Search Results (37)

In this paper, we clarify several issues concerning the abstract geometrical formulation of thermodynamics on non-compact symmetric spaces $\mathrm{U}/\mathrm{H}$ that are the mathematical model of hidden layers in the new paradigm of Cartan Neural Networks. We introduce a clear-cut distinction between the generalized thermodynamics associated with Integrable Dynamical Systems and the challenging proposal of Gibbs probability distributions on $\mathrm{U}/\mathrm{H}$ provided by generalized thermodynamics à la Souriau. Our main result is the proof that $\mathrm{U}/\mathrm{H}$.s supporting such Gibbs distributions are only the Kähler ones. Furthermore, for the latter, we solve the problem of determining the space of temperatures, namely, of Lie algebra elements for which the partition function converges. The space of generalized temperatures is the orbit under the adjoint action of $\mathrm{U}$ of a positivity domain in the Cartan subalgebra $C_c\subset \mathbb{H}$ of the maximal compact subalgebra $\mathbb{H}\subset \mathbb{U}$. We illustrate how our explicit constructions for the Poincaré and Siegel planes might be extended to the whole class of Calabi–Vesentini manifolds utilizing Paint Group symmetry. Furthermore, we claim that Rao’s, Chentsov’s, and Amari’s Information Geometry and the thermodynamical geometry of Ruppeiner and Lychagin are the very same thing. In particular, we provide an explicit study of thermodynamical geometry for the Poincaré plane. The key feature of the Gibbs probability distributions in this setup is their covariance under the entire group of symmetries U. The partition function is invariant against $\mathrm{U}$ transformations, and the set of its arguments, namely the generalized temperatures, can always be reduced to a minimal set whose cardinality is equal to the rank of the compact denominator group $\mathrm{H}\subset \mathrm{U}$. Full article

Between 1900 and 1940, African American participants in transatlantic public exhibitions reclaimed a medium that often oppressed non-White bodies: the diorama. This essay traces a transatlantic conversation among African American artists about how to render Black history in diorama form, leveraging the miniature format to make political arguments. In diorama series which circulated on both sides of the Atlantic, such as those designed by Thomas W. Hunster for the Exhibit of American Negroes in the Paris Universal Exposition in 1900 and the Pan-American Exposition in 1901, Meta Vaux Warrick Fuller for the Jamestown Ter-Centennial Exposition in 1907, and Charles C. Dawson for the American Negro Exposition in Chicago in 1940, African American makers selectively used architectural models to signify histories of oppression and liberation as they told transatlantic stories about Black migration and enslavement. This essay argues that this set of dioramas is entwined, growing from 9 to 14 to 33, and that Hunster, Fuller, and Dawson all rendered archetypal buildings, such as slave cabins or plantation homes, to designate the wide and encompassing scope of oppression, while they reference singular buildings associated with public institutions from government to universities—the M Street School in Washington DC, Carnegie Library at Howard University, Mother Bethel AME Church in Philadelphia, the Old Massachusetts State House, and the White House—to signify and emplace spaces of Black liberation. Building on research on the layered functions of miniatures and drawing on burgeoning scholarship on entwinements between race and architecture, the article speculates on how architecture style signifies through the models to reinforce what James C. Scott has parsed as dominant narratives and hidden transcripts. Seeking to build Black futurity, all three series facilitated community participation and collaboration to produce an intersocial construction of transatlantic African American history built through mobile models of architecture. Full article

In this paper we will be concerned with zeta-symmetry—the functional equation for the (Riemann) zeta-function (equivalents to which are called modular relations)—and reveal the reason why so many results are intrinsic to PFE (Partial Fraction Expansion) for the cotangent function. The hidden reason is that the cotangent function (as a function in the upper half-plane, say) is the polylogarithm function of order 0 (with complex exponential argument), and therefore it shares properties intrinsic to the Lerch zeta-function of order 0. Here we view the Lerch zeta-function defined in the unit circle as a zeta-function in a wider sense, as a function defined in the upper and lower half-planes. As evidence, we give a plausibly most natural proof of Ramanujan’s formula, including the eta transformation formula as a consequence of the modular relation via the cotangent function, speculating the reason why Ramanujan had been led to such a formula. Other evidence includes the pre-Poisson summation formula as the pick-up principle (which in turn is a generalization of the argument principle). Full article

In the ontological argument for the existence of God, Descartes famously argues that the idea of God is the idea of a perfect being. As such, the idea of God must combine all of the perfections. Now, as (necessary) existence is a perfection, God must exist. Leibniz criticized Descartes’ argument, pointing out that it rests upon the hidden assumption that God is possible. Leibniz argues, however, that God is really possible because realities cannot oppose one another, and so there could be no real opposition between the perfections. So, at least in the case of God, conceivability entails real possibility. Kant rejects this assumption and insists that the non-contradictoriness of an idea is not an adequate criterion for the real possibility of the object of the idea, for although predicates may be combined in thought to form a concept, this does not entail the properties they indicate may be so combined in reality. For this reason, Kant believes that it is impossible to prove the real possibility of God, and so the ontological argument is not sound. In this paper, I examine Kant’s reasons for reaching this conclusion. I pay particular attention to Kant’s argument in the Amphiboly, which deals with the concepts of agreement and opposition, and where Kant stresses the importance of the distinction between logical and real opposition. I will argue that this distinction plays a crucial role in Kant’s rejection of the ontological argument and rationalist Leibnizian–Wolffian metaphysics in general. I also show how Kant’s rejection of the possibility of what he calls the complete determination of a concept in the Ideal of Pure Reason, plays a role in his rejection of the conceivability entails real possibility principle. Full article

Fractional-order chaotic systems have emerged as powerful tools in secure communications and multimedia protection owing to their memory-dependent dynamics, large key spaces, and high sensitivity to initial conditions. However, most existing fractional-order image encryption schemes rely on fixed-order chaos and conventional solvers, which limit their complexity and reduce unpredictability, while also neglecting the potential of variable fractional-order (VFO) dynamics. Although similar phenomena have been reported in some fractional-order systems, the coexistence of hidden attractors and stable equilibria has not been extensively investigated within VFO frameworks. To address these gaps, this paper introduces a novel discrete variable fractional-order dark matter–dark energy (VFODM-DE) chaotic system. The system is discretized using the piecewise constant argument discretization (PWCAD) method, enabling chaos to emerge at significantly lower fractional orders than previously reported. A comprehensive dynamic analysis is performed, revealing rich behaviors such as multistability, symmetry properties, and hidden attractors coexisting with stable equilibria. Leveraging these enhanced chaotic features, a pseudorandom number generator (PRNG) is constructed from the VFODM-DE system and applied to grayscale image encryption through permutation–diffusion operations. Security evaluations demonstrate that the proposed scheme offers a substantially large key space (approximately $2^{249}$) and exceptional key sensitivity. The scheme generates ciphertexts with nearly uniform histograms, extremely low pixel correlation coefficients (less than 0.04), and high information entropy values (close to 8 bits). Moreover, it demonstrates strong resilience against differential attacks, achieving average NPCR and UACI values of about 99.6% and 33.46%, respectively, while maintaining robustness under data loss conditions. In addition, the proposed framework achieves a high encryption throughput, reaching an average speed of 647.56 Mbps. These results confirm that combining VFO dynamics with PWCAD enriches the chaotic complexity and provides a powerful framework for developing efficient and robust chaos-based image encryption algorithms. Full article

In the Timaeus, Plato explores the topic of cosmology. The demiurge creates a perfect cosmos by imitating the eternal being and using necessity as an auxiliary cause. The unique cosmos not only contains immortal gods, but also mortal living beings. Concerning the academic research on cosmology in Plato’s Timaeus, scholars have explored it through reason, good, and necessity, and they have conducted in-depth analyses of multiple dimensions, such as human organs and diseases. Nonetheless, we should acknowledge the significance of fate, a hidden thread that runs through all of Plato’s cosmology. Whether it is the immortal cosmos created by the demiurge or the mortal humans created by the lesser gods, both demonstrate the significance of fate. This article takes the horizon of divine providence and uses eikos logos as the argument pattern to explore characteristics of determinism contained in the hidden concept of fate in the Timaeus. We cannot ignore the crucial significance of freedom in the thought of fate. Without freedom, the demiurge cannot achieve the overall goodness of the cosmos. Full article

Does determinism (or even the incompleteness of quantum mechanics) follow from locality and perfect correlations? In a 1964 paper, John Bell gave the first demonstration that quantum mechanics is incompatible with local hidden variables. Since then, a vigorous debate has rung out over whether he relied on an assumption of determinism or instead, as he later claimed in a 1981 paper, derived determinism from assumptions of locality and perfect correlation. This paper aims to bring clarity to the debate via simple examples and rigorous results. It is first recalled, via quantum and classical counterexamples, that the weakest statistical form of locality consistent with Bell’s 1964 paper (parameter independence) is insufficient for the derivation of determinism. Attention is then turned to critically assess Bell’s appeal to the Einstein–Rosen–Podolsky (EPR) incompleteness argument to support his claim. It is shown that this argument is itself incomplete, via counterexamples that expose two logical gaps. Closing these gaps via a strong “counterfactual” reality criterion enables a rigorous derivation of both determinism and parameter independence, and in this sense justifies Bell’s claim. Conversely, however, it is noted that whereas the EPR argument requires a weaker “measurement choice” assumption than Bell’s demonstration, it nevertheless leads to a similar incompatibility with quantum predictions rather than quantum incompleteness. Full article

Thermal infrared imaging could detect hidden faults in various types of high-voltage power equipment, which is of great significance for power inspections. However, there are still certain issues with thermal-imaging-based abnormal heating detection methods due to varying appearances of abnormal regions and complex temperature interference from backgrounds. To solve these problems, a contour-based instance segmentation network is first proposed to utilize thermal (T) and visual (RGB) images, realizing high-accuracy segmentation against complex and changing environments. Specifically, modality-specific features are encoded via two-stream backbones and fused in spatial, channel, and frequency domains. In this way, modality differences are well handled, and effective complementary information is extracted for object detection and contour initialization. The transformer decoder is further utilized to explore the long-range relationships between contour points with background points, and to achieve the deformation of contour points. Then, the auto-encoder-based reconstruction network is developed to learn the distribution of power equipment using the proposed random argument strategy. Meanwhile, the UNet-like discriminative network directly explores the differences between the reconstructed and original image, capturing the deviation of poor reconstruction regions for abnormal heating detection. Many images are acquired in transformer substations with different weathers and day times to build the datasets with pixel-level annotation. Several extensive experiments are conducted for qualitative and quantitative evaluation, while the comparison results fully prove the effectiveness and robustness of the proposed instance segmentation method. The practicality and performance of the proposed abnormal heating detection method are evaluated on image patches with different kinds of insulators. Full article

This essay assesses the relevance of Søren Kierkegaard’s non-pseudonymous, edifying writings for considering themes of desire, detachment, and humility within the religious context of Christian spiritual formation. Building on the argument of recent scholars who identify in Kierkegaard’s writings an account of a fundamental desire for God “implanted” in the human being, I explore the influence of this vision on Kierkegaard’s depiction of desire and detachment in his “Discourses on the Lilies and the Birds”. I then turn to how this relates to the perspective of humility that emerges from Kierkegaard’s reflections on the biblical story of “the widow’s mite”. In each case, these edifying writings aim to stir the reader into a process of interrogating faulty self-perceptions based on arbitrary measures of value. I read this mode of communication as able to initiate a “counter-experience”, provoking the reader to reorient her horizon of prior self-valuations so she might come to recognize the hidden significance of things and, ultimately, achieve a more accurate sense of oneself in relation to the authentic source of the self’s desire. Insofar as this reorientation of the self informs the practice of detachment or the development of humility, people might experience this same process in diverse ways. In this respect, the relevance of Kierkegaard’s edifying writings for reflecting on Christian spirituality is not that they provide a thoroughgoing account of detachment or humility that should replace the insights of various spiritual traditions. Rather, I argue that his discourses—when read alongside these traditions—offer a supplemental resource for reflecting on how our positionalities, dispositions, and proximate contexts will inform the divergent ways we might experience the practice of detachment or the manifestation of humility in each new life circumstance. Full article

The transformation formula under the action of a general linear fractional transformation for a generalized Dedekind eta function has been the subject of intensive study since the works of Rademacher, Dieter, Meyer, and Schoenberg et al. However, the (Hecke) modular relation structure was not recognized until the work of Goldstein-de la Torre, where the modular relations mean equivalent assertions to the functional equation for the relevant zeta functions. The Hecke modular relation is a special case of this, with a single gamma factor and the corresponding modular form (or in the form of Lambert series). This has been the strongest motivation for research in the theory of modular forms since Hecke’s work in the 1930s. Our main aim is to restore the fundamental work of Rademacher (1932) by locating the functional equation hidden in the argument and to reveal the Hecke correspondence in all subsequent works (which depend on the method of Rademacher) as well as in the work of Rademacher. By our elucidation many of the subsequent works will be made clear and put in their proper positions. Full article

This article draws on case studies or ‘microhistories’ from the author’s own research to explore the ethical responsibility of family historians to represent the experiences of those whose lives have been ‘hidden from history’, and in particular the lives of one’s female ancestors, as a way of correcting the omissions and erasures of official histories. It also discusses the ethical dilemmas posed by the discovery that one’s ancestors were involved in activities that are now regarded as morally suspect, such as profiting from the ownership of slaves. Finally, the article debates ethical arguments about respecting the rights of the dead to privacy. Full article

Rurality is rarely integrated into analyses of educational inequalities and this article presents an alternative perspective on rural–urban attainment and highlights the impact of rurality on educational outcomes. The traditional narrative of urban–rural educational disadvantage is that urban pupils do less well in the English exam system. Decontextualised data across different English exam performance measures demonstrate how rural pupils outperform their urban counterparts. Socioeconomic disadvantage (SED) has the most significant impact on attainment and this analysis explores the rural–urban attainment gap through this SED lens. An analysis of the Department for Education (DfE) data explores possible factors that might explain the emerging rural educational gap and presents an argument that rurality is another limiting factor that intersects with SED. This article demonstrates how rural underachievement in England has been hidden by the relative sizes and SED distribution of rural and urban populations. Full article

Early warning systems (EWS) facilitate societies’ preparedness and effective response capabilities to climate risks. Climate risks embody hazards, exposure, and vulnerability associated with a particular geographical area. Building an effective EWS requires consideration of the factors above to help people with coping mechanisms. The objective of this paper is to propose an approach that can enhance EWSs and ensure an effective climate risk resilience development. The paper focuses on the Southern African Development Community (SADC) region and highlights the issues with EWS, identifying weaknesses and characteristics of EWS to help in climate risk adaptation strategies. The SADC region was chosen as the context because it is a climate variability and change hotspot with many vulnerable populations residing in rural communities. Trending themes on building climate risk resilience were uncovered through scientific mapping and network analysis of published articles from 2008 to 2022. This paper contributes to on-going research on building climate risks resilience through early warning systems to identify hidden trends and emerging technologies from articles in order to enhance the operationalization and design of EWS. This review provides insight into technological interventions for assessing climate risks to build preparedness and resilience. From the review analysis, it is determined that there exists a plethora of evidence to support the argument that involving communities in the co-designing of EWS would improve risk knowledge, anticipation, and preparedness. Additionally, Fourth Industrial Revolution (4IR) technologies provide effective tools to address existing EWS’ weaknesses, such as lack of real-time data collection and automation. However, 4IR technology is still at a nascent stage in EWS applications in Africa. Furthermore, policy across societies, institutions, and technology industries ought to be coordinated and integrated to develop a strategy toward implementing climate resilient-based EWS to facilitate the operations of disaster risk managers. The Social, Institutional, and Technology model can potentially increase communities’ resilience; therefore, it is recommended to develop EWS. Full article

How to disentangle the possible genuine quenching of $g_A$ caused by scale anomaly of QCD parameterized by the scale-symmetry-breaking quenching factor $q_{ssb}$ from nuclear correlation effects is described. This is accomplished by matching the Fermi-liquid fixed point theory to the “Extreme Single Particle (shell) Model” (acronym ESPM) in superallowed Gamow–Teller transitions in heavy doubly-magic shell nuclei. The recently experimentally observed indication for $(1-q_{ssb})\ne 0$—that one might identify as “fundamental quenching (FQ)”—in certain experiments seems to be alarmingly significant. I present arguments for how symmetries hidden in the matter-free vacuum can emerge and suppress such FQ in strong nuclear correlations. How to confirm or refute this observation is discussed in terms of the superallowed Gamow–Teller transition in the doubly-magic nucleus ${}^{100}$Sn and in the spectral shape in the multifold forbidden $\beta$ decay of ${}^{115}$In. Full article

Divine hiddenness appears today as one of the most important and serious religious problems. This problem has been posed most clearly by the proponents of the “argument from hiddenness”. They point to religious diversity as an important element working in the background of this argument and strengthening the force of its impact. In turn, religious diversity is seen as a result of the ambiguity of religious phenomena and the lack of conclusive testimony in favor of religious beliefs. In my paper, I pose the thesis that the ambiguity of religious phenomena can be counted among the “benefits of divine hiddenness”. This will be possible when the ambiguity of religious phenomena becomes the basis for the formation of interreligious solidarity. I define the concept of interreligious solidarity and show the theoretical aspects of this attitude. In discussing the theoretical aspect of interreligious solidarity, I draw attention to the possible role of phenomenology. I also argue that in the context of divine hiddenness, the most important question is not the one concerning the genesis of this problem (“why are religious phenomena not more unambiguous?”), but the question concerning the meaning of this problem (“what to do with the ambiguity of religious phenomena?”). Full article