Representation Theory Research Articles

Asa, Allyson, and Davies: Three Amazons of Tonal Integrity in Yoruba Vocal Music

The existing body of literature has engaged the translation of English hymns to the Yorùbá language by European missionaries sung to European tunes, which constituted linguistic distortion of the Yorùbá language. Little or no attention has been given to this phenomenon in Yorùbá vocal music outside core liturgical settings. Despite the distorted singing of Yorùbá words in the church and its influence on Christian and popular Yorùbá singers, there remains a school of Yorùbá composers and singers, whose music has continued to align with Yorùbá speech tone pattern. Anchored on the theory of cultural representation, this study investigates three selected female icons of contemporary Yorùbá music – Bukola Elemide, Sola Allyson Obaniyi and Yinka Davies, who have demonstrated strong allegiance to Yorùbá tonal integrity in their musical vocalisations. Purposive sampling was employed in selecting two songs from each of the artists and subjected to content analysis. The music of the three selected singers conforms to Yorùbá tonal integrity, thereby promoting appropriateness in Yorùbá vocal music composition and performance. Their music has continued to create awareness, serving as an avenue for advocacy in the proper approach to composing and singing Yoruba music.

The AGM of Gauss, Ramanujan’s corresponding theory, and spectral bounds of self-adjoint operators

Abstract We study the spectral bounds of self-adjoint operators on the Hilbert space of square-integrable functions, arising from the representation theory of the Heisenberg group. Interestingly, starting either with the von Neumann lattice or the hexagonal lattice of density 2, the spectral bounds obey well-known arithmetic–geometric mean iterations. This follows from connections to Jacobi theta functions and Ramanujan’s corresponding theories. As a consequence, we rediscover that these operators resemble the identity operator as the density of the lattice grows. We also prove that the conjectural value of Landau’s constant is obtained as half the cubic arithmetic–geometric mean of $$\root 3 \of {2}$$ 2 3 and 1, which we believe to be a new result.

Representation theory of topological full groups of étale groupoids and paradoxicality

Abstract We provide a unified treatment of several results concerning full groups of ample groupoids and paradoxical decompositions attached to them. This includes a criterion for the full group of an ample groupoid being amenable as well as comparison of its orbit, Koopman and groupoid-left-regular representations. Besides that, we unify several recent results about paradoxicality in semigroups and groupoids, relating embeddings of Thompson’s group V into full groups of ample étale groupoids.

Flexible framework of computing binding free energy using the energy representation theory of solution.

Host-guest binding plays a crucial role in the functionality of various systems, and its efficiency is often quantified using the binding free energy, which represents the free-energy difference between the bound and dissociated states. Here, we propose a methodology to compute the binding free energy based on the energy representation (ER) theory of solution, which enables us to evaluate the free-energy difference between the systems of interest with the molecular dynamics (MD) simulations. Unlike the other free-energy methods, such as the Bennett acceptance ratio (BAR), the ER theory does not require the MD simulations for hypothetical intermediate states connecting the systems of interest, leading to reduced computational costs. By constructing the thermodynamic cycle of the binding process that is suitable for the ER theory, a robust calculation of the binding free energy is realized. We apply the present method to the self-association of N-methylacetamide in different solvents and the binding of aspirin to β-cyclodextrin (CD) in water. In the former case, the present method estimates that the binding free energy decreases as the solvent polarity decreases. This trend is consistent with the experimental finding. For the latter system, the binding free energies for the two representative CD-aspirin bound complexes, primary (P) and secondary (S) complexes, are estimated to be -5.2 ± 0.1 and -5.03 ± 0.09kcalmol-1, respectively. These values are satisfactorily close to those from the BAR method [-4.2 ± 0.2 and -4.1 ± 0.2kcalmol-1 for P and S, respectively]. Furthermore, the interaction-energy component analysis reveals that the van der Waals interaction between aspirin and CD dominantly contributes to the stabilization of the bound complexes, which is in harmony with the well-known binding mechanism in the CD systems.

The impact of platform affordance on the representation of iconic architecture: a case study of Markthal across visual social media

PurposeThis paper explores how platforms shape the representation of iconic architecture across visual social media platforms, particularly how their unique features and affordances impact these representations.Design/methodology/approachThis paper develops an integrated framework connecting iconic architecture representation, platform affordance and triadic spatial theory. Taking Rotterdam’s Markthal as a case study and collecting multimodal data from TikTok, Instagram and Google Maps, the paper uses a mixed-methods approach that integrates content analysis with qualitative coding and quantitative image/video label detection and image clustering.FindingsTikTok is more associated with enriching lived space by enabling users to share vibrant, personal experiences and activities. Instagram influences perceived space more by shaping how users view and experience the physical environment through curated visual content. Meanwhile, Google Maps effectively shapes conceived and perceived space by users’ feedback of place ratings and reviews.Research limitations/implicationsUnderstanding how platform affordances influence the representation of iconic architecture helps designers and researchers generate design strategies and guides marketers in strategically selecting effective social media platforms for architecture promotion.Originality/valueThis research addresses the gap in understanding the impact of platform affordances on social media representations, especially through comparisons across multiple visual social media platforms. Its novel contribution is introducing the concept of affordance from media studies to architecture and urban studies while enhancing traditional text analysis with computational methods for analysing videos and images.

Analyzing the Theme of The Everlasting Regret from the Perspective of Segmented Discourse Representation Theory

This research conducts a thematic analysis of The Everlasting Regret based on Segmented Discourse Representation Theory (SDRT), aiming to uncover its deeper meanings by exploring the text's discourse structure and rhetorical relations. Unlike traditional literary criticism approaches, this study adopts the SDRT framework, with a focus on analyzing the rhetorical relations between Compound Discourse Units (CDUs). The academic debate surrounding the theme of The Everlasting Regret is extensive, with major perspectives including allegorical, romantic, and dual-theme interpretations. Through detailed analysis, this research argues that The Everlasting Regret does not present a dual theme, but rather a single one. Moreover, this theme is not a celebration of love, but rather a subtle and nuanced form of satire. Additionally, the research offers an in-depth examination of key discourse units within the text, revealing that the rhetorical relations among them can be interpreted as Contrast, Result, and Narration. This not only highlights the complexity of discourse coherence and textual structure, but also suggests a potential intrinsic link among these three rhetorical relations.

Cataland: Why the Fuß?

The three main objects in noncrossing Catalan combinatorics associated to a finite Coxeter system are noncrossing partitions, clusters, and sortable elements. The first two of these have known Fuß-Catalan generalizations. We provide new viewpoints for both and introduce the missing generalization of sortable elements by lifting the theory from the Coxeter system to the associated positive Artin monoid. We show how this new perspective ties together all three generalizations, providing a uniform framework for noncrossing Fuß-Catalan combinatorics. Having developed the combinatorial theory, we provide an interpretation of our generalizations in the language of the representation theory of hereditary Artin algebras.

Edge Laplacians and Edge Poisson Transforms for Graphs

Abstract For a finite graph, we establish natural isomorphisms between eigenspaces of a Laplace operator acting on functions on the edges and eigenspaces of a transfer operator acting on functions on one-sided infinite non-backtracking paths. Interpreting the transfer operator as a classical dynamical system and the Laplace operator as its quantization, this result can be viewed as a quantum-classical correspondence. In contrast to previously established quantum-classical correspondences for the vertex Laplacian which exclude certain exceptional spectral parameters, our correspondence is valid for all parameters. This allows us to relate certain spectral quantities to topological properties of the graph such as the cyclomatic number and the 2-colorability. The quantum-classical correspondence for the edge Laplacian is induced by an edge Poisson transform on the universal covering of the graph which is a tree of bounded degree. In the special case of regular trees, we relate both the vertex and the edge Poisson transform to the representation theory of the automorphism group of the tree and study associated operator valued Hecke algebras.

The Theory of Social Representation: Its Various Models and Their Imbrication

The Theory of Social Representation: Its Various Models and Their Imbrication

Affine Root Systems, Stable Tubes, and a Conjecture by Geiss–Leclerc–Schröer

Abstract Associated to a symmetrizable Cartan matrix $C$, Geiss–Leclerc–Schröer constructed and studied a class of Iwanaga–Gorenstein algebras $H$. They proved a generalized version of Gabriel’s Theorem, that is, the rank vectors of $\tau $-locally free $H$-modules are the positive roots of type $C$ when $C$ is of finite type, and conjectured that this is true for any $C$. In this paper, we investigate this conjecture specifically for the case when $C$ is of affine type. We explicitly construct stable tubes, some of which are inhomogeneous tubes with non-rigid mouth modules. This characteristic is not presented in the representation theory of quivers (with no relations). We deduce that any positive root of type $C$ is the rank vector of some $\tau $-locally free $H$-module. However, the converse is not generally true. Our construction shows that there are $\tau $-locally free $H$-modules whose rank vectors are not roots, when $C$ is of type $\operatorname{\widetilde{\mathbb{B}}}_{n}$, $\operatorname{\widetilde{\mathbb{C}\mathbb{D}}}_{n}$, $\operatorname{\widetilde{\mathbb{F}}}_{41}$ and $\operatorname{\widetilde{\mathbb{G}}}_{21}$, and so the conjecture fails for these four types.

Social Representations of pregnancy among trans men.

to understand the meanings and experiences of pregnancy among trans men in light of the Theory of Social Representations. this is a qualitative, descriptive and exploratory study, carried out with trans men selected for convenience and availability. Data production took place from September to October 2021, via the Google Meet® platform, based on interviews with a semi-structured script. Interview lexicographic textual analysis was performed using the Reinert method and instrumented by IRAMUTEQ version 7.0. social representations of pregnancy involved a wide field of meanings, in which efforts were articulated to accept opportune and solitary pregnancy, fear of the parturition process and influence of physical and emotional changes. the study reinforces the importance of advanced nursing practice in assisting the pregnancy-puerperal cycle, based on the perspective of comprehensive care, equity in access to services and respect for differences.

Feed-Forward Neural Network-Based Prediction of Flutter Speed of 3 DOF 2D Wing Model

IntroductionThe application of artificial intelligence, particularly neural network models, has expanded throughout various fields of academic and industrial studies, recently. This research focuses to investigate aeroelastic phenomena and predict flutter speeds without expensive computational and experimental methods utilizing these algorithms, specifically the artificial neural network (ANN).MethodsFundamentally, the approach involves an ANN algorithm to navigate the complexities of aeroelastic systems, achieved by layering multiple ANNs. The network's neurons effectively interpret diverse flight data by this structure. The study also incorporates state-space representation and Theodorsen's unsteady aerodynamic theory to create a comprehensive dataset on aeroelastic flutter speed across different wing parameters. In order to forecast the flutter speeds, a feed-forward neural network (FFNN) model, which is an approach of ANN method, containing sigmoid hidden neurons and a linear output neuron has been proposed for the conditions above.ResultsThe proposed model accomplished a regression value of 0.92 for flutter speeds according to the experimental findings. As presented, the suggested FFNN model is successful and can be employed to predict the flutter speed estimation. The findings of the FFNN structure are validated with the previous work for aeroelastic flutter speed analysis in the literature.DiscussionFinally, the findings indicate that the FFNN model formulated in this study is highly accurate in predicting flutter speeds with the accordance of numerical results of aeroelastic structure modeled with unsteady aerodynamic theory. In addition, the correctness of the predicted flutter speeds demonstrates that analyzing without expensive tests and high computational costs is in the near future.

Memory Development, Configurations, Conjunctions, and the Hippocampal Index.

When I began my career, I had no idea that much of it would center around the hippocampus. Here I discuss some of the history of how this happened. I briefly mention my early undergraduate life and the problems it posed for getting into graduate school. I describe the unique circumstances that led me to Allan Wagner's laboratory and changed my career trajectory. My path to the hippocampus began with a decision to study memory development. This led to a collaboration with Rob Sutherland that produced the configural theory of the hippocampus. The idea was that the hippocampus facilitated the construction of representations of the co-occurring stimulus elements currently experienced by the organism. Thus, if two elements, A and B, occurred together, a representation, AB, could be constructed that could be discriminated from its elements, A and B. This idea was partially correct, but we missed an important property of the hippocampal system that was recognized by O'Keefe and Nadel, 1978 that is, that the hippocampus is an unmotivated, rapid learning system. Randy O'Reilly and I addressed this issue in what we called conjunctive representation theory and put forth a detailed cortical-hippocampus computational theory to explain how this could work I later realized that our ideas were remarkably like Tim Teyler's indexing theory of how the hippocampal system supports memory. At a Park City meeting, a chance encounter with Tim (whom I had never met) resulted in the opportunity to write a paper with Tim updating the indexing theory, It is my favorite theoretical paper.

The properties on F-manifold color algebras and pre-F-manifold color algebras

<p>The concept of F-manifold algebras is an algebraic expression of F-manifolds. In this paper, we provide the definition of an F-manifold color algebra, which can be viewed as a natural generalization of an F-manifold algebra. We develop the representation theory of an F-manifold color algebra and show that F-manifold color algebras admitting non-degenerate symmetric bilinear forms are coherence F-manifold color algebras. The concept of pre-F-manifold color algebras is also presented, and using this definition one can construct F-manifold color algebras. These results extend some properties of F-manifold algebras.</p>

Acts from the cracks: Representations and positions of the decolonial in the geopolitical (de)construction of power-entangled knowledge.

This paper examines the geopolitical implications of knowledge production in psychology through two studies that respond to the growing body of work on the 'Decolonisation of Knowledge' and the 'Decolonisation of Psychology' over the past two decades. By adopting a constructivist approach, particularly through the lens of Social Representation Theory (SRT), these studies explore the ways in which geopolitical contexts shape decolonial activism within psychological and scientific discourse. The first study sheds light on the lexical divergences in the construction of knowledge within the domains of psychology. We reviewed 300 article abstracts related to decolonial studies using lexicometric analysis based on the Reinhart method (IraMuTeq). Four clusters were identified: Educational Reform, Historical Temporalities, Social Actors, and Epistemological Discourse. These clusters suggest differences in knowledge production within different geopolitical localities. The second study explores these variations by immersing itself in the perspectives and representations articulated by decolonial scholars. The second study is conducted using 12 semi-structured interviews with academics actively engaged in decolonial efforts. The aim of the two studies is to demonstrate regional variations in decolonial discourse and highlight the ongoing influence of geopolitical factors on scientific inquiry.

Group Theory Explanation of Microscopic Superconductivity Theory

In 1911, Dutch physicist Onnes discovered that after liquefying helium gas. At around 15 K, the resistance of mercury drops sharply to zero, which is named superconductivity and marks the beginning of human research on superconductors. So far, over a hundred types of superconducting materials have been discovered. With the discovery of superconducting materials and phenomena, many theoretical models have emerged to explain superconducting phenomena, promoting human understanding of condensed matter micro magnetism and other fields. Group theory is a mathematical concept. In mathematics and abstract algebra, group theory studies the algebraic structure of groups. In the study of physics and chemistry, many different physical structures, such as crystal structures and hydrogen atomic structures, can be modeled using group theory methods. So group theory and related group representation theory have a lot of applications in physics and chemistry. This article will elaborate on the phonon model that explains superconductivity theory, Cooper’s model. And attempt to construct a model using molecular point group crystal dynamics knowledge to explore micro superconducting phenomena and theories.

Root of unity quantum cluster algebras and discriminants

AbstractWe describe a connection between the subjects of cluster algebras, polynomial identity algebras, and discriminants. For this, we define the notion of root of unity quantum cluster algebras and prove that they are polynomial identity algebras. Inside each such algebra we construct a (large) canonical central subalgebra, which can be viewed as a far reaching generalization of the central subalgebras of big quantum groups constructed by De Concini, Kac, and Procesi and used in representation theory. Each such central subalgebra is proved to be isomorphic to the underlying classical cluster algebra of geometric type. When the root of unity quantum cluster algebra is free over its central subalgebra, we prove that the discriminant of the pair is a product of powers of the frozen variables times an integer. An extension of this result is also proved for the discriminants of all subalgebras generated by the cluster variables of nerves in the exchange graph. These results can be used for the effective computation of discriminants. As an application we obtain an explicit formula for the discriminant of the integral form over of each quantum unipotent cell of De Concini, Kac, and Procesi for arbitrary symmetrizable Kac–Moody algebras, where is a root of unity.

What is a theory of neural representation for?

What is a theory of neural representation for?

Cowards and the beloved: newspaper representations of the Jamaican diaspora

ABSTRACT On 11 August 2022, the Deputy Mayor of Montego Bay, Jamaica, Richard Vernon, made controversial remarks about the Jamaican Diaspora, implying that ‘only cowards run away to go to America because they are seeking out opportunities’. On Jamaica's media landscape, these remarks angered several individuals and morphed into a proxy for a larger debate concerning the diaspora's allegiance to Jamaica. Anchored by Social Representation Theory (SRT), this study investigates the content and meanings within newspaper representations of the Jamaican Diaspora from 2004 to 2023. The findings are based on content analysis of stories (N = 2358) from the Jamaica Gleaner and Jamaica Observer newspapers. The frequency with which these newspapers portray the Jamaican Diaspora offers frames from which people draw their understandings of emigration, the diaspora, and support for the Jamaican government's policies and posture towards the diaspora. These portrayals can reveal potential misrepresentations that may affect how the diaspora's contributions are leveraged for national development. This study finds that the portrayal of the Jamaican Diaspora in media coverage is predominantly positive. It suggests that newspaper portrayals contribute to the construction of narratives surrounding the Jamaican Diaspora. Media representations influence public opinion and identity, positioning the diaspora as a crucial component of Jamaican society. The notion of Jamaicaness has implications for national identity and diaspora engagement. It shapes how Jamaicans at home and abroad perceive their role in the nation's narrative, influencing feelings of belonging and collective responsibility. This study has implications for policymakers aiming to improve diaspora engagement and national cohesion.

‘With a Gesture, a Smile, a Glance’: Felix Salten Performing Vienna and Decoding Acculturation

Abstract This article accompanies Felix Salten, author of Bambi and popular journalist in fin-de-siècle Vienna, in his efforts to observe, negotiate, and perform social role performances in the modern city. Linking Jewish Cultural Studies with theatre theory, it argues that Salten developed an understanding for the performative qualities of society through his sensibility as a theatre critic, and that he positioned Jewish belonging within this performative framework as thoroughly corporeal. His writings, thus, articulate his Jewish experiences for his Vienna contemporaries as a physical practice of socialization—thereby decentring acculturation as a merely Jewish practice, while also unravelling a praxeology of belonging via attention, gaze, and posture.