Set Of Triples Research Articles

Joint Entity and Relation Extraction With Set Prediction Networks.

Joint entity and relation extraction is an important task in natural language processing, which aims to extract all relational triples mentioned in a given sentence. In essence, the relational triples mentioned in a sentence are in the form of a set, which has no intrinsic order between elements and exhibits the permutation invariant feature. However, previous seq2seq-based models require sorting the set of relational triples into a sequence beforehand with some heuristic global rules, which destroys the natural set structure. In order to break this bottleneck, we treat joint entity and relation extraction as a direct set prediction problem, so that the extraction model is not burdened with predicting the order of multiple triples. To solve this set prediction problem, we propose networks featured by transformers with non-autoregressive parallel decoding. In contrast to autoregressive approaches that generate triples one by one in a specific order, the proposed networks are able to directly output the final set of relational triples in one shot. Furthermore, we also design a set-based loss that forces unique predictions through bipartite matching. Compared with cross-entropy loss that highly penalizes small shifts in triple order, the proposed bipartite matching loss is invariant to any permutation of predictions; thus, it can provide the proposed networks with a more accurate training signal by ignoring triple order and focusing on relation types and entities. Various experiments on two benchmark datasets demonstrate that our proposed model significantly outperforms the current state-of-the-art (SoTA) models. Training code and trained models are now publicly available at https://github.com/DianboWork/SPN4RE.

Geometry of smooth extremal surfaces

We study the geometry of smooth projective surfaces defined by Frobenius forms, a class of homogenous polynomials in prime characteristic recently shown to have minimal possible F-pure threshold among forms of the same degree. We call these surfaces extremal surfaces, and show that their geometry is reminiscent of the geometry of smooth cubic surfaces, especially non-Frobenius split cubic surfaces. For instance, extremal surfaces have many lines but no triangles, hence many “star points” analogous to Eckardt points on a cubic surface. We generalize the classical notion of a double six for cubic surfaces to a double 2d on an extremal surface of degree d. We show that, asymptotically in d, smooth extremal surfaces have at least 116d14 double 2d's. A key element of the proofs is the large automorphism group of an extremal surface, which we show to act transitively on many associated sets, such as the set of triples of skew lines on the extremal surface.

The Field of Free Time as Tertiary Agency of Socialisation

Abstract Introduction: The authors examine the agencies of socialisation and attempt to reveal a pattern among these agents. They differentiate social elements and agencies of socialisation, and they endow the latter with three conditions: the requirements of scope, time and intensity and specific set of rules. Purpose: The purpose of the paper is to examine which factors satisfy this triple set of requirements. Methods: Explanatory method to expose the issue, based on desk research and secondary analysis was used. Results: Near the family and the school, the free time space meets the three conditions of the socialization environment (scope, time-intensity, specific set of rules). Discussion: The authors believe that these three conditions are not met by any other socialization area. Conclusions: All this means that in postmodern society, the institution of the family, which has been with us since pre-modernity, and the institution of the school, which has been with us since modernity, is accompanied by a third socialization macro-agency.

The Farey Sum of Pythagorean and Eisenstein Triples

A composition law, inspired by the Farey addition, is introduced on the set of Pythagorean triples. We study some of its properties as well as two symmetric matrices naturally associated to a given Pythagorean triple. Several examples are discussed, some of them involving the degenerated Pythagorean triple $(1, 0, 1)$. The case of Eisenstein triples is also presented.

Embedding Ontologies in the Description Logic ALC by Axis-Aligned Cones

This paper is concerned with knowledge graph embedding with background knowledge, taking the formal perspective of logics. In knowledge graph embedding, knowledge— expressed as a set of triples of the form (a R b) (“a is R-related to b”)—is embedded into a real-valued vector space. The embedding helps exploiting geometrical regularities of the space in order to tackle typical inductive tasks of machine learning such as link prediction. Recent embedding approaches also consider incorporating background knowledge, in which the intended meanings of the symbols a, R, b are further constrained via axioms of a theory. Of particular interest are theories expressed in a formal language with a neat semantics and a good balance between expressivity and feasibility. In that case, the knowledge graph together with the background can be considered to be an ontology. This paper develops a cone-based theory for embedding in order to advance the expressivity of the ontology: it works (at least) with ontologies expressed in the description logic ALC, which comprises restricted existential and universal quantifiers, as well as concept negation and concept disjunction. In order to align the classical Tarskian Style semantics for ALC with the sub-symbolic representation of triples, we use the notion of a geometric model of an ALC ontology and show, as one of our main results, that an ALC ontology is satisfiable in the classical sense iff it is satisfiable by a geometric model based on cones. The geometric model, if treated as a partial model, can even be chosen to be faithful, i.e., to reflect all and only the knowledge captured by the ontology. We introduce the class of axis-aligned cones and show that modulo simple geometric operations any distributive logic (such as ALC) interpreted over cones employs this class of cones. Cones are also attractive from a machine learning perspective on knowledge graph embeddings since they give rise to applying conic optimization techniques.

A large-scale evaluation of NLP-derived chemical-gene/protein relationships from the scientific literature: Implications for knowledge graph construction.

One area of active research is the use of natural language processing (NLP) to mine biomedical texts for sets of triples (subject-predicate-object) for knowledge graph (KG) construction. While statistical methods to mine co-occurrences of entities within sentences are relatively robust, accurate relationship extraction is more challenging. Herein, we evaluate the Global Network of Biomedical Relationships (GNBR), a dataset that uses distributional semantics to model relationships between biomedical entities. The focus of our paper is an evaluation of a subset of the GNBR data; the relationships between chemicals and genes/proteins. We use Evotec's structured 'Nexus' database of >2.76M chemical-protein interactions as a ground truth to compare with GNBRs relationships and find a micro-averaged precision-recall area under the curve (AUC) of 0.50 and a micro-averaged receiver operating characteristic (ROC) curve AUC of 0.71 across the relationship classes 'inhibits', 'binding', 'agonism' and 'antagonism', when a comparison is made on a sentence-by-sentence basis. We conclude that, even though these micro-average scores are modest, using a high threshold on certain relationship classes like 'inhibits' could yield high fidelity triples that are not reported in structured datasets. We discuss how different methods of processing GNBR data, and the factuality of triples could affect the accuracy of NLP data incorporated into knowledge graphs. We provide a GNBR-Nexus(ChEMBL-subset) merged datafile that contains over 20,000 sentences where a protein/gene-chemical co-occur and includes both the GNBR relationship scores as well as the ChEMBL (manually curated) relationships (e.g., 'agonist', 'inhibitor') -this can be accessed at https://doi.org/10.5281/zenodo.8136752. We envisage this being used to aid curation efforts by the drug discovery community.

Use of viscera from hunted roe deer by vertebrate scavengers in summer in central European mountainous mixed forest

Carrion is a valuable resource in forests, providing sustenance for vertebrate and invertebrate scavenger communities and contributing to ecosystem functions, such as nutrient cycling. Intensive ungulate hunting, and thereby extraction of carcasses, removes large quantities of potential carrion from the system, denying a valuable resource from scavenger fauna. It may be possible to reduce the loss and negative consequences to forest biodiversity by retaining evisceration residues from hunted deer, where full carcasses cannot be retained. However, what roll evisceration residues play as a resource for scavengers in temperate forests is not well understood. In this study, we exposed 47 carrion samples from hunted roe deer, in front of triple sets of camera traps, to examine how hunting remains are removed and fed upon by vertebrate scavengers. Overall, 70% of the samples were completely removed from experimental sites by vertebrates. We detected twelve vertebrate taxa feeding on evisceration residues, including martens (Martes spp.), red kites Milvus milvus and garden dormice Eliomys quercinus. Common buzzards Buteo buteo and Eurasian jays Garrulus glandarius were the most frequent feeders on carrion samples, while red foxes Vulpes vulpes displaced the largest proportion of samples. Finally, we found a range of insectivorous bird and mammal species using hunting remains as a source for invertebrate prey, while not scavenging on the remains directly. We demonstrate that evisceration residues can be a valuable resource for a wide range of taxa and suggest that viscera retention from hunted game may contribute to resource provisioning for scavengers in forest ecosystems.

Quantifying Intramolecular Basis Set Superposition Errors.

We show that medium-sized Gaussian basis sets lead to significant intramolecular basis set superposition errors at Hartree-Fock and density functional levels of theory, with artificial stabilization of compact over extended conformations for a 186 atom deca-peptide. Errors of ∼80 and ∼10 kJ/mol are observed, with polarized double zeta and polarized triple zeta quality basis sets, respectively. Two different procedures for taking the basis set superposition error into account are tested. While both reduce the error, it appears that polarized quadruple zeta basis sets are required to reduce the error below a few kJ/mol. Alternatively, the basis set superposition error can be eliminated using multiresolution methods based on Multiwavelets.

Language Classes of Extended Distributed Reaction Systems

Reaction systems are well-known formal models of interactions between biochemical reactions. A reaction system is a finite set of triples (reactants, inhibitors, products) that represent chemical reactions, where the reactants, the inhibitors, and the products are objects corresponding to the chemicals. The reactions may facilitate or inhibit each other. A distributed reaction system consists of a finite set of reaction systems that interact with their environment (function in a given context). The environment is a finite set of reactants provided by a context automaton. In the preceding paper, we studied distributed reaction systems where in each step, the context automaton provided a separate set of reactants to the component reaction systems. We assigned languages to these distributed reaction systems and provided representations of some well-known language classes by these constructs. In this paper, the context is provided for the whole distributed reaction system and the component reaction systems distribute the context among each other in different ways (the same context is valid for each component, or the context is split among the components). As in the preceding paper, we assign languages to these new types of distributed reaction systems and provide representations of well-known language classes (the class of right-linear simple matrix languages, the recursively enumerable language class).

The group of primitive Pythagorean triples over Gaussian integers

A group structure of the set of primitive Pythagorean triples over Gaussian integers is investigated. In addition, we show that it is a free abelian group. Base on the study, the construction and enumeration of the primitive Pythagorean triples having the same hypotenuse are established.

Double scaling limits of Dirac ensembles and Liouville quantum gravity

In this paper we study ensembles of finite real spectral triples equipped with a path integral over the space of possible Dirac operators. In the noncommutative geometric setting of spectral triples, Dirac operators take the center stage as a replacement for a metric on a manifold. Thus, this path integral serves as a noncommutative analogue of integration over metrics, a key feature of a theory of quantum gravity. From these integrals in the so-called double scaling limit we derive critical exponents of minimal models from Liouville conformal field theory coupled with gravity. Additionally, the asymptotics of the partition function of these models satisfy differential equations such as Painlevé I, as a reduction of the KDV hierarchy, which is predicted by conformal field theory. This is all proven using well-established and rigorous techniques from random matrix theory.

On Neutrosophic Relations in Group Theory

In this paper, we study neutrosophic of some triple relations or neutrosophic triple set (NTS) and related to the homomorphism groups. Various properties like equivalent relation, product, intersection and the union are studied. We showed several equivalent relations in group theory with new examples about neutrosophic homomorphism. Finally, some definitions, examples and other remarks of neutrosophic of these relations are given.

Knowledge grounded medical dialogue generation using augmented graphs

Smart healthcare systems that make use of abundant health data can improve access to healthcare services, reduce medical costs and provide consistently high-quality patient care. Medical dialogue systems that generate medically appropriate and human-like conversations have been developed using various pre-trained language models and a large-scale medical knowledge base based on Unified Medical Language System (UMLS). However, most of the knowledge-grounded dialogue models only use local structure in the observed triples, which suffer from knowledge graph incompleteness and hence cannot incorporate any information from dialogue history while creating entity embeddings. As a result, the performance of such models decreases significantly. To address this problem, we propose a general method to embed the triples in each graph into large-scalable models and thereby generate clinically correct responses based on the conversation history using the recently recently released MedDialog(EN) dataset. Given a set of triples, we first mask the head entities from the triples overlapping with the patient’s utterance and then compute the cross-entropy loss against the triples’ respective tail entities while predicting the masked entity. This process results in a representation of the medical concepts from a graph capable of learning contextual information from dialogues, which ultimately aids in leading to the gold response. We also fine-tune the proposed Masked Entity Dialogue (MED) model on smaller corpora which contain dialogues focusing only on the Covid-19 disease named as the Covid Dataset. In addition, since UMLS and other existing medical graphs lack data-specific medical information, we re-curate and perform plausible augmentation of knowledge graphs using our newly created Medical Entity Prediction (MEP) model. Empirical results on the MedDialog(EN) and Covid Dataset demonstrate that our proposed model outperforms the state-of-the-art methods in terms of both automatic and human evaluation metrics.

Is explicitly correlated double-hybrid density functional theory advantageous for vibrational frequencies?

We have investigated the effect of F12 geminals on the basis set convergence of harmonic frequencies calculated using two representative double-hybrid density functionals, namely, B2GP-PLYP and revDSD-PBEP86-D4. Like previously found for energetics (Mehta N.; Martin J. M. L. J. Chem. Theory Comput. 2022, 18, 5978), one sees an acceleration by two zeta steps, such that even the cc-pVDZ-F12 basis set is quite close to the complete basis set (CBS) limit. However, the basis set convergence problem is not as acute as for energetics, and compared with experimental harmonic frequencies, conventional orbital calculations with augmented triple zeta quality basis set are acceptably close to the CBS limit, and can be carried out using analytical second derivatives. An efficient implementation of double-hybrid F12 analytical derivatives would make the F12 approach attractive in the sense that even an spd orbital basis set would be adequate. For the accurate revDSD-PBEP86-D4 functional, the role of differing local correlation terms (Perdew–Zunger 1981 versus VWN5) in different electronic structure programs has been investigated, while optimal double-hybrid parameters and performance statistics for energetics as well as frequencies differ slightly between the two implementations; these differences are insignificant for practical purposes.

A de Bruijn and Erdös property in quasi-metric spaces with four points

It is a classic result that a set of n non-collinear points in the Euclidean plane defines at least n different lines. Chen and Chvátal conjectured in 2008 that the same results is true in metric spaces for an adequate definition of line. More recently, this conjecture was studied in the context of quasi-metric spaces.One way to study lines in an space is though its betweenness. Given a quasi-metric space (V,ρ), its induced quasi-metric be-tweenness is the set of triples (x, y, z) ϵ V3 such that ρ(x, z) = ρ(x, y) +ρ(y, z). In this work, we prove the existence of a quasi-metric space on four points a, b, c and d whose quasi-metric betweenness is ẞ = {(c, a, b), (a, b, c), (d, b, a), (b, a, d)}. This space has only three lines, none of which has four points. Moreover, we show that the betweenness of any quasi-metric space on four points with this property is isomorphic to B. Since B is not metric, we conclude that Chen and Chvatal's conjecture is valid for any metric space on four points.

Enhancing Text Classification by Graph Neural Networks With Multi-Granular Topic-Aware Graph

Text classification based on graph neural networks (GNNs) has been widely studied by virtue of its potential to capture complex and across-granularity relations among texts of different types from learning on a text graph. Existing methods typically construct text graphs based on words-documents to capture relevant intra-class document representations among the same documents via words-words and words-documents propagation. However, a natural problem is that polysemy words in documents may become an information medium between documents of different categories, promoting heterophily information propagation. The performance of text classification will be somewhat constrained by this issue. This paper proposes a novel text classification method based on GNN from multi-granular topic-aware perspective, referred to as Text-MGNN. Specifically, topic nodes are introduced to build a triple node set of “word, document, topic,” and multi-granularity relations are modeled on a text graph for this triple node set. The introduction of topic nodes has three significant advantages. The first is to strengthen the propagation of topics, words, and documents. The second is to enhance class-aware representation learning. The final is to mitigate the effect of heterophily information caused by polysemy words. Extensive experiments are conducted on three real-world datasets. Results validate that our proposed method outperforms 11 baselines methods.

An Online Parsing Framework for Semistructured Streaming System Logs of Internet of Things Systems

This article presents a novel log abstraction framework based on neural open information extraction (OpenIE) and dynamic word embedding principles. Though various log parsing frameworks are proposed in the literature, the existing frameworks are modeled on predefined heuristics or auto-regressive methodologies that work well in offline scenarios. However, these frameworks are less suitable for dynamic self-adaptive systems, such as the Internet of Things (IoT), where the log outputs have diverse contextual variations and disparate time irregularities. Therefore, it is essential to move away from these traditional approaches and develop a systematic model that can effectively analyze log outputs in real-time and increase the system up-time of IoT networks so that they are almost always available. To address these needs, the proposed framework used OpenIE along with term frequency/inverse document frequency (TF/IDF) vectorization for constructing a set of relational triples (aka triple-sets). Additionally, a dynamic pretrained encoder–decoder architecture is utilized to imbibe the positional and contextualized information in its resultant outputs. The adopted methodology has enabled the proposed framework to extract richer word representations with dynamic contextualization of time-sensitive event logs to enhance further downstream activities, such as failure prediction and prognostic analysis of IoT networks. The proposed framework is evaluated on the system event log traces accumulated from a long range wide-area network (LoRaWAN) IoT gateway to proactively determine the probable causes of its various failure scenarios. Additionally, the study also provided a comparative analysis of its mathematical representations with that of the current state-of-the-art (SOTA) approaches to project the advantages and benefits of the proposed model, particularly from its data analytics standpoint.

On strongly walk regular graphs, triple sum sets and their codes

Strongly walk regular graphs (SWRGs or s-SWRGs) form a natural generalization of strongly regular graphs (SRGs) where paths of length 2 are replaced by paths of length s. They can be constructed as coset graphs of the duals of projective three-weight codes whose weights satisfy a certain equation. We provide classifications of the feasible parameters of these codes in the binary and ternary case for medium size code lengths. For the binary case, the divisibility of the weights of these codes is investigated and several general results are shown. It is known that an s-SWRG has at most 4 distinct eigenvalues k> theta _1> theta _2 > theta _3, and that the triple (theta _1, theta _2, theta _3) satisfies a certain homogeneous polynomial equation of degree s - 2 (Van Dam, Omidi, 2013). This equation defines a plane algebraic curve; we use methods from algorithmic arithmetic geometry to show that for s = 5 and s = 7, there are only the obvious solutions, and we conjecture this to remain true for all (odd) s ge 9.

Ab initio relativistic potential energy surface with analytical long-range part of benzene-Rn complex and its application to intermolecular vibrations

We study the benzene-Rn (BzRn) complex in its electronic ground state using an ab initio scalar relativistic method in the framework of the coupled-cluster level of theory with single, double, and perturbative triple excitations [CCSD(T)]. Two different approaches to treat the scalar relativistic effects have been tested — the small-core pseudopotential (PP) and the Douglas–Kroll–Hess (DKH) Hamiltonian. These methods were used with the augmented Dunning’s double zeta basis set for C and H atoms, and the augmented triple PP basis set for Rn supplemented by midbond functions. Additionally, the effects of the basis extension for C and H atoms and the extension of the correlation space to include the internal orbitals of Rn and C have been tested. The comparison of the binding energy De and the equilibrium coordinate ze found with different methods has allowed to choose the optimal one based on PP for the construction of the analytical potential energy surface (PES). The long-range part of the potential has been fitted separately and the obtained long-range coefficients have been compared to their counterparts calculated from the first principles using the CCSD polarization propagator. The vibrational energy level pattern of BzRn has been studied, and the revealed polyad structure of the complex has been compared to the previously studied benzene-Kr and benzene-Xe complexes. A Python code that yields the interaction energy at any Rn position is provided.

GCP: Graph Encoder With Content-Planning for Sentence Generation From Knowledge Bases.

A knowledge base is a large repository of facts usually represented as triples, each consisting of a subject, a predicate, and an object. The triples together form a graph, i.e., a knowledge graph. The triple representation in a knowledge graph offers a simple interface for applications to access the facts. However, this representation is not in a natural language form, which is difficult for humans to understand. We address this problem by proposing a system to translate a set of triples (i.e., a graph) into natural sentences. We take an encoder-decoder based approach. Specifically, we propose a Graph encoder with Content-Planning capability (GCP) to encode an input graph. GCP not only works as an encoder but also serves as a content-planner by using an entity-order aware topological traversal to encode a graph. This way, GCP can capture the relationships between entities in a knowledge graph as well as providing information regarding the proper entity order for the decoder. Hence, the decoder can generate sentences with a proper entity mention ordering. Experimental results show that GCP achieves improvements over state-of-the-art models by up to 3.6%, 4.1%, and 3.8% in three common metrics BLEU, METEOR, and TER, respectively. The code is available at (https://github.com/ruizhang-ai/GCP/).