Continuous Curve Research Articles

Infinitesimally Helicoidal Motions with Fixed Pitch of Oriented Geodesics of a Space Form

Let \(\mathscr{G}\) be the manifold of all (unparametrized) oriented lines of \(\mathbb{R}^{3}\). We study the controllability of the control system in \(\mathscr{G}\) given by the condition that a curve in \(\mathscr{G}\) describes at each instant, at the infinitesimal level, an helicoid with prescribed angular speed \(\alpha \). Actually, we pose the analogous more general problem by means of a control system on the manifold \(\mathscr{G}_{\kappa }\) of all the oriented complete geodesics of the three dimensional space form of curvature \(\kappa \): \(\mathbb{R}^{3}\) for \(\kappa =0\), \(S^{3}\) for \(\kappa =1\) and hyperbolic 3-space for \(\kappa =-1\). We obtain that the system is controllable if and only if \(\alpha ^{2}\neq \kappa \). In the spherical case with \(\alpha =\pm 1\), an admissible curve remains in the set of fibers of a fixed Hopf fibration of \(S^{3}\).We also address and solve a sort of Kendall’s (aka Oxford) problem in this setting: Finding the minimum number of switches of piecewise continuous curves joining two arbitrary oriented lines, with pieces in some distinguished families of admissible curves.

Universal Criterion for Interpreting Capacity from Load Tests on Piles

Interpretation of field load tests on piles has many important practical and financial implications in foundation engineering practice. However, identifying the ultimate capacity or resistance on a continuous load settlement curve remains elusive. The geotechnical engineering literature abounds with over 40 criteria to aid in interpreting the ultimate capacity from static load tests on deep foundations. These include settlement, settlement rate, offset, and creep criteria, among others. Since the 1990s criteria proposed by Davisson, AASHTO, and New York City Building Code as well as the 5% and 10% of diameter criteria have evolved to become the most routinely specified for all foundations, without assessing their performance or what they have been intended for. This study provides a side-by-side comparison of the performance of these methods in relation to usability, accuracy, precision, and length and diameter effects. In addition, the performance is also compared with the recently developed NYU criterion where the capacity is taken as the smallest of (i) a settlement corresponding to the elastic compression plus 0.75 in.; (ii) the capacity at plunging or strain-softening; or (iii) settlement corresponding to 5% of the pile diameter, unless the settlement threshold is modified by the structural engineer of record. Assessment is made possible using a database of 350 load tests conducted on square and round concrete piles, open and closed steel pipe piles, as well as H-piles. Comparison suggests that the NYU criterion is the most versatile, precise, and accurate among the examined methods.

Three-Dimensional Quantification of Cam Resection Using MRI Bone Models: A Comparison of 2 Techniques.

Background:The current clinical standard for the evaluation of cam deformity in femoroacetabular impingement syndrome is based on radiographic measurements, which limit the ability to quantify the complex 3-dimensional (3D) morphology of the proximal femur.Purpose:To compare magnetic resonance imaging (MRI)–based metrics for the quantification of cam resection as derived using a best-fit sphere alpha angle (BFS-AA) method and using 3D preoperative-postoperative surface model subtraction (PP-SMS).Study Design:Descriptive laboratory study.Methods:Seven cadaveric hemipelvises underwent 1.5-T MRI before and after arthroscopic femoral osteochondroplasty, and 3D bone models of the proximal femur were reconstructed from the MRI scans. The alpha angles were measured radially along clockfaces using a BFS-AA method from the literature and plotted as continuous curves for the pre- and postoperative models. The difference between the areas under the curve for the pre- and postoperative models was then introduced in the current study as the BFS-AA–based metric to quantify the cam resection. The cam resection was also quantified using a 3D PP-SMS method, previously described in the literature using the metrics of surface area (FSA), volume (FV), and height (maximum [FHmax] and mean [FHmean]). Bivariate correlation analyses were performed to compare the metrics quantifying the cam resection as derived from the BFS-AA and PP-SMS methods.Results:The mean ± standard deviation maximum pre- and postoperative alpha angle measurements were 59.73° ± 15.38° and 48.02° ± 13.14°, respectively. The mean for each metric quantifying the cam resection with the PP-SMS method was as follows: FSA, 540.9 ± 150.7 mm2; FV, 1019.2 ± 486.2 mm3; FHmax , 3.6 ± 1.0 mm; and FHmean, 1.8 ± 0.5 mm. Bivariate correlations between the BFS-AA–based and PP-SMS–based metrics were strong: FSA (r = 0.817, P = .012), FV (r = 0.888, P = .004), FHmax (r = 0.786, P = .018), and FHmean (r = 0.679, P = .047).Conclusion:Strong positive correlations were appreciated between the BFS-AA and PP-SMS methods quantifying the cam resection.Clinical Relevance:The utility of the BFS-AA technique is primarily during preoperative planning. The utility of the PP-SMS technique is in the postoperative setting when evaluating the adequacy of resection or in patients with persistent hip pain with suspected residual impingement. In combination, the techniques allow surgeons to develop a planned resection while providing a means to evaluate the depth of resection postoperatively.

Brownian regularity for the Airy line ensemble, and multi-polymer watermelons in Brownian last passage percolation

The Airy line ensemble is a positive-integer indexed system of random continuous curves whose finite dimensional distributions are given by the multi-line Airy process. It is a natural object in the KPZ universality class: for example, its highest curve, the Airy 2 _2 process, describes after the subtraction of a parabola the limiting law of the scaled energy of a geodesic running from the origin to a variable point on an anti-diagonal line in such problems as Poissonian last passage percolation. The ensemble of curves resulting from the Airy line ensemble after the subtraction of the same parabola enjoys a simple and explicit spatial Markov property, the Brownian Gibbs property. In this paper, we employ the Brownian Gibbs property to make a close comparison between the Airy line ensemble’s curves after affine shift and Brownian bridge, proving the finiteness of a superpolynomially growing moment bound on Radon-Nikodym derivatives. We also determine the value of a natural exponent describing in Brownian last passage percolation the decay in probability for the existence of several near geodesics that are disjoint except for their common endpoints, where the notion of ‘near’ refers to a small deficit in scaled geodesic energy, with the parameter specifying this nearness tending to zero. To prove both results, we introduce a technique that may be useful elsewhere for finding upper bounds on probabilities of events concerning random systems of curves enjoying the Brownian Gibbs property. Several results in this article play a fundamental role in a further study of Brownian last passage percolation in three companion papers (Hammond 2017a,b,c), in which geodesic coalescence and geodesic energy profiles are investigated in scaled coordinates.

Is there a low-mass triple system orbiting around the massive semi-detached binary ZZ Cassiopeiae?

Abstract ZZ Cassiopeiae (ZZ Cas) is an early spectral B-type close binary with an orbital period of 1.243527 d. By analyzing the continuous light curve obtained by TESS, and the spectroscopic data with low resolution observed by the 2.16 m telescope in Xinglong station, we found that it is a semi-detached binary; the secondary component fulfills the critical Roche lobe, while the more massive one is detached from the lobes with a fraction of the third light $1.82\%$. Our O-C diagram time spanning 32.6 yr shows a cyclical oscillation with a semi-amplitude of 0.0255(±0.0010) d and a period of 19.11(±0.27) yr superimposed on an upward parabolic curve with a period increase rate of dP/dt = +2.93 × 10−8 d yr−1. The upward parabolic variation and photometric solutions reveal that ZZ Cas is undergoing a late Case A mass transfer process on the nuclear timescale of the secondary component, and it was formed from originally detached binary systems. Its evolution is different from that of V606 Cen in the massive binaries. Meanwhile, the cyclic change in the O-C curve can be interpreted by the light-travel-time effect via the presence of a tertiary body. The tertiary companion with a minimal mass of M3 = 4.23(±0.22) M⊙ orbits around the central eclipsing binary in an eccentric orbit (e = 0.62). The estimation of an extremely low luminosity ratio of the primary component and the tertiary body may reveal that the additional component is a low-mass triple system or a compact object candidate.

Developing a functional index to dynamically examine the spatio-temporal disparities of China’s inclusive green growth

Inclusive green growth strategy has become a worldwide consensus on sustainable development for its highlight on the coordination between social equity, economic growth quality, and environmental stability. In-depth understanding of the temporal disparity in inclusive green growth is vital for developing countries with regional imbalances to devise scientific and sustainable development strategies. Motivated by the need for continuously monitoring the time-varying process of inclusive green growth and to overcome the shortfalls of conventional inclusive green growth index in dynamic assessment, we developed a functional inclusive green growth index (IGGI(t)) in the context of continuous curves. The inclusive green growth in China comprises four functional sub-indices and is built upon four pillars, namely the economic development, social opportunity equity, sustainable production and consumption, and eco-environmental protection. All normalized indicators within each pillar are individually smoothed into dynamically evolving curves, and then are objectively aggregated using the functional Shannon's entropy weights. Applying the IGGI(t) to examine disparities in China's provincial inclusive green growth from 2000 to 2019 demonstrates significant disparity in the absolute level of inclusive green growth among the three regions in China, whereas disparities in the velocity and acceleration of regional inclusive green growth are not significant. Furthermore, the overall and structural inequality of China's inclusive green growth was decomposed via the extended functional Dagum index and targeted policies for reducing regional inequality and improving China's overall inclusive green growth are proposed based on discussions of empirical results. Finally, a sensitivity analysis was conducted to verify the robustness of conclusions derived from using the IGGI(t). We contributed to proposing a dynamic framework for evaluating the quality of green growth and providing a reference for developing countries, including China, to coordinate economic development, social inclusiveness, and eco-environmental protection.

Baseline-sensitivity of Botrytis cinerea to pydiflumetofen and its efficacy on tomato gray mold in Hebei Province, China

Tomato gray mold (TGM), a worldwide destructive disease, is caused by Botrytis cinerea, and fungicide treatments are effective for its control. Pydiflumetofen is a new fungicide of succinate dehydrogenase inhibitors. In this research, 153 B. cinerea isolates were collected from eight different cities in Hebei Province from 2015 to 2017. The sensitivity of these 153 isolates to pydiflumetofen was determined by spore germination assays and mycelial growth rate assays. The results indicated that for these tested isolates, the EC50 values of pydiflumetofen ranged from 0.0036 to 0.0822 mg/L (on conidia germination), and 0.0287–1.2659 mg/L (on mycelial growth rate), with average EC50 values of 0.0327 ± 0.0213 mg/L and 0.3717 ± 0.2744 mg/L, respectively. The frequency distribution of the sensitivity of these 153 isolates to pydiflumetofen was a continuous single-peak curve, and could be used as the baseline for testing the sensitivity of B. cinerea to pydiflumetofen. No cross-resistance existed between pydiflumetofen and the other six botryticides such as diethofencarb, pyrimethanil, iprodione, pyrisoxazole, and fludioxonil, apart from fluopyram. The control efficacy of pydiflumetofen against TGM was determined using detached leaves and in field trials. Pydiflumetofen exhibited good control efficacy against TGM and the preventive effect was better than the curative effect. In the field trials, the control efficacy of pydiflumetofen against TGM was higher than 80%, both on leaves and fruits, at doses of 120, 160 and 200 g a.i./ha. It was significantly better than pyrimethanil. This study showed that pydiflumetofen had high activity and could effectively control the prevalence of TGM, but it should be administered carefully.

Phase behavioral study of binary systems for the vinyl Benzoate, vinyl pivalate and vinyl octanoate with carbon dioxide at high-pressure

The experimental phase-behavior data is reported at high-pressure for the mixtures of vinyl benzoate, vinyl pivalate and vinyl octanoate with supercritical carbon dioxide (sc-CO2) at pressure and temperature array of 3.42 MPa to 22.19 MPa and 313.2 K to 393.2 K respectively. In pressure vs temperature space, the binary mixtures show the continuous critical curves between carbon dioxide critical point and that of other component critical point exhibiting maximum in between. The solubility of vinyl benzoate, vinyl pivalate and vinyl octanoate in sc-CO2 is observed to increase with increasing temperature. Moreover, the (sc-CO2 + vinyl benzoate), (sc-CO2 + vinyl pivalate), and (sc-CO2 + vinyl octanoate) systems demonstrate type-I phase performance.The experimental outcomes are modeled with Goderao-Dalvi-Narayan (G-D-N) and Peng-Robinson (P-R) cubic equations of state. The pressure vs composition (P vs x) isotherms were predicted with Van der Waals one-fluid mixing rules having pair of interaction parameters. The theoretical (P vs x) isotherms of the (sc-CO2 + vinyl benzoate), (sc-CO2 + vinyl pivalate), and (sc-CO2 + vinyl octanoate) systems in range of temperature 313.2 K–393.2 K are in decent agreement with the experimentally derived data.

Asteroseismology Across the Hertzsprung–Russell Diagram

Asteroseismology has grown from its beginnings three decades ago to a mature field teeming with discoveries and applications. This phenomenal growth has been enabled by space photometry with precision 10–100 times better than ground-based observations, with nearly continuous light curves for durations of weeks to years, and by large-scale ground-based surveys spanning years designed to detect all time-variable phenomena. The new high-precision data are full of surprises, deepening our understanding of the physics of stars. ▪ This review explores asteroseismic developments from the past decade primarily as a result of light curves from the Kepler and Transiting Exoplanet Survey Satellite space missions for massive upper main sequence OBAF stars, pre-main-sequence stars, peculiar stars, classical pulsators, white dwarfs and subdwarfs, and tidally interacting close binaries. ▪ The space missions have increased the numbers of pulsators in many classes by an order of magnitude. ▪ Asteroseismology measures fundamental stellar parameters and stellar interior physics—mass, radius, age, metallicity, luminosity, distance, magnetic fields, interior rotation, angular momentum transfer, convective overshoot, core-burning stage—supporting disparate fields such as galactic archeology, exoplanet host stars, supernovae progenitors, gamma-ray and gravitational wave precursors, close binary star origins and evolution, and standard candles. ▪ Stars are the luminous tracers of the Universe. Asteroseismology significantly improves models of stellar structure and evolution on which all inference from stars depends.

A Fast Mean-Preserving Spline for Interpolating Interval Data

Abstract Interpolation of interval data where the mean is preserved, e.g., estimating smoothed, pseudodaily meteorological variables based on monthly means, is a common problem in the geosciences. Existing methods for mean-preserving interpolation are computationally intensive and/or do not readily accommodate bounded interpolation, where the interpolated data cannot exceed a threshold value. Here we present a mean-preserving, continuous, easily implementable, and computationally efficient method for interpolating one-dimensional interval data. Our new algorithm provides a straightforward solution to the interpolation problem by utilizing Hermite cubic splines and midinterval control points to interpolate interval data into smaller partitions. We further include adjustment schemes to restrict the interpolated result to user-specified minimum and maximum bounds. Our method is fast, portable, and broadly applicable to a range of geoscientific data, including interpolating unbounded time series such as mean temperature, and bounded data including mean wind speed or cloud-cover fraction. Significance Statement Interpolation is often utilized to mathematically estimate smaller time step values when such data are not readily available, for example, the estimation of daily temperature when only monthly temperature values are available. We propose a novel interpolation method based on linking segments of flexible continuous curves that ensures the average of interpolated result will be the same as the original value, which is important for minimizing interpolation errors. We find that our new method takes significantly less computational time when compared with other existing methods, while retaining a similar degree of precision. Furthermore, we outline an additional procedure for users to specify the minimum and maximum bounds of interpolated results if applicable.

Assembly mechanism of the pleomorphic immature poxvirus scaffold

In Vaccinia virus (VACV), the prototype poxvirus, scaffold protein D13 forms a honeycomb-like lattice on the viral membrane that results in formation of the pleomorphic immature virion (IV). The structure of D13 is similar to those of major capsid proteins that readily form icosahedral capsids in nucleocytoplasmic large DNA viruses (NCLDVs). However, the detailed assembly mechanism of the nonicosahedral poxvirus scaffold has never been understood. Here we show the cryo-EM structures of the D13 trimer and scaffold intermediates produced in vitro. The structures reveal that the displacement of the short N-terminal α-helix is critical for initiation of D13 self-assembly. The continuous curvature of the IV is mediated by electrostatic interactions that induce torsion between trimers. The assembly mechanism explains the semiordered capsid-like arrangement of D13 that is distinct from icosahedral NCLDVs. Our structures explain how a single protein can self-assemble into different capsid morphologies and represent a local exception to the universal Caspar-Klug theory of quasi-equivalence.

A Generalized Conditional Gradient Method for Dynamic Inverse Problems with Optimal Transport Regularization

We develop a dynamic generalized conditional gradient method (DGCG) for dynamic inverse problems with optimal transport regularization. We consider the framework introduced in Bredies and Fanzon (ESAIM: M2AN 54:2351–2382, 2020), where the objective functional is comprised of a fidelity term, penalizing the pointwise in time discrepancy between the observation and the unknown in time-varying Hilbert spaces, and a regularizer keeping track of the dynamics, given by the Benamou–Brenier energy constrained via the homogeneous continuity equation. Employing the characterization of the extremal points of the Benamou–Brenier energy (Bredies et al. in Bull Lond Math Soc 53(5):1436–1452, 2021), we define the atoms of the problem as measures concentrated on absolutely continuous curves in the domain. We propose a dynamic generalization of a conditional gradient method that consists of iteratively adding suitably chosen atoms to the current sparse iterate, and subsequently optimizing the coefficients in the resulting linear combination. We prove that the method converges with a sublinear rate to a minimizer of the objective functional. Additionally, we propose heuristic strategies and acceleration steps that allow to implement the algorithm efficiently. Finally, we provide numerical examples that demonstrate the effectiveness of our algorithm and model in reconstructing heavily undersampled dynamic data, together with the presence of noise.

Quantitative spatial analysis of thermal infrared radiation temperature fields by the standard deviational ellipse method for the uniaxial loading of sandstone

Previous studies focused mainly on the temporal analyses of thermal infrared radiation variations based on statistical parameters for rocks under loading conditions, and the spatial features were qualitatively obtained by visual interpretation. Hence, quantitative studies on the infrared radiation temperature fields on rock surfaces caused by stress variations and fracture activity remain scarce. Therefore, the standard deviational ellipse algorithm was introduced into spatial statistical analysis based on a temporal analysis. First, the abnormal infrared temperature points with values exceeding three times the standard deviation were extracted according to the statistical results for the entire calculated region, and the spatial coordinates of those abnormal points at different loading times were obtained. Second, the standard deviational ellipse was plotted based on the spatial coordinates of the abnormal points, and the lengths of the axes parallel and perpendicular to the loading direction, the coordinates of the ellipse center, and the area and ellipticity of the ellipse can be calculated at a certain loading moment. Then, the continuous temporal curves of the ellipse parameters during the whole loading process can be plotted, and quantitative analysis can be carried out on the spatiotemporal characteristics. The ellipse parameters changed steadily in the elastic stage, and the inflection point on the curves of the ellipse parameters occurred earlier than the inflection point on the curves of the average infrared radiation temperature and standard deviation in the microfracture development stage. The length of the coordinate axis perpendicular to the loading direction exhibited a decreasing trend. In the fracture development stage, the area of the ellipse decreased, and the ellipticity increased; the coverage region decreased, and the shape of the ellipse changed from circular to elongated. The ellipse parameters can quantitatively describe the evolution trend of the infrared radiation temperature field on the rock surface from a uniform random distribution to a centralized distribution in the fracture area, and the moving direction of the ellipse center can roughly indicate the macrofracture location. These research results are expected to provide experimental data-based guidance for the comprehensive quantitative analysis of temporal-spatial characteristics for the monitoring of rock stress disasters by thermal infrared remote sensing.

Vector field guidance for standoff target tracking

This work presents a guidance algorithm for standoff target tracking by unmanned aerial vehicles using the traditional Lyapunov guidance vector field framework. Unlike the past work, this guidance law is the function of the minimum radius of curvature, and, hence, it can act more flexibly for different maneuverable vehicles. Moreover, normalized even and odd functions are proposed here as circulation and convergence terms to improve performance in terms of optimality. The presence of wind is also considered for real world applications. As the proposed guidance law generates paths of continuous curvature, the designed path is flyable by fixed-wing unmanned vehicles. Simulation results are presented to validate the proposed guidance law.

Identifying the Dynamic Influence of Economic Policy Uncertainty on Enterprise Investment Using Functional Data Analysis

Economic policy uncertainty (EPU) is one of the important influencing factors for enterprise investment. By its nature, enterprise investment is dynamically affected by uncertainty. We examine the time-varying impact of EPU on the level of corporate investment by introducing functional data analysis (FDA). Based on smoothing the discrete data of 106 China Securities Index (CSI) 300 firms into the continuous curve, we examine the dynamic relationship between EPU on corporate investment level and investment efficiency. In addition, we explore the effect of EPU on the level of corporate investment and investment efficiency after grouping regressions in a functional model. The findings show the following: Firstly, there is a suppressive effect of rising EPU on the level of corporate investment. However, when the EPU is low, it has a significant promoting effect on the level of corporate investment and gradually decreases with the increase of uncertainty level. Secondly, elevated EPU has a promoting effect on the efficiency of corporate investment. The inhibitory effect on firm investment efficiency is observed at low EPU and changes to a promotional effect at high EPU. Thirdly, increasing EPU has a greater inhibitory role in the investment level of nonstate firms and a greater promotional role in the investment efficiency of state firms. We seek to expand the research on the impact of macrouncertainty on microfirm investment and introduce FDA to provide a meaningful reference to solve the current controversial issue.

The spatial decay of human capital externalities - A functional regression approach with precise geo-referenced data

This paper analyzes human capital externalities from high-skilled workers by applying functional regression to precise geocoded register data. Functional regression enables us to describe the concentration of high-skilled workers around workplaces as continuous curves and to efficiently estimate a spillover function determined by distance. Furthermore, our rich panel data allow us to address the sorting of workers and disentangle human capital externalities from supply effects by using an extensive set of time-varying fixed effects. Our estimates reveal that human capital externalities attenuate with increasing distance and disappear after 25 km. Externalities from the immediate neighborhood of an establishment are twice as large as externalities from surroundings 10 km away.

Bifurcation of symmetric solutions for the sublinear Moore-Nehari differential equation

We study the bifurcation of symmetric nodal solutions for the equation u″+h(x,λ)|u|p−1u=0 in (−1,1) with u(−1)=u(1)=0, where 0<p<1, h(x,λ)=0 for |x|<λ and h(x,λ)=1 for λ≤|x|≤1 and λ∈(0,1) is a bifurcation parameter. For a non-negative integer n, we call a solution u(x)n-nodal if it has exactly n zeros in (−1,1). We call a solution u symmetric if it is even or odd. For each n, the equation has a unique n-nodal symmetric solution un(x,λ), which is a continuous curve of λ∈(0,1). We prove that when n is even, this curve does not bifurcate and when n is odd, it bifurcates.

Short wave diffraction on a contour with a Hölder singularity of the curvature

Formulas are constructed for the short-wave asymptotics in the problem of diffraction of a plane wave on a contour with continuous curvature that is smooth everywhere except for one point near which it has a power-like behavior. The wave field is described in the boundary layers surrounding the singular point of the contour and the limit ray. An expression for the diffracted wave is found.

Detection and computation of conservative kernels of models consisting of freeform curves and surfaces, using inequality constraints

We present an algorithm to compute a tight-as-needed conservative approximation of the kernel domain of freeform curves in R2 and freeform surfaces in R3. Inequality constraints to detect the interior of the kernel domain are formulated as multivariates, and solved with a subdivision-based approach to find the domains in R2 or R3 that satisfy the inequalities and are in the kernel. The convex hull of the computed domains is also included in the kernel, and adopted as the approximated kernel domain. We can apply the presented algorithm to detect the kernel domain of not only C1 continuous closed regular curves and surfaces, but also the kernel domains of multiple piecewise C1 continuous regular freeform curves and surfaces. Further, the presented algorithm can be applied to find the gamma-kernel as well as the kernel domain of open curves and surfaces, under some assumptions. We demonstrate our experimental result using various freeform curves and surfaces, and compare it with the kernel computation algorithm presented in Elber et al. (2006).

Pregnancy-specific Continuous Reference Intervals for Haematology Parameters from an Australian Dataset: A Step Toward Dynamic Continuous Reference Intervals

(Aust N Z J Obstet Gynaecol. 2021;61:223–231) Reference intervals (RIs) in pregnancy are usually only reported in terms of trimesters or for specific weeks gestational age. RIs are also usually treated in a static manner, while pediatric growth charts and now fetal growth charts use smoothed centile curves to detect growth issues. This study aimed to derive continuous centile curves for 6 hematological parameters in pregnancy and compare the indirect RIs from those curves to previously published direct RIs.