Canonical Scaling Research Articles

Quantum field theories of relativistic Luttinger fermions

We propose relativistic Luttinger fermions as a new ingredient for the construction of fundamental quantum field theories. We construct the corresponding Clifford algebra and the spin metric for relativistic invariance of the action using the spin-base invariant formalism. The corresponding minimal spinor has 32 complex components, matching with the degrees of freedom of a standard-model generation including a right-handed neutrino. The resulting fermion fields exhibit a canonical scaling different from Dirac fermions and thus support the construction of novel relativistic and perturbatively renormalizable, interacting quantum field theories. In particular, new asymptotically free self-interacting field theories can be constructed, representing first examples of high-energy complete quantum field theories based on pure matter degrees of freedom. Gauge theories with relativistic Luttinger fermions exhibit a strong paramagnetic dominance, requiring large non-Abelian gauge groups to maintain asymptotic freedom. We comment on the possibility to use Luttinger fermions for particle physics model building and the expected naturalness properties of such models. Published by the American Physical Society 2024

Triaxial Schwarzschild models of NGC 708: a 10-billion solar mass black hole in a low-dispersion galaxy with a Kroupa IMF

ABSTRACT We report the discovery of a (1.0 ± 0.28) × 1010 M⊙ supermassive black hole (BH) at the centre of NGC 708, the Brightest Cluster Galaxy of Abell 262. Such high BH masses are very rare and allow to investigate BH–host galaxy scaling relations at the high mass end, which in turn provide hints about the (co)evolution of such systems. NGC 708 is found to be an outlier in all the canonical scaling relations except for those linking the BH mass to the core properties. The galaxy mass-to-light ratio points to a Kroupa IMF rather than Salpeter, with this finding confirmed using photometry in two different bands. We perform this analysis using our novel triaxial Schwarzschild code to integrate orbits in a five-dimensional space, using a semiparametric deprojected light density to build the potential and non-parametric line-of-sight velocity distributions (LOSVDs) derived from long-slit spectra recently acquired at Large Binocular Telescope (LBT) to exploit the full information in the kinematic. We find that the galaxy geometry changes as a function of the radius going from prolate, nearly spherical in the central regions to triaxial at large radii, highlighting the need to go beyond constant shape profiles. Our analysis is only the second of its kind and will systematically be used in the future to hunt supermassive BH in giant ellipticals.

A Causality-Driven Graph Convolutional Network for Postural Abnormality Diagnosis in Parkinsonians.

Abnormal posture is a common movement disorder in the progress of Parkinson's disease (PD), and this abnormality can increase the risk of falls or even disabilities. The conventional assessment approach depends on the judgment of well-trained experts via canonical scales. However, this approach requires extensive clinical expertise and is highly subjective. Considering the potential of quantitative susceptibility mapping (QSM) in PD diagnosis, this study explored the QSM-based method for the automated classification between PD patients with and without postural abnormalities. Nevertheless, a major challenge is that unstable non-causal features typically lead to less reliable performance. Therefore, we propose a causality-driven graph-convolutional-network framework based on multi-instance learning, where performance stability is enhanced through the invariant prediction principle and causal interventions. Specifically, we adopt an intervention strategy that combines a non-causal intervenor with causal prediction. A stability constraint is proposed to ensure robust integrated prediction under different interventions. Moreover, an intra-class homogeneity constraint is enforced for each individually-learned causality scoring module to promote the extraction of group-level general features, and hence achieve a balance between subject-specific and group-level features. The proposed method demonstrated promising performance through extensive experiments on a real clinical dataset. Also, the features extracted by our method coincide with those reported in previous medical studies on PD posture abnormalities. In general, our work provides a clinically-valuable approach for automated, objective, and reliable diagnosis of postural abnormalities in Parkinsonians. Our source code is publicly available at https://github.com/SJTUBME-QianLab/CausalGCN-PDPA.

Effects of Bubble Plumes on Lake Dynamics, Near‐Bottom Turbulence, and Transfer of Dissolved Oxygen at the Sediment‐Water Interface

AbstractWe quantify the lake dynamics, near‐bottom turbulence, flux of dissolved oxygen (DO) across the sediment‐water interface (SWI) and their interactions during oxygenation in two lakes. Field observations show that the lake dynamics were modified by the bubble plumes, showing enhanced mixing in the near‐field of the plumes. The interaction of the bubble‐induced flow with the internal density structure resulted in downwelling of warm water into the hypolimnion in the far‐field of the plumes. Within the bottom boundary layer (BBL), both lakes show weak oscillating flows primarily induced by seiching. The vertical profile of mean velocity within 0.4 m above the bed follows a logarithmic scaling. One lake shows a larger drag coefficient than those in stationary BBLs, where the classic law‐of‐the‐wall is valid. The injection of oxygen elevated the water column DO and hence, altered the DO flux across the SWI. The gas transfer velocity is driven by turbulence and is correlated with the bottom shear velocity. The thickness of the diffusive boundary layer was found to be consistent with the Batchelor length scale. The dynamics of the surface renewal time follow a log‐normal distribution, and the turbulent integral time scale is comparable to the surface renewal time. The analyses suggest that the effect of bubble plumes on the BBL turbulence is limited and that the canonical scales of turbulence emerge for the time‐average statistics, validating the turbulence scaling of gas transfer velocity in low‐energy lakes.

ВЗАИМОДЕЙСТВИЯ НЕЛИНЕЙНЫХ ГЕОМЕХАНИЧЕСКИХ И ГАЗООБМЕННЫХ ПРОЦЕССОВ ПРИ ОТРАБОТКЕ МЕСТОРОЖДЕНИЙ УГЛЕВОДОРОДНОГО РЯДА

In the canonical scale of hierarchical representations V.N. Oparin was first introduced and successfully verified by A.S. Tanaino is a generalized indicator of a quantitative description of the petrographic properties of coals, using which a classification is given and the distribution of petrographic groups of coal seams in the Kuzbass regions is described. This is important not only for mapping sections of mine fields when identifying potentially hazardous zones for emissions of coal, rocks and gas, but also for geotechnological zoning based on the most important physical and chemical properties of the productive properties of the rock massifs being mined.

Stochastic theory of gravitational relaxation and Lévy-fractional Klein-Kramers equation

This paper reports a stochastic theory of gravitational relaxation based on a Lévy-fractional Klein-Kramers equation with self-consistent entropy term. The use of fractional derivatives in this equation is motivated by nonequilibrium phase-space dynamics breaking the restrictive assumptions of Gaussianity, lack of correlation and nearness to virialized state. Astrophysical applications of the theory concern gravitational evolution of galaxy clusters with non-minimally coupled cold dark matter. One hard result pertaining to the statistical model is that position correlations between galaxies are attracted by the power law r −7/4, which approximates the canonical scaling r −1.8 found in observations. The kinetic description, considered in this paper's work, is compatible with an idea that the relaxation of galaxy clusters to virialized state could be collisionless and mediated by hypothetical “dark waves,” collective excitations of the coupled baryonic-dark matter system driven by the variation of local curvature on suitably small spatial scales.

On transition density functions of skew Brownian motions with two-valued drift

In this article, based on the results in Gairat and Shcherbakov (2017), we derive two-sided bounds for the full family of transition density functions of skew Brownian motion (SBM in abbreviation) with two-valued drift for all t>0. As an important step of this result, it is also shown in this paper that SBM with two-valued drift is a strong Markov process by finding its symmetrizing measure and canonical scale function, from which one can tell what values of the drift make such a process transient or recurrent.

Canonical scale separation in two-dimensional incompressible hydrodynamics

The rules that govern a two-dimensional inviscid incompressible fluid are simple. Yet, to characterise the long-time behaviour is a knotty problem. The fluid fulfils Euler's equations: a nonlinear Hamiltonian system with an infinite number of conservation laws. In both experiments and numerical simulations, coherent vortex structures emerge after an initial stage. These formations dominate the large-scale dynamics, but small scales also emerge and persist. The resulting scale separation resembles Kraichnan's theory of forward and backward cascades of enstrophy and energy. Previous attempts to model the double cascade use filtering techniques that enforce separation from the outset. Here, we show that Euler's equations possess an intrinsic, canonical splitting of the vorticity function. The splitting is remarkable in four ways: (i) it is defined solely by the Poisson bracket and the Hamiltonian; (ii) it characterises steady flows; (iii) it innately separates scales, enabling the dynamics behind Kraichnan's qualitative description; and (iv) it accounts for ‘broken line’ energy spectra observed in both experiments and numerical simulations. The splitting originates from Zeitlin's truncated model of Euler's equations in combination with a standard quantum tool: the spectral decomposition of Hermitian matrices. In addition to theoretical insight, the scale separation dynamics enables stochastic model reduction, where multiplicative noise models small scales.

Are there ALPs in the asymptotically safe landscape?

We investigate axion-like particles (ALPs) in the context of asymptotically safe gravity-matter systems. The ALP-photon interaction, which facilitates experimental searches for ALPs, is a dimension-5-operator. Quantum fluctuations of gravity lower its scaling dimension, and the ALP-photon coupling can become asymptotically free or even asymptotically safe. However, quantum fluctuations of gravity need to be strong to overcome the canonical scaling and this strong-gravity regime is in tension with the weak-gravity bound in asymptotic safety. Thus, we tentatively conclude that fundamental ALPs can likely not be accommodated in asymptotically safe gravity-matter systems. In turn, an experimental discovery of an ALP would thus shed valuable light on the quantum nature of gravity.

Hausdorff dimensions for shared endpoints of disjoint geodesics in the directed landscape

Within the Kardar–Parisi–Zhang universality class, the space-time Airy sheet is conjectured to be the canonical scaling limit for last passage percolation models. In recent work [27] of Dauvergne, Ortmann, and Virág, this object was constructed and, upon a parabolic correction, shown to be the limit of one such model: Brownian last passage percolation. The limit object without parabolic correction, called the directed landscape, admits geodesic paths between any two space-time points (x,s) and (y,t) with s<t. In this article, we examine fractal properties of the set of these paths. Our main results concern exceptional endpoints admitting disjoint geodesics. First, we fix two distinct starting locations x1 and x2, and consider geodesics traveling (x1,0)→(y,1) and (x2,0)→(y,1). We prove that the set of y∈R for which these geodesics coalesce only at time 1 has Hausdorff dimension one-half. Second, we consider endpoints (x,0) and (y,1) between which there exist two geodesics intersecting only at times 0 and 1. We prove that the set of such (x,y)∈R2 also has Hausdorff dimension one-half. The proofs require several inputs of independent interest, including (i) connections to the so-called difference weight profile studied in [10]; and (ii) a tail estimate on the number of disjoint geodesics starting and ending in small intervals. The latter result extends the analogous estimate proved for the prelimiting model in [40].

Canonical Grading Scales of Corneal and Conjunctival Staining Based on Psychophysical and Physical Attributes.

PurposeIn this study, we apply psychophysical scaling principles based on physical (photometric) attributes of images to better understand the factors involved in clinician judgement of ocular surface staining and, using that knowledge, to develop photographic scales for the assessment of staining for dry eye (DE) and related conditions.MethodsSubjects with noninfectious ocular surface staining were enrolled at five clinical sites. Following instillation of fluorescein, photographs of corneal staining were taken every 30 seconds for at least 5 minutes. The same procedure was followed for conjunctival staining after instillation of 2 µl of 1% lissamine green. A subset of the best corneal and bulbar conjunctival staining images were anonymized and a spectroradiometer measured photometric attributes (luminance and chromaticity). The images were scaled psychophysically by study investigators, who participated in constructing grading scales based on physical and psychophysical analyses. The final grading scales were refined following consultation with outside DE experts.ResultsPhotographs were collected from 142 subjects (81% women), with an average age of 58 ± 17 years; 89% were diagnosed with DE. There was a monotonic relationship between between physical measurements and psychophysically scaled staining of both corneal (fluorescein) and bulbar (lissamine green) staining. Michelson contrast and u’ (chromaticity) accounted for 66% and 64% of the variability in the psychophysically scaled images of fluorescein corneal and lissamine green conjunctival staining, respectively.Translational RelevanceThis paper provides examples of the first ever clinically usable ocular surface staining scales validated using psychophysical scaling and the physical attributes (luminance and chromaticity) of the staining itself. In addition, it provides a generalizable method for the development of other clinical scales of ocular appearance.

Estimating Dissipation Rates Associated With Double Diffusion

AbstractDouble diffusion refers to a variety of turbulent processes in which potential energy is released into kinetic energy, made possible in the ocean by the difference in molecular diffusivities between salinity and temperature. Here, we present a new method for estimating the kinetic energy dissipation rates forced by double‐diffusive convection using temperature and salinity data alone. The method estimates the up‐gradient diapycnal buoyancy flux associated with double diffusion, which is hypothesized to balance the dissipation rate. To calculate the temperature and salinity gradients on small scales we apply a canonical scaling for compensated thermohaline variance (or ‘spice’) on sub‐measurement scales with a fixed buoyancy gradient. Our predicted dissipation rates compare favorably with microstructure measurements collected in the Chukchi Sea. Fine et al. (2018), https://doi.org/10.1175/jpo-d-18-0028.1, showed that dissipation rates provide good estimates for heat fluxes in this region. Finally, we show the method maintains predictive skill when applied to a sub‐sampling of the Conductivity, Temperature, Depth (CTD) data.

Canonical tensor scaling

In this paper we generalize the canonical positive scaling of rows and columns of a matrix to the scaling of selected-rank subtensors of an arbitrary tensor. We expect our results and framework will prove useful for sparse-tensor completion required for generalizations of the recommender system problem beyond a matrix of user-product ratings to multidimensional arrays involving coordinates based both on user attributes (e.g., age, gender, geographical location, etc.) and product/item attributes (e.g., price, size, weight, etc.).

Full-frequency GW without frequency.

Efficient computer implementations of the GW approximation must approximate a numerically challenging frequency integral; the integral can be performed analytically, but doing so leads to an expensive implementation whose computational cost scales as O(N6), where N is the size of the system. Here, we introduce a new formulation of the full-frequency GW approximation by exactly recasting it as an eigenvalue problem in an expanded space. This new formulation (1) avoids the use of time or frequency grids, (2) naturally obviates the need for the common "diagonal" approximation, (3) enables common iterative eigensolvers that reduce the canonical scaling to O(N5), and (4) enables a density-fitted implementation that reduces the scaling to O(N4). We numerically verify these scaling behaviors and test a variety of approximations that are motivated by this new formulation. The new formulation is found to be competitive with conventional O(N4) methods based on analytic continuation or contour deformation. In this new formulation, the relation of the GW approximation to configuration interaction, coupled-cluster theory, and the algebraic diagrammatic construction is made especially apparent, providing a new direction for improvements to the GW approximation.

Two-Speed Solutions to Non-convex Rate-Independent Systems

We consider evolutionary PDE inclusions of the form $$\begin{aligned} -\lambda {\dot{u}}_\lambda + \Delta u - \mathrm {D}W_0(u) + f \ni \partial \mathscr {R}_1({\dot{u}}) \quad \text {in}\,\,{ (0,T) \times \Omega ,} \end{aligned}$$ where $$\mathscr {R}_1$$ is a positively 1-homogeneous rate-independent dissipation potential and $$W_0$$ is a (generally) non-convex energy density. This work constructs solutions to the above system in the slow-loading limit $$\lambda \downarrow 0$$ . Our solutions have more regularity both in space and time than those that have been obtained with other approaches. On the “slow” time scale we see strong solutions to a purely rate-independent evolution. Over the jumps, we obtain a detailed description of the behavior of the solution and we resolve the jump transients at a “fast” time scale, where the original rate-dependent evolution is still visible. Crucially, every jump transient splits into a (possibly countable) number of rate-dependent evolutions, for which the energy dissipation can be explicitly computed. This, in particular, yields a global energy equality for the whole evolution process. It also turns out that there is a canonical slow time scale that avoids intermediate-scale effects, where movement occurs in a mixed rate-dependent/rate-independent way. In this way, we obtain precise information on the impact of the approximation on the constructed solution. Our results are illustrated by examples, which elucidate the effects that can occur.

Small cap decouplings

We develop a toolbox for proving decouplings into boxes with diameter smaller than the canonical scale. As an application of this new technique, we solve three problems for which earlier methods have failed. We start by verifying the small cap decoupling for the parabola. Then we find sharp estimates for exponential sums with small frequency separation on the moment curve in $$\mathbb {R}^3$$ . This part of the work relies on recent improved Kakeya-type estimates for planar tubes, as well as on new multilinear incidence bounds for plates and planks. We also combine our method with the recent advance on the reverse square function estimate, in order to prove small cap decoupling into square-like caps for the two dimensional cone. The Appendix by Roger Heath-Brown contains an application of the new exponential sum estimates for the moment curve, to the Riemann zeta-function.

Abelian-Higgs cosmic string evolution with CUDA

Topological defects form at cosmological phase transitions by the Kibble mechanism, with cosmic strings—one-dimensional defects—being the most studied example. A rigorous analysis of their astrophysical consequences is limited by the availability of accurate numerical simulations, and therefore by hardware resources and computation time. Improving the speed and efficiency of existing codes is therefore important. All current cosmic string simulations were performed on Central Processing Units. In previous work we presented a General Purpose Graphics Processing Unit implementation of the evolution of cosmological domain wall networks. Here we discuss an analogous implementation for local Abelian-Higgs string networks. We discuss the implementation algorithm (including the discretisation used and how to calculate network averaged quantities) and then showcase its performance and current bottlenecks. We validate the code by directly comparing our results for the canonical scaling properties of the networks in the radiation and matter eras with those in the literature, finding very good agreement. We finally highlight possible directions for improving the scalability of the code.

Implied Volatility Structure in Turbulent and Long-Memory Markets

We consider fractional stochastic volatility models that extend the classic Black--Scholes model for asset prices. The models are general and motivated by recent empirical results regarding the behavior of realized volatility. While such models retain the semimartingale property for the asset price the associated European option pricing problem becomes complex, with no explicit solution. In a number of canonical scaling regimes it is possible, however, to derive asymptotic and sparse representations for the option price and the associated implied volatility, that are parameterized by a few effective parameters and that involve power law dependences on time to maturity. These effective parameters may depend in a complicated way on the volatility model, but they can be easily estimated from the observation of a few option prices. The effective parameters associated with a particular underlying asset can be calibrated with respect to liquid contracts written on this asset and then used for pricing less liquid contracts written on the same underlying asset. Therefore, the effective parameters provide a robust link between financial products written on a particular underlying asset.

Kinematic-Structure-Preserved Representation for Unsupervised 3D Human Pose Estimation

Estimation of 3D human pose from monocular image has gained considerable attention, as a key step to several human-centric applications. However, generalizability of human pose estimation models developed using supervision on large-scale in-studio datasets remains questionable, as these models often perform unsatisfactorily on unseen in-the-wild environments. Though weakly-supervised models have been proposed to address this shortcoming, performance of such models relies on availability of paired supervision on some related task, such as 2D pose or multi-view image pairs. In contrast, we propose a novel kinematic-structure-preserved unsupervised 3D pose estimation framework, which is not restrained by any paired or unpaired weak supervisions. Our pose estimation framework relies on a minimal set of prior knowledge that defines the underlying kinematic 3D structure, such as skeletal joint connectivity information with bone-length ratios in a fixed canonical scale. The proposed model employs three consecutive differentiable transformations namely forward-kinematics, camera-projection and spatial-map transformation. This design not only acts as a suitable bottleneck stimulating effective pose disentanglement, but also yields interpretable latent pose representations avoiding training of an explicit latent embedding to pose mapper. Furthermore, devoid of unstable adversarial setup, we re-utilize the decoder to formalize an energy-based loss, which enables us to learn from in-the-wild videos, beyond laboratory settings. Comprehensive experiments demonstrate our state-of-the-art unsupervised and weakly-supervised pose estimation performance on both Human3.6M and MPI-INF-3DHP datasets. Qualitative results on unseen environments further establish our superior generalization ability.

Dynamic allometry in coastal overwash morphology

Abstract. Allometry refers to a physical principle in which geometric (and/or metabolic) characteristics of an object or organism are correlated to its size. Allometric scaling relationships typically manifest as power laws. In geomorphic contexts, scaling relationships are a quantitative signature of organization, structure, or regularity in a landscape, even if the mechanistic processes responsible for creating such a pattern are unclear. Despite the ubiquity and variety of scaling relationships in physical landscapes, the emergence and development of these relationships tend to be difficult to observe – either because the spatial and/or temporal scales over which they evolve are so great or because the conditions that drive them are so dangerous (e.g. an extreme hazard event). Here, we use a physical experiment to examine dynamic allometry in overwash morphology along a model coastal barrier. We document the emergence of a canonical scaling law for length versus area in overwash deposits (washover). Comparing the experimental features, formed during a single forcing event, to 5 decades of change in real washover morphology from the Ria Formosa barrier system, in southern Portugal, we find differences between patterns of morphometric change at the event scale versus longer timescales. Our results may help inform and test process-based coastal morphodynamic models, which typically use statistical distributions and scaling laws to underpin empirical or semi-empirical parameters at fundamental levels of model architecture. More broadly, this work dovetails with theory for landscape evolution more commonly associated with fluvial and alluvial terrain, offering new evidence from a coastal setting that a landscape may reflect characteristics associated with an equilibrium or steady-state condition even when features within that landscape do not.