Category Theory Research Articles

Computational infrastructure for concepts discovery in science and technology

Automated scientific discovery, a topic in artificial intelligence has mainly been used to generate scientific insight from data. Our work follows the knowledge-driven discovery approach and introduces the use of category theory as the foundation for modeling diverse engineering fields represented with combinatorial representation. We show how category theory provides support for all stages of the discovery process starting from modeling the engineering knowledge. We demonstrate the use of the approach to rediscover previous discoveries in mechanics and discover new devices, some of which need to be realized to be appreciated. Category theory allows expanding the process to disciplines not modeled with combinatorial representations. We intend to demonstrate this in future studies.

Development of a Platform for Distributed Energy Resources Management on the Basis of a Digital Twin

The paper discusses the development of a platform for distributed energy resources management based on digital twins. The platform use cases include demand response, electric vehicle charging, peer-to-peer energy trading, storage scheduling, virtual power plant, and so on. Thanks to the digital twin, the platform can perform the use cases controlling either real operation-stage equipment or virtual design-stage simulation models. The platform offers mass distributed energy resources owners and operators to improve the power supply quality (including stability), reduce costs (including transaction overhead), and gain emerging market opportunities (including participation in various aggregators' programs). Software and equipment vendors are interested in the platform's capability to quickly assemble distributed energy management systems almost without programming. The digital twin and the platform are designed with the viewpoint-based approach established by the international systems engineering standard ISO/IEC/IEEE 42010. The typical power system digital twin architecture is described. The major kinds of mathematical models as part of digital twins are presented: physical models based on numerical solutions of differential equations and optimization problems, machine learning models, knowledge-based models. The interoperability of such heterogeneous models is ensured on the basis of the ontological model of distributed energy. The platform architecture is represented from three key viewpoints: functional, information, and software. To formalize and ultimately automate the integration of heterogeneous models, we propose novel mathematical methods of model-based system engineering based on category theory, including universal constructions and the multicomma. The multicomma category is shown to be constructed using standard product, exponent, and pushout constructions, which makes it possible to establish a number of its practically significant properties.

Universal Causality

Universal Causality is a mathematical framework based on higher-order category theory, which generalizes previous approaches based on directed graphs and regular categories. We present a hierarchical framework called UCLA (Universal Causality Layered Architecture), where at the top-most level, causal interventions are modeled as a higher-order category over simplicial sets and objects. Simplicial sets are contravariant functors from the category of ordinal numbers Δ into sets, and whose morphisms are order-preserving injections and surjections over finite ordered sets. Non-random interventions on causal structures are modeled as face operators that map n-simplices into lower-level simplices. At the second layer, causal models are defined as a category, for example defining the schema of a relational causal model or a symmetric monoidal category representation of DAG models. The third layer corresponds to the data layer in causal inference, where each causal object is mapped functorially into a set of instances using the category of sets and functions between sets. The fourth homotopy layer defines ways of abstractly characterizing causal models in terms of homotopy colimits, defined in terms of the nerve of a category, a functor that converts a causal (category) model into a simplicial object. Each functor between layers is characterized by a universal arrow, which define universal elements and representations through the Yoneda Lemma, and induces a Grothendieck category of elements that enables combining formal causal models with data instances, and is related to the notion of ground graphs in relational causal models. Causal inference between layers is defined as a lifting problem, a commutative diagram whose objects are categories, and whose morphisms are functors that are characterized as different types of fibrations. We illustrate UCLA using a variety of representations, including causal relational models, symmetric monoidal categorical variants of DAG models, and non-graphical representations, such as integer-valued multisets and separoids, and measure-theoretic and topological models.

Functional diversity and team innovation: A study on the mediating role of social cohesion in primary care teams.

Bringing together professionals with different knowledge and skills comes with the opportunity to spur the innovativeness of primary care teams. Nevertheless, empirical evidence shows that it is not self-evident that these innovations are also realized. The social categorization theory suggests that a better understanding of whether these potential team innovations are realized can be obtained by looking at the social cohesion of such teams. The aim of this study was to study the relationship between functional diversity and team innovation in primary care teams by examining the mediating role of social cohesion. Survey responses and administrative data of 887 primary care professionals and 75 supervisors in 100 primary care teams were analyzed. Structural equation modeling was used to examine a curvilinear mediated relationship among functional diversity and team innovation through social cohesion. The findings show a positive relationship between social cohesion and team innovation as expected. Contrary to the expectations, the relationship between functional diversity and social cohesion is insignificant, and the results show an inverted U-shaped relationship between functional diversity and team innovation instead. This study reveals an unexpected inverted U-shaped relationship between functional diversity and team innovation. This relationship is not mediated by social cohesion; however, social cohesion is still a significant predictor of team innovation. Policymakers should be aware of the relevance as well as the complexity of creating social cohesion in functionally diverse primary care teams. As long as it remains unknown how social cohesion is stimulated in functionally diverse teams, it seems best for the team innovation to prevent bringing together too many, but also too few, different functions.

From opportunity to threat: the non‐linear relationship between voice frequency and job performance via voice endorsement

How managers evaluate employees' ideas and when they endorse or reject them have always been concerns. Based on categorization theory, we theorize that middle managers with multiple responsibilities and limited resources tend to label excessive voices as threats instead of opportunities. We thus propose an inverted U‐shaped relationship between voice frequency and voice endorsement that sequentially influences job performance. Further, perceived task interdependence, related to how an individual makes sense of issues in the team, will influence voice content and moderate the curvilinear relationship between voice frequency and job performance through voice endorsement. A three‐wave time‐lagged survey of Chinese firms, including 299 employees and 37 supervisors, provided convergent support for this theoretical model. Our research contributes to the voice literature by exploring how middle managers' limited resources and multiple responsibilities influence their voice evaluation process. This research thus has practical implications for both organizations and employees, as it suggests organizations allocate resources to facilitate managers' implementation of voice and provides suggestions for effective voice experience.

Convergence of sewing conformal blocks

In a recent work [On factorization and vector bundles of conformal blocks from vertex algebras, preprint (2019), arXiv:1909.04683], Damiolini et al. showed that for a [Formula: see text]-cofinite rational vertex operator algebra [Formula: see text], sheaves of conformal blocks are locally free and satisfy the factorization property. In this paper, we prove that if [Formula: see text] is [Formula: see text]-cofinite, the sewing of conformal blocks is convergent. This proves a conjecture proposed by Zhu [Global vertex operators on Riemann surfaces, Commun. Math. Phys. 165(3) (1994) 485–531] and Huang [Some open problems in mathematical two-dimensional conformal field theory, preprint (2016), arXiv:1606.04493], generalizing previous results on the convergence of products, iterates, and traces (but not pseudo-traces) of vertex operators and intertwining operators in [Y. Zhu, Modular invariance of characters of vertex operator algebras, J. Amer. Math. Soc. 9(1) (1996) 237–302; Y. Z. Huang, A theory of tensor products for module categories for a vertex operator algebra, IV, J. Pure Appl. Algebra 100(1–3) (1995) 173–216; Y. Z. Huang, Differential equations, duality and modular invariance, Commun. Contemp. Math. 7(05) (2005) 649–706; Y. Z. Huang, J. Lepowsky and L. Zhang, Logarithmic tensor category theory, VII: Convergence and extension properties and applications to expansion for intertwining maps, preprint (2011), arXiv:1110.1929] and on the convergence of projective factors related to the central charge of the Virasoro algebra in [Y. Z. Huang, Two-Dimensional Conformal Geometry and Vertex Operator Algebras, Vol. 148 (Springer Science & Business Media, 1997)].

Cognitive technologies of the subject area based on ontology

An important problem of the automated construction of ontologies as a knowledge system is intellectualization, as well as the related data integration and qualitative information search. In this connection, the task of automated formation of ontologies is quite urgent. The most common quality criterion of the ontology is based on the assessment of the convenience and efficiency of working with it, and the presence of a connection between cognitive and semantic processes, which contributes to the process of its construction and actualization. The main difference of the conducted analysis, the results of which are presented in this work, are cognitive information technologies of the subject area, cognitive-semantic analysis based on the theory of categories, mathematical logic and universal algebra, construction of an ontological dictionary and ontological constructions. The informational interaction of the intellectual environment of the object with the subject is defined. For the formation of the concept in the intellectual environment due to the attached information space, the possibility is determined and the application of the concept and its features within the framework of the problem is substantiated. The construction of ontologies is based on the connection of cognitive processes with semantic ones and actualization – description and identification of sources of cognitive information in intellectual environments of subject areas. Linguistic-semantic analyzer is the main method of analyzing the emergence of new concepts, identification of semantically compatible concepts from various sources of knowledge, formation of textual stereotypes, prototypes and invariants in the form of text written with the words of this dictionary and terms contained in the thesaurus – by searching in text arrays of varying degrees of structuring of minimal semantic units and the use of object-oriented multivariate analysis in the construction of a system of templates with fuzzy calculations for class fields.

A mathematical framework for operational fine tunings

In the framework of ontological models, the inherently nonclassical features of quantum theory always seem to involve properties that are fine tuned, i.e. properties that hold at the operational level but break at the ontological level. Their appearance at the operational level is due to unexplained special choices of the ontological parameters, which is what we mean by a fine tuning. Famous examples of such features are contextuality and nonlocality. In this article, we develop a theory-independent mathematical framework for characterizing operational fine tunings. These are distinct from causal fine tunings – already introduced by Wood and Spekkens in [NJP,17 033002(2015)] – as the definition of an operational fine tuning does not involve any assumptions about the underlying causal structure. We show how known examples of operational fine tunings, such as Spekkens' generalized contextuality, violation of parameter independence in Bell experiment, and ontological time asymmetry, fit into our framework. We discuss the possibility of finding new fine tunings and we use the framework to shed new light on the relation between nonlocality and generalized contextuality. Although nonlocality has often been argued to be a form of contextuality, this is only true when nonlocality consists of a violation of parameter independence. We formulate our framework also in the language of category theory using the concept of functors.

Remember me? The role of gender and racial attributes in memory

Remembering people is at the core of many social and economic relationships. We present evidence of systematic biases in the way we remember people, based on two experiments. The first experiment is conducted in a real professional setting - academia. Participants of two academic conferences are asked to recall ‘who presented what’ a month after attending the conferences. The second experiment is a controlled version of the first. Participants are shown pictures of people, matched with the title of a paper. We exogenously vary the relative shares of women and non-white individuals. In both experiments, we find evidence that women and ethnic minorities are more likely to be remembered in settings where they are in a small minority. In contrast, they are more likely to be confused with each other when they are in larger fraction. These findings are in line with a theory of categorization. People with minority attributes appear to be “blended together.” We conjecture that these biases in remembering could have important implications for the formation of professional networks.

Down closed-quasi-injectivity of partially ordered acts

Action of a pomonoid on partially ordered sets ([Formula: see text]-posets) has beautiful aspects in practical subjects such as automata theory, projection algebra and theoretical computer science which makes it always capture the interest of mathematicians. On the other hand, the study of different kinds of weakly injectivity (which category theory inherited from homological and commutative algebra) is an interesting subject for mathematicians. One of the important kinds of weakly injectivity is quasi-injectivity. In this paper, we study quasi-injectivity in the category of [Formula: see text]-posets with respect to special kind of order embeddings, namely, down-closed embeddings (dc-quasi-injectivity).

Category theory and organic electronics

Inorganic semiconductors and conducting polymers are described by band conduction models with delocalized electrons, whereas small-molecule organic compounds are described by hopping conduction between localized molecular orbitals. However, the latter devices can reproduce fully the characteristics of semiconductor devices. Why are they so different and yet so similar? We will try to answer this question using Category theory and considering the meaning of electrical transport in electronic materials. The meaning of the category theory in physics is to consider different mathematical entities under a common mathematical structure.In this paper, the basic idea of category theory is first explained in detail using the example of complex impedance, and then four examples of its application are discussed. The derivation of the Mott-Gurney equation and the negative capacitance in OLED are discussed as examples of solving problems by moving to different categories. After those simple examples of formal rewriting from physical entity to mathematical entity, it is shown that electrical connection and electrical contact lead to direct sums and direct products of conducting states, based on the duality concept. We conclude that small-molecule organic compounds are not a mere branch of semiconductors, but rather equal counterparts of semiconductors in duality that are necessary to clarify the origin of the difference and similarity between organic electronics and semiconductor physics. Finally, by considering the electrical responses of OLEDs and OFETs in the immittance category, we show that they can be described under a common operating dynamic and propose a new operating model for OFETs.

Formalising Autonomous Construction Sites with the Help of Abstract Mathematics

With the rapid development of modern technologies, autonomous or robotic construction sites are becoming a new reality in civil engineering. Despite various potential benefits of the automation of construction sites, there is still a lack of understanding of their complex nature combining physical and cyber components in one system. A typical approach to describing complex system structures is to use tools of abstract mathematics, which provide a high level of abstraction, allowing a formal description of the entire system while omitting non-essential details. Therefore, in this paper, autonomous construction is formalised using categorical ontology logs enhanced by abstract definitions of individual components of an autonomous construction system. In this context, followed by a brief introduction to category theory and ologs, exemplary algebraic definitions are given as a basis for the olog-based conceptual modelling of autonomous construction systems. As a result, any automated construction system can be described without providing exhausting detailed definitions of the system components. Existing ologs can be extended, contracted or revised to fit the given system or situation. To illustrate the descriptive capacity of ologs, a lattice of representations is presented. The main advantage of using the conceptual modelling approach presented in this paper is that any given real-world or engineering problem could be modelled with a mathematically sound background.

Category of Generalized Modules Over Two Different Rings

In this paper,a method of enriched category theory to form a closed symmetricmonoidal structure on the category of generalized modules CR= (modR,Ab) have been implemented. Further, a new kind of generalized module category defined on two commutativerings R and S, denoted by CRS = (modR,modS) is constructed.Finally, the authors studied a localization on this type of categories, both of them are Grothendieck

Mixed reactions to multicultural (vs. Colorblind) diversity approach signals: A lay theories of culture perspective.

Despite its popularity, signaling a multicultural approach to racial-ethnic diversity is often faced with both positive and negative reactions. In this article, we sought insights into what may contribute to the mixed reactions and why. Drawing on social categorization theories and mindset research, we proposed that an underexplored factor influencing stakeholders' reactions to organizations' diversity approach was their lay theories or mindsets of culture. Specifically, we argued that those who believe that racial-ethnic groups represent unchangeable deep-seated essences-a fixed (vs. malleable) cultural mindset-would react negatively toward the intergroup differentiations and comparisons evoked by multicultural approach signals. Three experiments manipulated organizational diversity approach signals. Results consistently showed that a fixed cultural mindset was negatively related to organizational attraction (Studies 1 and 2) and support for diversity-promoting policies (Study 3) in reaction to a multicultural (vs. colorblind) approach. In addition, Study 3 tested and showed that ethnocentrism, a self-protective mechanism, mediated the negative reactions. Together, the findings support lay theories of culture as a moderating factor that affects reactions toward a multicultural approach. Organizations should take individuals' theories of culture into consideration in their efforts to maximize attraction and support for diversity. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Fukugoukakujoshi ~wo moto ni shite dan ~ni motodzuite dalam Kalimat Bahasa Jepang: Menelisik Jenis Nomina, Verba, dan Genre Kalimat

This research aims to determine the nouns, verbs, and sentence genres contained in Japanese sentences that contained fukugoukakujoshi of ~wo moto ni shite and ~ni motodzuite. This was conducted due to the similar meaning between fukugoukakujoshi ~wo moto ni shite and ~ni motodzuite when translated into Indonesian, which is "based on". Nevertheless, each word essentially has its own differences. This research uses a qualitative descriptive method with data collection techniques in the form of note-taking techniques, and direct-elements divide analysis technique based on experts’ theories. The used theories are noun type theory, verb type theory, phrase theory, and sentence genre seen from the theory of grammatical categories in the predicate. Based on the analysis results, the nouns, verbs, and sentence genres in Japanese sentences containing fukugoukakujoshi ~wo moto ni shite and ~ni motodzuite have similarities and differences.

Ethnic minority CEO turnover: Resource‐based and leadership categorization perspectives

SummaryWe use the resource‐based theory and leadership categorization theory to develop hypotheses about ethnic minority CEO turnover. Using survival analysis, we test the hypotheses and find that, as a group, ethnic minority CEOs at US firms experience only about half of the risk of turnover at any time as do nonethnic minority CEOs. However, the risk is not spread evenly across ethnic minority subgroups. Asian and Hispanic CEOs experience lower risk of turnover than nonethnic minority CEOs. Black CEOs of US firms do not share this reduced risk of turnover. We find that the resource‐based theory is consistent with the turnover experience of Asian and Hispanic ethnic minority CEOs, but that it is not useful for explaining Black CEO turnover. Some implications of our findings are the following: (1) In research, all minorities should not be treated as a single homogenous group, and (2) in practice, it may be useful to increase CEO social capital to lengthen tenure.

A category-theoretic proof of the ergodic decomposition theorem

AbstractThe ergodic decomposition theorem is a cornerstone result of dynamical systems and ergodic theory. It states that every invariant measure on a dynamical system is a mixture of ergodic ones. Here, we formulate and prove the theorem in terms of string diagrams, using the formalism of Markov categories. We recover the usual measure-theoretic statement by instantiating our result in the category of stochastic kernels. Along the way, we give a conceptual treatment of several concepts in the theory of deterministic and stochastic dynamical systems. In particular, ergodic measures appear very naturally as particular cones of deterministic morphisms (in the sense of Markov categories), and the invariant$\sigma $-algebra of a dynamical system can be seen as a colimit in the category of Markov kernels. In line with other uses of category theory, once the necessary structures are in place, our proof of the main theorem is much more intuitive than traditional approaches. In particular, it does not use any quantitative limiting arguments, and it does not rely on the cardinality of the group or monoid indexing the dynamics. We hope that this result paves the way for further applications of category theory to dynamical systems, ergodic theory, and information theory.

Similarity of Musical Timbres Using FFT-Acoustic Descriptor Analysis and Machine Learning

Musical timbre is a phenomenon of auditory perception that allows the recognition of musical sounds. The recognition of musical timbre is a challenging task because the timbre of a musical instrument or sound source is a complex and multifaceted phenomenon that is influenced by a variety of factors, including the physical properties of the instrument or sound source, the way it is played or produced, and the recording and processing techniques used. In this paper, we explore an abstract space with 7 dimensions formed by the fundamental frequency and FFT-Acoustic Descriptors in 240 monophonic sounds from the Tinysol and Good-Sounds databases, corresponding to the fourth octave of the transverse flute and clarinet. This approach allows us to unequivocally define a collection of points and, therefore, a timbral space (Category Theory) that allows different sounds of any type of musical instrument with its respective dynamics to be represented as a single characteristic vector. The geometric distance would allow studying the timbral similarity between audios of different sounds and instruments or between different musical dynamics and datasets. Additionally, a Machine-Learning algorithm that evaluates timbral similarities through Euclidean distances in the abstract space of 7 dimensions was proposed. We conclude that the study of timbral similarity through geometric distances allowed us to distinguish between audio categories of different sounds and musical instruments, between the same type of sound and an instrument with different relative dynamics, and between different datasets.

Logical-semantic definition of a production process digital twin

Objectives . A methodology currently being developed for generalizing and presenting knowledge about studied subject-oriented areas is based on a “model hypothesis” for determining the distinguished objects and their relationships. Such system models can be used in any information system to define the knowledge about subject-oriented areas. Systems engineering methods already make it possible to create information models of real objects supplemented by virtual components, and vice versa, i.e., models of virtual objects supplemented by real components. So, for example, the availability of information models of technological and production facilities and their connections with real equipment allow the creation and management of real-virtual production processes (PP) in accordance with Industry 4.0 methodologies. From a theoretical aspect, the development of system models of objects and their connections in subject-oriented areas is based on the problem of a formal consistent description (grammatical calculus) of the functional regularities of a given set of objects and their relationships. The purpose of the study is to develop an approach and principles of methodology for system modeling of production facilities and their connections to provide closed-loop control (forecasting, planning, accounting, regulation, etc.) in the production environments of machinery enterprises taking the form of their digital twins (DTs). Methods . The basic provisions of the theory of sets and graph theory—in particular, the provisions of the theory of categories of sets—are used according to the formal logic and control theories. System Engineering methods are also applied in the organization and management of machinery production. Results . The approach to the formation of a metastructure of production process digital twin (PPDT) based on the models of production facilities and their relationships is substantiated. The procedure and rules for constructing a PPDT system model are developed along with an approach to the structural and parametric identification of DT models, taking logical and semantic restrictions into account. Conclusions . A presented example for identifying the basic set of objects of the organization of the PPDT based on the logical-semantic analysis of production activities and the provisions of the unified standards of the unified system for technological preparation of production of machinery production as a researched subject area confirms the main provisions of the proposed methodology for constructing the PPDT.

A comparative study of the cognitive load of basic-level category, superordinate category and subordinate category.

Some cognitive linguists (Rosch et al. Cognit Psychol 8:382-439, 1976; Ungerer and Schmid An introduction to cognitive linguistics, Pearson Education Limited, London, England, 2006) believe the basic level category has cognitive economy because the basic level category allows obtaining the maximum amount of information about an item with the lowest cognitive effort. Whether it is also true for L2 learners has not been verified so far. This study examined whether Chinese English learners' cognitive load of basic level category is lower than that of superordinate category and subordinate category. The eye movement data, including that of total duration of fixations, total number of fixations, duration of first fixation, and average duration of fixations, generated by 31 Chinese English learners while reading sentences with different levels of category words, were collected and analyzed. The results showed that Chinese English learners' cognitive load of the basic level category was the lowest. This study provides cross-linguistic experimental evidence for the basic level category theory, and also shows the cognitive economy of basic level categories is an intrinsic psychological property, no matter whether it is the first language or the second language that the readers use.