Formulation Of Theory Research Articles

Corpus Studies, Sonata Typology, and the Nineteenth-Century Violin Concerto: Viotti, Saint-Saëns, and the Challenge of Recapitulatory Compression

Abstract A corpus study of first-movement form in the nineteenth-century violin concerto, encompassing works from Viotti to Elgar, addresses: the New Formenlehre’s lack of attention to the genre, the pitfalls of formal theory’s focus on canonical Austro-German repertoire; and the question of how concepts derived from late eighteenth-century practice need to adapt to nineteenth-century evolutions. In some geographic subcategories of the corpus, recapitulatory compression is as prevalent as the presumably normative tonic return of P and S. Composers explore multiple alternatives: bypassing recapitulation of either of these zones, merging them, or recapitulating neither in a truncated form that flows into the slow movement. These practices unsettle the tendency to treat the Mozartian type 5 form as a yardstick, reveal a heretofore unrecognized type 2 lineage originating in the eighteenth century and stretching across the nineteenth, and expose the shortcomings of over-reliance on canonical repertoire. Two case studies of Viotti and Saint-Saëns highlight related practices across the corpus’s long chronological span and counterbalance the corpus’s bird’s eye view with attention to the aesthetically compelling formal complexities revealed by close reading of individual compositions.

Relational dynamics and Page-Wootters formalism in group field theory

Group field theory posits that spacetime is emergent and is hence defined without any background notion of space or time; dynamical questions are formulated in relational terms, in particular using (scalar) matter degrees of freedom as time. Unlike in canonical quantisation of gravitational systems, there is no obvious notion of coordinate transformations or constraints, and established quantisation methods cannot be directly applied. As a result, different canonical formalisms for group field theory have been discussed in the literature. We address these issues using a parametrised version of group field theory, in which all (geometry and matter) degrees of freedom evolve in a fiducial parameter. There is a constraint associated to the freedom of reparametrisation and the Dirac quantisation programme can be implemented. Using the "trinity of relational dynamics", we show that the resulting "clock-neutral" theory is entirely equivalent to a deparametrised canonical group field theory, interpreted in terms of the Page-Wootters formalism. Our results not only show that the deparametrised quantisation is fully covariant and can be seen as encoding the dynamics of joint quantum matter and geometry degrees of freedom, they also appear to be the first application of the Page-Wootters formalism directly to non-perturbative quantum gravity. We show extensions to a setting in which many independent gauge symmetries are introduced, which connects to the "multi-fingered time" idea in quantum gravity and provides a somewhat novel extension of the Page-Wootters formalism.

How Microeconomics Works Within a Firm

While it is a widespread practice for business majors to take the microeconomics course in the early years of their college education, for most students it is followed by courses in other disciplines such as accounting, finance, and marketing. In turn, in these disciplines, the formulation of theory, models and examples involve use of nomenclature specific to that discipline such as accounting and financial performances. Sometimes the word “economic” measure does appear in these discipline specific courses. Many of these concepts and models with resulting measures though perceived to be developed in different business disciplines, they originate from or developed utilizing the micro economic theory. In this study, we plan to link together the microeconomic theory and its applications in development of concepts and models in other disciplines so that student and practitioners will be able tie in a seamless manner, and if necessary, modify these concepts to apply and solve business issues in a firm.

Nonrenormalizable theories and finite formulation of QFT

In this paper, we show how the finite formulation of quantum field theory based on Callan-Symanzik equations can be generalized to the case of nonrenormalizable theories. We derive an equation for effective action for an arbitrary single scalar field theory, allowing us to perform computations without running in intermediate divergencies. We illustrate the method with the use of λϕ4+ϕ6/M2 theory by the explicit (and fully finite) calculations of the effective potential as well as two-, four- and six-point correlation functions at one-loop level and demonstrate that no quantum corrections to scalar mass m2, depending on M2 scale, are generated. Published by the American Physical Society 2025

Typology of trust in micro-health and fitness influencers

Purpose Health and fitness influencers who directly affect one’s well-being through their messages create situations of vulnerability that require trust. To understand the various dimensions of trust, this study integrated a typology of trust into source credibility theory. The purpose of the study is to explore the typology’s four trust dimensions concomitant with the perceived attractiveness and expertise of such influencers to identify consumers’ attitudes toward micro-health and fitness influencers. Design/methodology/approach This study used a manipulated-stimuli online survey and gathered 414 micro-influencer evaluations. Variance-based structural equation modeling was used to analyze the data. Findings The results supported the four of trust building. However, a less complex trust formation process was revealed, thereby contrasting the original trust theory formulation. Specifically, the effect of disposition to trust on institution-based trust was higher for regular than for heavy social media users. Also, compared to regular social media users, trusting intentions had a greater impact on heavy social media users’ attitudes toward micro-influencers. In addition, the effect of institution-based trust on trusting beliefs was higher for older than for younger participants. Furthermore, placement of congruent compared to noncongruent products created differences in perceived attitudes toward micro-influencers. In particular, disposition to trust had a larger effect on institution-based trust for noncongruent than for congruent product placements. Originality/value This study extended source credibility theory by including alternative trust dimensions – notably, non-situation-specific disposition to trust and institution-based trust, as well as situation-specific trusting beliefs and trusting intentions – into source credibility.

Reproduction and Senescence: The Meeting of Thomistic Philosophy and Modern Biogerontological Evolutionary Theories

Abstract The explosive increase in life expectancy over the 20th century led to the formulation of multiple gerontological theories. Of these, it is the evolutionary theories of senescence that enjoy the greatest theoretical and empirical support today. It is striking that these models put reproduction at the center of their postulates, an emphasis shared with the Aristotelian and Thomistic doctrines of the living being; this meeting point inspires our model. In particular, we hypothesize that the corporeal living being, precisely because of its mortality, can only fulfill the universal vocation to similitudo Dei through the generation of another living being of the same species. Once this purpose is fulfilled, its biological organization – understood here as a minimal entitative disposition that allows the actualization of matter by substantial form – decays and is exposed to random damage, as predicted by evolutionary models. This gradual decline is what is known as senescence. Such an approach opens up the possibility of addressing aging positively, with an emphasis on organizational prolongation resulting in a healthier old age. At the same time, such a perspective could illuminate our current understanding of biological organization and the pathologies that affect it.

THE SYNERGIC ELECTROWEAK SYNCHROTRON RADIATION

The power spectral formula is derived for radiation of neutral electroweak bosons from an electron in a weak external homogeneous electromagnetic field. The calculation method is based on the source theory formulation of quantum field theory introduced by Schwinger. For ultra-relativistic electrons, it is derived that the Z0 emission rate is suppressed relative to photon emission. This implies that the decay of electron into W-boson and neutrino is also exponentially small under similar conditions. The article is written in the form of mathematical simplicity and the Schwinger pedagogical clarity.

Plane-parallel waves as Jacobi–Lie models

Abstract T-duality and its generalizations are widely recognized either as symmetries or solution-generating techniques in string theory. Recently introduced Jacobi--Lie T-plurality is based on Leibniz algebras whose structure constants fab c, fc ab, Za, Za satisfy further conditions. Low dimensional Jacobi--Lie bialgebras were classified a few years ago. We study four- and six-dimensional algebras with structure constants fb ba = Za = 0 and show that there are several classes consisting of mutually isomorphic algebras.

Using isomorphisms between Jacobi--Lie bialgebras we investigate three- and four-dimensional sigma models related by Jacobi--Lie T-plurality with and without spectators. In the Double Field Theory formulation constant generalized fluxes FA are used in the literature to transform dilaton field. We extend the procedure to non-constant fluxes and verify that obtained backgrounds and dilatons solve Supergravity Equations. Most of the resulting backgrounds have vanishing curvature scalars and, as can be seen by finding Brinkmann coordinates, represent plane-parallel waves.

The Univalence Principle

The Univalence Principle is the statement that equivalent mathematical structures are indistinguishable. We prove a general version of this principle that applies to all set-based, categorical, and higher-categorical structures defined in a non-algebraic and space-based style, as well as models of higher-order theories such as topological spaces. In particular, we formulate a general definition of indiscernibility for objects of any such structure, and a corresponding univalence condition that generalizes Rezk’s completeness condition for Segal spaces and ensures that all equivalences of structures are levelwise equivalences. Our work builds on Makkai’s First-Order Logic with Dependent Sorts, but is expressed in Voevodsky’s Univalent Foundations (UF), extending previous work on the Structure Identity Principle and univalent categories in UF. This enables indistinguishability to be expressed simply as identification, and yields a formal theory that is interpretable in classical homotopy theory, but also in other higher topos models. It follows that Univalent Foundations is a fully equivalence-invariant foundation for higher-categorical mathematics, as intended by Voevodsky.

Formalising Graph Algorithms with Coinduction

Graphs and their algorithms are fundamental to computer science, but they can be difficult to formalise, especially in dependently-typed proof assistants. Part of the problem is that graphs aren’t as well-behaved as inductive data types like trees or lists; another problem is that graph algorithms (at least in standard presentations) often aren’t structurally recursive. Instead of trying to find a way to make graphs behave like other familiar inductive types, this paper builds a formal theory of graphs and their algorithms where graphs are treated as coinductive structures from the beginning. We formalise our theory in Agda. This approach has its own unique challenges: Agda is more comfortable with induction than coinduction. Additionally, our formalisation relies on quotient types, which tend to make coinduction even harder to deal with. Nonetheless, we develop reusable techniques to deal with these difficulties, and the simple graph representation at the heart of our work turns out to be flexible, powerful, and formalisable.

Atypical oscillatory and aperiodic signatures of visual sampling in developmental dyslexia

Temporal processing deficits in Developmental Dyslexia (DD) have been documented extensively at the behavioral level, leading to the formulation of neural theories positing that such anomalies in parsing multisensory input rely on aberrant synchronization of neural oscillations or to an excessive level of neural noise. Despite reading being primarily supported by visual functions, experimental evidence supporting these theories remains scarce. Here, we tested 26 adults with DD (9 females) and 31 neurotypical controls (16 females) with a temporal segregation/integration task that required participants to either integrate or segregate two rapidly presented displays while their EEG activity was recorded. We confirmed behaviorally a temporal sampling deficit in DD, which affected specifically the rapid segregation of visual input. While the ongoing alpha frequency and the excitation/inhibition (E/I) ratio (i.e., an index of neural noise quantified by the aperiodic exponent) were differently modulated based on task demands in typical readers, DD participants exhibited an impairment in alpha speed modulation and an altered E/I ratio that affected their rapid visual sampling. Nonetheless, an association between visual temporal sampling accuracy and both alpha frequency and the E/I ratio measured at rest were evident in the DD group, further confirming an anomalous interplay between alpha synchronization, the E/I ratio and active visual sampling. These results provide evidence that both trait- and state-like differences in alpha-band synchronization and neural noise levels coexist in the dyslexic brain and are synergistically responsible for cascade effects on visual sampling and reading.

Testing the necessity of complex numbers in traditional quantum theory with quantum computers

A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers. To motivate the experiment, we present a basic construction for real-valued quantum theory. The real-valued description is shown to predict correlations identical to those of complex-valued quantum mechanics for two types of Bell tests based on the Clauser–Horne–Shimony–Holt inequality. A slight modification to one test, however, results in different predictions for the real- and complex-valued constructions. While noisier devices are incapable of delivering convincing results, it is shown that certain devices possess sufficiently small error rates to falsify real-valued formulations of quantum theory for composite states. The results obtained with quantum computers are consistent with published experiments. This work demonstrates the feasibility of using freely available quantum devices to explore foundational features of quantum mechanics with minimal technical expertise. Accordingly, this treatment could inspire novel projects for undergraduate students taking a course on quantum mechanics.

Recurrence rates for shifts of finite type

Let ΣA be a topologically mixing shift of finite type, let σ:ΣA→ΣA be the usual left-shift, and let μ be the Gibbs measure for a Hölder continuous potential that is not cohomologous to a constant. In this paper we study recurrence rates for the dynamical system (ΣA,σ) that hold μ-almost surely. In particular, given a function ψ:N→N we are interested in the following setRψ={i∈ΣA:in+1…in+ψ(n)+1=i1…iψ(n)for infinitely manyn∈N}.We provide sufficient conditions for μ(Rψ)=1 and sufficient conditions for μ(Rψ)=0. As a corollary of these results, we discover a new critical threshold where the measure of Rψ transitions from zero to one. This threshold was previously unknown even in the special case of a non-uniform Bernoulli measure defined on the full shift. The proofs of our results combine ideas from Probability Theory and Thermodynamic Formalism. In our final section we apply our results to the study of dynamics on self-similar sets.

Topology-Based Reconstruction Prevention for Decentralised Learning

Decentralised learning has recently gained traction as an alternative to federated learning in which both data and coordination are distributed over its users. To preserve the confidentiality of users' data, decentralised learning relies on differential privacy, multi-party computation, or a combination thereof. However, running multiple privacy-preserving summations in sequence may allow adversaries to perform reconstruction attacks. Unfortunately, current reconstruction countermeasures either cannot trivially be adapted to the distributed setting, or add excessive amounts of noise. In this work, we first show that passive honest-but-curious adversaries can infer other users' private data after several privacy-preserving summations. For example, in subgraphs with 18 users, we show that only three passive honest-but-curious adversaries succeed at reconstructing private data 11.0% of the time, requiring an average of 8.8 summations per adversary. The success rate depends only on the adversaries' direct neighbourhood, and is independent of the size of the full network. We consider weak adversaries that do not control the graph topology, cannot exploit the inner workings of the summation protocol, and do not have auxiliary knowledge; and show that these adversaries can still infer private data. We develop a mathematical understanding of how reconstruction relates to topology and propose the first topology-based decentralised defence against reconstruction attacks. Specifically, we show that reconstruction requires a number of adversaries linear in the length of the network's shortest cycle. Consequently, exact reconstruction attacks over privacy-preserving summations are impossible in acyclic networks. Our work is a stepping stone for a formal theory of topology-based decentralised reconstruction defences. Such a theory would generalise our countermeasure beyond summation, define confidentiality in terms of entropy, and describe the interactions with (topology-aware) differential privacy.

실재에 의한 교과의 정당화 논의의 의미와 한계

Formal discipline theory can be understood as a justification based on means-ends relation, as it regards school subjects as means to development of general abilities. While the formal discipline theory emphasizes usefulness of general abilities, some metaphysical discussions suggest that school subjects are paths to ‘metaphysical reality’ which transcends everyday life. These discussions regard metaphysical reality as a goal which is established before educational activities, and justify school subjects as means to reach that reality. In this sense, these discussions belong to justification based on means-ends relation, and thus, they share the same disadvantages with the formal discipline theory.

Brownian motion in the Hilbert space of quantum states along with the Ricci flow and stochastically emergent Einstein–Hilbert action: Formulating a well-defined Feynman’s path-integral measure for quantum fields in the presence of gravity

In this paper, we aim to interpret the background gravitational effects appearing in quantum field theory on curved space-time by studying the Brownian motion of quantum states along with the Hamilton–Perelman Ricci flow. It has been shown that the Wiener measure automatically contains the Einstein–Hilbert action and the path-integral formulation of the scalar quantum field theory on curved space-time at the first order of local approximations. This provides a well-defined formulation of the path-integral measure for quantum field theory in the presence of gravity. However, we establish that the emergence of Einstein–Hilbert action is independent of the matter field interactions and is a merely entropic/geometric effect stemming from the nature of the Ricci flow of the universe geometry. We also extract an explicit formula for the cosmological constant in terms of the Ricci flow and Hamilton’s theorem for 3-manifolds. Then, we discuss the cosmological features of the FLRW solution in [Formula: see text]CDM Model via the derived equations of the Ricci flow. We also argue the correlation between our formulations and the entropic aspects of gravity. Finally, we provide some theoretical evidence that proves the second law of thermodynamics is the basic source of gravity and probably a more fundamental concept.

Association Kinetics for Perfluorinated n-Alkyl Radicals.

Radical-radical reaction channels are important in the pyrolysis and oxidation chemistry of perfluoroalkyl substances (PFAS). In particular, unimolecular dissociation reactions within unbranched n-perfluoroalkyl chains, and their corresponding reverse barrierless association reactions, are expected to be significant contributors to the gas-phase thermal decomposition of families of species such as perfluorinated carboxylic acids and perfluorinated sulfonic acids. Unfortunately, experimental data for these reactions are scarce and uncertain. Furthermore, obtaining reliable theoretical predictions for such reactions is a laborious and computationally intensive task. In this work, the chemical kinetics of the various association/decomposition reactions producing/decomposing the C2-C4 series of unbranched n-perfluoroalkanes (C2F6, C3F8, and C4F10) are examined using state-of-the-art ab initio transition-state-theory-based master-equation calculations. The variable-reaction-coordinate transition-state theory (VRC-TST) formalism is employed in computing the microcanonical and canonical rates for the association reactions. Reaction thermochemistry is obtained via composite quantum chemistry calculations and the laddering of error-canceling reaction schemes via a connectivity-based hierarchy approach employing ANL1/ANL0-style reference energies. Lennard-Jones collision model parameters for the considered systems were estimated by a direct dynamics approach, and collisional energy transfer parameters were obtained from analogies to systems of similar size and heavy-atom connectivity. A one-dimensional master equation approach was used to convert the microcanonical rate coefficients from the VRC-TST analysis into temperature- and pressure-dependent rate constants for the association reactions and the reverse dissociation reactions. The data are reported in standardized formats for usage in comprehensive chemical kinetic models for PFAS thermal destruction.

Balancing Universality and Cultural Diversity in the Search for Inclusive Moral Frameworks

Purpose. The article aims to draw the attention of researchers to the creation of an ethical framework that harmoniously incorporates universal principles and cultural diversity taking into account the rights and dignity of every individual as a key actor in ethical discussions. It argues that an effective ethical framework gives the opportunity to each person to take part in moral deliberations and ethical decision-making. Theoretical basis. The article, based on the approach of Kant, Rolls, Singer and others, insists on the need to define and agree on the universal principles. They should form the basis of all subsequent ethical discussions. The protection of personal identity is emphasized through intercultural sensitivity (Herskovits, Benedict). People with diverse cultural contexts should be included in ethical debates. The importance in research of the flexibility of ethical concepts in accordance with the cosmopolitanism of Appiah and the approach to the capabilities of Nussbaum is also emphasized. Ethical theories need to balance between cultural pluralism and universality. Cultural sensitivity in ethical theories must recognize, respect, and give space to other moralities, paving the way for the formulation of open ethical theories. Anthropological and philosophical insights contribute to achieving the necessary balance between core principles and flexibility to create avenues for dialogue and consensus. Finally, while attempting to achieve universality, cultural sensitivity, and adaptability, ethical frameworks in an interconnected world should apply the principles across various societies, respect diversity in values, and take into account changes in those societies. Originality. The article outlines the contours of a possible balanced approach emphasizing universality as the central core of ethical theory and cross-cultural sensitivity, flexibility, and adaptability. That allows each person to preserve identity and feel to be involved in ethics. Conclusions. The article demonstrated that it is necessary to promote such qualities as understanding cultural specificity, empathy for other cultures and cooperation in solving moral dilemmas on the path towards ethical excellence. Only a balanced approach that combines universal principles and takes into account cultural diversity recognizes the rights and dignity of each person and transcends cultural differences.

Effect of chiral imbalance on the electrical conductivity of hot and dense quark matter using Green–Kubo method within the 2-flavour gauged NJL model

The electrical conductivity of hot and dense quark matter is calculated using the 2-flavour gauged Nambu–Jona–Lasinio (NJL) model in the presence of a chiral imbalance quantified in terms of a chiral chemical potential (CCP). To this end, the in-medium spectral function corresponding to the vector current correlator is evaluated employing the real time formulation of finite temperature field theory. Taking the long wavelength limit of the spectral function we extract the electrical conductivity using the Green–Kubo relation. The thermal widths of the quarks/antiquarks that appear in the expression of electrical conductivity are calculated by considering the 2→2 scattering in the NJL model. The scattering amplitudes containing the polarization functions of the mesonic modes in the scalar and pseudoscalar channels are also evaluated by considering finite value of CCP. We find that the ratio of electrical conductivity to temperature has significant dependence on CCP especially in the low temperature region.

Exploring perturbative constraints in higher-order curvature gravity theories

Abstract In the realm of general relativity (GR) and extended theories of gravity, obtaining solutions for scenarios of physical interest is a highly intricate challenge. By employing the formalism of mathematical perturbation theory within the GR framework, we demonstrate that, for a significant class of vacuum f ( R , R μ ν R μ ν ) theories, the corresponding solutions do not yield additional effects beyond those predicted by GR’s perturbation theory. However, models characterized by terms of the form f ( R , R μ ν R μ ν , R μ ν σ δ R μ ν σ δ ) exhibit distinctive contributions not present in GR. We assert that fundamental limitations exist, explaining why solutions of certain f ( R , R μ ν R μ ν ) models can deviate from their GR counterparts, indicating non-connected solutions or non-analytic behavior. Conversely, in the models f ( R , R μ ν R μ ν , R μ ν σ δ R μ ν σ δ ) , the solutions seamlessly connect with those of GR. This distinction highlights the nuanced interplay between higher-order curvature terms and their impact on gravitational dynamics, offering new insights into the landscape of modified gravity theories.