Intrinsic Notion Research Articles

Long-lived heavy neutral leptons at lepton colliders as a probe of left-right-symmetric models

Left-right symmetric models (LRSM) were proposed to reconcile the apparent parity violation in weak interactions with our intrinsic notion of fundamental parity symmetry. It was quickly realized that LRSM offers a viable framework for explaining neutrino masses by incorporating right-handed neutrinos, N, into its spectrum. In this study, we investigate for the first time the potential of future lepton colliders (including the FCC-ee, CEPC, ILC, CLIC, and a muon collider) to detect signals stemming from N’s, focusing primarily on displaced vertex signals, and on prompt signals to a lesser degree. Our results demonstrate that these signals can effectively probe the characteristic scales of LRSM, providing evidence that would be unobtainable through any other experimental means. Published by the American Physical Society 2024

Positive Definite Kernels for Partitions

This paper presents a comprehensive exploration of various families of positive definite kernels for comparing partitions. It not only reviews existing examples from the literature but also introduces novel classes of positive definite kernels. These new classes include kernels based on agreement and ones designed using the concept of hidden variables. The study also focuses on assessing the compatibility of these kernels with structural properties that capture the intrinsic notion of proximity between partitions. Notably, agreement-based kernels are demonstrated to align well with this notion. Moreover, the paper provides two generic procedures for designing hidden-feature-based kernels that also adhere to the specified structural properties.

Towards regenerative business models: A necessary shift?

Regeneration has become a debated topic in organizational studies, yet its characteristics and distinctions from sustainability and circular business models remain unclear. This study aims to provide an initial framework for regenerative business models and differentiate them from sustainable or circular models. Employing literature reviews, six focus groups with international and indigenous participants, and comparisons with seminal articles on sustainable and circular models, this study finds that organizations with regenerative business models focus on planetary health and societal wellbeing. They create and deliver value at multiple stakeholder levels—including nature, societies, customers, suppliers and partners, shareholders and investors, and employees—through activities promoting regenerative leadership, co-creative partnerships with nature, and justice and fairness. Capturing value through multi-capital accounting, they aim for a net positive impact across all stakeholder levels. Regenerative business models share some design approaches with sustainable and circular models but differ in their main goals and systemic perspectives. Achieving regenerative business models requires strong and contested policy frameworks, including animal and nature rights and true pricing. Further research is needed to explore how organizations can incorporate intrinsic notions of value beyond capital and avoid new forms of greenwashing when adopting regeneration and net positive impact narratives.

Symmetry of intrinsically singular solutions of double phase problems

We continue the study of positive singular solutions of PDEs arising from double phase functionals started in [6]. In particular, we consider the case $p < q < 2$, and we relax the assumption on the capacity of the singular set using an intrinsic notion of capacity.

Hairer-Quastel universality in non-stationarity via energy solution theory

The paper addresses probabilistic aspects of the KPZ equation and stochastic Burgers equation by providing a solution theory that builds on the energy solution theory [15, 19, 20, 23]. The perspective we adopt is to study the stochastic Burgers equation by writing its solution as a probabilistic solution [22] plus a term that can be studied with deterministic PDE considerations. One motivation is universality of KPZ and stochastic Burgers equations for a certain class of stochastic PDE growth models, first studied in [28]. For this, we prove universality for SPDEs with general nonlinearities, thereby extending [28, 29], and for many non-stationary initial data, thereby extending [21]. Our perspective lets us also prove explicit rates of convergence to white noise invariant measure of stochastic Burgers for non-stationary initial data, in particular extending the spectral gap result of [23] beyond stationary initial data, though for non-stationary data our convergence will be measured in Wasserstein distance and relative entropy, not via the spectral gap as in [23]. Actually, we extend the spectral gap in [23] to a log-Sobolev inequality. Our methods can also analyze fractional stochastic Burgers equations [23]; we discuss this briefly. Lastly, we note our perspective on the KPZ and stochastic Burgers equations gives a first intrinsic notion of solutions for general continuous initial data, in contrast to Hölder regular data needed for regularity structures [26], paracontrolled distributions [14], and Hölder-regular Brownian bridge data for energy solutions [19, 20].

Indicators of Higher Education and the Public Good in Africa: A Dashboard Approach

Indicators and metrics have gained increasing prominence in international higher education in recent years, and global rankings have become a powerful force in shaping ideas of what the university is and should be. Yet these measures do a poor job of capturing the broad role of the institution, and particularly in recognising its actions in promoting the public good and addressing inequalities. African higher education institutions have struggled to perform well in the conventional rankings, whose indicators rely on extensive resources for high-level research. This article explores the possibilities of alternative metrics for understanding the public good contribution of universities in the context of four African countries: Ghana, Kenya, Nigeria and South Africa. After assessing the shortcomings of the existing indicators and metrics, and the challenges of the availability of data, it puts forward a dashboard approach as a possible new model. Dashboards have the advantage of avoiding the conflation of diverse qualities of importance and allow different profiles of an institution to be compared. The article proposes six main elements for the dashboard: solidarity with society, equitable access and deliberative space (which correspond to the intrinsic notion of public good and graduate destinations, knowledge production and community engagement (which correspond to instrumental notions). Finally, the challenges of implementing public good metrics in practice are discussed.

On the numerical computation of Fisher–Rao based distances and KL-divergences between Gaussian random fields

Random fields are among the mathematical models used in the study of non-deterministic and non-linear complex systems. A fundamental aspect in the characterization of such models is to define intrinsic properties and to understand how these measures change over time. In this paper, we propose an information-geometric framework to analyze Gaussian–Markov random fields (GMRF’s) by the definition of a Fisher information based space. With this approach, it is possible to measure the variations in each component of the metric tensor that equips the underlying parametric space, when visiting different entropic states. Using Markov Chain Monte Carlo simulations, we propose a method based on infinitesimal displacements to compute distances between two systems operating in different regimes using the Fisher metric. Moreover, we derive an expression for the KL-divergence (relative entropy) between two GMRF models, showing that, it symmetrized version works reasonably well as a replacement for the Fisher information based distance. Finally, information cycles that relate components of the metric tensor and the system’s entropy reveal an asymmetric pattern of evolution when the system moves towards different entropic states, indicating that the simple interaction between several Gaussian random variables can lead to the emergence of an intrinsic notion of time in the evolution of a random field, based in the geometric properties of its parametric space.

Intrinsic holonomy and curved cosets of Cartan geometries

We provide an intrinsic notion of curved cosets for arbitrary Cartan geometries, simplifying the existing construction of curved orbits for a given holonomy reduction. To do this, we intrinsically define a holonomy group, which is shown to coincide precisely with the standard definition of the holonomy group for Cartan geometries in terms of an associated principal connection. These curved cosets retain many characteristics of their homogeneous counterparts, and they behave well under the action of automorphisms. We conclude the paper by using the machinery developed to generalize the de Rham decomposition theorem for Riemannian manifolds and give a potentially useful characterization of inessential automorphism groups for parabolic geometries.

Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces

In vector optimization, it is of increasing interest to study problems where the image space (a real linear space) is preordered by a not necessarily solid (and not necessarily pointed) convex cone. It is well-known that there are many examples where the ordering cone of the image space has an empty (topological/algebraic) interior, for instance in optimal control, approximation theory, duality theory. Our aim is to consider Pareto-type solution concepts for such vector optimization problems based on the intrinsic core notion (a well-known generalized interiority notion). We propose a new Henig-type proper efficiency concept based on generalized dilating cones which are relatively solid (i.e., their intrinsic cores are nonempty). Using linear functionals from the dual cone of the ordering cone, we are able to characterize the sets of (weakly, properly) efficient solutions under certain generalized convexity assumptions. Toward this end, we employ separation theorems that are working in the considered setting.

The young child’s journey of ‘the will’: A synthesis of child-centered and inclusive principles in international Waldorf early childhood education

Within the education academic arena, there is almost no established research on the alternative Waldorf (or Steiner) education movement in the US or UK. This primary research investigates Rudolf Steiner’s philosophy of early childhood Waldorf education, and its child-centered and inclusive core. Ten kindergarten teachers in the US and UK educating children ages three through seven were interviewed on their values and practices, and on intrinsic notions of inclusion, which are scrutinized according to Lani Florian's inclusive pedagogy. Contrasting interpretation among practitioners on educating diverse learners emerge. US and UK Waldorf education appear situationally different, and yet the underlying educational ethos fundamentally remains the same. An anthroposophical understanding of the human being, and ‘the will’ of the kindergarten child who learns through imitation and play, underlies this far-sighted, holistic basis. Recommendation is for Waldorf early childhood studies to enhance transnational networks among themselves, and to make connections with broader academic educational clusters, in particular those on inclusion.

Not All Structure and Dynamics Are Equal.

The hard problem of consciousness has been a perennially vexing issue for the study of consciousness, particularly in giving a scientific and naturalized account of phenomenal experience. At the heart of the hard problem is an often-overlooked argument, which is at the core of the hard problem, and that is the structure and dynamics (S&D) argument. In this essay, I will argue that we have good reason to suspect that the S&D argument given by David Chalmers rests on a limited conception of S&D properties, what in this essay I’m calling extrinsic structure and dynamics. I argue that if we take recent insights from the complexity sciences and from recent developments in Integrated Information Theory (IIT) of Consciousness, that we get a more nuanced picture of S&D, specifically, a class of properties I’m calling intrinsic structure and dynamics. This I think opens the door to a broader class of properties with which we might naturally and scientifically explain phenomenal experience, as well as the relationship between syntactic, semantic, and intrinsic notions of information. I argue that Chalmers’ characterization of structure and dynamics in his S&D argument paints them with too broad a brush and fails to account for important nuances, especially when considering accounting for a system’s intrinsic properties. Ultimately, my hope is to vindicate a certain species of explanation from the S&D argument, and by extension dissolve the hard problem of consciousness at its core, by showing that not all structure and dynamics are equal.

Renormalization Group Approach to the Continuum Limit of Matrix Models of Quantum Gravity With Preferred Foliation

This contribution is not intended as a review but, by suggestion of the editors, as a glimpse ahead into the realm of dually weighted tensor models for quantum gravity. This class of models allows one to consider a wider class of quantum gravity models, in particular one can formulate state sum models of spacetime with an intrinsic notion of foliation. The simplest one of these models is the one proposed by Benedetti and Henson [1], which is a matrix model formulation of two-dimensional Causal Dynamical Triangulations (CDT). In this paper we apply the Functional Renormalization Group Equation (FRGE) to the Benedetti-Henson model with the purpose of investigating the possible continuum limits of this class of models. Possible continuum limits appear in this FRGE approach as fixed points of the renormalization group flow where the size of the matrix acts as the renormalization scale. Considering very small truncations, we find fixed points that are compatible with analytically known results for CDT in two dimensions. By studying the scheme dependence of our results we find that precision results require larger truncations than the ones considered in the present work. We conclude that our work suggests that the FRGE is a useful exploratory tool for dually weighted matrix models. We thus expect that the FRGE will be a useful exploratory tool for the investigation of dually weighted tensor models for CDT in higher dimensions.

On a rough perturbation of the Navier–Stokes system and its vorticity formulation

We introduce a rough perturbation of the Navier–Stokes system and justify its physical relevance from balance of momentum and conservation of circulation in the inviscid limit. We present a framework for a well-posedness analysis of the system. In particular, we define an intrinsic notion of strong solution based on ideas from the rough path theory and study the system in an equivalent vorticity formulation. In two space dimensions, we prove that well-posedness and enstrophy balance holds. Moreover, we derive rough path continuity of the equation, which yields a Wong–Zakai result for Brownian driving paths, and show that for a large class of driving signals, the system generates a continuous random dynamical system. In dimension three, the noise is not enstrophy balanced, and we establish the existence of local in time solutions.

Intrinsic diophantine approximation in Carnot groups and in the Siegel model of the Heisenberg group

We study an intrinsic notion of Diophantine approximation on a rational Carnot group G. If G has Hausdorff dimension Q, we show that its Diophantine exponent is equal to $$(Q+1)/Q$$, generalizing the case $$G=\mathbb {R}^n$$. We furthermore obtain a precise asymptotic on the count of rational approximations. We then focus on the case of the Heisenberg group $$\mathbf {H}^n$$, distinguishing between two notions of Diophantine approximation by rational points in $$\mathbf {H}^n$$: Carnot Diophantine approximation and Siegel Diophantine approximation. We provide a direct proof that the Siegel Diophantine exponent of $$\mathbf {H}^1$$ is equal to 1, confirming the general result of Hersonsky-Paulin, and then provide a link between Siegel Diophantine approximation, Heisenberg continued fractions, and geodesics in the Picard modular surface. We conclude by showing that Carnot and Siegel approximation are qualitatively different: Siegel-badly approximable points are Schmidt winning in any complete Ahlfors regular subset of $$\mathbf {H}^n$$, while the set of Carnot-badly approximable points does not have this property.

On uniform measures in the Heisenberg group

We study uniform measures in the first Heisenberg group H equipped with the Korányi metric dH. We prove that 1-uniform measures are proportional to the spherical 1-Hausdorff measure restricted to an affine horizontal line, while 2-uniform measures are proportional to spherical 2-Hausdorff measure restricted to an affine vertical line. We also show that each 3-uniform measure which is supported on a vertically ruled surface is proportional to the restriction of spherical 3-Hausdorff measure to an affine vertical plane, and that no quadratic x3-graph can be the support of a 3-uniform measure. According to a result of Merlo, every 3-uniform measure is supported on a quadratic variety; in conjunction with our results, this shows that all 3-uniform measures are proportional to spherical 3-Hausdorff measure restricted to an affine vertical plane. We establish our conclusions by deriving asymptotic formulas for the measures of small extrinsic balls in (H,dH) intersected with smooth submanifolds. The coefficients in our power series expansions involve intrinsic notions of curvature associated to smooth curves and surfaces in H.

Persistent homology for low-complexity models

We show that recent results on randomized dimension reduction schemes that exploit structural properties of data can be applied in the context of persistent homology. In the spirit of compressed sensing, the dimension reduction is determined by the Gaussian width of a structure associated with the dataset, rather than its size, and such a reduction can be computed efficiently. We further relate the Gaussian width to the doubling dimension of a finite metric space, which appears in the study of the complexity of other methods for approximating persistent homology. We can, therefore, literally replace the ambient dimension by an intrinsic notion of dimension related to the structure of the data.

How algorithmic popularity bias hinders or promotes quality

Algorithms that favor popular items are used to help us select among many choices, from top-ranked search engine results to highly-cited scientific papers. The goal of these algorithms is to identify high-quality items such as reliable news, credible information sources, and important discoveries–in short, high-quality content should rank at the top. Prior work has shown that choosing what is popular may amplify random fluctuations and lead to sub-optimal rankings. Nonetheless, it is often assumed that recommending what is popular will help high-quality content “bubble up” in practice. Here we identify the conditions in which popularity may be a viable proxy for quality content by studying a simple model of a cultural market endowed with an intrinsic notion of quality. A parameter representing the cognitive cost of exploration controls the trade-off between quality and popularity. Below and above a critical exploration cost, popularity bias is more likely to hinder quality. But we find a narrow intermediate regime of user attention where an optimal balance exists: choosing what is popular can help promote high-quality items to the top. These findings clarify the effects of algorithmic popularity bias on quality outcomes, and may inform the design of more principled mechanisms for techno-social cultural markets.

On Γ-TS-Acts Over Ternary Γ-Semigroups

We generalise the notion of acts over ternary semigroups to the Γ-TS-acts for a ternary Γ-semigroup T. Certain intrinsic notions of Γ-TS-acts are studied.

On the Navier–Stokes equation perturbed by rough transport noise

We consider the Navier–Stokes system in two and three space dimensions perturbed by transport noise and subject to periodic boundary conditions. The noise arises from perturbing the advecting velocity field by space–time-dependent noise that is smooth in space and rough in time. We study the system within the framework of rough path theory and, in particular, the recently developed theory of unbounded rough drivers. We introduce an intrinsic notion of a weak solution of the Navier–Stokes system, establish suitable a priori estimates and prove existence. In two dimensions, we prove that the solution is unique and stable with respect to the driving noise.

Augustine on Creation, Providence and Motion

AbstractAugustine's theology of creation has been criticized for its Platonic tendency to denigrate matter and for a supposedly extrinsic view of divine providence that is reminiscent of design and even deism. This article counters such criticism and argues that Augustine explicitly blends extrinsic and intrinsic notions of providential teleological order. For Augustine, God ‘administers externally the natures he has created internally’ by inscribing the rationes seminales within creatures and conferring motion through the mediation of measure, number and weight. By resisting a dualism of intrinsic and extrinsic teleological order, Augustine avoids many of the problems that characterize modern theologies of creation and provides a more coherent account of divine providence.