Thomas Theorem Research Articles

Product Structure Extension of the Alon–Seymour–Thomas Theorem

Product Structure Extension of the Alon–Seymour–Thomas Theorem

Belief in Meritocracy Reexamined: Scrutinizing the Role of Subjective Social Mobility

Despite decreasing intergenerational mobility, strengthening the ties between family background and children’s economic outcomes, Western citizens continue to believe in meritocracy. We study how meritocratic beliefs about success relate to individuals’ social mobility experiences: Is subjective upward mobility associated with meritocratic attributions of success and downward mobility with structuralist views? Whereas previous studies addressed the relevance of individuals’ current position or objective mobility, we leverage diagonal reference models to disentangle the role of subjective mobility, origin, and destination. Surveying a representative Dutch sample (n = 1,507), we find, echoing the Thomas theorem, that if people experience social mobility as real, it is real in its consequences: subjective upward mobility is associated with stronger meritocratic beliefs, and downward mobility is associated with stronger structuralist beliefs—but has no bearing on people’s meritocracy beliefs. This helps understand the muted political response to growing inequality: a small share of upwardly mobile individuals may suffice to uphold public faith in meritocracy.

The complexity of frugal colouring

A t-frugal colouring of a graph G is an assignment of colours to the vertices of G, such that each colour appears at most t times in the neighbourhood of any vertex. A dichotomy theorem for the complexity of deciding whether a graph has a 1-frugal colouring with k colours was found by McCormick and Thomas, and then later extended to restricted graph classes by Kratochvil and Siggers. We generalize the McCormick and Thomas theorem by proving a dichotomy theorem for the complexity of deciding whether a graph has a t-frugal colouring with k colours, for all pairs of positive integers t and k. We also generalize bounds of Lih et al. for the number of colours needed in a 1-frugal colouring of a given K_4-minor-free graph with maximum degree Delta to t-frugal colourings, for any positive integer t.

The Schur-Weyl graph and Thoma's theorem.

В работе определяется градуированный граф, названный графом Шура-Вейля, который естественно возникает при одновременном рассмотрении алгоритма RSK и классической двойственности между симметрической и полной линейной группами. В качестве одного из первых применений этого графа мы даем новое доказательство полноты списка дискретных неразложимых характеров бесконечной симметрической группы.

On the question of the exact formulation of “The Thomas theorem”

On the question of the exact formulation of “The Thomas theorem”

ЖИЛИЩНО-КОММУНАЛЬНОЕ ХОЗЯЙСТВО В РОССИИ: СОЦИАЛЬНЫЕ ЗАКОНЫ, ГИПОТЕЗЫ И ТЕОРЕМЫ В ДЕЙСТВИИ

Целью исследования является попытка в жанре научного памфлета дать социологическую интерпретацию отдельным процессам и явлениям в системе жилищно-коммунального хозяйства России, применив известные социальные законы, гипотезы и теоремы. Жилищно-коммунальное хозяйство считается по праву наиболее противоречивой отраслью российской экономики и находится в процессе постоянного реформирования, что объясняет актуальность исследований в этой сфере различных общественных наук, включая социологию.
 Методологическую базу исследования составили закон разделения функций и специализации, теорема Томаса и ее следствия, гипотеза лингвистической относительности Сепира-Уорфа, закон возвышения потребностей, теория разбитых окон Уилсона-Келлинга, закон интеллектуального развития, число Данбара, концепция жилищных классов Рекса-Мура и др. При этом на современном этапе жилищных исследований усматривается недооцененность именно социологического инструментария к исследованию жилищно-коммунальных проблем в России.
 Результаты исследования отражают применение социологического инструментария к объяснению отдельных процессов и явлений в области управления многоквартирными домами в России. По ходу исследования анализируются результаты применения подобного метода. Руководствуясь методологическим принципом бритвы Оккама, сделан вывод о достаточной практичности подобного научного подхода к исследованию сферы жилищно-коммунального хозяйства в рамках жилищной социологии.
 Перспективу исследования составляет дальнейший социологический анализ с применением представленного инструментария на более глубоком эмпирическом уровне с целью верификации представленных выводов, уточнения результатов, а также формулирования новых гипотез.

To Regulate or Not: A Social Dynamics Analysis of an Idealised AI Race

Rapid technological advancements in Artificial Intelligence (AI), as well as the growing deployment of intelligent technologies in new application domains, have generated serious anxiety and a fear of missing out among different stake-holders, fostering a racing narrative. Whether real or not, the belief in such a race for domain supremacy through AI, can make it real simply from its consequences, as put forward by the Thomas theorem. These consequences may be negative, as racing for technological supremacy creates a complex ecology of choices that could push stake-holders to underestimate or even ignore ethical and safety procedures. As a consequence, different actors are urging to consider both the normative and social impact of these technological advancements, contemplating the use of the precautionary principle in AI innovation and research. Yet, given the breadth and depth of AI and its advances, it is difficult to assess which technology needs regulation and when. As there is no easy access to data describing this alleged AI race, theoretical models are necessary to understand its potential dynamics, allowing for the identification of when procedures need to be put in place to favour outcomes beneficial for all. We show that, next to the risks of setbacks and being reprimanded for unsafe behaviour, the time-scale in which domain supremacy can be achieved plays a crucial role. When this can be achieved in a short term, those who completely ignore the safety precautions are bound to win the race but at a cost to society, apparently requiring regulatory actions. Our analysis reveals that imposing regulations for all risk and timing conditions may not have the anticipated effect as only for specific conditions a dilemma arises between what is individually preferred and globally beneficial. Similar observations can be made for the long-term development case. Yet different from the short-term situation, conditions can be identified that require the promotion of risk-taking as opposed to compliance with safety regulations in order to improve social welfare. These results remain robust both when two or several actors are involved in the race and when collective rather than individual setbacks are produced by risk-taking behaviour. When defining codes of conduct and regulatory policies for applications of AI, a clear understanding of the time-scale of the race is thus required, as this may induce important non-trivial effects.
 
 
 This article is part of the special track on AI and Society.
 
 

The Thomas theorem and the Efimov States within a generalized Bohr model

Using a generalized Bohr model and the hyper-spherical formalism for a three-body system, we derive the universal energy functions. We apply our model to 4He atom where only the Coulomb potential is dominant and find that its binding energy is well reproduced (less than 5.5% difference). Later, we focus on the equal mass three-body systems and derive the Thomas theorem assuming a simple interaction depending on the range of the potential. We discuss the conditions for which an unbound two-body system produces a bound three-body system and apply our model to 4He and triton atoms as well as to the triton nucleus. Using their scattering lengths and effective ranges, we are able to reproduce the two-body or the three-body binding energies (less than 5% difference) with only one parameter fitted. Prediction for excited (Efimov) levels are also given and in particular we demonstrate that for some hyper-angles two equal minima appear which indicate a phase (shape) transition similar to the Landau’s theory of phase transition. We suggest that the observed excited levels in two different experiments for the triton nucleus are indeed Efimov levels and there may be more surprises.

Зміна влади та боротьба з корупцією в Україні: погляд крізь призму теореми Томаса

The article examines contemporary Ukrainian political realities, namely the coming to power following the presidential and parliamentary elections of a new political force and its prospects in the fight against corruption. The forecasting for further developments in the fight against corruption is proposed based on Thomas theorem. In particular, the author looks at the perspectives […]

Trademarks in the Light of the Thomas Theorem: a model of a social object ontology

The paper considers the reasons for the existence of trademarks as a social phenomenon. The authors reveal three dominant functional explanations: rationalistic, stratification and semantic. A rationalistic model describes a trademark in terms of identifying the source of the goods (the trademark allows the consumer to identify the goods of a particular manufacturer). The stratification explanation defines the function of the trademark in terms of demonstratively maintaining social differentiation and the distribution of prestige. The semantic approach focuses on the trademark as a mental cell in the consumer’s memory archive, which contains information about the product and its associations. All three approaches are characterized by common problems of functional explanation, namely: the logical circle and internal connection with the homeostatic image of the social system. To overcome these problems, the authors propose an approach to the social ontology of trademarks based on the well-known “Thomas theorem”, which allows to establish causal relationships between the subjective and objective world on the basis of the postulation of equality between reality and perception at the level of formation of human actions. The authors demonstrate the explanatory power of the “Thomas theorem” on example of self-fulfilling prophecies that can be observed in the practice of using trademarks, considering the rationalistic, prestigious and semantic functions of trademarks through the prism of this principle.

OF BOUNDARIES, PLACES, AND SITUATIONS

ABSTRACTThomas F. Gieryn's Truth‐Spots: How Places Make Us Believe presents eight case studies to support his historical‐sociological thesis that “Places … have agency and exert a force of their own on the direction and pace of knowledge and belief” (18). Gieryn adds a new angle to a century‐old discourse on the social construction of truth: the emplacement of credibility in narrated material locations. Throughout his career, Gieryn has contributed extensively to the spatial and placeful analysis of knowledge and social power: from advancing the concept of discursive “boundary‐work” in the 1980s, to a refined method of “cultural cartography” in the 1990s, and in the twenty‐first century, toward investigations of places: defined as meaning‐enriched material locations. He has now advanced “truth‐spots” as a type of place that credibilizes truth‐claims. This essay reviews the key concepts in the career of this historical sociologist of scientific knowledge, through a mapping of Gieryn's own trajectory within the arc of a long pragmatist tradition in US social science. I shall use Gieryn's own case studies to test two key claims in his account of how place operates in the social‐cultural construction of belief: (1) The model of “place” that Gieryn proposed in 2000, and has used consistently ever since (termed here a “Gieryn‐place”), and (2) Gieryn's claim that features of “truth‐spots” exhibit an observably independent (“agentic”) effect on the credibility of claims made there. I argue that both Gieryn‐places and truth‐spots suffer from incomplete specification of the ways in which people attach meanings to locations; of the boundaries of places; and of the sites of conscious encounter with places. They suffer also from his own boundary‐work to exclude imaginary, cultural, and virtual spaces from his conception of place. This essay argues that a credible account of how place operates in/as history will require a focus on situation and situatedness, drawing on the pragmatist tradition of the Thomas Theorem. The concept of situation completes the circuit between meaning‐production and the attachment of meaning to places and opens a gate for historical investigation, across the boundary between imagined, virtual, and conceptual spaces, and lived, material embodied places.

Positive specializations of symmetric Grothendieck polynomials

It is a classical fundamental result that Schur-positive specializations of the ring of symmetric functions are characterized via totally positive functions whose parametrization describes the Edrei–Thoma theorem. In this paper, we study positive specializations of symmetric Grothendieck polynomials, K-theoretic deformations of Schur polynomials.

Culture of Critical Discourse on Education and Science

The article addresses the problems concerning the formation of the methodology of critical analysis of Russian strategies, which are aimed at reforming and managing of education and science on the basis of modern social science and Humanities studies and the principles of the interdisciplinary approach. The authors state the change of the critique vector – the transition from value-loaded political statements to scientific analysis of the objective factors determining social pathologies in education system. The situation today is characterized by the attempts to find and formulate an objectivated language to describe social reality. In particular, the researchers actively use the methodological potential of such concepts as “converted form”, “red tapes”, “Goodhart’s law”, “Thomas theorem” that are implemented as conceptual tools to comprehend and describe the specificity of educational system. The general meaning of the forming analytical strategy applied to education and science is that all the management actions are subject to “corrective” influence of these principles and laws. Within the framework of this approach critique of education (and the process of its reforming) is indivisible from the constructive analysis of education as a whole system with its immanent dimensions. This approach orients researchers towards studying the “ontological” and “essential” problems of education.

To share or not to share: Incentivizing data sharing in life science communities.

Most scientists recognize the importance of sharing data online in an open fashion. Nonetheless, many studies have documented the concerns that accompany data sharing activities, including loss of credit or IP, misuse and the time needed to curate interoperable data. To this end, discussions around data sharing often identify incentives that could potentially ameliorate these disincentivising concerns. Nonetheless, current Open Data discussions often rely on evidence-based studies to identify the disincentives to overcome. This results in highly specific and directed interventions. In contrast, this paper offers a different interpretation of these concerns. To do so, it makes use of the Thomas Theorem which suggests that: "If men define situations as real, they are real in their consequences". Using empirical evidence from sub-Saharan African (bio)chemistry laboratories, this paper illustrates how individual perceptions of research environments - whether associated with evidence or not - are highly influential in shaping data sharing practices. It concludes with the suggestion that discussion on incentivising data sharing amongst scientific communities need to take a broader set of concerns into account and offer a more creative approach to ameliorating environmental disincentives.

The motivational peculiarities of bribe-takers

Criminology (as the scientific study of criminal behaviour on the individual and social level) and psychology (as the science, which seeks to understand individuals and groups) pay special attention to motivation – a theoretical construction, used to explain behaviour. In this article the motivation of recipients of bribery is widely investigated. In addition to such well-established motives as greediness, selfishness, prevalence of personal interest, the author analyzes also other criminal behaviour determinants. The works, which are used in this research are of the following authors: John Broadus Watson, Edward Lee Thorndike (Behavioural); Sigmund Freud, Erich Fromm (Psychoanalysis); Carl Rogers, Abraham Maslow (Existential-humanistic theories); William Isaac Thomas (Thomas theorem); Florian Witold Znaniecki (sociological theory); Erik Homburger Erikson (theory on psychosocial development of human beings); Jean William Fritz Piaget (theory of cognitive development); Herbert Lefcourt, Ronald Smith (Locus of Control) etc. As the result of this research the author has concluded that bribe-takers’ behaviour is determined by such psychological constructs as the desire for power, fear, envy, mental deflections, mania, feeling of exclusion, the need for extreme, oppressed creativity.

Thoma type results for discrete quantum groups

Thoma's theorem states that a group algebra [Formula: see text] is of type I if and only if [Formula: see text] is virtually abelian. We discuss here some similar questions for the quantum groups, our main result stating that, under suitable virtually abelianity conditions on a discrete quantum group [Formula: see text], we have a stationary model of type [Formula: see text], with [Formula: see text] being a finite quantum group, and with [Formula: see text] being a compact group. We discuss then some refinements of these results in the quantum permutation group case, [Formula: see text], by restricting the attention to the matrix models which are quasi-flat, in the sense that the images of the standard coordinates, known to be projections, have rank [Formula: see text].

Resurrecting an Abandoned “Standpoint”: An Exploratory Application of W. I. Thomas’ Abandoned “Four Wishes” and the “Definition of the Situation” to Adolescent Shoplifters’ Cases

This is a novel, qualitative application of W. I. Thomas’ (1863-1948) historically significant ideas about human motivation to the study of shoplifters. Nineteen short cases of self-reported adolescent shoplifting are presented here under the organization of Thomas’ (1923) “Four Wishes” and discussed from Thomas’s symbolic interactionist perspective, the “Definition of the Situation.” While the “Thomas Theorem” (Merton, 1948) has long been abandoned as an action theory and is rarely used by sociologists, this researcher found Thomas’ “standpoints” useful in gaining an understanding of what was going on in the mind of the adolescents as they shoplifted and in explicating the meaning shoplifting had to them.

Racism: A Virulent But Curable Social Disease

In this paper, we argue that race is a destructive biological illusion that is better understood as a form of Durkheimian deviance. There are significant differences among human social groups, however, those differences are sociological rather than biological in nature. We will analyze the tennis careers of Venus and Serena Williams to illustrate that excellence is determined by sociological success factors rather than biological attributes. Further, we will emphasize that the deleterious consequences of socio-racial differentiation are aggravated by the Thomas Theorem (“If men define situations as real, then they are real in their consequences”). We will conclude by drawing upon Jane Elliot’s work to illustrate that racism is rooted in malevolent social constructions, and, as such, racism is a curable ― or “deconstructable” ― social disease.

Boolean Witt vectors and an integral Edrei–Thoma theorem

A subtraction-free definition of the big Witt vector construction was recently given by the first author. This allows one to define the big Witt vectors of any semiring. Here we give an explicit combinatorial description of the big Witt vectors of the Boolean semiring. We do the same for two variants of the big Witt vector construction: the Schur Witt vectors and the $p$-typical Witt vectors. We use this to give an explicit description of the Schur Witt vectors of the natural numbers, which can be viewed as the classification of totally positive power series with integral coefficients, first obtained by Davydov. We also determine the cardinalities of some Witt vector algebras with entries in various concrete arithmetic semirings.

Меркантилизм: разрушительное созидание, финансы и машинерия теоремы Томаса

Меркантилизм: разрушительное созидание, финансы и машинерия теоремы Томаса