Ternary Relation Research Articles

Triadic concept analysis for insights extraction from longitudinal studies in health

In the health field, longitudinal studies involve the recording of clinical observations of the same sample of patients over successive periods, referred to as waves. This type of database serves as a valuable source of information and insights, particularly when examining the temporal aspect, allowing the extraction of relevant and non-obvious knowledge. The triadic concept analysis theory has been proposed to describe the ternary relationships between objects, attributes, and conditions. In this study, we present a methodology for exploring longitudinal health databases using both the triadic theory and triadic rules, which are similar to association rules but incorporate temporal relations. Through four case studies, we demonstrate the potential of applying triadic analysis to longitudinal databases to identify risk patterns, enhance decision-making processes, and deepen our understanding of temporal dynamics. These findings suggest a promising approach for describing longitudinal databases and obtaining insights to improve clinical decision-support systems for disease treatment.

Adaptive multi-graph contrastive learning for bundle recommendation

Recently, recommending bundles - sets of items that complement each other - instead of individual items to users has drawn much attention in both academia and industry. Models based on Graph Neural Networks (GNNs) for bundle recommendation have achieved great success in capturing users’ preferences by modeling pairwise correlations among users, bundles, and items via information propagation on graphs. However, a notable limitation lies in their insufficient focus on explicitly modeling intricate ternary relationships. Additionally, the loose combination of node embeddings from different graphs tends to introduce noise, as it fails to consider disparities among the graphs. To this end, we propose a novel approach called Adaptive Multi-Graph Contrastive Learning for Bundle Recommendation (AMCBR). Specifically, AMCBR models ternary interactions by constructing multiple graphs, including a bundle preference graph based on direct user-bundle interactions, a collaborative neighborhoods graph featuring user-level and bundle-level subgraphs, and an item-level preference hypergraph capturing indirect user-bundle relationships through items. Then, (hyper)graph convolution is applied to each (hyper)graph to encode diverse potential preferences into node embeddings. To enhance the model’s robustness, an adaptive aggregation module is employed to assign varying weights to node embeddings from different graphs during the fusion process, which enriches the semantic and comprehensive information in the embeddings while mitigating potential noise. Finally, a contrastive learning strategy is proposed to jointly optimize the model, strengthening collaborative links between individual graphs. Extensive experiments on three real datasets demonstrate that AMCBR can outperform the state-of-the-art baselines on the Top-K recommendations.

Simplified Semantics for Further Relevant Logics I

This paper shows that the relevant logics E and Π′ are strongly sound and complete with regards to a version of the “simplified” Routley-Meyer semantics. Such a semantics for E has been thought impossible. Although it is impossible if an admissible rule of E  the rule of restricted assertion or equivalently Ackermann’s δ-rule  is solely added as a primitive rule, it is very much possible when E is axiomatized in the way Anderson and Belnap did. The simplified semantics for E and Π′ requires unreduced frames. Contra what has been claimed, however, no additional frame component is required over and above what’s required to model other relevant logics such as T and R. It is also shown how to modify the tonicity requirements of the ternary relation so as to allow for the standard truth condition for both fusion – the intensional conjunction ◦ – as well as the converse conditional ←.

Bacterial Susceptibility to Ceria Nanoparticles: The Critical Role of Surrounding Molecules.

Investigating the ternary relationship among nanoparticles (NPs), their immediate molecular environment, and test organisms rather than the direct interaction between pristine NPs and test organisms has been thrust into the mainstream of nanotoxicological research. Diverging from previous work that predominantly centered on surrounding molecules affecting the toxicity of NPs by modulating their nanoproperties, this study has unveiled a novel dimension: surrounding molecules altering bacterial susceptibility to NPs, consequently impacting the outcomes of nanobio interaction. The study found that adding nitrate as the surrounding molecules could alter bacterial respiratory pathways, resulting in an enhanced reduction of ceria NPs (nanoceria) on the bacterial surfaces. This, in turn, increased the ion-specific toxicity originating from the release of Ce3+ ions at the nanobio interface. Further transcriptome analysis revealed more mechanistic details underlying the nitrate-induced changes in the bacterial energy metabolism and subsequent toxicity patterns. These findings offer a new perspective for the deconstruction of nanobio interactions and contribute to a more comprehensive understanding of NPs' environmental fate and ecotoxicity.

Drug repurposing based on the DTD-GNN graph neural network: revealing the relationships among drugs, targets and diseases

MotivationThe rational modelling of the relationship among drugs, targets and diseases is crucial for drug retargeting. While significant progress has been made in studying binary relationships, further research is needed to deepen our understanding of ternary relationships. The application of graph neural networks in drug retargeting is increasing, but further research is needed to determine the appropriate modelling method for ternary relationships and how to capture their complex multi-feature structure.ResultsThe aim of this study was to construct relationships among drug, targets and diseases. To represent the complex relationships among these entities, we used a heterogeneous graph structure. Additionally, we propose a DTD-GNN model that combines graph convolutional networks and graph attention networks to learn feature representations and association information, facilitating a more thorough exploration of the relationships. The experimental results demonstrate that the DTD-GNN model outperforms other graph neural network models in terms of AUC, Precision, and F1-score. The study has important implications for gaining a comprehensive understanding of the relationships between drugs and diseases, as well as for further research and application in exploring the mechanisms of drug-disease interactions. The study reveals these relationships, providing possibilities for innovative therapeutic strategies in medicine.

Paired relation feature network for spatial relation recognition

Recognizing relations between objects in an image is challenging for neural networks because some relations may not have obvious dedicated visual features. This paper proposes a Paired Relation Feature Network (PRFN), where all spatial and semantic features are extracted from the subject–object pair jointly, without using any hand-crafted features. PRFN includes a paired 2D spatial feature module that can learn the representative features from a pair of bounding boxes. By focusing on the paired depth feature between the subject and object, the problem of depth feature extraction is simplified to the recognition of a ternary relation {−1, 0, 1}, which is much easier to learn from training data. Experimental results demonstrate the effectiveness of PRFN for both the cases of RGB-D images and RGB images with estimated depth.

Traces of Ternary Relations Based on Bandler–Kohout Compositions

Recently, we have introduced and studied all possible four-point compositions (one degree of freedom) and five-point compositions (two degrees of freedom) of ternary relations in analogy with the usual composition of binary relations. In this paper, we introduce and study new types of compositions of ternary relations inspired by the compositions of binary relations introduced by Bandler and Kohout (BK-compositions, for short). Moreover, we pay particular attention to the link between BK-compositions and the traces of binary relations and use it as source of inspiration to introduce traces of ternary relations. Moreover, we show that these new notions of BK-compositions and traces are useful tools to solve some relational equations in an unknown ternary relation.

An Invitation to Higher Arity Science

Analytical thinking is dominated by binary ideas. From pairwise interactions to algebraic operations, to compositions of processes, to network models, binary structures are deeply ingrained in the fabric of most current scientific paradigms. In this paper, we introduce arity as the generic conceptualization of the order of an interaction between a discrete collection of entities and argue that there is a rich universe of higher arity ideas beyond binarity waiting to be explored. To illustrate this, we discuss several higher-order phenomena appearing in a wide range of research areas, paying special attention to instances of ternary interactions. From the point of view of formal sciences and mathematics, higher arity thinking opens up new paradigms of algebra, symbolic calculus and logic. In particular, we delve into the special case of ternary structures, as that itself reveals ample surprises: new notions of associativity (or lack thereof) in ternary operations of cubic matrices, ternary isomorphisms and ternary relations, the integration problem of 3-Lie algebras, and generalizations of adjacency in 3-uniform hypergraphs. All these are open problems that strongly suggest the need to develop new ternary mathematics. Finally, we comment on potential future research directions and remark on the transdisciplinary nature of higher arity science.

About One Linguistic Problem

Introduction. The article continues a series of publications on R-linguistics and is dedicated to the ternary hypothesis and the problem of modeling the world associated with it. The essence of the ternary hypothesis is based on the assumption that any natural language does not use verbs with arity (valency) above three. This hypothesis creates an epistemological problem, the essence of which lies in the mismatch between the constraints of the dimensionality of thinking and the dimensionality of some phenomena and processes of the surrounding world. The indicated problem is directly related to language, since language reflects human thinking and the structure of the world model.Methodology and sources. The results obtained in the previous parts of the series are used as research tools. To develop the necessary mathematical representations for verbs with high valence, the categorization axioms formulated earlier in the series are used.Results and discussion. It has been shown that cases of multiple indirect objects are related to data dependencies in the sentence. Methods of categorization have been developed for ternary relations and relations with higher arity. It has been demonstrated that even in this case, all conditional categorizations and conditional verbs can be reduced to a single categorization.Conclusion. The ternary hypothesis and the ternary problem are formulated. Based on the study of data dependencies, it is shown that the ternary hypothesis is most likely true for all natural languages. Based on the study of methods of categorizing relations with arity higher than three, it is demonstrated that in this case linguistic spaces show stability regardless of the location of categories in the sentence, which makes it possible to describe highdimensional interactions using subordinate clauses. Thus, the appearance of subordinate clauses in all languages of the world is associated with the need to describe highdimensional interactions in the world model human.

A dual source switched-capacitors multilevel inverter topology with extended voltage levels and voltage gain

The switched-capacitors multi-level inverters (SCMLI) are widely used in renewable energy resources for enhancing the quality and reliability of generated power. This paper suggests a new topology of extendable voltage levels and voltage gain units using switched capacitors SC with a dual DC source. The proposed unit can be extended by a modular pattern to increase the output voltage levels and voltage-boosting gain of the inverter. The main feature of this work is presenting a unit topology that utilizes multiple and modular sub-cells to increase the voltage gain at the output by increasing the number of the sub-cell components. A ternary relationship of the voltage magnitudes between the two asymmetrical DC sources is mandatory. Furthermore, all the capacitors are self-balanced, so there is no need for any additional and complex control circuit. Moreover, to decrease the cost factor of the inverter, a low IGBT switch count is taken into consideration and no passive diodes are used in the proposed structure. The H-bridge is connected to the unit to achieve bipolar voltage at the output. The operational analysis of the inverter is delineated in detail. A comparative study with state-of-art MLIs in different terms such as the number of components, the total standing voltage, the cost factor, and the gain shows the particularity of the proposed topology. The simulation of the proposed MLI is performed using PSCAD-EMTDC software. An experimental prototype is built to validate the simulation results.

Application of bacteriophage φPaP11-13 attenuates rat Cutibacterium acnes infection lesions by promoting keratinocytes apoptosis via inhibiting PI3K/Akt pathway.

Acne vulgaris caused by antibiotic-resistant Cutibacterium acnes (C. acnes) infection is difficult to treat conventionally. Phages have been suggested as a potential solution, but research on the mechanism of phage treatment is inadequate. This research investigates the underlying molecular mechanisms of phage φPaP11-13 attenuating C. acnes-induced inflammation in rat models. We found that rats infected with C. acnes had higher average ear thickness, greater enrichment of inflammatory cells as shown by hematoxylin-eosin (HE) staining, and fewer TUNEL (TdT-mediated dUTP Nick-End Labeling)-positive keratinocytes visualized by IF staining. Moreover, an increase of IGF-1 and IGF-1 receptor (IGF-1r) was detected using the immunohistochemical (IHC) staining method, Western blot (WB), and quantitative real-time PCR (qRT-PCR) when infected with C. acnes, which was decreased after the application of phage φPaP11-13. By applying the IGF-1 antibody, it was demonstrated that the severity of C. acnes-induced inflammation was relevant to the expression of IGF-1. Through WB and qRT-PCR, activation of the PI3K/Akt pathway and a down-regulation of the BAD-mediated apoptosis pathway were discovered after C. acnes infection. Subsequently, it was shown that the activation of the PI3K/Akt pathway against BAD-mediated apoptosis pathway was alleviated after applying phage φPaP11-13. Furthermore, applying the IGF-1r inhibitor, Pan-PI3K inhibitor, and Akt inhibitor reversed the changing trends of BAD induced by C. acnes and phage φPaP11-13. This study demonstrates that one of the critical mechanisms underlying the attenuation of acne vulgaris by phage φPaP11-13 is lysing C. acnes and regulating keratinocyte apoptosis via the PI3K/Akt signaling pathway.IMPORTANCECutibacterium acnes infection-induced acne vulgaris may cause severe physical and psychological prognosis. However, the overuse of antibiotics develops drug resistance, bringing challenges in treating Cutibacterium acnes. Bacteriophages are currently proven effective in MDR (multiple drug-resistant) Cutibacterium acnes, but there is a significant lack of understanding of phage therapy. This study demonstrated a novel way of curing acne vulgaris by using phages through promoting cell death of excessive keratinocytes in acne lesions by lysing Cutibacterium acnes. However, the regulation of this cell cycle has not been proven to be directly mediated by phages. The hint of ternary relation among "phage-bacteria-host" inspires huge interest in future phage therapy studies.

Process Path for Reducing Carbon Emissions from Steel Industry—Combined Electrification and Hydrogen Reduction

This review focuses on the energy structure of iron and steel production and a feasible development path for carbon reduction. The process path and feasible development direction of carbon emission reduction in the iron and steel industry have been analyzed from the perspective of the carbon–electricity–hydrogen ternary relationship. Frontier technologies such as “hydrogen replacing carbon” are being developed worldwide. Combining the high efficiency of microwave electric-thermal conversion with the high efficiency and pollution-free advantages of hydrogen-reducing agents may drive future developments. In this review, a process path for “microwave + hydrogen” synergistic metallurgy is proposed. The reduction of magnetite powder by H2 (CO) in a microwave field versus in a conventional field is compared. The driving effect of the microwave field is found to be significant, and the synergistic reduction effect of microwaves with H2 is far greater than that of CO.

ЭМПИРИЧЕСКАЯ ТЕОРИЯ ФОРМИРОВАНИЯ ЭМОЦИОНАЛЬНОГО И ВОЛЕВОГО ДЕФИЦИТА ПРИ ШИЗОФРЕНИИ С ПРЕОБЛАДАНИЕМ НЕГАТИВНЫХ РАССТРОЙСТВ, ПОЛУЧЕННАЯ НА ОСНОВЕ АНАЛИЗА СВЯЗИ КЛИНИЧЕСКИХ И ГЕНЕТИЧЕСКИХ ДАННЫХ С ПРИМЕНЕНИЕМ ДСМ-МЕТОДА АВТОМАТИЗИРОВАННОЙ ПОДДЕРЖКИ ИССЛЕДОВАНИЙ

The study attempted to test experts' assumptions about the difference in the genetic mechanisms of the formation of emotional and volitional deficits in schizophrenia with predominance of negative disorders. The aim of the study is to create empirical theory of these two phenomena using an approach based on JSM-method for automated research support (JSM-method ARS). Polymorphisms of four genes associated with schizophrenia (BDNF, 5HTR2A, HTTLPR, ZNF804A) and clinical data presented as PANSS score were used as empirical data. The use of generalized JSM-method ARS, which generates ternary relationships “cause-blocker-effect”, allows us considering in detail the interaction of specific gene variants for emotional and volitional deficits in negative schizophrenia. The result of the study is confirmation of the experts' hypothesis about the difference in the mechanisms of these clinical manifestations. This conclusion was based on a comparison of knowledge fragments for two phenomena. The utilized approach can be extrapolated to a larger number of genes. We suggest that the use of the generalized JSM-method ARS is a promising approach to studying gene interactions in schizophrenia.

Towards a finer classification of strongly minimal sets

Let M be strongly minimal and constructed by a ‘Hrushovski construction’ with a single ternary relation. If the Hrushovski algebraization function μ is in a certain class T (μ triples) we show that for independent I with |I|>1, dcl⁎(I)=∅ (* means not in dcl of a proper subset). This implies the only definable truly n-ary functions f (f ‘depends’ on each argument), occur when n=1. We prove for Hrushovski's original construction and for the strongly minimal k-Steiner systems of Baldwin and Paolini that the symmetric definable closure, sdcl⁎(I)=∅ (Definition 2.7). Thus, no such theory admits elimination of imaginaries. As, we show that in an arbitrary strongly minimal theory, elimination of imaginaries implies sdcl⁎(I)≠∅. In particular, such strongly minimal Steiner systems with line-length at least 4 do not interpret a quasigroup, even though they admit a coordinatization if k=pn. The case structure depends on properties of the Hrushovski μ-function. The proofs depend on our introduction, for appropriate G⊆aut(M) (setwise or pointwise stabilizers of finite independent sets), the notion of a G-normal substructure A of M and of a G-decomposition of any finite such A. These results lead to a finer classification of strongly minimal structures with flat geometry, according to what sorts of definable functions they admit.

Genome wide identification and characterization of fertility associated novel CircRNAs as ceRNA reveal their regulatory roles in sheep fecundity

Reproductive traits play a vital role in determining the production efficiency of sheep. Maximizing the production is of paramount importance for breeders worldwide due to the growing population. Circular RNAs (circRNAs) act as miRNA sponges by absorbing miRNA activity through miRNA response elements (MREs) and participate in ceRNA regulatory networks (ceRNETs) to regulate mRNA expression. Despite of extensive research on role of circRNAs as miRNA sponges in various species, their specific regulatory roles and mechanism in sheep ovarian tissue are still not well understood. In this study, we performed whole genome sequencing of circRNAs, miRNA and mRNA employing bioinformatic techniques on ovine tissues of two contrasting sheep breeds "Small tail Han (X_LC) and Dolang sheep (D_LC)", which results into identification of 9,878 circRNAs with a total length of 23,522,667 nt and an average length of 2,381.32 nt. Among them, 44 differentially expressed circRNAs (DECs) were identified. Moreover, correlation between miRNA-mRNA and lncRNA-miRNA provided us with to prediction of miRNA binding sites on nine differentially expressed circRNAs and 165 differentially expressed mRNAs using miRanda. miRNA-mRNA and lncRNA-miRNA pairs with negative correlation were selected to determine the ceRNA score along with positively correlated pairs from lncRNA and mRNA network. Integration of ceRNA score and positively correlated pairs exhibit a significant ternary relationship among circRNAs-miRNA-mRNA demonestrated by ceRNA, comprising of 50 regulatory pairs sharring common nodes and predicted potential differentially expressed circRNAs-miRNAs-mRNAs regulatory axis. Based on functional enrichment analysis shortlisted key ceRNA regulatory pairs associated with reproduction including circRNA_3257-novel579_mature-EPHA3, circRNA_8396-novel130_mature-LOC101102473, circRNA_4140- novel34_mature > novel661_mature-KCNK9, and circRNA_8312-novel339_mature-LOC101110545. Furthermore, expression profiling, functional enrichments and qRT-PCR analysis of key target genes infer their implication in reproduction and metabolism. ceRNA target mRNAs evolutionary trajectories, expression profiling, functional enrichments, subcellular localizations following genomic organizations will provide new insights underlying molecular mechanisms of reproduction, and establish a solid foundation for future research.Graphical Graphical abstract summarizing the scheme of study

A Unified Interpretation of the Semantics of Relevance Logic

Abstract I introduce a novel and quite intuitive interpretation of the ternary relation that figures in the relational semantics of many relevance logics. Conceptually, my interpretation makes use only of incompatibility and parthood relations, defined over a set of states. In this way, the proposed interpretation—of the ternary relation and the conditional—extends Dunn’s and Restall’s works on negation and the Routley star operator. Therefore, the interpretation is unified, and hence not only intuitive but also parsimonious. Additionally, the interpretation provides us with a cogent argument to the effect that a ternary relation is indispensable, and we cannot merely do with a binary relation.

Contrastive Intentions

AbstractThis paper introduces and argues for contrastivism about intentions. According to contrastivism, intention is not a binary relation between an agent and an action. Rather, it is a ternary relation between an agent, an action, and an alternative. Contrastivism is introduced via a discussion of cases of known but (apparently) unintended side effects. Such cases are puzzling. They put pressure on us to reject a number of highly compelling theses about intention, intentional action, and practical reason. And they give rise to a puzzle about rather-than constructions such as ‘I intend to ϕ rather than ψ’: In side effect cases it can seem wrong to claim that the subject intends to ϕ yet acceptable to claim that they intend to ϕ rather than ψ. This cries out for explanation. Contrastivism provides a unified response to all of these problems.

Modular labelled calculi for relevant logics


 
 
 In this article, we perform a detailed proof theoretic investigation of a wide number of relevant logics by employing the well-established methodology of labelled sequent calculi to build our intended systems. At the semantic level, we will characterise relevant logics by employing reduced Routley-Meyer models, namely, relational structures with a ternary relation between worlds along with a unique distinct element considered as the real (or actual) world. This paper realizes the idea of building a variety of modular labelled calculi by reflecting, at the syntactic level, semantic informations taken from reduced Routley-Meyer models. Central results include proofs of soundness and completeness, as well as a proof of cut- admissibility.
 
 

Transitivity-like Postulates of Ternary Relation on Four Points

In this paper, we firstly analyse the position relation on four points from four cases, that is, (i) both x and y are on the outside side of m and n, (ii) either x or y is on the inner side of m and n, (iii) both x and y are on the inner side of m and n, (iv) both x and y are on the same side of m and n. Then we acquire eight kinds of transitivity-like postulates from the four cases. What is more, we discuss the interrelationships between eight transitivity-like postulates and get some important deductibility theorems. Finally, we give a few counter-examples to show that the inverse of the deductibility theorems do not hold and get a summary diagram to show the relationships among these transitivity-like postulates.

Catoids and modal convolution algebras

We show how modal quantales arise as convolution algebras Q^X of functions from catoids X, multisemigroups equipped with source and target maps, into modal quantales value or weight quantales Q. In the tradition of boolean algebras with operators we study modal correspondences between algebraic laws in X, Q and Q^X. The catoids introduced generalise Schweizer and Sklar’s function systems and single-set categories to structures isomorphic to algebras of ternary relations, as they are used for boolean algebras with operators and substructural logics. Our correspondence results support a generic construction of weighted modal quantales from catoids. This construction is illustrated by many examples. We also relate our results to reasoning with stochastic matrices or probabilistic predicate transformers.