Category Structure Research Articles

A taxometric analysis of panic disorder

ABSTRACT Panic disorder is costly, and while evidence-based interventions for panic disorder are effective, obtaining a diagnosis often precludes access to such treatments. This is problematic because the categorical diagnosis of panic disorder (i.e. “you have it, or you don’t”) supported by modern diagnostic manuals contradicts empirically supported dimensional models of panic disorder. Taxometric analyses, which test the dimensional or categorical latent structure of constructs, have consistently revealed dimensional latent structures when applied to other anxiety disorders and panic-related processes, but taxometric analyses have never been applied to panic disorder. To address this gap in the literature, three nonredundant taxometric procedures were applied to seven theoretically-relevant indicators of panic disorder derived from Panic Disorder Severity Scale data collected from 663 participants recruited via Amazon Mechanical Turk. Simulated comparison plots and objective fit indices were also evaluated. The collective results provided consistent empirical support for a dimensional model of panic disorder, with an overall mean CCFI score of .39. The implications of the present findings for the measurement, assessment, diagnosis, and treatment of panic disorder are discussed.

Study of the Framework and Attributes of Ethical Standards in Journalism

It has always been difficult to create fair evaluation criteria for journalists, especially when it comes to judging morality and ethical conduct in news reporting. These guidelines function as yardsticks for gauging the ethics of news topics and the objectivity of journalistic techniques. These criteria are becoming more and more difficult as journalism changes, especially in the digital age. Fostering ethical journalism requires an understanding of its categorization and internal structure. This analysis employs a conceptual framework to explore the evaluation standards of news ethics. The method involves: Literature Review: Examining existing academic literature, ethical codes, and industry guidelines to outline the prevailing evaluation standards in journalism. Thematic Analysis: Identifying and categorizing the components of evaluation standards into normative and quality standards, assessing their relevance to different aspects of journalistic practice. Case Studies: Analyzing specific instances where journalistic ethics were put to the test, allowing for a practical understanding of how these standards function in real-world scenarios. The primary objective of this study is to clarify the internal structure of journalistic ethics evaluation standards and highlight the distinctions between normative and quality standards. By doing so, the analysis aims to provide insights into how these standards can be effectively applied to evaluate news behaviors and moral character in journalism. What is deemed ethical in one context may not hold the same weight in another. This relativity underscores the importance of understanding the specific circumstances surrounding journalistic practices. Historical Context: The evolution of journalistic ethics is tied to historical events and societal changes. Standards that once sufficed may need reevaluation to address contemporary challenges, particularly with the rise of digital media and misinformation. Complex Internal Structure: The internal structure of evaluation standards can be multi-layered, with different levels of criteria applied depending on the context and specific ethical dilemmas faced by journalists. This complexity requires continuous dialogue and adjustment as new ethical challenges arise. Practical Implications: Journalists and media organizations must engage with these standards actively, incorporating them into training and policy development. By fostering an understanding of both normative and quality standards, the industry can promote a more ethical and accountable journalism practice.

The constraints of sedimentary environment on the evolution of bauxite reservoir characteristics within the benxi formation in the Linxing area, Ordos Basin, China

AbstractThe breakthrough of bauxite natural gas in the Taiyuan Formation in the Longdong area of the Ordos Basin makes bauxite natural gas gradually become a new exploration direction. However, the complex sedimentary conditions and diverse developmental strata of the Linxing region present difficulties for the exploration of bauxite gas. In this research, samples of bauxite cores from significant drilling sections in the Linxing area were obtained for comprehensive geochemical, mineralogical, and pore structure analysis. This study investigates the impact of sedimentary environments on the physical properties of bauxite reservoirs within the Benxi Formation, focusing on lithofacies categorization, mineral composition, and pore structure. This study established a lithofacies categorization system that iron minerals, aluminum minerals + titanium minerals, clay minerals as three end‐member components. The study identified four lithofacies types: pure bauxite, clayey bauxite, mixed bauxite, and bauxite mudstone. According to geochemical analysis, the bauxite rock in the study area is deposited in a semi‐enclosed bay with terrestrial freshwater input. The physical properties of bauxite reservoir in the study area are relatively poor, among which the physical properties of bauxite reservoir are the best. Authigenic minerals like pyrite are often filled in dissolution pores. The constraint of sedimentary environment on bauxite reservoir is mainly manifested as the influence on the formation of diaspore mineral framework, and its acidity and alkalinity are very important for the formation of diaspore. Hence, diaspore commonly forms in the shallow lake environments characterized by pure bauxite rock, exhibiting favorable reservoir conditions. This research examines the impact of mineral composition on bauxite reservoirs through the lens of lithofacies and sedimentary environments. The variations in bauxite rock reservoirs across distinct sedimentary environments have been elucidated. It provides a new guidance for the exploration of natural gas in Benxi Formation bauxite in Ordos Basin.

Automatic differentiation for ML-family languages: Correctness via logical relations

Abstract We give a simple, direct, and reusable logical relations technique for languages with term and type recursion and partially defined differentiable functions. We demonstrate it by working out the case of automatic differentiation (AD) correctness: namely, we present a correctness proof of a dual numbers style AD code transformation for realistic functional languages in the ML-family. We also show how this code transformation provides us with correct forward- and reverse-mode AD. The starting point is to interpret a functional programming language as a suitable freely generated categorical structure. In this setting, by the universal property of the syntactic categorical structure, the dual numbers AD code transformation and the basic $\boldsymbol{\omega } \mathbf{Cpo}$ -semantics arise as structure preserving functors. The proof follows, then, by a novel logical relations argument. The key to much of our contribution is a powerful monadic logical relations technique for term recursion and recursive types. It provides us with a semantic correctness proof based on a simple approach for denotational semantics, making use only of the very basic concrete model of $\omega$ -cpos.

The mining of China's policies against COVID-19 based on a policy target and tool co-evolution framework

Mining all COVID-19 policies issued by China can provide valuable lessons for both China and other countries in future pandemic control efforts. In this paper, we introduce a novel framework for mining the co-evolution of policy targets and policy tools. We employ bibliometric methods, text mining, and network analysis to explore the entire evolution of China's COVID-19 policies. Examining 1154 central government policies, (a) we extract policy targets from each policy, uncovering their evolution across different stages of the pandemic; (b) propose to identify the policy tool used in each policy unit by integrating an automatic identification model and active learning. We also reveal the categorical structure of these tools; (c) characterize the co-evolution pattern between policy targets and policy tools, shedding light on their dynamic relationship. Our findings indicate that policy targets have shifted across various stages, revealing unique characteristics in China's COVID-19 prevention and control efforts. Notably, there is a self-paradox between prevention measures and economic development. We identify the inadequateness in the distribution and utilization of policy tools. Ensuring the alignment of policy targets with appropriate tools is crucial. This synchronization and co-evolution between policy targets and tools are essential for enhancing the functional approach to policy implementation. This paper is the first systematic mining and review about the COVID-19 policies issued by the Chinese government, and our policy target and tool co-evolution mining framework provides a new quantitative framework for policy mining, especially an improved large language model and active learning theory are integrated to identify the policy tools automatically.

Simultaneous confidence interval construction for many-to-one of proportion ratios of bilateral correlated data.

In ophthalmology and otolaryngology, data collected from paired body parts are typically reformatted into categorical bilateral data structures for subsequent research. This article applies Donner's equal correlation coefficient model and obtains nine simultaneous confidence intervals (SCI) of proportion ratios under three asymptotic statistical methods and three ways of multiplicity adjustment. The empirical coverage probability and mean interval width are evaluated through Monte Carlo simulations. A real example is used to demonstrate the proposed methods.

Galois theory and homology in quasi-abelian functor categories

Given a finite category T, we consider the functor category AT, where A can be any quasi-abelian category. Examples of quasi-abelian categories are given by any abelian category but also by non-exact additive categories as the categories of torsion(-free) abelian groups, topological abelian groups, locally compact abelian groups, Banach spaces and Fréchet spaces. In this situation, the categories of various internal categorical structures in A, such as the categories of internal n-fold groupoids, are equivalent to functor categories AT for a suitable category T. For a replete full subcategory S of T, we define F to be the full subcategory of AT whose objects are given by the functors F:T→A with F(T)=0 for all T∉S. We prove that F is a torsion-free Birkhoff subcategory of AT. This allows us to study (higher) central extensions from categorical Galois theory in AT with respect to F and generalized Hopf formulae for homology.

On the non-measurability of $$\omega $$-categorical Hrushovski constructions

AbstractWe study $$\omega $$ ω -categorical MS-measurable structures. Our main result is that a certain class of $$\omega $$ ω -categorical Hrushovski constructions, supersimple of finite SU-rank is not MS-measurable. These results complement the work of Evans on a conjecture of Macpherson and Elwes. In constrast to Evans’ work, our structures may satisfy independent n-amalgamation for all n. We also prove some general results in the context of $$\omega $$ ω -categorical MS-measurable structures. Firstly, in these structures, the dimension in the MS-dimension-measure can be chosen to be SU-rank. Secondly, non-forking independence implies a form of probabilistic independence in the measure. The latter follows from more general unpublished results of Hrushovski, but we provide a self-contained proof.

A Coupled Hidden Markov Model framework for measuring the dynamics of categorization

We introduce a new framework for measuring the dynamics of category learning using Coupled Hidden Markov Models (CHMMs). The key assumptions of the framework are that people maintain a latent assignment of every stimulus to a category, and that they can update the assignments for all stimuli whenever they encounter any stimulus. These assumptions contrast with many existing accounts of category learning, which either do not allow for what is learned about one stimulus to influence the category association of others, or allow only for indirect influence. The CHMM framework allows tailored models to be developed for specific category learning tasks, taking as input the stimulus sequence and category responses people make, and producing as output inferences about the underlying dynamics of category assignments and the mechanics of the response processes. We demonstrate the framework by applying it to a categorization task considered by Lee and Navarro (2002), showing how the model measures the change in participants’ latent category assignments as they learn the category structure. We conclude by discussing potential applications of the CHMM framework to category learning situations involving prior knowledge, changing category structures, and category learning tasks that involve the consideration of multiple stimuli at one time.

Dynamic Short-Term Perspective Estimation Based on Formal Concept Analysis

In online shopping, user perspectives transit dynamically from abstract categories to concrete subcategories within a short period. We propose a perspective-estimation system that estimates the dynamic, short-term perspectives of users by inferring a hierarchy of categories based on their actions. The proposed system analyzes the wish list rankings of users and their operational histories to extract the categories emphasized at that moment. It then employs formal concept analysis to infer the hierarchical structure of categories, thereby visualizing the dynamic short-term perspective. In experiments involving 57 participants, the proposed method rates its match with user perspectives on a seven-point scale, achieving an average score of 4.84, outperforming the feature estimation method using latent Dirichlet allocation (LDA), which scored 4.36. The statistical significance was confirmed through the Wilcoxon rank-sum test with a statistic W=4.80 and a p-value of 1.56×10-6. Compared with LDA, the proposed system is statistically significant in terms of the degree of agreement with the perspectives.

The category $\Theta_{2}$, derived modifications, and deformation theory of monoidal categories

A complex C^{\bullet}(C,D)(F,G)(\eta,\theta) , generalising the Davydov–Yetter complex of a monoidal category (Davydov (1998) and Yetter (1998)), is constructed. Here, C,D are \Bbbk -linear (corresp., dg) bicategories, F,G\colon C\to D are \Bbbk -linear (corresp., dg) strong functors, and \eta,\theta\colon F\Rightarrow G are strong natural transformations. Morally, it is a complex of “derived modifications” \eta\Rrightarrow\theta ; likewise for the case of dg categories, one has the complex of “derived natural transformations” F\Rightarrow G , given by the Hochschild cochain complex of C with coefficients in C -bimodule D(F-,G=) .The complex C^{\bullet}(C,D)(F,G)(\eta,\theta) naturally arises from a 2-cocellular dg vector space A(C,D)(F,G)(\eta,\theta)\colon\Theta_{2}\to C^{\bullet}(\Bbbk) , as its \Theta_{2} -totalisation (here, \Theta_{2} is the category dual to the category of Joyal 2-disks (Joyal (1997))).It is shown that for a \Bbbk -linear monoidal category C , the third cohomology vector space H^{3}(C^{\bullet}(C,C)(\mathrm{Id},\mathrm{Id})(\mathrm{id},\mathrm{id})) is isomorphic to the vector space of the outer (modulo twists) infinitesimal deformations of the \Bbbk -linear monoidal category which we call the full deformations. It means that the following data is to be deformed: (a) the underlying dg category structure, (b) the monoidal product on morphisms (the monoidal product on objects is a set-theoretical datum and is maintained under the deformation), and (c) the associator. The data (a), (b), (c) is subject to the (infinitesimal versions of) numerous monoidal compatibilities, which we interpret as the closeness of the corresponding degree 3 element. Similarly, H^{2}(C^{\bullet}(C,D)(F,F)(\mathrm{id},\mathrm{id})) is isomorphic to the vector space of the outer infinitesimal deformations of the strong monoidal functor F .A relative totalisation Rp_{*}A(C,D)(F,F)(\mathrm{id},\mathrm{id}) along the projection p\colon\Theta_{2}\to\Delta is defined, and it is shown to be a cosimplicial monoid, which fulfils the Batanin–Davydov 1-commutativity condition (Batanin and Davydov (2023)). Then it follows from loc. cit. that C^{\bullet}(C,D)(F,F)(\mathrm{id},\mathrm{id}) is a C_{\bullet}(E_{2};\Bbbk) -algebra. Conjecturally, C^{\bullet}(C,C)(\mathrm{Id},\mathrm{Id})(\mathrm{id},\mathrm{id}) is a C_{\bullet}(E_{3};\Bbbk) -algebra; however, the proof requires more sophisticated methods.

Effect of fast frequency double pulse current on microstructural characteristics and mechanical properties of wire arc additively manufactured Ti-6Al-4V alloy

This study introduces an innovative technique known as fast-frequency double pulse wire arc metal additive manufacturing (FFDP-WAAM). This method employs periodic fluctuations in arc plasma and force to enhance the stirring effect within the molten pool, resulting in the fragmentation of β grains and the formation of finer prior-β grains. The microstructure primarily comprises α', attributed to the high cooling rates and minimal heat accumulation. Compared to the conventional gas tungsten arc welding-based WAAM (CGT-WAAM) process, FFDP-WAAM significantly reduces α-variant selection, thereby achieving a more uniform α phase orientation distribution. Additionally, ultrasonic vibration in the FFDP-WAAM process facilitates recrystallization and mitigates residual strain. The tensile strength and elongation of the FFDP-WAAM specimens reached 939.2 MPa and 9.0 %, respectively, whereas the CGT-WAAM specimens showed a lower tensile strength of 830 MPa and elongation of 9.2 %. The enhanced strength, fatigue life and microhardness of Ti-6Al-4V produced by FFDP-WAAM is ascribed to the refined grain-size distribution. Furthermore, the low Schmid factor (SF) distribution and the stable triangular structure of Category I α-clusters are anticipated to contribute to the increased strength of the FFDP-WAAM-fabricated wall.

Psycho-semantic analysis of job advertisements as a communicative tool of educational marketing

Introduction. The relevance of the study of job advertisements for teachers and psychologists is associated with the need to find tools for regulating communication within the modern educational environment with dynamic, constantly changing working conditions. The publication of employer requirements sets the direction for changing the criteria for the success of the specialist, which changes the entire educational environment. The purpose of the study: to identify the categorical semantic structure of job advertisements for teachers (using the example of the "Infrastructure of Scientific Research Data" platform). Materials and methods. The object of the study was a corpus of teacher job vacancies from the "Infrastructure of Scientific Research Data" platform, published in 2023 in 83 regions of Russia (5561 vacancies). The job postings included descriptions of candidate requirements, information about the offered salary, and the region in which the vacancy was available. As a comparison group, a corpus of psychologist job vacancies (2076 vacancies) was considered. The following methods were used in the study: 1) Latent Dirichlet Allocation (LDA) method for identifying and analyzing the structure of requirements presented in teacher and psychologist job vacancies; 2) Term Frequency-Inverse Document Frequency (TF-IDF) method for categorical semantic analysis of the structure of teacher and psychologist job vacancies and description of the semantic framework (frame) of the job description; 3) Descriptive statistical methods for analyzing the needs of professionals in helping professions in different regions of Russia and the conditions offered to them. The results of the study. The regions of the Russian Federation with the greatest need for teachers and psychologists have been identified. Based on the statistical significance in the collection of text documents, the most demanded skills of teachers by employers are identified: methodological development and design of an individual educational route (0.167), work with children with disabilities (0.144), organization of the educational process (0.089). For vacancies of psychologists, the most significant were: work on investigative actions (0.319), methodical work in an educational organization (0.187), psychological and pedagogical support for successful development and training (0.129). The main meanings governing professional pedagogical activity are more focused on meta-skills based on the values of inclusion and continuous improvement of education, as well as on flexible skills (Soft skills) that increase competitiveness in various fields of pedagogical activity. In the vacancies of psychologists, professional skills (Hard skills) are relevant, applicable in specific areas, which somewhat narrows the scope of professional implementation. Conclusion. The results of the empirical study allow for considering job vacancy advertisements as one of the communicative tools of educational marketing. Analyzing the significant professional skills from the employer's perspective will enable the development of recommendations for the development of professional communication for teachers, which can be considered in the system of continuous professional education, as well as in regulating interaction within the educational environment. Automated analysis of job vacancies can become a successful interactive diagnostic tool for educational marketing, necessary for the development of the educational space and the improvement of the competitiveness of educational institutions.

Individual differences in the perception of phonetic category structure predict speech-in-noise performance.

Speech sounds exist in a complex acoustic-phonetic space, and listeners vary in the extent to which they are sensitive to variability within the speech sound category ("gradience") and the degree to which they show stable, consistent responses to phonetic stimuli. Here, we investigate the hypothesis that individual differences in the perception of the sound categories of one's language may aid speech-in-noise performance across the adult lifespan. Declines in speech-in-noise performance are well documented in healthy aging, and are, unsurprisingly, associated with differences in hearing ability. Nonetheless, hearing status and age are incomplete predictors of speech-in-noise performance, and long-standing research suggests that this ability draws on more complex cognitive and perceptual factors. In this study, a group of adults ranging in age from 18 to 67 years performed online assessments designed to measure phonetic category sensitivity, questionnaires querying recent noise exposure history and demographic factors, and crucially, a test of speech-in-noise perception. Results show that individual differences in the perception of two consonant contrasts significantly predict speech-in-noise performance, even after accounting for age and recent noise exposure history. This finding supports the hypothesis that individual differences in sensitivity to phonetic categories mediates speech perception in challenging listening situations.

Lie algebras arising from two-periodic projective complex and derived categories

Let A be a finite-dimensional C-algebra of finite global dimension and A be the category of finitely generated right A-modules. By using of the category of two-periodic projective complexes C2(P), we construct the motivic Bridgeland's Hall algebra for A, where structure constants are given by Poincaré polynomials in t, then construct a C-Lie subalgebra g=n⊕h at t=−1, where n is constructed by stack functions about indecomposable radical complexes, and h is by contractible complexes. For the stable category K2(P) of C2(P), we construct its moduli spaces and a C-Lie algebra g˜=n˜⊕h˜, where n˜ is constructed by support-indecomposable constructible functions, and h˜ is by the Grothendieck group of K2(P). We prove that the natural functor C2(P)→K2(P) together with the natural isomorphism between Grothendieck groups of A and K2(P) induces a Lie algebra isomorphism g≅g˜. This makes clear that the structure constants at t=−1 provided by Bridgeland in [5] in terms of exact structure of C2(P) precisely equal to that given in [30] in terms of triangulated category structure of K2(P).

Psychometric Properties of Fine Motor Function Measure in Children With Cerebral Palsy: A Rasch Analysis.

Our study utilized Rasch Analysis to examine the psychometric properties of 61-items fine motor function measure (FMFM) in children with cerebral palsy (CP). Partial credit model (PCM) was utilized to test the reliability and validity of FMFM. The response pattern of this samples displayed acceptable fitness to PCM. The analysis results supported the assumption of 1-dimensionality of FMFM. Disordered category thresholds were found in 30 items. Differential item functioning (DIF) was detected in 23 items. Participants with different CP subtypes in different age groups may perform in differently responses patterns. The Rasch analysis produces reliable evidence to support the clinical application of FMFM. Some items may produce inaccurate measurements originated from category structures. Difference in age groups and symptom topography may be associated with variation in fine motor ability among children with CP and leading to unnecessary assessment bias. Hence, FMFM items need modifications to calibrate the former item formulation.

Phrase prosody of a southern Russian dialect: Rogovatoe

This paper deals with the phrase intonation of the Southern Russian dialect spoken in the village of Rogovatoe, in the Starooskol’sky district of the Belgorod region. The study is devoted to the analysis of the prosodic structure of various communicative categories: statements, yes-no questions, wh-questions, non-finality, imperative, and vocative. Based on the examination of more than 7000 sentences, I argue that the dialect of Rogovatoe uses only two monotonal pitch accents — H* and L* — as opposed to three bitonal accents of Modern Standard Russian. I also postulate two final boundary tones — H% and L% — for this dialect, while no proof of a phonological distinction between the high and the low phrase accents was found. Finally, the idiom of Rogovatoe employs the phonological distinction between the high and the low initial boundary tone — %H and %L. Therefore, the prosodic system of this Southern Russian dialect is much more focused on the level tones than Modern Standard Russian utilizing predominantly contour (rising and falling) tones.

Mind Melds: Verbal Labels Induce Greater Representational Alignment.

What determines whether two people represent something in a similar way? We examined the role of verbal labels in promoting representational alignment. Across two experiments, three groups of participants sorted novel shapes from two visually dissimilar categories. Prior to sorting, participants in two of the groups were pre-exposed to the shapes using a simple visual matching task designed to reinforce the visual category structure. In one of these groups, participants additionally heard one of two nonsense category labels accompanying the shapes. Exposure to these redundant labels led people to represent the shapes in a more categorical way, which led to greater alignment between sorters. We found this effect of label-induced alignment despite the two categories being highly visually distinct and despite participants in both pre-exposure conditions receiving identical visual experience with the shapes. Experiment 2 replicated this basic result using more even more stringent testing conditions. The results hint at the possibly extensive role that labels may play in aligning people's mental representations.

Coderived and contraderived categories of locally presentable abelian DG-categories

The concept of an abelian DG-category, introduced by the first-named author in Positselski (Exact DG-categories and fully faithful triangulated inclusion functors. arXiv:2110.08237 [math.CT]), unites the notions of abelian categories and (curved) DG-modules in a common framework. In this paper we consider coderived and contraderived categories in the sense of Becker. Generalizing some constructions and results from the preceding papers by Becker (Adv Math 254:187–232, 2014. arXiv:1205.4473 [math.CT]) and by the present authors (Positselski and Št’ovíček in J Pure Appl Algebra 226(#4):106883, 2022. arXiv:2101.10797 [math.CT]), we define the contraderived category of a locally presentable abelian DG-category B\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{B}$$\\end{document} with enough projective objects and the coderived category of a Grothendieck abelian DG-category A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{A}$$\\end{document}. We construct the related abelian model category structures and show that the resulting exotic derived categories are well-generated. Then we specialize to the case of a locally coherent Grothendieck abelian DG-category A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{A}$$\\end{document}, and prove that its coderived category is compactly generated by the absolute derived category of finitely presentable objects of A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{A}$$\\end{document}, thus generalizing a result from the second-named author’s preprint (Št’ovíček in On purity and applications to coderived and singularity categories. arXiv:1412.1615 [math.CT]). In particular, the homotopy category of graded-injective left DG-modules over a DG-ring with a left coherent underlying graded ring is compactly generated by the absolute derived category of DG-modules with finitely presentable underlying graded modules. We also describe compact generators of the coderived categories of quasi-coherent matrix factorizations over coherent schemes.

Unsupervised discriminative projection based on contrastive learning

Feature extraction can effectively alleviate the curse of dimensionality on high-dimensional data. Contrastive learning, as a self-supervised learning method, has garnered widespread attention in recent years. In this study, we propose a new unsupervised feature extraction model based on contrastive learning. We integrate the principle of contrastive learning into the feature extraction model in a novel way without data augmentation or negative samples, defining positive samples more accurately and flexibly. Additionally, we propose new structure preserving terms based on the selected positive samples to preserve the distribution structure of specific categories. An iterative algorithm is designed to solve the proposed model. Numerical experiments on four real datasets demonstrate that our method outperforms existing methods, highlighting its potential in handling high-dimensional data and extracting discriminative features.