Representations Of Group Research Articles

On n-Dimensional Maxwell and Dirac Equations in Curved Space-Time and Its Applications in SO(P,Q) Group Theoretic Image Processing

Maxwell equations in p time and q spatial dimensions are formulated. Properties of the Green’s function for the associated (p,q)-wave operator are derived based on contour integration. The notions of electric and magnetic fields in (p,q)-dimensions is explored by analogy with four dimensional physics and the problem of far field computation of the radiation field generated by charges and currents in \((1,n-1)\) space-time is analyzed. SO(p,q) invariance properties of the Maxwell equations are deduced and used to formulate SO(p,q)-group theoretic image processing problems in (p,q)-dimensions. Dirac’s equation in (p,q)-dimensional space-time is derived using the Clifford algebra of the Dirac gamma matrices. SO(p,q)-invariance of the Dirac equation based on the spinor representation of \(SO(p,q)\) is mentioned. The Maxwell’s equations in (p,q)-dimensional curved space-time is analyzed using perturbation theory in the context of maximally symmetric spaces which play a fundamental role in \((p,q)\)-dimensional cosmological models for homogeneous and isotropic spaces. The Einstein-Maxwell equations for (p,q)-dimensional gravity and electromagnetism is studied and used to derive the equations of motion of point charges carrying mass moving under mutual gravitational and electromagnetic interactions in general relativity. Finally, Dirac’s equation in (p,q)-dimensional curved space-time interacting with the (p,q)-dimensional electromagnetic field is looked at. \(U(1)\)-Gauge, local SO(p,q) Lorentz and diffeomorphism invariance of this equation is analyzed. Local \(SO(p,q)\) invariance of the curved space-time Dirac equation is deduced based on transformation properties of the Dirac matrices under the spinor representation. The appendix presents some applications of group representation theoretic statistical image processing on a manifold to the situation when the image field is described by the six component electromagnetic field tensor on which the Lorentz group acts.

Representations of groups on Banach spaces

We establish a general framework for representability of a metric group on a (well-behaved) class of Banach spaces. More precisely, let G \mathcal {G} be a topological group, and A \mathcal {A} a unital symmetric C ∗ C^* -subalgebra of U C ( G ) \mathrm {UC}(\mathcal {G}) , the algebra of bounded uniformly continuous functions on G \mathcal {G} . Generalizing the notion of a stable metric, we study A \mathcal {A} -metrics δ \delta , i.e., the function δ ( e , ⋅ ) \delta (e, \cdot ) belongs to A \mathcal {A} ; the case A = W A P ( G ) \mathcal {A}=W\hskip -0.7mm A\hskip -0.2mm P(\mathcal {G}) , the algebra of weakly almost periodic functions on G \mathcal {G} , recovers stability. If the topology of G G is induced by a left invariant metric d d , we prove that A \mathcal {A} determines the topology of G \mathcal {G} if and only if d d is uniformly equivalent to a left invariant A \mathcal {A} -metric. As an application, we show that the additive group of C [ 0 , 1 ] C[0,1] is not reflexively representable; this is a new proof of Megrelishvili [Topological transformation groups: selected topics, Elsevier, 2007, Question 6.7] (the problem was already solved by Ferri and Galindo [Studia Math. 193 (2009), pp. 99–108] with different methods and later the results were generalized by Yaacov, Berenstein, and Ferri [Math. Z. 267 (2011), pp.129–138]). Let now G \mathcal {G} be a metric group, and assume A ⊆ L U C ( G ) \mathcal {A}\subseteq \mathrm {LUC}(\mathcal {G}) , the algebra of bounded left uniformly continuous functions on G \mathcal {G} , is a unital C ∗ C^* -algebra which is the uniform closure of coefficients of representations of G \mathcal {G} on members of F \mathscr {F} , where F \mathscr {F} is a class of Banach spaces closed under ℓ 2 \ell _2 -direct sums. We prove that A \mathcal {A} determines the topology of G \mathcal {G} if and only if G \mathcal {G} embeds into the isometry group of a member of F \mathscr {F} , equipped with the weak operator topology. As applications, we obtain characterizations of unitary and reflexive representability.

What are the Leadership and Management Positions in Medical Education? A Scoping Review

Leadership can be defined as a combination of position, responsibilities, attitude, skills, and behaviours contributing to sustainable success. Despite extensive research on the representation of various groups, including genders and personal qualities, in leadership and management positions in medical education, there remains a lack of clarity regarding what these positions exactly are. In this scoping review, we aimed to determine these positions by following Levac et al.'s framework. We searched four databases; PubMed, ERIC, Scopus, and Web of Science until March 23, 2023, resulting in 558 records for screening after removing duplicates and applying some exclusions. The review included 266 studies for data extraction and synthesis. In addition to the leadership positions, we revealed the studies’ countries, main context, discipline, and year. We identified 396 leadership and management positions in medical education under four categories: academic, administrative, journal- related, and society-related positions. Additionally, the majority of the studies (59.77%) were on gender-related topics, followed by those focusing on underrepresented minorities. The articles covered 40 different disciplines, with the surgical fields exhibiting the highest frequencies, such as orthopaedic surgery, neurosurgery, and plastic and reconstructive surgery. The systematically developed list of positions in our study may be considered as a valuable resource for future research, especially in studies that aim to determine the representation of women and underrepresented minorities in leadership and management positions in medical education.

Реконструкция медийных социальных представлений с использованием показателей статистики текста (на материале медиадискурса о пандемии)

<p style="text-align: justify;"><strong>Objective. </strong>The aim is to present an algorithm to reconstruct media social representations based on indicators of text statistics and to conduct a comparative analysis of the construction of semantically similar media joint ventures, such as “pandemic”, “coronavirus”, “COVID-19” in Russian media. <br><strong>Background</strong>. Social representations perform the most important functions in the process of social functioning of an individual and a group, serve as a tool for cognition, adaptation and regulation of behavior and are formed taking into account the influence of media social representations. Methods for studying social representations for various social groups are presented in psychological studies, however, methods for studying media social representations are discussed in single scientific work. The presented scientific project is based on the theory of social representations by S. Moskovici and generalizations by B. Hoyer regarding the construction of media social representations (naming, emotional attachment, thematic attachment, metaphorical attachment and attachment through basic antinomies). <br><strong>Study design</strong>. The phenomenon of the coronavirus pandemic, presented in media discourse, was used as the signified in the study. The signifier is a trio of semantically similar concepts (“pandemic”, “COVID”, “coronavirus”). <br><strong>Measurements</strong>. To reconstruct media social representations, statistically stable collocations were identified to indicate the measure of association, logically close to the associative experiment. Hence, it was possible to identify thematic networks, axiological and evaluative components, components-characteristics of activity. The research material is represented by texts about the COVID-19 pandemic (January 2020-March 2022: “Rossiyskaya Gazeta”: 19471 texts, 7,97 million words; “Kommersant”: 1482 texts, 1,07 million words, “Novaya Gazeta”: 705 texts, 0,9 million words) and processed using BootCat, TreeTagger, AntConc (lemmatization, frequency analysis). <br><strong>Results</strong>. The associative fields of the joint ventures are different and contain anchoring and objectification resources when using concepts, only few elements of the associative field are similar. Thus, depending on the concept used to signify the intent of the text, stories about the fear of infection, the treatment of the disease, or resistance to the harsh elements are created. <br><strong>Conclusions</strong>. The similar algorithm based on media text statistics can be used to reconstruct any media social representation.</p>

Retraction Note: Curves with prescribed symmetry and associated representations of mapping class groups

Retraction Note: Curves with prescribed symmetry and associated representations of mapping class groups

Good Guys Became Bad Guys? Changing Representations of Asians and Other Races in Crime News During COVID-19

During COVID-19, Asian Americans were perceived as a threat to the American society, which could have led to heightened media scrutiny and a shift in media portrayals. This study examines this question with a quantitative analysis of crime stories sampled from five newspapers (2019–2021). Our results suggested that large-scale social events such as COVID-19 might have transformed media representations of Asians and other racial groups, with noteworthy variability: (a) When considering all types of crimes, during the pandemic, news about lawbreaking activities by Asian perpetrators almost doubled that of before-COVID period. No significant change was uncovered in the coverage of Asian victims. (b) However, on two types of crimes—“crimes against persons” and “violent crimes”—that have more newsworthiness and social import, stories about Asian victims during the COVID-19 were higher than those of the before-COVID period. (c) When comparing media representations with the Federal Bureau of Investigation (FBI) data, the percentage of Asian perpetrators and victims in newspapers did not differ from that of the FBI in 2019 and 2020; however, Asians were overrepresented as victims in 2021.

ATTENTION TO PROBLEMATIC SOCIAL GROUP REPRESENTATION IN GUIDANCE FOR USING MASS MEDIA IN ENGLISH EDUCATION

While media studies amply document problematic social group representation in mass media materials, how English language educators are equipped to address these issues when they engage in the common practice of appropriating such artifacts for teaching is unclear. This research responds by collecting 319 prominent Internet sources providing guidance on using mass media materials for language learning and subjecting them to a content analysis. This analysis draws upon ten forms of problematic social group portrayal in the mass media as a conceptual lens. Analysis results indicate little attention to ableism, ageism, Christonormativity, classism, colorism, gender bias, heternormativity, lookism/sizeism, racism, and urbanormativity with articles universally acclaiming the integration of mass media materials into language teaching, primarily on the grounds of “authenticity.” Defined as materials authored by and for native speakers, this is an authenticity insensitive to authentic social group representation. This research is significant because of teacher reliance on the Internet as a source of materials, because of the global reach of English language teaching, the power of mass media, especially for youth socialization, and because there is a lack of previous research concerning how language teachers are trained to consider problematic social group representation in mass media artifacts.

Sociodemographic and patient reported outcomes by racial and ethnicity status among participants in a randomized controlled trial for methamphetamine use disorder

BackgroundThere has been a significant increase in methamphetamine use and methamphetamine use disorder (Meth UD) in the United States, with evolving racial and ethnic differences. ObjectivesThis secondary analysis explored racial and ethnic differences in baseline sociodemographic and clinical characteristics as well as treatment effects on a measure of substance use recovery, depression symptoms, and methamphetamine craving among participants in a pharmacotherapy trial for Meth UD. MethodsThe ADAPT-2 trial (ClinicalTrials.gov number, NCT03078075; N=403; 69% male) was a multisite, 12-week randomized, double-blind, trial that employed a two-stage sequential parallel design to evaluate the efficacy of combination naltrexone (NTX) and oral bupropion (BUP) vs. placebo for Meth UD. Treatment effect was calculated as the weighted mean change in outcomes in the NTX-BUP minus placebo group across the two stages of treatment. ResultsOf the 403 participants in the ADAPT-2 trial, the majority (65%) reported non-Hispanic White, while 14%, 11% and 10% reported Hispanic, non-Hispanic Black, and non-Hispanic other racial and ethnic categories respectively. At baseline non-Hispanic Black participants reported less severe indicators of methamphetamine use than non-Hispanic White. Treatment effects for recovery, depression symptoms and methamphetamine cravings did not significantly differ by race and ethnicity. ConclusionsAlthough we found racial and ethnic differences at baseline, our findings did not show racial and ethnic differences in treatment effects of NTX-BUP on recovery, depression symptoms and methamphetamine cravings. However, our findings also highlight the need to expand representation of racial and ethnic minority groups in future trials.

Generalized charges, part I: Invertible symmetries and higher representations

qq-charges describe the possible actions of a generalized symmetry on qq-dimensional operators. In Part I of this series of papers, we describe qq-charges for invertible symmetries; while the discussion of qq-charges for non-invertible symmetries is the topic of Part II. We argue that qq-charges of a standard global symmetry, also known as a 0-form symmetry, correspond to the so-called (q+1)(q+1)-representations of the 0-form symmetry group, which are natural higher-categorical generalizations of the standard notion of representations of a group. This generalizes already our understanding of possible charges under a 0-form symmetry! Just like local operators form representations of the 0-form symmetry group, higher-dimensional extended operators form higher-representations. This statement has a straightforward generalization to other invertible symmetries: qq-charges of higher-form and higher-group symmetries are (q+1)(q+1)-representations of the corresponding higher-groups. There is a natural extension to higher-charges of non-genuine operators (i.e. operators that are attached to higher-dimensional operators), which will be shown to be intertwiners of higher-representations. This brings into play the higher-categorical structure of higher-representations. We also discuss higher-charges of twisted sector operators (i.e. operators that appear at the boundary of topological operators of one dimension higher), including operators that appear at the boundary of condensation defects.

The Colonialism and Stereotypes Based on Race and Religion: Representation of Papua in Indonesian Elementary Textbook School

Implementing anti-racist pedagogy in Islamic schools, particularly for Muslim teachers, involves unique challenges. Their behaviour is closely scrutinized, making it crucial to emphasize positive Islamic behaviour, including antiracism efforts, to contribute to a more just society. This research explained the root of racism and equality in Islam. In addition, this research add explanation on how Islamic education has significant role as well as antiracism paedagogy through school text book. School textbooks are effective media for conveying educational messages or values to children. Besides being made as an educational medium, books are also deliberately designed to represent the ideal interests according to their creator, especially books published by the state. The content can undoubtedly describe what is suitable for each country. Through school textbooks, we can look at the state's perspective on ethnicity critically. Based on this, this study will describe the representation of an ethnic group, especially the Papuan ethnic group. This research is not only limited to the study of texts but will try to do interdiscussion with the existing social context. By using Critical Discourse Analysis (CDA) this research will provide a complete picture of how the text is formed and what discourses are present in the formation of the text. The text in this study consisted of 2 related types, namely picture text and narrative text. In addition, this research is necessary because the findings will provide an overview of the content of school textbooks related to how regional representation is described. This is important to note as one of the instruments to build contemporary Indonesian identity especially in the national and Islamic education sector.

Algebra environments II. Algebra homomorphisms and derivations

Algebra environments provide requisites for studying objects of interest in operator algebra theory, group representation theory, spin geometry, Clifford analysis, and several variable operator theory. The concept is analyzed by developing an algebraic geometry approach. Specific algebraic sets, called structure manifolds of algebra environments, and their Zariski tangent spaces are introduced and described by using as critical tools derivations on algebras. Structure manifolds of tensor environments in particular yield spaces of algebra homomorphisms. Consequently, such spaces could be investigated as algebraic manifolds. Related issues include characterizations of their Zariski tangent spaces and of derivations that preserve algebra homomorphisms.

A service-oriented approach to clinical trial recruitment for dementia and brain health: Methods and case examples of MyAlliance for Brain Health.

Recruitment of sufficient and diverse participants into clinical research for Alzheimer's disease and related dementias remains a formidable challenge. The primary goal of this manuscript is to provide an overview of an approach to diversifying research recruitment and to provide case examples of several methods for achieving greater diversity in clinical research enrollment. The University of Kansas Alzheimer's Disease Research Center (KU ADRC) developed MyAlliance for Brain Health (MyAlliance), a service-oriented recruitment model. MyAlliance comprises a Primary Care Provider Network, a Patient and Family Network, and a Community Organization Network, each delivering tailored value to relevant parties while facilitating research referrals. We review three methods for encouraging increased diversity in clinical research participation. Initial outcomes reveal an increase in underrepresented participants from 17% to 27% in a research registry. Enrollments into studies supported by the research registry experienced a 51% increase in proportion of participants from underrepresented communities. MyAlliance shifts power, resources, and knowledge to community advocates, promoting brain health awareness and research participation, and demands substantial financial investment and administrative commitment. MyAlliance offers valuable lessons for building sustainable, community-centered research recruitment infrastructure, emphasizing the importance of localized engagement and cultural understanding. MyAlliance led to a significant increase in the representation of underrepresented racial and ethnic groups and individuals from rural areas.The service-oriented approach facilitated long-term community engagement and trust-building, extending partnerships between an academic medical center and community organizations.While effective, MyAlliance required substantial financial investment, with costs including infrastructure development, staff support, partner organization compensation, and promotional activities, underscoring the resource-intensive nature of inclusive research recruitment efforts.

Realization of unitary representations of the Lorentz group on de Sitter space

This paper builds on our previous work in which we showed that, for all connected semisimple linear Lie groups G acting on a non-compactly causal symmetric space M=G/H, every irreducible unitary representation of G can be realized by boundary value maps of holomorphic extensions in distributional sections of a vector bundle over M. In the present paper we discuss this procedure for the connected Lorentz group G=SO1,d(R)e acting on de Sitter space M=dSd. We show in particular that the previously constructed nets of real subspaces satisfy the locality condition. Following ideas of Bros and Moschella from the 1990’s, we show that the matrix-valued spherical function that corresponds to our extension process extends analytically to a large domain Gℂcut in the complexified group Gℂ=SO1,d(ℂ), which for d=1 specializes to the complex cut plane ℂ∖(−∞,0]. A number of special situations is discussed specifically: (a) The case d=1, which closely corresponds to standard subspaces in Hilbert spaces, (b) the case of scalar-valued functions, which for d>2 is the case of spherical representations, for which we also describe the jump singularities of the holomorphic extensions on the cut in de Sitter space, (c) the case d=3, where we obtain rather explicit formulas for the matrix-valued spherical functions.

Parameters of Hecke algebras for Bernstein components of [formula omitted]-adic groups

Let G be a reductive group over a non-archimedean local field F. Consider an arbitrary Bernstein block Rep(G)s in the category of complex smooth G-representations. In earlier work the author showed that there exists an affine Hecke algebra H(O,G) whose category of right modules is closely related to Rep(G)s. In many cases this is in fact an equivalence of categories, like for Iwahori-spherical representations.In this paper we study the q-parameters of the affine Hecke algebras H(O,G). We compute them in many cases, in particular for principal series representations of quasi-split groups and for classical groups.Lusztig conjectured that the q-parameters are always integral powers of the cardinality of the residue field of F, and that they coincide with the q-parameters coming from some Bernstein block of unipotent representations. We reduce this conjecture to the case of absolutely simple p-adic groups, and we prove it for most of those.

ALGEBRA ENVIRONMENTS I.

Algebra environments capture properties of non–commutative conditional expectations in a general algebraic setting. Their study relies on algebraic geometry, topology, and differential geometry techniques. The structure algebraic and Banach manifolds of algebra environments and their Zariski and smooth tangent vector bundles are particular objects of interest. A description of derivations on algebra environments compatible with geometric structures is an additional issue. Grassmann and flag manifolds of unital involutive algebras and spaces of projective compact group representations in C∗–algebras are analyzed as structure manifolds of associated algebra environments.

Local Galois representations associated to additive polynomials

For an additive polynomial and a positive integer, we define an irreducible smooth representation of a Weil group of a non-archimedean local field. We study several invariants of this representation. We obtain a necessary and sufficient condition for it to be primitive.

Multiplier systems for Siegel modular groups

Deligne proved in [Extensions centrales non résiduellement finies de groupes arithmetiques, C. R. Acad. Sci. Paris 287 (1978) 203–208] (see also 7.1 in [R. Hill, Fractional weights and non-congruence subgroups, in Automorphic Forms and Representations of Algebraic Groups Over Local Fields, eds. H. Saito and T. Takahashi, Surikenkoukyuroku Series, Vol. 1338 (2003), pp. 71–80]) that the weights of Siegel modular forms on any congruence subgroup of the Siegel modular group of genus [Formula: see text] must be integral or half integral. Actually he proved that for a system [Formula: see text] of complex numbers of absolute value 1 [Formula: see text] can be an automorphy factor only if [Formula: see text] is integral. We give a different proof for this. It uses Mennicke’s result [Zur Theorie der Siegelschen Modulgruppe, Math. Ann. 159 (1965) 115–129] that subgroups of finite index of the Siegel modular group are congruence subgroups and some techniques from [Solution of the congruence subgroup problem for [Formula: see text] and [Formula: see text], Publ. Math. Inst. Hautes Études Sci. 33 (1967) 59–137] of Bass–Milnor–Serre.

Effective interventions to increase representation of under-served groups in randomised trials in UK and Ireland: a scoping literature review.

Participants in clinical trials often do not reflect the populations that could benefit from the treatments being investigated. There are known barriers to trial participation for under-served groups, but limited evidence on strategies to alleviate these barriers to improve representation. This scoping review aimed to identify effective interventions and design features that improve the representation `of under-served groups in trials, focusing on the UK and Ireland. We included methodological research studies that reported interventions to improve representation of ethnic minority groups, socioeconomically disadvantaged groups, older people, or those with impaired capacity to consent to randomised controlled trials, conducted in the UK and Ireland, published between 2000-2021. Systematic searches were conducted in November 2021 and data were independently extracted by two authors and narratively synthesised. Seven studies were included: one randomised controlled study embedded in five trials, one mixed-methods study, and five studies reporting 'lessons learnt' from one trial. We categorised the 47 reported interventions or strategies into nine broad themes: Recruitment sites, recruitment settings, community engagement, and communication with participants, incentives, inclusion criteria, flexibility, patient documentation, and the consent process. Only 28/47 interventions were evaluated, 23 of which were comparison of recruitment pathways.The randomised study found that a £100 incentive mentioned in the invitation letter increased positive responses overall across drug trials in cardiovascular disease and hypertension, but not for older people or those living in the most deprived areas. Invitation letters via GPs and working with communities were reported as successful recruitment pathways in recruiting different under-served populations. Interventions aiming to improve the recruitment of under-served groups in the UK and Ireland were reported across seven papers, but their effectiveness was rarely rigorously evaluated. Included studies were context specific. Using a variety of recruitment methods is likely to help achieve a more diverse cohort.

Some Infinite-Dimensional Representations of Certain Coxeter Groups

Some Infinite-Dimensional Representations of Certain Coxeter Groups

Towards Fairer Centroids in K-means Clustering

There has been much recent interest in developing fair clustering algorithms that seek to do justice to the representation of groups defined along sensitive attributes such as race and sex. Within the centroid clustering paradigm, these algorithms are seen to generate clusterings where different groups are disadvantaged within different clusters with respect to their representativity, i.e., distance to centroid. In view of this deficiency, we propose a novel notion of cluster-level centroid fairness that targets the representativity unfairness borne by groups within each cluster, along with a metric to quantify the same. Towards operationalising this notion, we draw on ideas from political philosophy aligned with consideration for the worst-off group to develop Fair-Centroid; a new clustering method that focusses on enhancing the representativity of the worst-off group within each cluster. Our method uses an iterative optimisation paradigm wherein an initial cluster assignment is refined by reassigning objects to clusters such that the worst-off group in each cluster is benefitted. We compare our notion with a related fairness notion and show through extensive empirical evaluations on real-world datasets that our method significantly enhances cluster-level centroid fairness at low impact on cluster coherence.