Diametrically Opposed Research Articles

Towards complexity in de Sitter space from the doubled-scaled Sachdev-Ye-Kitaev model

How can we define complexity in dS space from microscopic principles? Based on recent developments pointing towards a correspondence between a pair of double-scaled Sachdev-Ye-Kitaev (DSSYK) models/ 2D Liouville-de Sitter (LdS2) field theory/ 3D Schwarzschild de Sitter (SdS3) space in [1–3], we study concrete complexity proposals in the microscopic models and their dual descriptions. First, we examine the spread complexity of the maximal entropy state of the doubled DSSYK model. We show that it counts the number of entangled chord states in its doubled Hilbert space. We interpret spread complexity in terms of a time difference between antipodal observers in SdS3 space, and a boundary time difference of the dual LdS2 CFTs. This provides a new connection between entanglement and geometry in dS space. Second, Krylov complexity, which describes operator growth, is computed for physical operators on all sides of the correspondence. Their late time evolution behaves as expected for chaotic systems. Later, we define the query complexity in the LdS2 model as the number of steps in an algorithm computing n-point correlation functions of boundary operators of the corresponding antipodal points in SdS3 space. We interpret query complexity as the number of matter operator chord insertions in a cylinder amplitude in the DSSYK, and the number of junctions of Wilson lines between antipodal static patch observers in SdS3 space. Finally, we evaluate a specific proposal of Nielsen complexity for the DSSYK model and comment on its possible dual manifestations.

$2$-nodal domain theorems for higher-dimensional circle bundles

We prove that the real parts of equivariant (but non-invariant) eigenfunctions of generic bundle metrics on non-trivial principal S^{1} bundles over manifolds of any dimension have connected nodal sets and exactly 2 nodal domains. This generalizes earlier results of the authors in the 3 -dimensional case. The failure of the results on for non-free S^{1} actions is illustrated on even-dimensional spheres by one-parameter subgroups of rotations whose fixed point set consists of two antipodal points.

A novel smooth quaternion-based attitude tracking control

The fact that two antipodal points in the quaternion characterize the same physical attitude depicts that the design of the global attitude control system is uneasy. This study deals with a smooth quaternion-based attitude tracking control system that is composed of a differential equation known as the augmented dynamical system. The augmented dynamical system plays such an important role that it is possible to conduct a novel perspective on viewing the set containing all possible motions as not a manifold. Therefore, the topological obstruction does not exist. The designed attitude tracking control system has a guarantee of stability in the large within a set containing all possible motions. It is able to avoid the unwinding phenomenon, and it is noise-induced chattering-free since there is no discontinuity. Furthermore, we show that the smooth attitude tracking control system has an integral input-to-state stability (iISS) guarantee in the presence of uncertainties in the moment of inertia and environmental disturbance. Simulations carried out show the effectiveness of the designed attitude tracking control system.

›Less Voice, more Viewpoint‹ – Towards a Cognitive Reconceptualization of the Centres of Orientation in Poetry

Abstract Analysing the centres of orientation in a literary text, narratologists since Genette have always worked with the distinction between voice (who speaks?) and viewpoint (who sees?). In contrast, nearly all lyricologists have remained entirely focussed on the category of voice, trying to identify, apart from the speaking voice, at best further speech instances in the poems under discussion. The present article challenges this voice-restricted tradition. It criticizes the deficiencies of various traditional one-voice-models (such as the identification of the speaking voice with the poet, a persona or the ›lyric I‹) as well as those of more recent voice-oriented approaches (by Hempfer and by Culler). It also discusses the blind spots of the multi-voice models developed in the course of lyricology’s ›narrative turn‹ (by Hühn and by Burdorf) and rejects Zymner’s recent suggestion to replace the notion of ›voice‹ by the purely textual concept of an ›addresser‹ as a ›structure of signs‹. Subsequently, the framework of an alternative, viewpoint-oriented lyricology is sketched by adopting from Cognitive Linguistics such key-concepts as viewpoint-multiplicity, mental spaces and deictic markers as well as from Cognitive Grammar the notions of ›viewing arrangement‹ and ›split conceptualiser‹. Further instruments that can help to account for those poems in which the centre of perception seems to unite in itself the viewpoints of different ›voices‹ are such concepts as ›viewpoint-blends‹ and ›viewpoint-zooms‹. More akin to cognition, in which there are no strict boundaries, but only transitions, they can help to overcome long-lasting, hardly successful attempts to establish rigid divisions in the lyric (e. g. between personal and impersonal, monologic and dialogic, biographical and non-biographical or lyric and narrative poems). Instead, the viewpoint-framework does justice to the fact that such binaries constitute no polar oppositions but mere scales of difference. Moreover, a viewpoint-approach makes possible a much more fine-grained analysis of poetry – in a way better even than an earlier attempt by Petzold (2012) to extend lyricology’s voice-centred methodology by integrating into it a Genette-inspired distinction of three types of focalization. The last section of this article is devoted to the complex problem of viewpoint-taking by the readers, which is aggravated by the underdetermined deixis and situational generality of many poems. As is finally illustrated by drawing on a poem with a particularly complicated deictic set-up (Eichendorff’s »Lockung« [»Lure«]), readers will admittedly not always be able to process all viewpoints contained in a text. Nevertheless, it can be shown with the help of this example that viewpoint-perception is often an indispensable prerequisite for a full understanding of a poem’s meaning.

Cosmological correlators for Bogoliubov initial states

We consider late-time correlators in de Sitter (dS) space for initial states related to the Bunch-Davies vacuum by a Bogoliubov transformation. We propose to study such late-time correlators by reformulating them in the familiar language of Witten diagrams in Euclidean anti-de Sitter space (EAdS), showing that they can be perturbatively re-cast in terms of corresponding dS boundary correlators in the Bunch-Davies vacuum and in turn, Witten diagrams in EAdS. Unlike the standard relationship between late-time correlators in the Bunch-Davies vacuum and EAdS Witten diagrams, this involves points on the upper and lower sheet of the EAdS hyperboloid which account for antipodal singularities of the two-point functions. Such Bogoliubov states include an infinite one parameter family of de Sitter invariant vacua as a special case, where the late-time correlators are constrained by conformal Ward identities. In momentum space, it is well known that their late-time correlators exhibit singularities in collinear (“folded”) momentum configurations. We give a position space interpretation of such solutions to the conformal Ward identities, where in embedding space they can be generated from the solution without collinear singularities by application of the antipodal map. We also discuss the operator product expansion (OPE) limit of late-time correlators in a generic dS invariant vacuum. Many results are derived using the Mellin space representation of late-time correlators, which in this work we extend to accommodate generic dS invariant vacua.

On Opposite Sides of the World – South African Expats’ Observations of the Society, Economy, Education and Ethics in South Korea

Abstract In this paper, a Comparative Historical Analysis (CHA) is made between South Korea and South Africa for the improvement of the South African politics, economy, society, and ethos. Through a mixed-methods approach, this study is making use of four case studies and a literature study to learn from the most prominent differences between RSA and ROK experienced by South African expats living in ROK (confirmed by other expats in ROK). The issues that form the basis of discussion of prominent differences between South Africa and South Korea are 1) the respect basis of society (the Korean focus on respect for others is viewed as a counter for racial superiority theories in RSA), 2) work ethics (the strong Korean commitment to hard work and proper remuneration corrects the lack of work ethics in small RSA enterprises), 3) education and innovation (the educational system in Korea is under less strain than in RSA because it receives high priority funding and support from the government), and 4) national cohesion (RSA’s diversity can be detrimental if leads to a lack of cohesion in the society). These issues are discussed from a CHA perspective for the purpose of contributing to the ongoing debate for the improvement of the South African society, economy and politics. By presenting case studies, this paper is limited in scope but makes an invaluable contribution to the wider debate on the improvement of RSA. The novel contribution of this paper is that it adds to the debate the observations of expatriates living in a country that has some similarities with RSA, but different from RSA, managed to improve their economy since their democratization in 1987.

Subclinical brain manifestations of repeated mild traumatic brain injury are changed by chronic exposure to sleep loss, caffeine, and sleep aids

IntroductionAfter mild traumatic brain injury (mTBI), the brain is labile for weeks and months and vulnerable to repeated concussions. During this time, patients are exposed to everyday circumstances that, in themselves, affect brain metabolism and blood flow and neural processing. How commonplace activities interact with the injured brain is unknown. The present study in an animal model investigated the extent to which three commonly experienced exposures—daily caffeine usage, chronic sleep loss, and chronic sleep aid medication—affect the injured brain in the chronic phase. MethodsSubclinical trauma by repeated mTBIs was produced by our head rotational acceleration injury model, which causes brain injury consistent with the mechanism of concussion in humans. Forty-eight hours after a third mTBI, chronic administrations of caffeine, sleep restriction, or zolpidem (sedative hypnotic) began and were continued for 70 days. On Days 30 and 60 post injury, resting state functional magnetic resonance imaging (fMRI) and diffusion tensor imaging (DTI) were performed. ResultsChronic caffeine, sleep restriction, and zolpidem each changed the subclinical brain characteristics of mTBI at both 30 and 60 days post injury, detected by different MRI modalities. Each treatment caused microstructural alterations in DTI metrics in the insular cortex and retrosplenial cortex compared with mTBI, but also uniquely affected other gray and white matter regions. Zolpidem administration affected the largest number of individual structures in mTBI at both 30 and 60 days, and not necessarily toward normalization (sham treatment). Chronic sleep restriction changed local functional connectivity at 30 days in diametrical opposition to chronic caffeine ingestion, and both treatment outcomes were different from sham, mTBI-only and zolpidem comparisons. The results indicate that commonly encountered exposures modify subclinical brain activity and structure long after healing is expected to be complete. ConclusionsChanges in activity and structure detected by fMRI are widely understood to reflect changes in the functions of the affected region which conceivably underlie mTBI neuropathology and symptomatology in the chronic phase after injury.

Thermal conductivity variation effects on Marangoni radiative hybridizedAg-ZrO2 and MoS2-ZrO2 nanofluid based-blood with oblique magnetic field

The objective of this examination is to explore the mathematical modeling of a hybridized nanofluid flowing, which involves the transference of biologically fluid via a stretchable sheet. The nanofluid contains of pure blood as the conventional fluid, and it is combined with two nanomolecules. The flow occurs through a porosity stretchable surface. This simulation has potential applications in drugs delivery. The present study relies on the Marangoni condition and the injection/suction properties of two hybrid nanofluids (Ag-ZrO2/blood and MoS2-ZrO2/blood) to explain the time-independent and incompressible flow and transport of energy. Adding magnetic and radiation terms helps develop the issue. Similarity variables are used to define the mathematical phenomena. By using the Fehlberg approach, the reorganized nonlinear model may be carried out. Displaying and elaborating on the roles performed by restrictions in determining engineering physical quantities. The key characteristics of the current analysis are the bigger speed profiles and lower temperatures that emerge in response to the tightening stretching limit. Declining trends in the solid volume percentage have been attributed to the skin friction factor, whereas rising temperatures have had the opposite effect. Nusselt numbers for volume fraction and radiation are the polar opposite of one another. Nusselt number values are also lower for blowing than they are for suction.

Constraint on the Cosmic Curvature in a Model with the Schwarzschild–de Sitter Metric from Supernovae and Gamma-Ray Burst Observational Data

In developing his cosmological model of 1917, de Sitter theoretically predicted the phenomenon of cosmological redshift (the de Sitter effect), which he did long before the discovery of this phenomenon in observations. The de Sitter effect is gravitational by its nature, as it is due to differences between the coordinate systems of the observer and the distant source. However, the relationship between the redshift and distance derived from the de Sitter metric is at odds with observations, since this relationship is nonlinear (quadratic) for small redshifts, while the observed relationship between the same quantities is strictly linear. This paper discusses the possibility that cosmological redshift is gravitational by its nature, as in de Sitter’s 1917 model. At the same time, here, as in de Sitter’s model, an elliptical space is used, the main characteristic of which is the identification of its antipodal points. But, unlike de Sitter’s model, here, in order to ensure strict linear dependence of the redshift on distance, the origin of the reference system is transferred to the observer’s antipodal point. The Schwarzschild–de Sitter metric used in this model allows you to estimate the curvature of space from observational data. To achieve this, a theoretical Hubble diagram is built within the framework of the model with the Schwarzschild–de Sitter metric, which is compared with observations from the Pantheon+ catalogue of type Ia supernovae and the Amati catalogue of gamma-ray bursts in the redshift range of 0<z<8. As a result of this comparison, we found that the lower estimate of the radius of curvature of space was quite large: 2.4×1015 Mpc. This means that the observational data indicate a negligible curvature of space.

Flipping the script: Action-plan modification during single- and multiple-action control

In this paper, we tested the idea that local changes in action demands (e.g., due to an invalid cue or trial-by-trial) result in frugal modifications of existing action plans via action-plan-modification operations. We implemented an experimental procedure making use of a cue that indicates the action requirements for an upcoming signal with a certain degree of reliability. Crucially, incongruent cue-stimulus pairs either require action-plan modification or “resetting” the prepared action plan and reselecting a new response from scratch. We systematically varied the proportion of valid cues over four experiments. There were four most basic response conditions: left button press, right button press, dual button presses, no action. Results support the concept of action-plan modification rather than reset-reselect: switching between a left and a right response was faster and less error-prone than any other type of switch, both between trials and between cue and signal. Thus, it appears that given two responses that can be conceived of as polar opposites (within the same single-action category), there is an action-plan-modification operation (“invert”) that transforms one into the other at a comparatively low cost. Furthermore, we observed a mixed pattern of dual-action costs and benefits. This indicates that participants represented dual actions holistically, that is, not based on a conjunction of single-action plans as building blocks. In addition, switching from null actions to overt actions appeared to require very similar action-plan-modification operations as other types of switches – thus, null actions are apparently not coded as empty sets, but rather represent actions in their own right. Finally, we observed strikingly similar patterns of results for trial-by-trial changes in action demands and intra-trial cue-signal incongruency. This implies that the mere cue-based formulation of an action plan – which is not actually executed – is sufficient to produce action-switching-like effects.

D. H. Lawrence, T. S. Eliot, and the Meaning of the Mythical Method

Abstract: There is a discrepancy between evidence of T. S. Eliot’s respect for D. H. Lawrence and F. R. Leavis’s account of their diametrical opposition. My goal is to establish and spell out the reasons for Eliot’s ambivalent posture. On the one hand, I argue that both authors tried to reconcile the contradiction between social unity and individual freedom, and they did so by resolving it into more basic concerns with morality, impersonality, and tradition. This parallel explains Eliot’s attraction to Lawrence. On the other hand, I argue that the different way they framed and understood these concerns accounts for his antipathy and, in turn, sheds new light on the mythical method in The Waste Land . When considered alongside Lawrence’s work and Eliot’s judgment of it, the mythical method comes across as no glorification of the past but instead as a critique of the present for repeating it.

Support of the Description and Art. 84 EPC: Why Reactive Amendments to the Description Harm Legal Certainty

Abstract In its granting procedures, the European Patent Office often requests that the patent description conforms to the claims granted. Amendments to the description are regularly motivated to comply with Art. 84 EPC, which requires support of the description. Decisions T 1024/18 and T 1989/18 form two prominent polar opposites of narrow and wide interpretation of the description support criterion according to Art. 84 EPC. T 1024/18 argues that support of the description should not involve a reader being confronted with any information conflicting with the wording of the claims. This means that embodiments of the invention which are not consistent with the claims must therefore be deleted. In this context, additional information of a further non-covered embodiment is regarded as conflicting information. However, any of these reactive amendments can give rise to various legal problems that could even lead to a later revocation of the patent. In contrast, the wide interpretation of T 1989/18 of the description support criterion does not require any post-grant amendments to the description and does not cause these legal problems.

Genie in a Cola Bottle: The Multiple Worlds (and Genres) of G. Willow Wilson's Alif the Unseen (2012)

Abstract: Winner of the 2013 World Fantasy Award for Best Novel, G. Willow Wilson's Alif the Unseen brings some new perspectives into the fantasy genre with its Middle Eastern setting and its basis in Islamic mythologies. It generates additional energies by mixing its fantastic elements with elements from other (very Western) genres (including cyberpunk science fiction and the technothriller). At the same time, it makes extensive use of the motif of parallel worlds, which has long been a staple in fantasy fiction. The parallel worlds of Alif the Unseen are particularly interesting in the way they converge, intersect, and bleed into one another at various points, just as the novel also collapses the boundaries between genres. Ultimately, the collapsing boundaries of Alif the Unseen deconstruct Orientalist polar oppositions between East and West by allowing worlds that might be associated with one or the other to meet and interact as equals within the novel.

The impact of the Hunga Tonga–Hunga Ha’apai volcanic eruption on the Peruvian atmosphere: from the sea surface to the ionosphere

The eruption of the Hunga Tonga Hunga Ha’apai volcano on 15 January 2022 significantly impacted the lower and upper atmosphere globally. Using multi-instrument observations, we described disturbances from the sea surface to the ionosphere associated with atmospheric waves generated by the volcanic eruption. Perturbations were detected in atmospheric pressure, horizontal magnetic field, equatorial electrojet (EEJ), ionospheric plasma drifts, total electron content (TEC), mesospheric and lower thermospheric (MLT) neutral winds, and ionospheric virtual height measured at low magnetic latitudes in the western South American sector (mainly in Peru). The eastward Lamb wave propagation was observed at the Jicamarca Radio Observatory on the day of the eruption at 13:50 UT and on its way back from the antipodal point (westward) on the next day at 07:05 UT. Perturbations in the horizontal component of the magnetic field (indicative of EEJ variations) were detected between 12:00 and 22:00 UT. During the same period, GNSS-TEC measurements of traveling ionospheric disturbances (TIDs) coincided approximately with the arrival time of Lamb and tsunami waves. On the other hand, a large westward variation of MLT winds occurred near 18:00 UT over Peru. However, MLT perturbations due to possible westward waves from the antipode have not been identified. In addition, daytime vertical plasma drifts showed an unusual downward behavior between 12:00 and 16:00 UT, followed by an upward enhancement between 16:00 and 19:00 UT. Untypical daytime eastward zonal plasma drifts were observed when westward drifts were expected. Variations in the EEJ are highly correlated with perturbations in the vertical plasma drift exhibiting a counter-equatorial electrojet (CEEJ) between 12:00 and 16:00 UT. These observations of plasma drifts and EEJ are, so far, the only ground-based radar measurements of these parameters in the western South American region after the eruption. We attributed the ion drift and EEJ perturbations to large-scale thermospheric wind variations produced by the eruption, which altered the dynamo electric field in the Hall and Pedersen regions. These types of multiple and simultaneous observations can contribute to advancing our understanding of the ionospheric processes associated with natural hazard events and the interaction with lower atmospheric layers.Graphical

Scalar Curvature Rigidity of Warped Product Metrics

We show scalar-mean curvature rigidity of warped products of round spheres of dimension at least 2 over compact intervals equipped with strictly log-concave warping functions. This generalizes earlier results of Cecchini-Zeidler to all dimensions. Moreover, we show scalar curvature rigidity of round spheres of dimension at least 3 with two antipodal points removed. This resolves a problem in Gromov's ''Four Lectures'' in all dimensions. Our arguments are based on spin geometry.

Interactions and Interferences of Italian and German Nationalist Regimes in Asia during the Interwar Period (1928–1937)

This article presents a comprehensive narration and interpretation of the political relations between nationalist regimes in Asia and Europe during the interwar history from 1928 to 1937. Authoritarian regimes with political affinities and similar autarchic economic strategies created the ground for an unprecedented collaboration among governments situated on the opposite side of the world. China, Italy, Germany had a prolonged political, military and economic dialogue which lasted for almost a decade and involved the active mediation of political leaders, scholars and highly professional military officers. The interaction with Japan disrupted that partnership and finally changed the perspectives of the strategic alliance. Ultimately, affinities and disagreements among these governments were relevant in leading the world into the abyss of the Second World War. The preparation of this article is supported by primary sources consulted at diplomatic and historical archives and historical literature written in three languages (English, German, and Italian).

A characterization of the Euclidean ball via antipodal points

A characterization of the Euclidean ball via antipodal points

Cucker–Smale type flocking models on a sphere

Cucker–Smale type flocking models on a sphere

Zur Funktion der „kleinen“ Rache in Prozessen moralischer Wiederherstellung – Warum Verzeihen und Rache nicht immer Gegensätze sind

ZusammenfassungAusgehend von der Beobachtung, dass die Rache heute von der Philosophie entweder ganz ignoriert oder mit ihren exzessiv gewalttätigen Formen gleichgesetzt und moralisch verurteilt wird, möchte der Beitrag ein differenzierteres Bild der Rache skizzieren. Dabei wird auch die Vorstellung kritisiert, Rache und Verzeihen seien in der sozialen Realität einander ausschließende Gegensätze. Im ersten Teil wende ich mich, ausgehend von verschiedenen neueren philosophischen Arbeiten, gegen ein essentialistisches und idealisiertes Verständnis des Verzeihens. Ich plädiere dafür, bei der Bewertung von Verzeihen und Rache auch ihre jeweilige Rolle mit Blick auf die Aufrechterhaltung oder Ausgleichung ungleicher Machtverhältnisse und ihre Funktion für die Selbstermächtigung von Opfern von Übergriffen und die Wiederherstellung ihrer Selbstachtung zu berücksichtigen. Im letzten Teil zeige ich an drei Beispielen, dass ein Prozess der moralischen Reparatur nicht selten kleine Racheelemente integrieren muss, um das Verzeihen zu ermöglichen.

Elliptical Space with the McVittie Metrics

The main feature of elliptical space—the topological identification of its antipodal points—could be fundamental for understanding the nature of the cosmological redshift. The physical interpretation of the mathematical (topological) structure of elliptical space is made by using physical connections in the form of Einstein-Rosen bridges (also called “wormholes”). The Schwarzschild metric of these structures embedded into a dynamic (expanding) spacetime corresponds to McVittie’s solution of Einstein’s field equations. The cosmological redshift of spectral lines of remote sources in this metric is a combination of gravitational redshift and the time-dependent scale factor of the Friedmann-Lemaitre-Robertson-Walker metric. I compare calculated distance moduli of type-Ia supernovae, which are commonly regarded as “standard candles” in cosmology, with the observational data published in the catalogue “Pantheon+”. The constraint based on these accurate data gives a much smaller expansion rate of the Universe than is currently assumed by modern cosmology, the major part of the cosmological redshift being gravitational by its nature. The estimated age of the Universe within the discussed model is 1.48·1012 yr, which is more than two orders of magnitude larger than the age assumed by using the standard cosmological model parameters.