Regular Points Research Articles

Holographic thermal correlators: a tale of Fuchsian ODEs and integration contours

We analyze real-time thermal correlation functions of conserved currents in holographic field theories using the grSK geometry, which provides a contour prescription for their evaluation. We demonstrate its efficacy, arguing that there are situations involving components of conserved currents, or derivative interactions, where such a prescription is, in fact, essential. To this end, we first undertake a careful analysis of the linearized wave equations in AdS black hole backgrounds and identify the branch points of the solutions as a function of (complexified) frequency and momentum. All the equations we study are Fuchsian with only regular singular points that for the most part are associated with the geometric features of the background. Special features, e.g., the appearance of apparent singular points at the horizon, whence outgoing solutions end up being analytic, arise at higher codimension loci in parameter space. Using the grSK geometry, we demonstrate that these apparent singularities do not correspond to any interesting physical features in higher-point functions. We also argue that the Schwinger-Keldysh collapse and KMS conditions, implemented by the grSK geometry, continue to hold even in the presence of such singularities. For charged black holes above a critical charge, we furthermore demonstrate that the energy density operator does not possess an exponentially growing mode, associated with ‘pole-skipping’, from one such apparent singularity. Our analysis suggests that the connection between the scrambling physics of black holes and energy transport has, at best, a limited domain of validity.

Effects of Harvest Maturity on Storability, Ripening Dynamics, and Fruit Quality of ‘Geneva 3’ Kiwiberries

Maturity at harvest is an important determinant of fruit quality in kiwiberry [Actinidia arguta (Siebold & Zucc.) Planch. ex Miq.], a climacteric fruit that is harvested after reaching physiological maturity but not yet ready-to-eat ripeness. Although a recommended cultivar for commercial kiwiberry producers in the northeastern United States is ‘Geneva 3’, no published research exists regarding recommended harvest and postharvest practices for this variety. In this study, conducted across two seasons, ‘Geneva 3’ kiwiberries were harvested at a range of mean maturities (6.5, 8.0, and 10.0°Brix), held in cold storage for various durations (4, 6, and 8 weeks), and then ripened at room temperature. At regular time points during ripening (0, 3, 6, 9, and 12 days), visual quality was assessed, and measurements were taken of soluble solids content, dry matter content, and firmness as a means of characterizing fruit quality. Results show that berries harvested at 6.5°Brix largely became visually unacceptable under cold storage conditions and resulted in lower overall quality fruit. Harvesting at 8.0°Brix resulted in high-quality fruit amenable to cold storage, and such quality was not enhanced by delaying harvest to 10.0°Brix. Fruit harvested at 8.0°Brix after 4 weeks in cold storage was found to be acceptable for consumption for, on average, a 3-day window after ripening at room temperature for 4 days. After 6 weeks in cold storage, the consumability window shortened to ∼2 days, starting after 3 days of ripening at room temperature. After 8 weeks in cold storage, the fruit were found to be largely visually unacceptable for fresh eating. In summary, the results indicate that harvesting ‘Geneva 3’ kiwiberries at 8.0°Brix produces berries with the greatest storability (at least 6 weeks in cold storage), the longest window of peak consumability, and the highest overall quality, while mitigating the risks associated with leaving physiologically mature fruit to ripen further in the field.

Статистические оценки параметров центров действия атмосферы в зимнем и летнем сезонах по данным реанализа за период 1992–2021 годов

The subject of the present study is climatological atmospheric centers of action (permanent and seasonal) of the Northern and Southern hemispheres for the central months of the winter and summer seasons. Data on 1000 hPa geopotential height from the NCEP/DOE AMIP-II reanalysis of atmospheric parameters for 1992-2021 are used as initial information. Software-implemented processing of long-term reanalysis data files made it possible to map of the distribution of synoptic centers of action at regular grid points (with a step of 2.5 in latitude and longitude). Statistical estimates of the parameters of atmospheric centers of action (location and intensity), including concentration ellipse characteristics, are presented. An analysis of the change in the characteristics as compared to the base climate period of 1961–1990 (according to the NCEP/NCAR reanalysis data) is given. The dynamics of the characteristics of the centers of action in the form of moving 10-year averages for 2000–2021 is demonstrated. Keywords: atmospheric center of action, reanalysis, geopotential height, concentration ellipse, moving average, trend

A Triangular Grid Filter Method Based on the Slope Filter

High-precision ground point cloud data has a wide range of applications in various fields, and the separation of ground points from non-ground points is a crucial preprocessing step. Therefore, designing an efficient, accurate, and stable ground extraction algorithm is highly significant for improving the processing efficiency and analysis accuracy of point cloud data. The study area in this article was a park in Guilin, Guangxi, China. The point cloud was obtained by utilizing the UAV platform. In order to improve the stability and accuracy of the filter algorithm, this article proposed a triangular grid filter based on the Slope Filter, found violation points by the spatial position relationship within each point in the triangulation network, improved KD-Tree-Based Euclidean Clustering, and applied it to the non-ground point extraction. This method is accurate, stable, and achieves the separation of ground points from non-ground points. Firstly, the Slope Filter is used to remove some non-ground points and reduce the error of taking ground points as non-ground points. Secondly, a triangular grid based on the triangular relationship between each point is established, and the violation triangle is determined through the grid; thus, the corresponding violation points are found in the violation triangle. Thirdly, according to the three-point collinear method to extract the regular points, these points are used to extract the regular landmarks by the KD-Tree-Based Euclidean Clustering and Convex Hull Algorithm. Finally, the dispersed points and irregular landmarks are removed by the Clustering Algorithm. In order to confirm the superiority of this algorithm, this article compared the filter effects of various algorithms on the study area and filtered the 15 data samples provided by ISPRS, obtaining an average error of 3.46%. The results show that the algorithm presented in this article has high processing efficiency and accuracy, which can significantly improve the processing efficiency of point cloud data in practical applications.

Non-line-of-sight imaging with arbitrary illumination and detection pattern

Non-line-of-sight (NLOS) imaging aims at reconstructing targets obscured from the direct line of sight. Existing NLOS imaging algorithms require dense measurements at regular grid points in a large area of the relay surface, which severely hinders their availability to variable relay scenarios in practical applications such as robotic vision, autonomous driving, rescue operations and remote sensing. In this work, we propose a Bayesian framework for NLOS imaging without specific requirements on the spatial pattern of illumination and detection points. By introducing virtual confocal signals, we design a confocal complemented signal-object collaborative regularization (CC-SOCR) algorithm for high-quality reconstructions. Our approach is capable of reconstructing both the albedo and surface normal of the hidden objects with fine details under general relay settings. Moreover, with a regular relay surface, coarse rather than dense measurements are enough for our approach such that the acquisition time can be reduced significantly. As demonstrated in multiple experiments, the proposed framework substantially extends the application range of NLOS imaging.

Spherical Induced Ensembles with Symplectic Symmetry

We consider the complex eigenvalues of the induced spherical Ginibre ensemble with symplectic symmetry and establish the local universality of these point processes along the real axis. We derive scaling limits of all correlation functions at regular points both in the strong and weak non-unitary regimes as well as at the origin having spectral singularity. A key ingredient of our proof is a derivation of a differential equation satisfied by the correlation kernels of the associated Pfaffian point processes, thereby allowing us to perform asymptotic analysis.

Electromagnetic Radiation Space Field Construction Collected along the Road Based on Layered Radial Basis Function

The electromagnetic radiation (EMR) data collected along a road have a largely empty region overall, while they have a linear distribution locally. Moreover, the traditional spatial interpolation method is not suitable for the electromagnetic radiation space field (EMR-SF) construction collected along the road. In this paper, a layered radial basis function (LRBF) method is proposed to generate the EMR-SF, which interpolates from outside to inside in a layered strategy. First, the regular grid points are constructed based on RBF within the range of sampling data and then are layered based on Ripley’s K function. Second, on the basis of layering, the EMR of grid points is generated layer by layer using the LRBF method. Finally, EMR-SF is constructed by using the sampling data and grid points. The LRBF method is applied to EMR data from an area of Yunnan Normal University in Kunming, China. The results show that the LRBF accuracy is higher than that of the ordinary kriging (OK) and inverse-distance-weighted (IDW) interpolation methods. The LRBF interpolation accuracy can be improved through the strategy of regular grid point construction and layering, and the EMR-SF constructed by LRBF is more realistic than OK and IDW.

Free boundary regularity in the multiple membrane problem in the plane

Abstract We study the regularity of free boundaries in the multiple elastic membrane problem in the plane. We prove the uniqueness of blow-ups, and that the free boundaries are C 1 , log {C^{1,\log}} -curves near a regular intersection point.

MFTR-Net: A Multi-Level Features Network with Targeted Regularization for Large-Scale Point Cloud Classification.

There are some irregular and disordered noise points in large-scale point clouds, and the accuracy of existing large-scale point cloud classification methods still needs further improvement. This paper proposes a network named MFTR-Net, which considers the local point cloud's eigenvalue calculation. The eigenvalues of 3D point cloud data and the 2D eigenvalues of projected point clouds on different planes are calculated to express the local feature relationship between adjacent point clouds. A regular point cloud feature image is constructed and inputs into the designed convolutional neural network. The network adds TargetDrop to be more robust. The experimental result shows that our methods can learn more high-dimensional feature information, further improving point cloud classification, and our approach can achieve 98.0% accuracy with the Oakland 3D dataset.

Singular effect of interfacial slip for an otherwise stable two-layer shear flow: analysis and computations

We consider instability of the flat interface in a two-layer Couette flow model developed earlier (Kalogirou & Papageorgiou, 2016, J. Fluid Mech. 802 , 5–36; Katsiavria & Papageorgiou, 2022, Wave Motion 114 , 103018. ( doi:10.1016/j.wavemoti.2022.103018 )) for a thin layer near one of the walls. For the case when the less viscous fluid resides next to the moving wall, we find that even a small slip effect at the interface can destabilize an otherwise highly stable flow to the Turing-type instability. The singular effect of small slip in an otherwise very stable configuration may have important ramifications in physical and technological applications. The neutral points of the dispersion relation give rise to travelling wave solutions that are continued to finite amplitude numerically and their linear stability properties identified for a set of parameter values for disturbances that include subharmonic modes with twice the wavelength of the nonlinear travelling wave. We determined Hopf and regular bifurcation points of travelling waves and rigorously justified their existence for some set of parameter values. Weakly nonlinear analysis close to bifurcation from a flat state is also presented for small amplitude waves in general. We also present global existence and regularity results for periodic initial conditions without any restriction on parameters.

Renal toxicity and biokinetics models after repeated uranium instillation

During nuclear fuel processing, workers can potentially be exposed to repeated inhalations of uranium compounds. Uranium nephrotoxicity is well documented after acute uranium intake, but it is controversial after long-term or protracted exposure. This study aims to analyze the nephrotoxicity threshold after repeated uranium exposure through upper airways and to investigate the resulting uranium biokinetics in comparison to reference models. Mice (C57BL/6J) were exposed to uranyl nitrate (0.03–3 mg/kg/day) via intranasal instillation four times a week for two weeks. Concentrations of uranium in urines and tissues were measured at regular time points (from day 1 to 91 post-exposure). At each exposure level, the amount of uranium retained in organs/tissues (kidney, lung, bone, nasal compartment, carcass) and excreta (urine, feces) reflected the two consecutive weeks of instillation except for renal uranium retention for the highest uranium dose. Nephrotoxicity biomarkers, KIM-1, clusterin and osteopontin, are induced from day 4 to day 21 and associated with changes in renal function (arterial fluxes) measured using non-invasive functional imaging (Doppler-ultrasonography) and confirmed by renal histopathological analysis. These results suggest that specific biokinetic models should be developed to consider altered uranium excretion and retention in kidney due to nephrotoxicity. The threshold is between 0.25 and 1 mg/kg/day after repeated exposure to uranium via upper airways.

Regularized limit, analytic continuation and finite-part integration

Finite-part integration is a recent method of evaluating a convergent integral in terms of the finite-parts of divergent integrals deliberately induced from the convergent integral itself [E. A. Galapon, The problem of missing terms in term by term integration involving divergent integrals, Proc. R. Soc. A 473 (2017) 20160567]. Within the context of finite-part integration of the Stieltjes transform of functions with logarithmic growths at the origin, the relationship is established between the analytic continuation of the Mellin transform and the finite-part of the resulting divergent integral when the Mellin integral is extended beyond its strip of analyticity. It is settled that the analytic continuation and the finite-part integral coincide at the regular points of the analytic continuation. To establish the connection between the two at the isolated singularities of the analytic continuation, the concept of regularized limit is introduced to replace the usual concept of limit due to Cauchy when the later leads to a division by zero. It is then shown that the regularized limit of the analytic continuation at its isolated singularities equals the finite-part integrals at the singularities themselves. The treatment gives the exact evaluation of the Stieltjes transform in terms of finite-part integrals and yields the dominant asymptotic behavior of the transform for arbitrarily small values of the parameter in the presence of arbitrary logarithmic singularities at the origin.

The Dorsal Nasal Complex in Asians: Anatomical Variations and Injection Guide for Botulinum Toxin Type A.

Multiple muscles contribute to the formation of dorsal nasal lines (DNLs) and affect nasal aesthetics. Few attempts have been made to explore the range of distribution of DNLs in relation to injection planning. The aim of this study was to classify the distribution types of DNLs and propose a refined injection technique validated by clinical study and cadaver dissection. Patients were classified into 4 types according to their DNL distribution type. Botulinum toxin type A injections were administered at 6 regular points and 2 optional points. The effect on wrinkle reduction was assessed. Patient satisfaction was recorded. Cadaver dissection was conducted to explore the anatomical evidence of DNL variation. The study included 349 treatments in 320 patients (269 females and 51 males), whose DNLs were classified into complex type, horizontal type, oblique type, and vertical type. The severity of DNLs was significantly reduced after treatment. Most patients were satisfied. From the cadaver study, connecting muscular fibers were clearly observed among the muscles involved in the formation of DNLs, and these muscles were collectively named the dorsal nasal complex (DNC) by the authors. Four anatomical variations of the DNC were discovered, corroborating the DNL classification system. A novel anatomical concept, the DNC, and a classification system for DNLs were proposed. Each of the 4 distribution types of DNLs corresponds to a specific anatomical variation of the DNC. A refined injection technique for DNLs was developed, and its efficacy and safety were demonstrated.

PSO-Based Target Localization and Tracking in Wireless Sensor Networks

Research of target localization and tracking is always a remarkable problem in the application of wireless sensor networks (WSNs) technology. There are many kinds of research and applications of target localization and tracking, such as Angle of Arrival (AOA), Time of Arrival (TOA), and Time Difference of Arrival (TDOA). The target localization accuracy for TOA, TDOA, and AOA is better than RSS. However, the required devices in the TOA, TDOA, and AOA are more expensive than RSS. In addition, the computational complexity of TOA, TDOA, and AOA is also more complicated than RSS. This paper uses a particle swarm optimization (PSO) algorithm with the received signal strength index (RSSI) channel model for indoor target localization and tracking. The performance of eight different method combinations of random or regular points, fixed or adaptive weights, and the region segmentation method (RSM) proposed in this paper for target localization and tracking is investigated for the number of particles in the PSO algorithm with 12, 24, 52, 72, and 100. The simulation results show that the proposed RSM method can reduce the number of particles used in the PSO algorithm and improve the speed of positioning and tracking without affecting the accuracy of target localization and tracking. The total average localization time for target localization and tracking with the RSM method can be reduced by 48.95% and 34.14%, respectively, and the average accuracy of target tracking reaches up to 93.09%.

Comparability of multi-temporal DTMs derived from different LiDAR platforms: Error sources and uncertainties in the application of geomorphic impact studies.

Multi-temporal digital terrain models (DTMs) derived from airborne or uncrewed aerial vehicle (UAV)-borne light detection and ranging (LiDAR) platforms are frequently used tools in geomorphic impact studies. Accurate estimation of mobilized sediments from multi-temporal DTMs is indispensable for hazard assessment. To study volumetric changes in alpine environments it is crucial to identify and discuss different kind of error sources in multi-temporal data. We subdivided errors into those caused by data acquisition, data processing, and spatial properties of the terrain. In terms of the quantification of surface changes, the propagation of errors can lead to high uncertainties. Three alpine catchments with different LiDAR point clouds of different origins (airborne laser scanning [ALS], UAV-borne laser scanning [ULS]), varying point densities, accuracies and qualities were analysed, and used as basis for interpolating DTMs. The workflow was developed in the Schöttlbach area in Styria and later applied to further catchments in Austria. The main aim of the presented work is a comprehensive DTM uncertainty analysis specially designed for geomorphic impact studies, with a resulting uncertainty analysis serving as input for a change detection tool. Our findings reveal that geomorphic impact studies need the careful distinction between actual surface changes and different data uncertainties. ULS combines the benefits of terrestrial laser scanning with all the benefits of ALS. However, the use of ULS data does not necessarily improve the results of the analysis since the high level of detail is not always helpful in geomorphic impact studies. In order to make the different point clouds and DTMs comparable the quality of the ULS point cloud had to be reduced to fit the accuracy of the reference data (older ALS point clouds). Using a point cloud with a high point density with a regular planimetric point spacing and less data gaps, in the best case collected during leaf-off conditions (e.g., cross-flight strategy) turned out to be sufficient for our geomorphic research purposes.

Sound Radiation Estimate from Vibration Measurements With Multiple Cameras

This paper presents experimental results on the estimate of the sound radiation by a thin flat plate from flexural vibration measurements taken with multiple cameras. The study considers the sound radiation into free-field by a baffled rectangular plate fixed on a rigid frame. The plate is excited by a tonal point force exerted by a shaker at the first three resonance frequencies of the plate flexural response. The resulting vibration field is measured with a set of six cameras suitably synchronised. More specifically, 3D point tracking is implemented on a regular NxM grid of small circular points marked on the plate. The transverse displacements at these points are thus reconstructed from triangulation with multiple (i.e. more than 2) view-points. The transverse displacements are then used to derive the sound radiation from a direct boundary integral formulation. More specifically, for the flat rectangular plate at hand, the sound radiation is derived from the Rayleigh integral, which is approximated into a finite sum over the mesh of rectangular elements centred at the NxM grid of points depicted on the plate. The flexural vibration field and the sound radiation field derived from the camera measurements are contrasted with measurements taken with a laser vibrometer and microphone-scanner probe. The initial results presented in this paper demonstrate the feasibility of the proposed measurement approach at low audio frequencies.

Pakistan's Trade Opportunities and Challenges with CARs:

Pakistan, Turkmenistan, and Kazakhstan are struggling from lack of trade diversification and post COVID-19 economic woes. These issues can be addressed via regional cooperation and expansion into each other's markets. Pakistan’s new geo-economics ambition and efforts to reach out to Central Asian Republics (CARs) is gaining momentum, with Gwadar port being touted as the go to port for CARs. Pakistan has a lot to offer these countries in terms of being a reliable source of imports, as well as being the closest outlet for their ocean trade. Presently, issue of access via unstable Afghanistan remains a major challenge, which has been a regular point of academic discussion. However, there hasn't been much discourse on the challenges and opportunities that await Pakistan, once stability in Afghanistan is regained and physical access issues between CARs and Pakistan are resolved. This work employs limited quantitative analysis to examine trade potential and proposes practical solutions to barriers to trade that must be addressed if these countries wish to be more than pawns in the New Great Game.

Study of the Hypergeometric Equation via Data Driven Koopman-EDMD Theory

We consider a data-driven method, which combines Koopman operator theory with Extended Dynamic Mode Decomposition. We apply this method to the hypergeometric equation which is the Fuchsian equation with three regular singular points. The space of solutions at any of its singular points is a two-dimensional linear vector space on the field of reals when the independent variable is restricted to take values in the real axis and the unknown function is restricted to be a real-valued function of a real variable. A basis of the linear vector space of solutions is spanned by the hypergeometric function and its products with appropriate powers of the independent variable or the logarithmic function depending on the roots of the indicial equation of the hypergeometric equation. With our work, we obtain a new representation of the fundamental solutions of the hypergeometric equation and relate them to the spectral analysis of the finite approximation of the Koopman operator associated with the hypergeometric equation. We expect that the usefulness of our results will come more to the fore when we extend our study into the complex domain.

PL Morse theory in low dimensions

Abstract We discuss a PL analog of Morse theory for PL manifolds. There are several notions of regular and critical points. A point is homologically regular if the homology does not change when passing through its level; it is strongly regular if the function can serve as one coordinate in a chart. Several criteria for strong regularity are presented. In particular, we show that in dimensions d ≤ 4 a homologically regular point on a PL d-manifold is always strongly regular. Examples show that this fails in higher dimensions d ≥ 5. One of our constructions involves an embedding of the dunce hat into 4-space and Mazur’s contractible 4-manifold. Finally, decidability questions in this context are discussed.

The set of mildly regular boundary points has full caloric measure

AbstractWe introduce a new kind of regularity in the Dirichlet problem for the heat equation, called mild regularity. The mildly regular boundary points include all types of regular points previously considered. Just as regular boundary points have barriers associated with them, the mildly regular boundary points have mild barriers, which are just as important. We consider whether the mild regularity of a boundary point for an open set is inherited by an open subset or superset. We detail the connection of mild regularity with the Green function. We consider, in particular, subdomains of an arbitrary open set that satisfy a certain connectivity condition which takes account of the special nature of the temporal variable, called zones of influence. Our main theorem states that, for any zone of influence, the set of boundary points that are not mildly regular is caloric measure null.