Derived representation schemes and Nakajima quiver varieties

We introduce a derived representation scheme associated with a quiver, which may be thought of as a derived version of a Nakajima variety. We exhibit an explicit model for the derived representation scheme as a Koszul complex and by doing so we show that it has vanishing higher homology if and only if the moment map defining the corresponding Nakajima variety is flat. In this case we prove a comparison theorem relating isotypical components of the representation scheme to equivariant K-theoretic classes of tautological bundles on the Nakajima variety. As a corollary of this result we obtain some integral formulas present in the mathematical and physical literature since a few years, such as the formula for Nekrasov partition function for the moduli space of framed instantons on $$S^4$$ S 4 . On the technical side we extend the theory of relative derived representation schemes by introducing derived partial character schemes associated with reductive subgroups of the general linear group and constructing an equivariant version of the derived representation functor for algebras with a rational action of an algebraic torus.

Consumer choice theory in economic theory

One of the components of social behaviour is rational action, which is that the consumer chooses optimal goals in accordance with his natural and social needs, thoroughly calculating the best way to meet all his needs.

A Study on Developing a Communicative Rational Action Scale

The aim of this study is to develop a Communicative Rational Action Scale and analyze its validity and reliability. The scale has been prepared for all administrators and especially for firm administrators based on Max Weber’s rationalizing theory and Jürgen Habermas’ communicative action theory. The scale reveals to what extent administrators’ behaviors are communicatively rational while deciding or acting. In total, 282 participants joined this study. The sample group consisted of senior administrators of 87 firms acting in Turkey’s different Organized Industrial Zones or Free Zones. Data were analyzed by the SPSS 21 and AMOS 22 programs. Exploratory factor analysis and confirmatory factor analysis were applied to the obtained data. In order to test item discrimination, total item correlations were calculated and items under the value of 0.40 were removed from the scale. Exploratory factor analysis revealed 21 articles and five factors. The correlation coefficient of the 21-article scale with a similar scale is 0.979 (p < 0.001). The Cronbach’s alpha value is 0.945 and the test–retest correlation parameter is r = 0.793 (p < 0.001). In conclusion, it was determined by confirmatory factor analysis that the Communicative Rational Action Scale has a good cohesion criterion, and it is a valid and reliable assessment instrument.

Inferring Actions, Intentions, and Causal Relations in a Neural Network

From a young age, we can select actions to achieve desired goals, infer the goals of other agents, and learn causal relations in our environment through social interactions. Crucially, these abilities are productive and generative: we can impute desires to others that we have never held ourselves. These abilities are often captured by only partially overlapping models, each requiring substantial changes to fit combinations of abilities. Here, in an attempt to unify previous models, we present a neural network underpinned by the linearly solvable Markov Decision Process (LMDP) framework which permits a distributed representation of tasks. The network contains two pathways: one captures the desirability of states, and another encodes the passive dynamics of state transitions in the absence of control. Interactions between pathways are bound by a principle of rational action, enabling generative inference of actions, goals, and causal relations supported by gradient updates to parts of the network.

Transformasi televisi sebagai media belajar di tengah pandemi dalam kacamata rasional instrumental

During the Covid-19 pandemic, various areas of life experienced changes and adjustments, including in the field of education by conducting distance learning. As a form of adjustment for distance learning, the government and educators use television as a learning medium. The transformation of television as a learning medium is aimed at every level of education, one of which is at the high school level. This study aims to determine the form of television transformation in the perspective of the instrumental rational theory as well as the perspective of students on learning through television. This research was conducted using descriptive qualitative methods with data collection techniques through observation and interviews. The results obtained in the form of structured programs during learning through television as a form of instrumental rational action during distance learning as well as the perspective of students with this transformation. Pada masa pandemi Covid-19 berbagai bidang dalam kehidupan mengalami perubahan serta penyesuaian, termasuk pada bidang pendidikan dengan mengadakan pembelajaran jarak jauh. Sebagai bentuk penyesuaian pembelajaran jarak jauh tersebut pihak pemerintah serta pendidik memanfaatkan televisi sebagai media belajar. Transformasi televisi sebagai media belajar ini ditujukan pada setiap jenjang pendidikan, salah satunya pada jenjang sekolah menengah. Penelitian ini bertujuan untuk mengetahui bentuk transformasi televisi dalam perspektif teori rasional instrumental tersebut serta perspektif peserta didik akan kegiatan belajar memelalui televisi. Penelitian ini dilakukan dengan menggunakan metode kualitatif deskriptif dengan teknik pengumpulan data melalui observasi serta wawancara. Hasil yang diperoleh berupa adanya program terstruktur selama pembelajaran melalui televisi sebagai bentuk tindakan rasional instrumental selama pembelajaran jarak jauh serta perspektif peserta didik dengan adanya transformasi tersebut.

BERTAHAN SEBAGAI ISTERI NARAPIDANA DI TANAH MINANG: Rasionalitas dan Tradisionalisme Isteri Narapidana di Kabupaten Tanah Datar Sumatera Barat

This paper discusses about women as wives of convicted criminals in Batusangkar, West Sumatra. This study concentrates on the reasons of their attitudes to stay at becoming wives of these convicted criminals. This study is an empirical research by utilizing the theory of social action of Max Weber. This article argues that the wives of convicted criminals have chosen to keep their household as a fruit of both traditional and rational action choices. The wife loyalty and the stigmatization of widow status are among traditional values which give strong influence to them. At the same time, some consider their age, their nuclear family and financial needs as rational reasons behind their choice.Tulisan ini membahas tentang perempuan yang menjadi isteri narapidana di Batusangkar, Sumatera Barat. Fokus kajian dalam tulisan ini adalah alasan mengapa mereka tetap memilih bertahan menjadi isteri narapidana. Dengan menggunakan teori tindakan sosial Max Weber, artikel ini menyatakan bahwa para perempuan tersebut tetap memilih bertahan untuk menjadi para isteri narapidana dikarenakan alasan tradisi dan alasan rasional. Kesetiaan perempuan dan stigma negatif terhadap status janda menjadi alasan tradisional yang melatari pilihan mereka. Sedangkan alasan rasional mereka dapat dilihat dari pernyataan di antara mereka yang mempertimbangkan usia mereka yang sudah lanjut. Sebagian lagi mempertimbangkan nasib anak-anak mereka. Terdapat pula sebagian isteri yang berargumen karena kebutuhan ekonomi mereka.

Record-Keeping and Cooperation in Large Societies

We introduce a new model of repeated games in large populations with random matching, overlapping generations, and limited records of past play. We prove that steady-state equilibria exist under general conditions on records. When the updating of a player’s record can depend on the actions of both players in a match, any strictly individually rational action can be supported in a steady-state equilibrium. When record updates can depend only on a player’s own actions, fewer actions can be supported. Here we focus on the prisoner’s dilemma and restrict attention to strict equilibria that are coordination-proof, meaning that matched partners never play a Pareto-dominated Nash equilibrium in the one-shot game induced by their records and expected continuation payoffs. Such equilibria can support full cooperation if the stage game is either “strictly supermodular and mild” or “strongly supermodular,” and otherwise permit no cooperation at all. The presence of “supercooperator” records, where a player cooperates against any opponent, is crucial for supporting any cooperation when the stage game is “severe.”

Agency in Circular City Ecosystems—A Rationalities Perspective

The concept of agency is increasingly used in the literature on sustainability transitions. In this paper, we add to that discussion by arguing that the concept of rationality opens new avenues to theorizing relational agency in transitions toward a circular economy. To this end, we compare rationality conceptions from management (e.g., collaboration and competition) with critical theory perspectives on rationality (e.g., instrumental and communicative rationality). This leads us to develop a typology matrix for describing plural rationalities underpinning relational agency. We illustrate this typology using excerpts from an in-depth case study of an ongoing city-coordinated ecosystem that develops a smart technology-enabled urban area based on the principles of circularity. The first contribution of this interdisciplinary paper is to offer a rational perspective on theorizing the antecedents of relational agency in circular economy transitions, where communicatively rational action enables agency and change. Secondly, our paper contributes to the literature on circular cities through conceptualizing circular transition as simultaneous collaboration and competition. Thirdly, our paper introduces a dyadic perspective on rationality to the literature on coopetition and provides an operating space from which professionals can navigate, depending on the type of coopetitive situation.

On the comprehensive indicator of the effectiveness of programs in the field of environmental safety and environmental development

The paper offers a comprehensive indicator for evaluating the effectiveness of the implementation of state policy in the field of environmental safety and environmental development. The indicator under consideration can be a flexible tool for justifying the effectiveness of strategic planning measures in the field of environmental development, taking into account current development trends. The idea of solving the optimization problem (bringing the values of the complex indicator to the maximum) of forming a rational action plan for the implementation of state policy in the field of environmental safety and environmental development is proposed.