irradiation chamber (UltraV360) for 30 minutes to complete cross-linking of the resin. After that, the obtained IB/GO 3D printed samples were thermally reduced in air at 200°C for 2 h and subsequently, at 300 ºC for 2 h. The thermal treatment converted the 3D-printed IB/GO into an IB/rGO conductive nanocomposite.

Characterizations:

The quality of the GO dispersion in the commercial resin was assessed by optical microscopy (Leica DM 2500P). The thermal stability of the resin has been characterized by thermogravimetric analysis (TGA) (TA TGA 5500). About 5 mg of sample were loaded into the aluminum bread and heated from room temperature up to 800ºC under air.

The UV-Visible spectra (Jasco V-730) of GO and rGO were recorded to compare the absorbance at 405 nm. All the experiments were performed with samples in PMMA cuvettes.

The sudy of the Jacobs curves, the formulations have been poured into the printing tank and 2x2 mm square patterns have been irradiated for different times. The power of the LCD's 3D printer has been measured with a Thorlab PM1000A power meter. It is 1.27 mW cm -2 . After irradiation, the non-crosslinked formulation was rinsed and removed with 2-propanol. The thickness of the photopolymerized resin was measured with a caliper.

The rheological measurements were performed at 25ºC using a controlled strain rheometer (TA AR2000) with a 40mm and 2º cone-plate geometry. The rheological tests were performed in the linear viscoelastic regime determined from steady state flow experiments. The frequencies were in the range of 0.1 to 100 s -1 .

The tensile mechanical properties of the composite before and after the heat treatments have been measured with a tensile test Zwick Z2S instrument with a 1 kN force sensor. ASTM D638 Type IV samples have been stretched at a speed of 1 mm/min to obtain the stress (MPa) as a function of strain ε (%). Young's modulus E was calculated from the slope of the stressstrain curve at small strains. The electrical conductivity of the thermally treated composites has been measured by a two-point method using a MX24B multimeter and an impedance analyzer (7260 Impedance Analyzer, Materials Mates Italia) under a voltage of 5 V in a frequency range of 1 Hz -10 6 Hz. Silver paint has been used in order to ensure good electrical contact between the sample and the electrodes.

Figure 1 .

 1 Figure 1. Scheme of the GO-based composites manufacture by Digital Light Processing. A monolayer GO dispersion is added to the resin and then, by UV 2D projections, the formulation is 3D printed. A final thermal post-treatment is applied in order to reduce GO and obtained a conductive composite.

Figure 2 .

 2 Figure 2. a) Poly(methyl methacrylate) (PMMA) cuvettes containing (from left to right) distilled water, 0.005% wt GO dispersed in water, 0.005% wt rGO stabilized with 0.35% wt bile salt (BS), b) Absorbance spectra of the (black) rGO dispersions, (brown) GO, and (blue) BS solution.

Figure 3 .

 3 Figure 3. Optical micrographs of the dispersions: a) 0.3 wt % rGO in the acrylic resin, b) GO ethanol-rich solution at 2.4 wt % under crossed polarizers. The axes of the polarizers are shown by white arrows. Birefringence reveals the liquid crystallinity of the solution c) 0.25 wt % and d) 0.45 wt % GO in the acrylic resin.

Figure 4 .

 4 Figure 4. a) Viscosity and b) shear stress as a function of shear rate for the acrylate resins containing different weight fractions of GO.

Figure 5 .

 5 Figure 5. Jacobs working curves for composites with different GO weight fractions at 405 nm (1.27 mW cm -2 ). Cd is the depth of polymerization. E0 is the irradiation energy.

Figure 6 .

 6 Figure 6. Digital model of a complex structure and photographs of a 3D printed of 0.15 wt % GO composite and 0.15 wt % MWCNTs composite. Red arrows show the failures during the 3D printing process. Scale bars: 1 cm

Figure 7 .

 7 Figure 7. a) 3D printed cube structures from left to right: pristine resin (transparent-yellow color), GO composite (dark brown color) and rGO composite (black color), b) 3D printed 4x4x4 tetrakaidecahedron cells of 0.35% wt GO composite before and after thermal reduction. Scale bars: 3 mm

Figure 8 .

 8 Figure 8. a) Photograph of the tensile test samples before (left) and after (right) thermal reduction and b) Young's moduli of the composites after and before thermal annealing as a function of GO fractions.

Figure 9 .

 9 Figure 9. a) Electrical conductivity as a function of the weight fraction of GO for the nanocomposites reduced at 200°C for 2h and at 200°C for 2h plus 300 ºC for 2h. The data are fitted by the scaling Equation (1). b) Frequency dependence of the alternating current conductivity of the nanocomposites before and after the thermal treatments.

Table 1 .

 1 The electrical properties of the rGO-based composites depend on the thermal annealing temperature. Fits to equation(1).

	Thermal annealing (ºC)	σmax (S m -1 )	σ0 (S m -1 )	ρc (% wt)	t
	200	9.93•10 -3	5.71•10 -3	0.15	1.72
	300	1.2•10 -2	6.85•10 -3	0.05	1.93

Acknowledgments

Funding from the AID (Agence Innovation Défense) and the Nouvelle Aquitaine Region are acknowledged.

Received: ((will be filled in by the editorial staff))

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Published online: ((will be filled in by the editorial staff))


Shouwen Zhang

Ari Setyan

Véronique Riffault

A laboratory

Introduction

 Particle size distribution is one of the most important physical properties of particles. A wide range of instruments have been developed to measure size distributions.  Four condensation particle counters (CPC) and three scanning mobility particle sizers (SMPS) (all commercial instruments) have been compared in terms of particle number concentration and size distribution.

Experimental setup

Setup for monodisperse aerosols Setup for polydisperse aerosols Solutions: NH 4 NO 3 10 -2 M for particles of selected sizes (50, 100, 200, 300 nm) NH 4 NO 3 10 -3 M for polydisperse aerosols PSL spheres (50, 200, 350, 500, 700, and

CPC vs. CPC:

All the instruments are very well correlated (r 2 > 0.99). However, CPC#1 measures much more particles than CPC#2 and CPC#4.

For CPC#1, the counting efficiency increases for large particles (>200 nm).

 SMPS vs. SMPS: SMPS#4(a and b) and SMPS#6 show different counting efficiencies, as a function of the particle size. For small particles, SMPS#6 counts much more particles than SMPS#4a. SMPS#5 measures particles larger than 300 nm and uses optical detector. Its correlation towards SMPS#4b, which uses butanol CPC, is low.

Conclusion

 All the instruments are very well correlated in terms of particle number concentrations (r 2 > 0.99). However, scatterplots have slopes very far from 1 in some cases.  Counting efficiencies of several instruments seem to depend highly on the particle size.  Good agreement between the different SMPS in terms of size distributions, except for SMPS#6 with monodisperse aerosols.  These discrepancies in particle counting between different instruments may be a serious problem in field campaigns or lab experiments, since people often bring just one SMPS or one CPC to calibrate instruments, and to measure particle concentrations and size distributions.  CPC vs. SMPS: SMPS#4a and SMPS#6 count much more particles than CPC#1 (slopes between 1.4 and 2.7). SMPS#6 vs. CPC#1 shows very large variation of the slope, as a function of the particle size.

Results and discussion

  has two different DMA (a and b), measuring two different size ranges. Diffusion loss correction has been applied for all the SMPS. Inter-comparisons: CPC vs. CPC: comparison of the particle number concentrations given by the CPC. CPC vs. SMPS: the SMPS size distribution is integrated over the entire size range. SMPS vs. SMPS: the SMPS size distributions are integrated over the same size range.

Acknowledgments

 The authors acknowledge financial support from the CaPPA project (Chemical and Physical Properties of the Atmosphere) which is funded by the French National Research Agency (ANR) through the PIA (Programme d'Investissements d'Avenir) under contract ANR-10-LABX-005.  S. Zhang is grateful for a PhD scholarship from the Nord-Pas de Calais Regional Council and Armines.


Shouwen Zhang

Ari Setyan

Véronique Riffault

A laboratory inter-comparison of CPC and SMPS measurements of submicron aerosols

Introduction

 Particle size distribution is one of the most important physical properties of particles. A wide range of instruments have been developed to measure size distributions.  Four condensation particle counters (CPC) and three scanning mobility particle sizers (SMPS) (all commercial instruments) have been compared in terms of particle number concentration and size distribution.

Experimental setup

Setup for monodisperse aerosols Setup for polydisperse aerosols Solutions: NH 4 NO 3 10 -2 M for particles of selected sizes (50, 100, 200, 300 nm) NH 4 NO 3 10 -3 M for polydisperse aerosols PSL spheres (50, 200, 350, 500, 700, and

CPC vs. CPC:

All the instruments are very well correlated (r 2 > 0.99). However, CPC#1 measures much more particles than CPC#2 and CPC#4.

For CPC#1, the counting efficiency increases for large particles (>200 nm).

 SMPS vs. SMPS: SMPS#4(a and b) and SMPS#6 show different counting efficiencies, as a function of the particle size. For small particles, SMPS#6 counts much more particles than SMPS#4a. SMPS#5 measures particles larger than 300 nm and uses optical detector. Its correlation towards SMPS#4b, which uses butanol CPC, is low.

Conclusion

 All the instruments are very well correlated in terms of particle number concentrations (r 2 > 0.99). However, scatterplots have slopes very far from 1 in some cases.  Counting efficiencies of several instruments seem to depend highly on the particle size.  Good agreement between the different SMPS in terms of size distributions, except for SMPS#6 with monodisperse aerosols.  These discrepancies in particle counting between different instruments may be a serious problem in field campaigns or lab experiments, since people often bring just one SMPS or one CPC to calibrate instruments, and to measure particle concentrations and size distributions.  CPC vs. SMPS: SMPS#4a and SMPS#6 count much more particles than CPC#1 (slopes between 1.4 and 2.7). SMPS#6 vs. CPC#1 shows very large variation of the slope, as a function of the particle size. Size distributions measured by SMPS#4a agree very well with those of NH 4 NO 3 selected by the electrostatic classifier. SMPS#6 has a very wide size distribution, and is obviously not suitable for the measurement of monodisperse aerosols.

Results and discussion

SMPS#4b and SMPS#6 have very similar size distributions, with a slight shift in the mode. SMPS#6 seems to measure size distributions of polydisperse aerosols much better than those of monodisperse aerosols.

SMPS have usually very poor size resolution beyond 300 nm. SMPS#4b and SMPS#5 see PSL particles in the range 300-1000 nm, but the integration of these signals has very large uncertainties.

  has two different DMA (a and b), measuring two different size ranges. Diffusion loss correction has been applied for all the SMPS. Inter-comparisons: CPC vs. CPC: comparison of the particle number concentrations given by the CPC. CPC vs. SMPS: the SMPS size distribution is integrated over the entire size range. SMPS vs. SMPS: the SMPS size distributions are integrated over the same size range.

Acknowledgments

 The authors acknowledge financial support from the CaPPA project (Chemical and Physical Properties of the Atmosphere) which is funded by the French National Research Agency (ANR) through the PIA (Programme d'Investissements d'Avenir) under contract ANR-10-LABX-005.  S. Zhang is grateful for a PhD scholarship from the Nord-Pas de Calais Regional Council and Armines.