Representation Theory Research Articles

Gender Bias in Residents’ Perceptions and Support of Rally Event Tourism: The Sierra Morena Rally of Córdoba, Spain

Motorsports have become a tourism resource for certain territories. Knowledge about the perception of impact and the support residents provide for their celebration contributes to ensuring their long-term success. The academic literature has so far focused on large-scale events, leaving a gap in knowledge regarding small-scale events. This study addresses the case of the Sierra Morena Rally in Córdoba, Spain. It is based on the principles of Social Exchange Theory (SET) and Social Representation Theory (SRT) to explore a gender bias in the perception of impact and support for the event. Using a sample of 753 residents, an Exploratory Factor Analysis is conducted, and Mann–Whitney U and Hedges’ G statistics are applied. The results confirm the existence of a gender bias in perception, which is discussed in the context of previous case studies.

Revictimization of women victims of intimate partner violence in the French press: A social representations approach.

This study aims to analyze how the press portrays cases of revictimization experienced by women in France, through the lens of social representation theory. An exploratory, descriptive study was conducted using a corpus of 157 online press articles. A total of 187,773 words and 5,240 segments were analyzed using Iramuteq version 7, employing top-down hierarchical classification and lexical similarity analysis. The analysis identified four classes: 1. Violent incidents (25.5%); 2. Political actions against violence (26%); 3. Institutional revictimization (26.6%) and 4. Violence and breaking the silence (21.9%). The findings illustrate how media portrayals contribute to the construction of social representations surrounding revictimization. Class 1 reveals a focus on extreme cases of violence, such as femicides, and highlights a potential gender bias in media reporting through the omission of terms like 'femicide'. Class 2 demonstrates the influence of ideological perspectives on the portrayal of political measures against violence, with conservative outlets framing such actions within traditional values, while progressive newspapers advocate for systemic reform. Class 3 shows a gap in the conceptualization of institutional revictimization in the French press compared to other countries, revealing how conservative portrayals can minimize systemic issues and perpetuate harmful stereotypes. Class 4 shows the role of female journalists in addressing various forms of violence, despite the limited impact of the #MeToo movement in recent coverage. Collectively, these findings elucidate how media representations shape public attitudes and institutional responses to gender-based violence through the lens of social representations.

The spectrum of Artin motives

We analyze the tt-geometry of derived Artin motives, via modular representation theory of profinite groups. To illustrate our methods, we discuss Artin motives over a finite field, in which case we also prove stratification.

Arithmetic properties of 5-regular partitions into distinct parts

A partition is said to be [Formula: see text]-regular if none of its parts is a multiple of [Formula: see text]. Let [Formula: see text] denote the number of 5-regular partitions into distinct parts (equivalently, into odd parts) of [Formula: see text]. This function has also close connections to representation theory and combinatorics. In this paper, we study arithmetic properties of [Formula: see text]. We provide full characterization of the parity of [Formula: see text], present several congruences modulo 4, and prove that the generating function of the sequence [Formula: see text] is lacunary modulo any arbitrary positive powers of 5.

The polarized “naturalizations” of the 2022 Freedom Convoy

During the month-long “Freedom Convoy” protest in Ottawa (Canada), protesters were ascribed many attributes (violent, extremist, hateful, disinformed) which they refuted. Protest organizers insisted the Freedom Convoy was peaceful, loving, and included “average Canadian citizens fighting for freedom”. This research is interested in the construction of this representational divide and its consequences. It analyzes the polarized social representations of the COVID-19 Freedom Convoy by using social representation theory, and more specifically, Negura and Plante’s model of “naturalization”. News articles (n = 516) from Canadian media and Freedom Convoy organizers’ Facebook posts (n = 611) were submitted to a rhetorical frame analysis. Results show how communications from organizers and the media both contributed to the naturalization of conflicting representations by (1) associating the movement with a desirable/undesirable identity, (2) neglecting nuanced perspectives, (3) instrumentalizing their representation to justify the legitimacy/illegitimacy of the protest, and (4) validating the representation by focusing on incidents that ratified the Freedom Convoy’s “goodness” or “badness”. We argue that this single protest became two opposed and morally charged “objects” impossible to reconcile, which prevented dialogue. Social implications of polarized naturalizations during epidemics are discussed.

Bearing fault diagnosis by sparse frequency spiral spectrum driven NAF-LDM under strong noise and small samples

Abstract The complexity of background noise and the scarcity of real fault samples seriously affect the diagnostic accuracy of the model. To address this, a noise-robust two-dimensional feature map, the sparse frequency spiral spectrum (SFSM), based on sparse representation theory, is proposed. A bridge penalty coefficient is applied to the sparse representation model to accurately select impact components, and the fast iterative shrinkage threshold algorithm is used to solve for sparse representation coefficients. Sparse reconstructed signals are obtained by convolving the impact patterns with these coefficients, leading to a sparse reconstruction algorithm with reduced computational complexity. Furthermore, the novel non-linear activation-free blocks (NAF Blocks) are embedded into the latent diffusion model to augment small samples, significantly improving image generation speed and quality. The integration of the Swin transformer for feature extraction and classification further enhances diagnostic performance. The superiority of this method is validated on the XJTU-SY dataset, a bearing experimental platform dataset, and enterprise engineering dataset. Experimental results demonstrate that the structural and generalization advantages of NAF Blocks are crucial for improving image quality and inference speed. The noise suppression capability of the proposed method, facilitated by the SFSM feature processing technique, is confirmed through ablation and noise robustness tests. Finally, the Swin transformer’s excellent feature extraction and classification capabilities for SFSM are verified. The proposed method achieves diagnostic accuracies of 99.10% and 98.7% on the XJTU-SY and experimental platform datasets, respectively.

US Higher Education's Civic Responsibility to Educate for Informal Political Representation

AbstractIn this paper, Caitlin Murphy Brust and Hannah Widmaier begin with the assumption that highly selective institutions of higher education in the United States have a duty to promote civic equality. They employ Wendy Salkin's theory of informal political representation to examine how highly selective institutions should go about promoting civic equality. According to Salkin's theory, someone serves as an informal political representative (IPR) when they speak or act on behalf of others, without having been selected to do so via a systematized selection procedure. Brust and Widmaier argue that as part of their civic educational missions, highly selective institutions should educate their students for informal political representation, and this includes equipping students to (1) serve as effective IPRs, (2) be responsible audience members to others' informal political representation, and (3) deliberate carefully and with open‐mindedness about when they should or should not take on the role of IPR. Brust and Widmaier examine two types of injustice that students from marginalized communities face at highly selective institutions, and they explore how education for informal political representation might ameliorate those injustices. The authors conclude by offering some practical suggestions to institutional policymakers and educators.

THE PORTRAYAL OF FEMALE VILLAINS: A REPRESENTATION STUDY ON CRUELLA

The portrayal of female villains in media and movies has evolved significantly, as evidenced through the lens of Stuart Hall's representation theory and film analysis concepts. Traditionally confined to one-dimensional roles perpetuating gender stereotypes, contemporary cinema showcases multi-dimensional characters like those in Cruella, challenging societal norms and defying traditional gender expectations. By employing narrative and non-narrative film analysis techniques, these characters are revealed as agents of subversion and empowerment, embodying a new archetype of female villains characterized by individual agency and autonomy. However, despite this progress, the lingering impact of gender stereotypes persists, influencing how female villains are depicted on screen. Thus, ongoing critical analysis and advocacy for more diverse and authentic representations of women in media remain crucial.

Enhancing relationship-based practice in the homeless sector by applying Hall’s representation theory (1997) and peer reviewed research

ABSTRACT A student essay for Clare Winnicott Essay Competition. A societal critique of the ongoing issues and complications for those experiencing homelessness in modern times, which applies both Stuart Hall’s Theory of Representation (1997) and peer reviewed research on social stigmas, to identify the effectiveness of relationship-based practice within the homeless sector.

We are Who we Represent: A Theory of “Immersive” Representation in Student Activism

Abstract Children and young people have a right to freedom of association and to have their views given due weight when they act collectively. However, when they come together in groups to engage in collective action, in school and elsewhere, they are often criticised for not being “representative” of all/other young people. The concept, while frequently cited, remains undefined and fails to incorporate how young people understand, experience and enact representation. This article presents data from an empirical study with youth activists who established a Secondary Schools Students’ Union during the Covid-19 pandemic to lobby for change in education decision-making. The study was carried out as a collaboration between two university-based researchers and two secondary school students who were founding members of the union. Drawing on focus groups and interviews with union executive members, this article presents findings that convey young people’s navigation of adults’ perceptions of their representativeness, focusing on issues of legitimacy and efficacy. Based on this study, we propose a new youth co-authored and youth-informed theory of representation that conceptualises it as immersive and mutually symbiotic and, we suggest, enables meaningful implementation of child and youth activists’ civil and political rights.

Recent advances in branching problems of representations

How does an irreducible representation of a group behave when restricted to a subgroup? This is part of branching problems, which are one of the fundamental problems in representation theory, and also interact naturally with other fields of mathematics. This expository paper is an up-to-date account on some new directions in representation theory highlighting the branching problems for real reductive groups and their related topics ranging from global analysis of manifolds via group actions to the theory of discontinuous groups beyond the classical Riemannian setting. This article is an outgrowth of the invited lecture that the author delivered at the commemorative event for the 70th anniversary of the re-establishment of the Mathematical Society of Japan, and originally appeared in Japanese in Sugaku 71 (2019).

Convolution Algebras of Double Groupoids and Strict 2-Groups

Double groupoids are a type of higher groupoid structure that can arise when one has two distinct groupoid products on the same set of arrows. A particularly important example of such structures is the irrational torus and, more generally, strict 2-groups. Groupoid structures give rise to convolution operations on the space of arrows. Therefore, a double groupoid comes equipped with two product operations on the space of functions. In this article we investigate in what sense these two convolution operations are compatible. We use the representation theory of compact Lie groups to get insight into a certain class of 2-groups.

Symmetries in particle physics: from nuclear isospin to the quark model

We present a concise pedagogic introduction to group representation theory motivated by the historical developments surrounding the advent of the Eightfold Way. definitions of groups and representations are avoided in favour of the physical intuition of symmetries of the nuclear interaction. The concept of nuclear isospin is used as a physical motivation to introduce SU(2) and discuss the main techniques of representation theory. The discovery of strange particles motivates extending the symmetry group to SU(3), at first in the context of the Sakata model. We highlight the successes in fitting mesons in the SU(3) octet, discuss the drawbacks of the Sakata model for baryonic classifications, and how the Eightfold Way finally led to the quark model. This approach has two major advantages: (i) the main concepts of the theory of Lie groups are introduced and discussed without ever losing touch with its applications in particle physics; (ii) it allows the beginner to study group theory while also becoming acquainted with the historical developments of particle physics that led to the concept of quarks. In particular, in this pedagogical path the quarks appear as yet another class of particles predicted from symmetry principles, rather than being introduced ad hoc for postulating an SU(3) symmetry, as usually done in the literature.

Habitual sentences with <em>costumar</em> ‘use to’: Issues of tense and interaction with frequentative adjuncts

This paper analyses the expression of habitual values in Portuguese, focusing on the auxiliary verb costumar ‘use to’. First, the concept of habituality (and its distinction from genericity, frequentativity, and iterativity) is discussed, and an overview of the various ways of signalling habituality in Portuguese is provided. Then, three topics take centre stage, one concerning tense and two concerning the interaction of costumar with temporal adjuncts of different types. With regard to tense, the versatility of the imperfective past of costumar is examined, noting that this tense form can convey values which are typically reserved to the perfective past and the pluperfect. Regarding the interaction with adjuncts, the combination of costumar with adjuncts that redundantly express habituality (e.g., habitualmente ‘usually’) is first addressed. Subsequently, the combination of costumar with a set of allied adjuncts, grouped under the cover term ‘frequentative’, is scrutinized. These include adjuncts that indicate whether exceptions to the habitual pattern are more or less frequent (e.g., muitas vezes ‘often’ vs. às vezes ‘sometimes’), and adjuncts expressing correlation between eventualities, frequency sensu stricto, or cyclicity (e.g., uma vez por semana ‘once a week’). Portuguese is systematically compared with English throughout the text. The neo-Reichenbachian framework of Discourse Representation Theory (Hans Kamp) is used for formal analyses.

On the classification of function algebras on subvarieties of noncommutative operator balls

We study algebras of bounded noncommutative (nc) functions on unit balls of operator spaces (nc operator balls) and on their subvarieties. Considering the example of the nc unit polydisk we show that these algebras, while having a natural operator algebra structure, might not be the multiplier algebra of any reasonable nc reproducing kernel Hilbert space (RKHS). After examining additional subtleties of the nc RKHS approach, we turn to study the structure and representation theory of these algebras using function theoretic and operator algebraic tools. We show that the underlying nc variety is a complete invariant for the algebra of uniformly continuous nc functions on a homogeneous subvariety, in the sense that two such algebras are completely isometrically isomorphic if and only if the subvarieties are nc biholomorphic. We obtain extension and rigidity results for nc maps between subvarieties of nc operator balls corresponding to injective spaces that imply that a biholomorphism between homogeneous varieties extends to a biholomorphism between the ambient balls, which can be modified to a linear isomorphism. Thus, the algebra of uniformly continuous nc functions on nc operator balls, and even its restriction to certain subvarieties, completely determine the operator space up to completely isometric isomorphism.

On the category 𝒪 of a hybrid quantum group

We study the representation theory of a hybrid quantum group at root of unity ζ \zeta introduced by Gaitsgory. After discussing some basic properties of its category O \mathcal {O} , we study deformations of the category O \mathcal {O} . For subgeneric deformations, we construct the endomorphism algebra of big projective object and compute it explicitly. Our main result is an algebra isomorphism between the center of deformed category O \mathcal {O} and the equivariant cohomology of ζ \zeta -fixed locus on the affine Grassmannian attached to the Langlands dual group.

Tensorial harmonic bases of arbitrary order with applications in elasticity, elastoviscoplasticity and texture-based modeling

In continuum mechanics, one regularly encounters higher-order tensors that require tensorial bases for theoretical or numerical calculations. By using results from [Formula: see text] representation theory, we present a method to derive tensorial harmonic bases which unifies existing approaches in one framework. Applying this convention to symmetric second-order tensors results in a second-order harmonic basis which, for example, simplifies the depiction and numerical handling of stiffness tensors for most common material symmetries and reduces the computational effort involved in implementations of incompressible elastoviscoplastic material laws. The same convention can be applied to texture analysis to yield tensorial texture coefficients for both polycrystals and fiber-reinforced composites. Rotations of higher-order tensors are particularly efficient in harmonic bases as both material and index symmetries can be exploited. While special attention is given here to the examples of small-strain material laws and texture analysis, the framework is entirely general and can be used to simplify calculations in other physical contexts involving tensors of arbitrary order and symmetry. A Python implementation of the harmonic basis convention defined in this work is available as a Supplementary Material.

Social representations of young people about people with disabilities and disabilities in an inclusive educational environment: the experience of cross-cultural research

Relevance. Interest in the study of social representations arose due to the development of inclusion in all spheres of life. This fact has an impact on the specifics of training Russian and foreign students in this field in a medical university, the development of their inclusive competence. The study of cross-cultural features of social representations of persons with disabilities and the disabled, the identification of universal and specific phenomena in respondents will contribute to understanding social and psychological phenomena at the individual level that determine social attitudes and behavior of individuals in an inclusive modern society, taking into account its sociocultural characteristics.The purpose of the study is to study the cross-cultural characteristics of social perceptions of people with disabilities and people with disabilities among Russian and foreign students.Objectives: to analyze the content characteristics and approaches to the study of social representations; to develop programs of empirical research; to describe the results of the study; to formulate conclusions.Methodology. This study is based on the provisions of the theory of social constructionism (P. Berger, T. Lukman; J.Douglas); E. Durkheim's concepts of collective representations; theories of social representations (S. Moscovici, D. Jodelet, etc.). Research methods: theoretical analysis of literature, research interview, method of verbal associations, testing, content analysis.Results. Both similar and specific phenomena in social representations of people with disabilities and people with disabilities in the samples of Russian and foreign students were revealed. Similar is the presence of tolerant attitudes towards people with disabilities and people with disabilities in both samples. The differences relate to the social level of social perceptions, as well as the characteristics of social distance in relation to respondents to this category of citizens.Conclusions. Along with a tolerant attitude towards people with disabilities and people with disabilities, respondents have insufficient professional awareness of this category of citizens, experience difficulties in interacting with them at the level of joint activities and professional relationships, which requires the development of additional programs and practices in the context of social, educational and volunteer activities to develop inclusive competence of students.

Coupled cluster degree of the Grassmannian

We determine the number of complex solutions to a nonlinear eigenvalue problem on the Grassmannian in its Plücker embedding. This is motivated by quantum chemistry, where it represents the truncation to single electrons in coupled cluster theory. We prove the formula for the Grassmannian of lines which was conjectured in earlier work with Fabian Faulstich. This rests on the geometry of the graph of a birational parametrization of the Grassmannian. We present a squarefree Gröbner basis for this graph, and we develop connections to toric degenerations from representation theory.

Symmetries and Wigner representations of operational theories

Abstract We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way to describe the theory in terms of some fixed observables; these observables are often picked to be position and momentum or spin observables. This allows us to introduce symmetries which transform the outcomes of the observables used to construct the Wigner representation; we obtain several results for when these symmetries are well defined or when they uniquely specify the Wigner representation.