Language Modeling with Reduced Densities

This work originates from the observation that today's state-of-the-art statistical language models are impressive not only for their performance, but also---and quite crucially---because they are built entirely from correlations in unstructured text data. The latter observation prompts a fundamental question that lies at the heart of this paper: What mathematical structure exists in unstructured text data? We put forth enriched category theory as a natural answer. We show that sequences of symbols from a finite alphabet, such as those found in a corpus of text, form a category enriched over probabilities. We then address a second fundamental question: How can this information be stored and modeled in a way that preserves the categorical structure? We answer this by constructing a functor from our enriched category of text to a particular enriched category of reduced density operators. The latter leverages the Loewner order on positive semidefinite operators, which can further be interpreted as a toy example of entailment.

Jordan permutation groups and limits of 𝐷-relations

We construct via Fraïssé amalgamation an 𝜔-categorical structure whose automorphism group is an infinite oligomorphic Jordan primitive permutation group preserving a “limit of 𝐷-relations”. The construction is based on a semilinear order whose elements are labelled by sets carrying a 𝐷-relation, with strong coherence conditions governing how these 𝐷-sets are inter-related.

(E,M)−estructuras inducidas en categorías topológicas

In this paper, we describe a convenient categorical structure with respect to a class of monomorphisms M and epimorphisms E for any topological category. We show in particular that the structure that we introduce here, which is induced by topological functors and their initial liftings, allows the study of some M−coreflective subcategories of a topological category. We pay special attention to projective structures.

A relational approach to consciousness: categories of level and contents of consciousness

Characterizing consciousness in and of itself is notoriously difficult. Here, we propose an alternative approach to characterize, and eventually define, consciousness through exhaustive descriptions of consciousness’ relationships to all other consciousness. This approach is founded in category theory. Indeed, category theory can prove that two objects A and B in a category can be equivalent if and only if all the relationships that A holds with others in the category are the same as those of B; this proof is called the Yoneda lemma. To introduce the Yoneda lemma, we gradually introduce key concepts of category theory to consciousness researchers. Along the way, we propose several possible definitions of categories of consciousness, both in terms of level and contents, through the usage of simple examples. We propose to use the categorical structure of consciousness as a gold standard to formalize empirical research (e.g. color qualia structure at fovea and periphery) and, especially, the empirical testing of theories of consciousness.

An interpretation of dependent type theory in a model category of locally cartesian closed categories

Locally cartesian closed (lcc) categories are natural categorical models of extensional dependent type theory. This paper introduces the “gros” semantics in the category of lcc categories: Instead of constructing an interpretation in a given individual lcc category, we show that also the category of all lcc categories can be endowed with the structure of a model of dependent type theory. The original interpretation in an individual lcc category can then be recovered by slicing. As in the original interpretation, we face the issue of coherence: Categorical structure is usually preserved by functors only up to isomorphism, whereas syntactic substitution commutes strictly with all type-theoretic structures. Our solution involves a suitable presentation of the higher category of lcc categories as model category. To that end, we construct a model category of lcc sketches, from which we obtain by the formalism of algebraically (co)fibrant objects model categories of strict lcc categories and then algebraically cofibrant strict lcc categories. The latter is our model of dependent type theory.

Categorical structure of the armenian image among russian students with different types of ethnic identity

Introduction. The article analyzes the specificity of the categorical structure of the Armenian image among Russian students of Barnaul with different types of ethnic identity. Representatives of the Armenian ethnic group are one of the numerous ethnic groups living in Russia, and the space of higher education seems to be one of the platforms where you can meet them. Thus, among modern students, the need to adapt both to the new educational space and to its multinationality is becoming actual. The process of such adaptation includes a number of difficulties that students of different nationalities face. In our opinion, such difficulties are also associated with the specifics of categorization by the indigenous population of members of different ethnic groups.Materials and Methods. The specificity of the categorical structure of the Armenian image is presented in the form of a structure of categories identified on the basis of the prevailing type of ethnic identity of the respondents. To achieve the goal of the study, the following methods were used: free associations, subjective scaling, factor analysis of data, the questionnaire "Types of ethnic identity" by G.U.Soldatova and S.V. Ryzhova. The selection consisted of 187 students of different specialties and different universities in Barnaul.Results. Four models have been obtained that reflect the categorical structure of the image of an Armenian in groups of Russian students with different types of ethnic identity. All groups of respondents categorize the Armenian on the basis of emotionality, sociability, strategy of behavior in the conflict, and the prevailing position in the group. The fullness of the selected categories is distinctive. Thus, Russian students with a pronounced normal ethnic identity note negative qualities of an Armenian, but positive characteristics prevail in the structure of the image (cheerful, talkative, expressive, compliant). Russian students with a pronounced hyperidentity also represent the Armenian in a complex way, highlighting their positive and negative characteristics, where the latter are mostly represented (competing, impulsive, cunning). In the structure of the image of an Armenian, the majority of respondents with predominantly ethnic indifference have negative characteristics, and the group of students with pronounced ethnonihilism almost completely represents the Armenian in a negative light.Discussion and Conclusions. Based on the results of the study, it was concluded that it is necessary to form a positive ethnic identity among students. It is assumed that the specificity of the categorization of a member of the Armenian ethnic group by Russian students will determine their nature of communication with a representative of this nationality.

“GOOD” AND “BAD” PERSON: SPECIFICS OF A CATEGORIZATION OF A PERSON BY ADULT INTERNET USERS

Scientific problem and relevance. The novelty and active introduction of digital technologies make psychological studies of the Internet impact on users of different age groups relevant. The study covers adult and senior age groups, whose psychological formation finished during the pre-digital era. Aim. The paper aims to reveal the specifics of a categorical structure of adult web-users’ consciousness regarding social perception. Methods. The results of an empirical research carried out in the tradition of the cognitive approach are as follows. The study involved 600 respondents. All the respondents were representatives of the intellectual labor and are from 35 to 60 years. Using an open-ended questionnaire, the respondents were divided into two contrasting groups: “the reading subjects” and “the active Internet users” (n=100 each). Modeling of the categorical structure of the respondents’ consciousness was carried out through the factor analysis. As the incentive material, the assessments of the features of a “good” and “bad” person were used. The leading criterion of the complexity of consciousness is the quantity of the categories that form the concept. Main results. The main conclusions are that the reading subjects have a more complex cognitive structure in the categorization of a personality. There are two parameters that indicate this complexity: the quantity of the categories that form the concept, and the quantity of the categories with a bipolar internal organization (p=0.05). Sphere of application. The data can state the rationale of online activity restrictions of adult Internet users. Conclusion. A simplification of a categorical structure in social cognition among the active Internet users can be a kind of deformation because of Internet impact.

THE ESSENCE AND ECONOMIC ROLE OF THE SPORTS AND HEALTH SPHERE OF THE REGION

Introduction. In the twentieth century, anthropocentric trends of social and economic growth stimulated interest in a healthy lifestyle and physical education. There have been processes that have made sports and physical culture an important sector of the economy of many countries. This actualizes the study of the essence, components and economic role of sports and health in ensuring the social and economic development of the region. Methods. The methods of theoretical and comparative analysis were used in the course of the research to reveal the essence and economic role of the sports and health sphere of the region. Results. The article carries out a comparative analysis of the concepts «sphere of physical culture and sports», «sports and health sphere», «physical culture and health services» and «sports and health services», «sports and health activities», «sports and health services market». It was found that according to the traditional approach, the field of physical culture and sports is considered by scientists in the context of its impact on the health and lifestyle of the population, the formation of an appropriate culture of behaviour. It is determined that the use of the term «sphere of physical culture and sports» places a significant emphasis on educational aspects – physical education and physical training. It is proved that the economic essence of sports and health is manifested primarily in the process of providing services to meet the needs of the population in physical activity and health. A schematic representation of the relationship between the concepts and the categorical structure of the sports and health sphere is given. The main components of the sports and health sphere are determined. It is proved that under the conditions of decentralization it is expedient to conduct research of the sports and health sphere at the level of regions. The author`s vision of the concept of sports and the health sphere of the region is offered. Discussion. Prospects for further research are to develop a concept for the development of sports and recreation, which should be based on the principles of comprehensiveness, achieving sustainable development goals, and be adapted to the conditions of decentralized management of sports and recreation. Keywords: sports and health sphere of the region, sports, physical culture, sports infrastructure, the market of sports, and health services.

Configuration as a Procedure of Intracultural Knowledge Transfer (Exemplified by the Dynamics of the Concept of Human in the Russian Linguistic Worldview)

Continuous development of technologies and globalization result in transfer of knowledge: knowledge about the world is transmitted between bearers of different linguocultures, as well as from generation to generation within one linguoculture. In the course of various transfer procedures, knowledge undergoes structural and qualitative changes. The nomenclature of possible transfer procedures and the essence of some procedures vary for different types of transfer. Configuration is one of the main procedures for knowledge transfer. Its implementation can be observed through structural changes in the units of knowledge transfer, such as works of art, terms, loanwords, etc. If a concept is considered as such a unit, configuration can be traced in the dynamics of the macrostructure, categorical structure and field description of the concept. Thus, the analysis of linguistic units representing a concept allows us to identify changes occurring in the minds of linguoculture-bearers over time. This paper aimed to study configuration as one of the main procedures of intracultural transfer of knowledge within the Russian worldview, with regard to everyday sphere of knowledge. The material of the research included representations of the concept of human in journalistic publications. The study is based on a complex methodology, including descriptive, comparative historical, and comparative methods, as well as statistical analysis and conceptual analysis. The research allowed us to identify the implementation of the configuration procedure in the course of knowledge transfer in the everyday sphere of knowledge, as well as to confirm its non-identity for the everyday and scientific spheres of knowledge by comparing our results with the data obtained earlier by other researchers. The study contributes to solving the problem of linguocultural transfer of knowledge and can be used in accomplishing many linguocognitive tasks.

Generalized Bounded Linear Logic and its Categorical Semantics

We introduce a generalization of Girard et al.’s called (and its affine variant ). It is designed to capture the core mechanism of dependency in , while it is also able to separate complexity aspects of . The main feature of is to adopt a multi-object pseudo-semiring as a grading system of the !-modality. We analyze the complexity of cut-elimination in , and give a translation from with constraints to with positivity axiom. We then introduce indexed linear exponential comonads (ILEC for short) as a categorical structure for interpreting the $${!}$$ ! -modality of . We give an elementary example of ILEC using folding product, and a technique to modify ILECs with symmetric monoidal comonads. We then consider a semantics of using the folding product on the category of assemblies of a BCI-algebra, and relate the semantics with the realizability category studied by Hofmann, Scott and Dal Lago.