Curvature Scale Research Articles

Numerical metrics, curvature expansions and Calabi-Yau manifolds

We discuss the extent to which numerical techniques for computing approximations to Ricci-flat metrics can be used to investigate hierarchies of curvature scales on Calabi-Yau manifolds. Control of such hierarchies is integral to the validity of curvature expansions in string effective theories. Nevertheless, for seemingly generic points in moduli space it can be difficult to analytically determine if there might be a highly curved region localized somewhere on the Calabi-Yau manifold. We show that numerical techniques are rather efficient at deciding this issue.

Modeling of the Loading–Unloading Contact of Two Cylindrical Rough Surfaces with Friction

The first fractal model for the loading–unloading process between two cylindrical surfaces with friction is presented. The nonlinear relation between the real contact area and the contact load in different deformation stages are deduced for a load–unload cycle. The impacts of parameters in the model are discussed. The numerical results show that for a given dimensionless contact load, the dimensionless real contact area of the loading–unloading process of cylindrical contact surface with friction, as well as the differences of the dimensionless real contact area between the loading and unloading processes, increase with the increase of the loading interference and fractal dimension, decrease of the profile scaling parameter and curvature radius, or the substitution of external contact for internal contact.

Open Curvature Scale Space Matching for Coronary Artery Identification in X-Ray Angiographic Images

Identification of the coronary artery in sequence angiograms is an important issue in the analysis and treatment of coronary angiography data, due to the ambiguities in the coronary vessels resulting from cardiac motion and the differences in the projection angles in angiograms. In this paper, we propose a novel coronary artery identification method based on curvature scale space image matching. First, points on the centerline of each coronary artery branch are convolved with Gaussian kernel functions of different scales to obtain the corresponding curvature scale space (CSS) image during the curve evolution. Then, a CSS image matching method for open curves, which uses a combination of open feature vectors and closed feature vectors, is proposed. Finally, curve matching transitivity is used to solve the problem of the inability to recognize the coronary artery when the difference in the imaging angles is too large. The experimental results demonstrate that the proposed method can recognize every coronary artery in different views, even when the difference in the imaging angles is 29.8°.

On the inflationary massive field with a curved field manifold

Massive fields during inflation provide an interesting opportunity to test new physics at very high energy scales. Meanwhile in fundamental realizations, the inflationary field space typically has a curved geometry, which may leave detectable imprints in primordial observables. In this paper we study an extension of quasi-single field inflation where the inflaton and the massive field belong to a curved field manifold. Because of the nontrivial field space curvature, the massive field here can get significant mass corrections of order the Hubble scale, thus the quasi-single field predictions on primordial non-Gaussianity are affected. We derive the same result in an equivalent approach by using the background effective field theory of inflation, where a dimension-6 operator is identified to play an important role and its cutoff scale is associated with the curvature scale of the field space. In addition, due to the slow-roll evolution of the inflaton, this type of mass correction has intrinsic time-dependence. Consequently, the running mass modifies the scaling behaviour in the squeezed limit of the scalar bispectrum, while the resulting running index measures the curvature of the internal field space. Therefore the minimal setup of a massive field within curved field space during inflation may naturally lead to new observational signatures of the field space geometry.

Method for segmentation of overlapping fish images in aquaculture

Individual fish segmentation is a prerequisite for feature extraction and object identification in any machine vision system. In this paper, a method for segmentation of overlapping fish images in aquaculture was proposed. First, the shape factor was used to determine whether an overlap exists in the picture. Then, the corner points were extracted using the curvature scale space algorithm, and the skeleton obtained by the improved Zhang-Suen thinning algorithm. Finally, intersecting points were obtained, and the overlapped region was segmented. The results show that the average error rate and average segmentation efficiency of this method was 10% and 90%, respectively. Compared with the traditional watershed method, the separation point is accurate, and the segmentation accuracy is high. Thus, the proposed method achieves better performance in segmentation accuracy and effectiveness. This method can be applied to multi-target segmentation and fish behavior analysis systems, and it can effectively improve recognition precision. Keywords: aquaculture, image processing, overlapping segmentation, corner detection, improved Zhang-Suen algorithm DOI: 10.25165/j.ijabe.20191206.3217 Citation: Zhou C, Lin K, Xu D M, Liu J T, Zhang S, Sun C H, et al. Method for segmentation of overlapping fish images in aquaculture. Int J Agric & Biol Eng, 2019; 12(6): 135–142.

Effective quantum extended spacetime of polymer Schwarzschild black hole

The physical interpretation and eventual fate of gravitational singularities in a theory surpassing classical general relativity are puzzling questions that have generated a great deal of interest among various quantum gravity approaches. In the context of loop quantum gravity (LQG), one of the major candidates for a non-perturbative background-independent quantisation of general relativity, considerable effort has been devoted to construct effective models in which these questions can be studied. In these models, classical singularities are replaced by a ‘bounce’ induced by quantum geometry corrections. Undesirable features may arise however depending on the details of the model. In this paper, we focus on Schwarzschild black holes and propose a new effective quantum theory based on polymerisation of new canonical phase space variables inspired by those successful in loop quantum cosmology. The quantum corrected spacetime resulting from the solutions of the effective dynamics is characterised by infinitely many pairs of trapped and anti-trapped regions connected via a space-like transition surface replacing the central singularity. Quantum effects become relevant at a unique mass independent curvature scale, while they become negligible in the low curvature region near the horizon. The effective quantum metric describes also the exterior regions and asymptotically classical Schwarzschild geometry is recovered. We however find that physically acceptable solutions require us to select a certain subset of initial conditions, corresponding to a specific mass (de-)amplification after the bounce. We also sketch the corresponding quantum theory and explicitly compute the kernel of the Hamiltonian constraint operator.

Corner detection based on gradient ghost imaging

Gradient ghost imaging (GGI) is a new imaging method that can directly extract the edge of a target from the correlation of light intensity fluctuations. However, there are problems of poor image quality and practicability in GGI. The corner point is an important target feature and has important applications in the fields of image processing and machine vision. In this paper, we propose a corner detection scheme that combines a corner detection algorithm based on curvature scale space with a GGI system, which can directly extract corner points from the reconstruction results of ghost imaging. A simulation and experimental results show that our method can acquire precise and robust corner information of an unknown target in undersampled cases, which promotes the practical development of ghost imaging.

Particle Acceleration in Kinetic Simulations of Nonrelativistic Magnetic Reconnection with Different Ion–Electron Mass Ratios

Abstract By means of fully kinetic particle-in-cell simulations, we study whether the proton-to-electron mass ratio m i /m e influences the energy spectrum and underlying acceleration mechanism during magnetic reconnection. While kinetic simulations are essential for studying particle acceleration during magnetic reconnection, a reduced m i /m e is often used to alleviate the demanding computing resources, which leads to artificial scale separation between electron and proton scales. Recent kinetic simulations with high mass ratios have suggested new regimes of reconnection, as electron pressure anisotropy develops in the exhaust region and supports extended current layers. In this work, we study whether different m i /m e changes the particle acceleration processes by performing a series of simulations with different mass ratio (m i /m e = 25–400) and guide field strength in a low-β plasma. We find that mass ratio does not strongly influence reconnection rate, magnetic energy conversion, ion internal energy gain, plasma energization processes, ion energy spectra, and the acceleration mechanisms for high-energy ions. Simulations with different mass ratios are different in electron acceleration processes, including electron internal energy gain, electron energy spectrum, and the acceleration efficiencies for high-energy electrons. We find that high-energy electron acceleration becomes less efficient when the mass ratio gets larger because the Fermi-like mechanism associated with particle curvature drift becomes less efficient. These results indicate that when particle curvature drift dominates high-energy particle acceleration, the further the particle kinetic scales are from the magnetic field curvature scales (∼d i ), the weaker the acceleration will be.

Computer Algorithm for Archaeological Projectile Points Automatic Classification

The manual archaeological projectile point morphological classification is an extensive and complex process since it involves a large number of categories. This article presents an algorithm that automatically makes this process, based on the projectile point digital image and using a classification scheme according to global archaeological approaches. The algorithm supports different conditions such as changes in scale and quality of the image. Moreover, it requires only a uniform background and an approximate north--south projectile point orientation. The principal computer methods that compose the algorithm are the curvature scale space map (CSS-map), the gradient contour on the projectile point, and the support vector machines (SVM) algorithm. Finally, the classifier was trained and tested on a dataset of approximately 800 projectile points images, and the results have shown a better performance than other shape descriptors such as Pyramid of Histograms of Orientation Gradients (PHOG), Histogram of Orientation Shape Context (HOOSC) (both used in a bag-of-words context), and geometric moment invariants (Hu moments).

Asymptotic safety casts its shadow

We set out to bridge the gap between regular black-hole spacetimes and observations of a black-hole shadow by the Event Horizon Telescope. We explore modifications of spinning and non-spinning black-hole spacetimes inspired by asymptotically safe quantum gravity which features a scale dependence of the Newton coupling. As a consequence, the predictions of our model, such as the shadow shape and size, depend on one free parameter determining the curvature scale at which deviations from General Relativity set in. In more general new-physics settings, it can also depart substantially from the Planck scale. In this case, the free parameter is constrained by observations, since the corresponding curvature scale is significantly below the Planck-scale. The leading new-physics effect can be recast as a scale-dependent black-hole mass, resulting in distinct observational signatures of our model. As a concrete example, we show that two mass-measurements, extracted from the size of the shadow and from Keplerian orbital motion of stars, allow to distinguish the classical from the modified, regular black-hole spacetime, yielding a bound on the free parameter. For spinning black holes, we further find that the singularity-resolving new physics puts a characteristic dent in the shadow. Finally, we argue, based on the underlying physical mechanism, that the effects we derive could be generic consequences of a large class of quantum-gravity theories.

Determination of Building Model Key Points Using Multidirectional Shaded Relief Images Generated from Airborne LiDAR Data

Light detection and ranging (LiDAR) data collected from airborne laser scanner system is one of the major sources to reconstruct Earth’s surface features. This paper presents a method for detecting model key points (MKPs) of the buildings using LiDAR point clouds. The proposed approach utilizes shaded relief images (SRIs) derived from the LiDAR data. The SRIs based on the concept of the shape from shading could provide unique information about individual surface patches of the building roofs. The main advantage of the proposed approach is to detect directly MKPs, which are primitives for 3D building modeling, without segmenting point clouds. Depending on the location of the light source, the SRIs are created differently. Therefore, integration of the multidirectional SRIs created from different locations of the light source could provide more reliable results. In addition, the vertical exaggeration (i.e., scaling Z-coordinates) is also beneficial because constituent surface patches of the roofs in the SRIs created with vertically exaggerated LiDAR data are more distinguishable. To determine the MKPs of the roofs, building data was separated from other objects using modified marker-controlled watershed algorithm in accordance with criteria to specify buildings such as area, height, and standard deviation. This process could remove the unnecessary objects such as trees, vegetation, and cars. The curvature scale space (CSS) corner detector was used to determine MKP since this method is robust to geometric changes such as rotation, translation, and scale. The proposed method was applied to simulated and real LiDAR datasets with various roof types. The experimental results show that the proposed method is effective in determining MKPs of various roof types with high level of detail (LoD).

Induced spatial geometry from causal structure

Motivated by the Hawking–King–McCarthy–Malament (HKMM) theorem and the associated reconstruction of spacetime geometry from its causal structure and local volume element , we define a one-parameter family of spatial distance functions on a Cauchy hypersurface using only and . The parameter corresponds to a ‘mesoscale’ cut-off which, when appropriately chosen, provides a distance function which approximates the induced spatial distance function to leading order. This admits a straightforward generalisation to the discrete analogue of a Cauchy hypersurface in a causal set. For causal sets which are approximated by continuum spacetimes, this distance function approaches the continuum induced distance when the mesoscale is much smaller than the scale of the extrinsic curvature of the hypersurface, but much larger than the discreteness scale. We verify these expectations by performing extensive numerical simulations of causal sets which are approximated by simple spacetime regions in 2 and 3 spacetime dimensions.

An almost complete curvature scale space representation: Euclidean case

Here, we intend to propose local shape curve features which are invariant under planar Euclidean transformations and independent with respect to the original curve parameterization. The present work generalizes the family of Curvature Scale Space descriptors in order to increase the shape information quantity to tend to the completeness property. For this, a more pragmatic criterion is introduced in this paper which we call the almost completeness. We define it as a pre-completeness for a given resolution of features. Such descriptors are formed by the curvatures on the set of curve points obtained from the antecedents of different curvature levels. This level set is fixed with a given rule. The idea of the almost completeness is to make a compromise between the cardinal of the set of curvature’s levels and the optimal number of scales. The rule is submitted to an unsupervised statistical study and the scales are obtained with a spectral analysis. Experiments are conducted on several known datasets. Promising results in the sense of shape retrieval and shape recognition rates are demonstrated.

Studies of 3D directed cell migration enabled by direct laser writing of curved wave topography

Cell migration, critical to numerous biological processes, can be guided by surface topography. Studying the effects of topography on cell migration is valuable for enhancing our understanding of directional cell migration and for functionally engineering cell behavior. However, fabrication limitations constrain topography studies to geometries that may not adequately mimic physiological environments. Direct Laser Writing (DLW) provides the necessary 3D flexibility and control to create well-defined waveforms with curvature and length scales that are similar to those found in physiological settings, such as the luminal walls of blood vessels that endothelial cells migrate along. We find that endothelial cells migrate fastest along square waves, intermediate along triangular waves, and slowest along sine waves and that directional cell migration on sine waves decreases as sinusoid wavelength increases. Interestingly, inhibition of Rac1 decreases directional migration on sine wave topographies but not on flat surfaces with micropatterned lines, suggesting that cells may utilize different molecular pathways to sense curved topographies. Our study demonstrates that DLW can be employed to investigate the effects and mechanisms of topography on cell migration by fabricating a wide array of physiologically-relevant surfaces with curvatures that are challenging to fabricate using conventional manufacturing techniques.

Curvature and topology dependency of the cosmological spectra

In this article we investigate dependency of the adiabatic and entropy spectral indices of the cosmological perturbations on the geometry and topology of the background universe. Our discussion includes the post-inflationary universe i.e. radiation-dust mixture era. For this purpose, we first extract an explicit equation describing evolution of the comoving curvature perturbation in the FLRW universe with arbitrary spatial sectional curvature. We may percept when $K\neq 0$, curvature scale would be as significant as the perturbations scales to recognize the behavior of the spectral indices. We also focus on the entropy perturbation in order to extract behavior of the isocurvature spectral index in terms of the curvature index and time. Our analysis shows that spectra of curvature and entropy perturbations in sub-horizon scales could be function of topology. Moreover, an accurate analysis makes clear that time-average of isocurvature index in case $K=0$ is about zero,so that imprint of entropy perturbation in time duration may be negligible. We also consider evolution of the cosmological indices for super-curvature modes in the case $K=-1$. In the most results dependency to curvature, initial conditions and scale modes are thoroughly vivid.

Method for segmentation of overlapping fish images in aquaculture

Individual fish segmentation is a prerequisite for feature extraction and object identification in any machine vision system. In this paper, a method for segmentation of overlapping fish images in aquaculture was proposed. First, the shape factor was used to determine whether an overlap exists in the picture. Then, the corner points were extracted using the curvature scale space algorithm, and the skeleton obtained by the improved Zhang-Suen thinning algorithm. Finally, intersecting points were obtained, and the overlapped region was segmented. The results show that the average error rate and average segmentation efficiency of this method was 10% and 90%, respectively. Compared with the traditional watershed method, the separation point is accurate, and the segmentation accuracy is high. Thus, the proposed method achieves better performance in segmentation accuracy and effectiveness. This method can be applied to multi-target segmentation and fish behavior analysis systems, and it can effectively improve recognition precision. Keywords: aquaculture, image processing, overlapping segmentation, corner detection, improved Zhang-Suen algorithm DOI: 10.25165/j.ijabe.20191206.3217 Citation: Zhou C, Lin K, Xu D M, Liu J T, Zhang S, Sun C H, et al. Method for segmentation of overlapping fish images in aquaculture. Int J Agric & Biol Eng, 2019; 12(6): 135–142.

Brachiopods classification based on fusion of contour and region based descriptors

In this paper, we propose a contour-region based shape descriptor for Brachiopods classification by using a combinations of Fourier descriptors and R-transform extracted from Radon transform. Fourier descriptors is supported by the well-developed and well-understood Fourier theory and are a powerful features for the recognition of two-dimensional connected shapes. We used the stable and complete Fourier descriptors proposed by Ghorbel to present the contour information. To depict shape interior content we used the R-transform. It is advantages lies in its low computational complexity and geometric invariance. We compared the proposed descriptor with curvature scale space, R-transform and Ghorbel descriptors using city block distance measure and our Brachiopods database. We present the experimental results to reveal the performance of the proposed descriptor which is independent on the starting points and efficient.

Nonsingular Schwarzschild–de Sitter black hole

We combine notions of a maximal curvature scale in nature with that of a minimal curvature scale to construct a non-singular Schwarzschild–de Sitter black hole. We present an exact solution within the context of two-dimensional dilaton gravity. For a range of parameters the solution approaches Schwarzschild–de Sitter at large values of the radial coordinate, asymptotically approaching a de Sitter metric with constant minimal curvature, while approaching a maximal constant curvature smooth spacetime as the radial coordinate approaches zero. The spacetime is geodesically complete and generically has both a black hole horizon and a cosmological horizon.

Nonlocal quantum effective actions in Weyl-Flat spacetimes

Virtual massless particles in quantum loops lead to nonlocal effects which can have interesting consequences, for example, for primordial magnetogenesis in cosmology or for computing finite N corrections in holography. We describe how the quantum effective actions summarizing these effects can be computed efficiently for Weyl-flat metrics by integrating the Weyl anomaly or, equivalently, the local renormalization group equation. This method relies only on the local Schwinger-DeWitt expansion of the heat kernel and allows for a re-summation of the anomalous leading large logarithms of the scale factor, log a(x), in situations where the Weyl factor changes by several e-foldings. As an illustration, we obtain the quantum effective action for the Yang-Mills field coupled to massless matter, and the self-interacting massless scalar field. Our action reduces to the nonlocal action obtained using the Barvinsky-Vilkovisky covariant perturbation theory in the regime R2 ≪ ∇2R for a typical curvature scale R, but has a greater range of validity effectively re-summing the covariant perturbation theory to all orders in curvatures. In particular, it is applicable also in the opposite regime R2 ≫ ∇2R, which is often of interest in cosmology.

Über-gravity and the cosmological constant problem

Abstract Recently, the idea of taking ensemble average over gravity models has been introduced. Based on this idea, we study the ensemble average over (effectively) all the gravity models (constructed from Ricci scalar) dubbing the name uber-gravity which is a fixed point in the model space. The uber-gravity has interesting universal properties, independent from the choice of basis: (i) it mimics Einstein–Hilbert gravity for high-curvature regime, (ii) it predicts stronger gravitational force for an intermediate-curvature regime, (iii) surprisingly, for low-curvature regime, i.e. R R 0 where R is Ricci scalar and R 0 is a given scale, the Lagrangian vanishes automatically and (iiii) there is a sharp transition between low- and intermediate-curvature regimes at R = R 0 . We show that the uber-gravity response is robust to all values of vacuum energy, ρ v a c when there is no other matter. So as a toy model, uber-gravity, gives a way to think about the hierarchy problems e.g. the cosmological constant problem. Due to the transition at R = R 0 there is a chance for uber-gravity to bypass Weinberg’s no-go theorem. The cosmology of this model is also promising because of its non-trivial predictions for small curvature scales in comparison to Λ CDM model.