Convex Curve Research Articles

Extremal interpolation of convex scattered data in ℝ3 by smooth edge convex minimum L∞‐norm networks: Characterization and solution

We consider the extremal problem of interpolation of convex scattered data in by smooth edge convex curve networks with minimal ‐norm of the second derivative for . The problem for was set and solved by Andersson et al. (1995). Vlachkova (2019) extended the results of Andersson et al. (1995) and solved the problem for . The minimum edge convex ‐norm network for is obtained from the solution to a system of nonlinear equations with coefficients determined by the data. The solution in the case is unique for strictly convex data. The corresponding extremal problem for remained open. The case is of particular interest in the context of applications since it has a solution which is a smooth curve network consisting of quadratic splines, that is, a smooth curve network of the lowest possible computational complexity. Here, we show that the extremal interpolation problem for always has a solution. We give a characterization of this solution. We show that a solution to the problem for can be found by solving a system of nonlinear equations in the case where it exists.

Determining the constant diffusion coefficient by Fourier series solution of the diffusion equation

The purpose of this study was to obtain the diffusion coefficient by calculating directly from the Fourier series solution of the diffusion equation, which has not been studied so far. The Fourier series solution is the sum of a steady-state solution and a transient solution. The steady-state solution is a linear function of distance. The transient solution is the product of a distance function and a time function. The Fourier sine series solution, a function of distance only, is negative for the steady-state solution. For the sublimation diffusion of disperse dye in paste into polyethylene terephthalate (PET) film using the film-roll method, the constant surface concentration and the diffusion distance were determined from the quadratic regression curve for the concentration distribution at a long time. The concentration distribution of the transient solution is a downwardly convex curve with negative values. The concentration distribution of the Fourier series solution is also a downwardly convex curve. The diffusion coefficient in the exponential term, a function of time only, was determined from the value of the exponential term obtained by the surface concentration and the diffusion distance. The constant diffusion coefficients determined from the Fourier series solution are reliable because they are very similar to those obtained from the error function solution and have excellent linearity of the linear regression lines for their Arrhenius plots.

Road Geometric Redesign used AutoCAD 2D A Case Jalan Majalengka-Rajagaluh

Majalengka-Rajagaluh road is a road located in several sub-districts which is a link to the city and also one of the connecting roads to Cirebon City. This design planning starts in Cigasong sub-district and continues to Rajagaluh sub-district with the length of Majalengka-Rajagaluh road is 5.3 kilometers. The geometric design results are visualized in the form of drawings using AutoCAD 2D. The design speed (Vd) was set at 60 km/h with a horizontal curve radius of 358 m, a maximum slope of 4%, and an elevation (e max) of 8%. Based on these design criteria, a spiral curve with a circular curve length (Lc) of 74.996 m was obtained. Furthermore, the results of the vertical alignment calculation of the length (L) of one type of convex curve in PPV were also calculated.

The polymyxin-B direct hemoperfusion OPTimal Initiation timing with Catecholamine PMX-OPTIC study: A multicenter retrospective observational study.

Polymyxin-B direct hemoperfusion (PMX-DHP) is an endotoxin adsorption column-based blood purification therapy. Since one of the most potent effects of PMX-DHP is blood pressure elevations, it may be the most effective when it is introduced at the time when the need for vasopressors is the greatest, which, in turn, may reduce mortality. A multicenter retrospective study was conducted at 24 ICUs in Japan. In each ICU, the 20 most recent consecutive cases of septic shock treated with PMX-DHP were analyzed. The duration between the time of the peak vasopressive agent dose, expressed as the noradrenaline equivalent dose (NEq), and the time of PMX initiation was evaluated. The primary outcome was 28-day mortality, and a multivariable analysis was performed to investigate factors associated with mortality. A total of 480 septic shock patients were included in the analysis. Among all patients, the 28-day mortality group was older, more severely ill, and had a higher body mass index. The NEq peak and NEq on PMX-DHP initiation were both higher in deceased patients. Regarding the timing of PMX-DHP initiation from the NEq peak, -4 << 4 h had more survivors (229/304, 75.3%) than ≤-4 h (50/75, 66.7%) and ≥4 h (66/101, 65.4%) (p = 0.085). When -4 << 4 h was assigned as a reference, the timing of PMX-DHP initiation from the NEq peak of ≤-4 h had an odds ratio of 1.96 (1.07-3.58), p = 0.029, while ≥4 h had an odds ratio of 1.64 (0.94-2.87), p = 0.082 for 28-day mortality, in the multivariable regression analysis. A spline curve of the relationship between the probability of death and the timing of PMX-DHP initiation from the NEq peak showed a downward convex curve with a nadir at timing = 0. The odds ratios of the timing of PMX-DHP initiation other than -4 << 4 h were significantly higher in an older age, male sex, lower BMI, more severe illness, and higher oxygenation. The induction of PMX-DHP at the time of the peak vasopressor dose correlated with lower mortality. PMX-DHP is one of the options available for elevating blood pressure in septic shock, and its initiation either too early or late for shock peak may not improve the outcome.

Tangential contact modeling to seal considering elastic-plastic for lubrication transition mechanism

Researches on the reciprocating seals lubrication under elastic-hydrodynamic lubrication (EHL) are mature, and leakage of failure criterion has been described with Couette flow for more than 30 years, which could not reflect to leakage mechanism in multiscale. Thus, it is necessary to explore seal leakage failure to focus on micro convex bodies of asperities model under contact pressure and cycle tangential friction stress in mixed lubrication. This is because convex bodies behaviors determine sealing effect and lubrication behaviors in microscale with subjecting to the dominant pressure. Interaction between convex bodies fatigue hysteresis curve and elastic-plastic strain are also calculated to explore sealing effect with leakage rate mechanism. We then design water seal at high pressure of 100 MPa with the speed of 0.1–1 m/s and medium temperature from 5 ℃ to 40 ℃. IWAN model of the convex bodies are calculated. Probability density function and Jenkin’s elements critical slip displacement are obtained. Convex bodies of radial and tangential deformation are also calculated through loading of contact pressure and friction stress with cycle strength coefficient to obtain seal fatigue lifespan. Ratio to seal stick and slip friction is calculated for evaluating the loading boundary. Seal leakage failure mechanism with fatigue characteristics is illustrated with macro lubrication parameters and micro convex bodies mechanics performance.

Foundational Engineering of Artificial Blood Vessels' Biomechanics: The Impact of Wavy Geometric Designs.

The design of wavy structures and their mechanical implications on artificial blood vessels (ABVs) have been insufficiently studied in the existing literature. This research aims to explore the influence of various wavy geometric designs on the mechanical properties of ABVs and to establish a foundational framework for advancing and applying these designs. Computer-aided design (CAD) and finite element method (FEM) simulations, in conjunction with physical sample testing, were utilized. A geometric model incorporating concave and convex curves was developed and analyzed with a symbolic mathematical tool. Subsequently, a total of ten CAD models were subjected to increasing internal pressures using a FEM simulation to evaluate the expansion of internal areas. Additionally, physical experiments were conducted further to investigate the expansion of ABV samples under pressure. The results demonstrated that increased wave numbers significantly enhance the flexibility of ABVs. Samples with 22 waves exhibited a 45% larger area under 24 kPa pressure than those with simple circles. However, the increased number of waves also led to undesirable high-pressure gradients at elevated pressures. Furthermore, a strong correlation was observed between the experimental outcomes and the simulation results, with a notably low error margin, ranging from 19.88% to 3.84%. Incorporating wavy designs into ABVs can effectively increase both vessel flexibility and the internal area under pressure. Finally, it was found that expansion depending on the wave number can be efficiently modeled with a simple linear equation, which could be utilized in future designs.

Parametric optimization for enhancing the electrical performance of hybrid photovoltaic/thermal and thermally regenerative electrochemical cycle system

Globally, the efficient utilization of solar energy has garnered significant attention. A hybrid system of photovoltaic/thermal (PV/T) modules integrated with thermally regenerative electrochemical cycle (TREC), i.e., PV/T-TREC has emerged recently and shows higher efficiency for solar-to-electrical conversion than a standalone PV system. However, there is a trade-off between the electricity generation from PV/T and TREC because the thermal energy from PV/T degrades the efficiency of the PV/T but improves that of TREC. Previous studies have failed to investigate this problem. This study therefore focuses on the key parameters that significantly affect the thermal output of PV/T, i.e., different PV materials, air gaps, heat storage tank volumes, and working fluids to investigate the maximum electrical efficiency of the hybrid system. The mathematical and transient-state numerical models are developed with the validation/refinement from the experiments. The results show that the hybrid system with PV material of cadmium telluride presents the best overall electrical efficiency of 25.37 %. The case of the air gap fosters the solar-to-electrical conversion. The electrical efficiency versus heat storage tank volume shows a convex curve, peaking at 200 L. The nanofluid performs the best. This study may help guide the practical application of such a high-efficiency electricity generation system.

Shape correction of deep-towed seismic arrays by using floaters and a cone-shaped drogue

Deep-towed multi-channel seismic arrays play vital role in marine geological exploration. However, these arrays often assume a "W" shape due to the weight of digital transmission units, adversely affecting hydrophone positioning and strata imaging. Floaters and a cone-shaped drogue are designed to correct the array shape, and numerical simulations are employed to validate the corrective effect in this paper. Additional drag forces induced by the floaters and drogue are identified using computational fluid dynamics, then they are integrated into the array model compiled to express the nonuniform mass distribution and concentrated loads based on absolute nodal coordinate formulation. Moreover, bending characteristics of arrays is fine-tuned through physical tests. Finally, simulation results indicate the floater has obvious effect than the drogue in the array shape correction, and the array shape becomes a simple convex curve with the presence of floaters and drogues under various towing conditions, facilitating hydrophone positioning. Furthermore, the array shape from the travel time positioning in sea trials also exhibit similar convex curves, and the signal-to-noise ratio of the seabed profile is much improved compare to previous one. This study also underscores the efficiency of numerical simulation in developing stabilization equipment for deep-towed multi-channel seismic arrays.

The Gradient Flow for Entropy on Closed Planar Curves

In this paper we consider the steepest descent L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2$$\\end{document}-gradient flow of the entropy functional. The flow expands convex curves, with the radius of an initial circle growing like the square root of time. Our main result is that, for any initial curve (either immersed locally strictly convex of class C2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^2$$\\end{document} or embedded of class W2,2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W^{2,2}$$\\end{document} bounding a strictly convex body), the flow converges smoothly to a round expanding multiply-covered circle.

Zero-shot classification of small target on sea bottom using model-agnostic meta-learning.

A model-agnostic meta-learning (MAML)-based active target classifier to identify small targets (e.g., mines) on the sea bottom in different ocean environments from those present in the training data is proposed. To better classify the targets deviating from those in the training set, MAML is applied to the out-of-distribution samples. Frequency-domain target and clutter scattering signals from various tasks with varying bottom types (silt/clay) and incident angles (low/moderate/high) are utilized as training data samples. MAML significantly outperforms conventional neural networks during the test. The improved generalization of MAML is explained using loss landscape in the form of a smooth convex curve.

Functional zoning of biodiversity profiles

AbstractSpatial mapping of biodiversity is crucial to investigate spatial variations in natural communities. Several indices have been proposed in the literature to represent biodiversity as a single statistic. However, these indices only provide information on individual dimensions of biodiversity, thus failing to grasp its complexity comprehensively. Consequently, relying solely on these single indices can lead to misleading conclusions about the actual state of biodiversity. In this work, we focus on biodiversity profiles, which provide a more flexible framework to express biodiversity through nonnegative and convex curves, which can be analyzed by means of functional data analysis. By treating the whole curves as single entities, we propose to achieve a functional zoning of the region of interest by means of a penalized model‐based clustering procedure. This provides a spatial clustering of the biodiversity profiles, which is useful for policy‐makers both for conserving and managing natural resources and revealing patterns of interest. Our approach is evaluated using a simulation study and discussed through the analysis of the Harvard Forest Data, which provides information on the spatial distribution of woody stems within a plot of the Harvard Forest.

A recursive method for fractional Hawkes intensities and the potential approach of credit risk

This article explores the potential approach for credit risk, which is an alternative to structural and reduced models. In the context of credit risk, it consists in assuming that the survival probability of a company is equal to the ratio of the expected value of a supermartingale divided by its initial value. This approach, that was previously used for modeling the term structure of interest rates, is extended by the use of a fractional self-exciting process, or fractional Hawkes process. This is a self-exciting process that is time-changed by the inverse of an alpha-stable subordinator. A self-exciting process allows to take into account the clustering of economic events such as defaults, whereas the time-change allows to properly fit highly convex survival probability curves. We derive a new recursive method that allows to compute all the moments of a self-exciting process intensity, as well as its time-changed counterpart. We show that this method can be used to approximate the survival probabilities in the potential approach. More specifically, we prove that the approximation converges and we provide a bound on the numerical error. Finally, we calibrate the model and show that it allows to properly fit survival probability curves that are highly convex.

When the Weibull model helps in deciphering bacterial resistance variability related to survival behaviour

Survival curves of bacterial vegetative cells or spores subjected to an inactivation process are often log-linear and then described by the d-value parameter. However, non log-linear, convex, shapes might be also observed particularly when mild inactivation treatments are applied. Our objective was to investigate whether the 3-parameters Weibull model (logN0, δ, p) could be used to go beyond a simple fitting of convex curve by providing information related to bacterial variability. First, survival curves were simulated to mimic the behaviour of a cocktail containing bacterial vegetative cells or spores undergoing an inactivation treatment, on which the Weibull model was fitted. Second, a mathematical model was developed to describe the link between the Weibull parameters p and delta with the d-values of sub-populations of bacterial vegetative cells or spores (considering as well the percentage of each sub-population). Based on this model, it was shown that the Weibull model can be used to go beyond a simple description of a convex curve. For instance, if p is estimated around 0.8, that means the presence of a resistant sub-population, but with a limited resistant variability (ratio of resistance from 1.5 to 4). In contrast, if p is estimated to 0.3–04 that means the presence of a resistant sub-population in a small proportion (less than 10 %) combined with a large resistant variability (ratio of 10 or more). This study shows that the Weibull model can be used in combination with the new model developed here to decipher vegetative cell or spore resistance variability, with application in food industry processes such as thermal or physical inactivation treatment as well as cleaning and disinfection verification procedure.

Remagnetization of magnetite-bearing rocks in the Eastern Qiangtang Terrane, Tibetan Plateau (China): Mechanism and diagnosis

Remagnetization is a common yet notorious phenomenon that interferes with paleogeographic reconstruction. Classical paleomagnetic field tests are helpful in detecting remagnetization but their diagnostic power is limited: remagnetization may occur before folding, the tilting age may be ambiguous, or protracted remagnetization may yield dual polarities. Rock magnetic information can provide other constraints on our understanding of the origin of natural remanent magnetization (NRM). Here we focus on the rock magnetic properties of acknowledged remagnetized limestones and unremagnetized rocks of the Zaduo area in the Eastern Qiangtang Terrane, Tibetan Plateau (China). Chemical remanent magnetization is suggested as a more frequent mechanism than the thermoviscous resetting of the NRM. The secondary NRM resides in authigenic magnetite of stable single domain and superparamagnetic (SP) size which grew during post-depositional burial processes. Both high-field and low-field thermomagnetic runs reveal the alteration of existing iron sulfides to magnetite in the remagnetized limestones. NRM decay curves show that the maximum unblocking temperature of the remagnetized samples is significantly lower than that of the unremagnetized samples. Component analysis of acquisition curves of the isothermal remanent magnetization (IRM) reveals a hard component that represents SP magnetite in remagnetized limestones. This component is absent in unremagnetized rocks. End-member modelling reveals a convex curve in the coefficient of determination versus the number of end-members plot for the unremagnetized limestones, whereas the remagnetized rocks exhibit both near-linear and convex shapes. In addition, quantitative analysis of the hysteresis loop shape for different lithologies indicates its validity in detecting remagnetization. Furthermore, we show the differences in the hysteresis data distributions of the two rock types on the Day plot, the Néel diagram, the Borradaile diagram, and the Fabian diagram. Our research emphasizes that rock magnetic properties can serve as tools to diagnose remagnetization in magnetite-dominated rocks. We recommend a comprehensive rock magnetic study to discriminate remagnetization, involving the Day plot, Fabian diagram, thermal demagnetization curves, IRM component analysis and end member modelling.

Representation formulae for linear hyperbolic curvature flows

In [19], Smoczyk showed that parabolic expansion of convex curves and hypersurfaces by the reciprocal of the harmonic mean curvature gives rise to a linear second order equation for the evolution of the support function, with corresponding representation formulae for solutions. In this article we obtain representation formula for the corresponding linear hyperbolic evolution equation for the support function of locally convex curves of general nonzero rotation number, finding some natural similarities and differences in behaviour of solutions as compared with the parabolic case. As applications, we consider linear hyperbolic flows that preserve length or generalised enclosed area of the evolving curve, flow of curves with Neumann boundary conditions inside cones and hyperbolic approaches to the Yau problem of flowing one curve to another. We also consider radial graphs evolving by similar linear equations and linear higher order hyperbolic equations. Our results may be compared with the corresponding parabolic cases consider by the first author, Schrader and Wheeler, in [17].

Phase Diagram Analysis of High-Pressure/High-Temperature Polymorphs of Ammonia Borane.

Ammonia borane (NH3BH3) is a promising hydrogen-storage material because of its high hydrogen density. It is employed as a hydrogen source when synthesizing superconducting polyhydrides under high pressure. Additionally, NH3BH3 is a crystallographically interesting compound that features protonic hydrogen (Hδ+) and hydridic hydrogen (Hδ-), and it forms a dihydrogen bond, which explains its stable existence as a solid. Herein, X-ray diffraction experiments were performed at high pressures (HPs) and high temperatures (HTs) of up to 30 GPa and 300 °C, respectively, to investigate the HP/HT phase diagram of NH3BH3. A new HP/HT phase (HPHT2) was identified above 9 GPa and 150 °C. Crystal-structure analysis using the Rietveld method and stability verification using density functional theory calculations revealed that HPHT2 has a P21/n (Z = 4) structure, similar to that of a previously reported HP/HT phase (HPHT) that appears at a lower pressure. HPHT2 is denser than the HP phases that appear at room temperature (HP1 and HP2) at the same pressure (up to ∼17 GPa). In the phase diagram, the phase-boundary line between HPHT and HP1 is a downward convex curve. These unconventional phenomena in the density and phase boundary can be attributed to the influence of dihydrogen bonding on the crystal structure and phase diagram.

Anisotropic area-preserving nonlocal flow for closed convex plane curves

Abstract We consider an anisotropic area-preserving nonlocal flow for closed convex plane curves, which is a generalization of the model introduced by Pan and Yang (J. Differential Equations 266 (2019), 3764–3786) when τ = 1. Under this flow, the evolving curve maintains its convexity and converges to a homothety of a smooth symmetric strictly convex plane curve in the C ∞ sense. The analysis of the asymptotic behavior of this flow implies the possibility of deforming one curve into another within the framework of Minkowski geometry.

A modified U-Net convolutional neural network for segmenting periprostatic adipose tissue based on contour feature learning

ObjectiveThis study trains a U-shaped fully convolutional neural network (U-Net) model based on peripheral contour measures to achieve rapid, accurate, automated identification and segmentation of periprostatic adipose tissue (PPAT). MethodsCurrently, no studies are using deep learning methods to discriminate and segment periprostatic adipose tissue. This paper proposes a novel and modified, U-shaped convolutional neural network contour control points on a small number of datasets of MRI T2W images of PPAT combined with its gradient images as a feature learning method to reduce feature ambiguity caused by the differences in PPAT contours of different patients. This paper adopts a supervised learning method on the labeled dataset, combining the probability and spatial distribution of control points, and proposes a weighted loss function to optimize the neural network's convergence speed and detection performance. Based on high-precision detection of control points, this paper uses a convex curve fitting to obtain the final PPAT contour. The imaging segmentation results were compared with those of a fully convolutional network (FCN), U-Net, and semantic segmentation convolutional network (SegNet) on three evaluation metrics: Dice similarity coefficient (DSC), Hausdorff distance (HD), and intersection over union ratio (IoU). ResultsCropped images with a 270 × 270-pixel matrix had DSC, HD, and IoU values of 70.1%, 27 mm, and 56.1%, respectively; downscaled images with a 256 × 256-pixel matrix had 68.7%, 26.7 mm, and 54.1%. A U-Net network based on peripheral contour characteristics predicted the complete periprostatic adipose tissue contours on T2W images at different levels. FCN, U-Net, and SegNet could not completely predict them. ConclusionThis U-Net convolutional neural network based on peripheral contour features can identify and segment periprostatic adipose tissue quite well. Cropped images with a 270 × 270-pixel matrix are more appropriate for use with the U-Net convolutional neural network based on contour features; reducing the resolution of the original image will lower the accuracy of the U-Net convolutional neural network. FCN and SegNet are not appropriate for identifying PPAT on T2 sequence MR images. Our method can automatically segment PPAT rapidly and accurately, laying a foundation for PPAT image analysis.

Uniform maximal Fourier restriction for convex curves

Uniform maximal Fourier restriction for convex curves

Latitudinal patterns and their climate drivers of the δ 13C, δ 15N, δ 34S isotope signatures of Spartina alterniflora across plant life-death status: a global analysis.

Isotopic signatures offer new methods, approaches, and perspectives for exploring the ecological adaptability and functions of plants. We examined pattern differences in the isotopic signatures (δ 13C, δ 15N, δ 34S) of Spartina alterniflora across varying plant life-death status along geographic clines. We extracted 539 sets of isotopic data from 57 publications covering 267 sites across a latitude range of over 23.8° along coastal wetlands. Responses of isotopic signatures to climate drivers (MAT and MAP) and the internal relationships between isotopic signatures were also detected. Results showed that the δ 13C, δ 15N, and δ 34S of S. alterniflora were -13.52 ± 0.83‰, 6.16 ± 0.14‰, and 4.01 ± 6.96‰, with a range of -17.44‰ to -11.00‰, -2.40‰ to 15.30‰, and -9.60‰ to 15.80‰, respectively. The latitudinal patterns of δ 13C, δ 15N, and δ 34S in S. alterniflora were shaped as a convex curve, a concave curve, and an increasing straight line, respectively. A decreasing straight line for δ 13C within the ranges of MAT was identified under plant life status. Plant life-death status shaped two nearly parallel decreasing straight lines for δ 34S in response to MAT, resulting in a concave curve of δ 34S for live S. alterniflora in response to MAP. The δ 15N of S. alterniflora significantly decreased with increasing δ 13C of S. alterniflora, except for plant death status. The δ 13C, δ 15N, and δ 34S of S. alterniflora are consistent with plant height, stem diameter, leaf traits, etc, showing general latitudinal patterns closely related to MAT. Plant life-death status altered the δ 15N (live: 6.55± 2.23‰; dead: -2.76 ± 2.72‰), latitudinal patterns of S. alterniflora and their responses to MAT, demonstrating strong ecological plasticity and adaptability across the geographic clines. The findings help in understanding the responses of latitudinal patterns of the δ 13C, δ 15N, and δ 34S isotope signatures of S. alterniflora in response plant life-death status, and provide evidence of robust ecological plasticity and adaptability across geographic clines.