Parameter Constraints Research Articles

High-accuracy emulators for observables in ΛCDM, Neff, Σmν, and w cosmologies

ABSTRACT We use the emulation framework CosmoPower to construct and publicly release neural network emulators of cosmological observables, including the cosmic microwave background (CMB) temperature and polarization power spectra, matter power spectrum, distance-redshift relation, baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) observables, and derived parameters. We train our emulators on Einstein–Boltzmann calculations obtained with high-precision numerical convergence settings, for a wide range of cosmological models including ΛCDM, wCDM, ΛCDM + Neff, and ΛCDM + Σmν. Our CMB emulators are accurate to better than 0.5 per cent out to ℓ = 104, which is sufficient for Stage-IV data analysis, and our P(k) emulators reach the same accuracy level out to $k=50 \, \, \mathrm{Mpc}^{-1}$, which is sufficient for Stage-III data analysis. We release the emulators via an online repository (CosmoPower Organisation), which will be continually updated with additional extended cosmological models. Our emulators accelerate cosmological data analysis by orders of magnitude, enabling cosmological parameter extraction analyses, using current survey data, to be performed on a laptop. We validate our emulators by comparing them to class and camb and by reproducing cosmological parameter constraints derived from Planck TT, TE, EE, and CMB lensing data, as well as from the Atacama Cosmology Telescope Data Release 4 CMB data, Dark Energy Survey Year-1 galaxy lensing and clustering data, and Baryon Oscillation Spectroscopic Survey Data Release 12 BAO and RSD data.

Reliability evaluation for Weibull distribution with heavily Type II censored data

AbstractThe lifetime data collected from the field are usually heavily censored, in which case, getting an accurate reliability evaluation based on heavily censored data is challenging. For heavily Type‐II censored data, the parameters estimation bias of traditional methods (i.e., maximum likelihood estimation (MLE) and least squares estimation (LSE)) are still large, and Bayesian methods are hard to specify the priors in practice. Therefore, considering the existing range of shape parameter for Weibull distribution, this study proposes two novel parameter estimation methods, the three‐step MLE method and the hybrid estimation method. For the three‐step MLE method, the initial estimates of shape and scale parameters are first respectively derived using MLE, then are updated by the single parameter MLE method with the range constraint of shape parameter. For the hybrid estimation method, the shape parameter is estimated by the LSE method with the existing range constraint of shape parameter, then the scale parameter estimate can be obtained by MLE. On this basis, two numerical examples are performed to demonstrate the consistency and effectiveness of the proposed methods. Finally, a case study on turbine engines is given to verify the effectiveness and applicability of the proposed methods.

Angular correlation function from sample covariance with BOSS and eBOSS LRG

The Baryon Acoustic Oscillations (BAO) are one of the most used probes to understand the accelerated expansion of the Universe. Traditional methods rely on fiducial model information within their statistical analysis, which may be a problem when constraining different families of models. This work aims to provide a method that constrains θBAO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{BAO}$$\\end{document} through a model-independent approach using the covariance matrix from the galaxy sample from thin redshift bins, later validated with a mock sample covariance matrix. We used widths of δz=0.002\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta z = 0.002$$\\end{document} separation for all samples as the basis for a sample covariance matrix weighted by the statistical importance of the redshift bin. Each sample belongs to the Sloan Digital Sky Survey: BOSS1, BOSS2, and eBOSS, with effective redshift zeff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z_{eff}$$\\end{document}: 0.35, 0.51, 0.71, and different numbers of bins with 50, 100, and 200. To get θBAO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{BAO}$$\\end{document}, we correct the angular separation from the polynomial fit (θfit\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{fit}$$\\end{document}) by comparing each bin correlation function with the correlation function of the whole set, a parameter named α~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ilde{\\alpha }$$\\end{document}. We also tested such correction by choosing the bin at zeff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z_{eff}$$\\end{document} and found that for eBOSS θBAO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{BAO}$$\\end{document} is in 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1 \\sigma $$\\end{document} agreement with the Planck 18 model. Finally, we found that the sample covariances are noisy compared to the mocks for lower z samples, something expected due to nonlinear effects. Such noise impact can be seen in the parameter constraints but does not affect the eBOSS covariance sample. It is shown that mocks’ results do tend to its chosen fiducial cosmology θBAO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{BAO}$$\\end{document}. BOSS1 and BOSS2 showed agreement with Planck 18 and an agreement with Pantheon + SH0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document}ES when α~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ilde{\\alpha }$$\\end{document} is based on the bin z=zeff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z=z_{eff}$$\\end{document}.

Inverse optimization in semi-definite programs to impute unknown constraint matrices

In a typical (forward) optimization problem, a decision-maker uses given values of model parameters to compute the values of decision variables. The goal in inverse optimization (IO) is instead to infer parameters that render given values of decision variables optimal. Most papers on IO utilize duality to impute objective function parameters. A corresponding literature for imputing constraint parameters is essentially non-existent, even for linear programs. The difficulty is that these IO problems include nonconvex bilinear constraints and/or objectives. We study inverse semi-definite programs (SDPs) where matrices on the left-hand-sides of constraints are unknown. These unknown matrices must satisfy some side constraints. We consider two types of such problems, depending on which SDP decision variable values are given: primal or dual. In each situation, we study three sub-cases based on whether both the right-hand-side coefficients and the objective function matrix are known or only one of these two is known. This creates six variants of the inverse problem. For each variant, we first look for sufficient conditions, either on the side constraints or on problem structure, under which the nonconvex bilinear inverse problem can be simplified substantially. In particular, it either has a trivial solution or can be reformulated as a (set of) convex program(s). When such conditions are not evident, we propose three tailored heuristics called the Convex–Concave Procedure, Sequential Semi-definite Programming, and Alternate Convex Search. We perform computational experiments to gain insights into the performance of these three methods.

Representative rupture stress-based parameter for characterizing the intensity of creep fracture constraint effect on creep crack growth rate

The introduction of creep fracture constraint parameter offers the possibility of accurately obtaining the CCG rate for specimens/structures subject to different constraint levels through the establishment of constraint-dependent CCG rate equation. However, experimental evidence indicates that the existing constraint-dependent CCG rate equation is generally material- and stress regime-dependent. It is noted that the dependencies may be attributed to the intrinsic difference in creep failure mechanisms of materials, which has not been fully considered by previous constraint parameters. To cope with the dependencies, a parameter, Kz, for characterizing the intensity of constraint effect is proposed in this work based on the representative rupture stress, which could better reflect the operative creep failure mechanism sustained by the material. To justify the parameter, finite element analysis is carried out for five different materials based on experimental data available in the literature. Results show that, compared to the existing constraint parameters, R* and Ac, the Kz is capable of characterizing the crack-tip constraint level under the influence of creep failure mechanism. Furthermore, a generalized constraint-dependent CCG rate equation is established based on the Kz, which overcomes the material and stress regime dependencies of the existing equation. Finally, to clarify the advantage of the Kz, further comparison between the new parameter and the existing parameters is made.

Numerical optimization of longitudinal collimator geometry for novel x-ray field

Objective. A novel x-ray field produced by an ultrathin conical target is described in the literature. However, the optimal design for an associated collimator remains ambiguous. Current optimization methods using Monte Carlo calculations restrict the efficiency and robustness of the design process. A more generic optimization method that reduces parameter constraints while minimizing computational load is necessary. A numerical method for optimizing the longitudinal collimator hole geometry for a cylindrically-symmetrical x-ray tube is demonstrated and compared to Monte Carlo calculations. Approach. The x-ray phase space was modelled as a four-dimensional histogram differential in photon initial position, final position, and photon energy. The collimator was modeled as a stack of thin washers with varying inner radii. Simulated annealing was employed to optimize this set of inner radii according to various objective functions calculated on the photon flux at a specified plane. Main results. The analytical transport model used for optimization was validated against Monte Carlo calculations using Geant4 via its wrapper, TOPAS. Optimized collimators and the resulting photon flux profiles are presented for three focal spot sizes and five positions of the source. Optimizations were performed with multiple objective functions based on various weightings of precision, intensity, and field flatness metrics. Finally, a select set of these optimized collimators, plus a parallel-hole collimator for comparison, were modeled in TOPAS. The evolution of the radiation field profiles are presented for various positions of the source for each collimator. Significance. This novel optimization strategy proved consistent and robust across the range of x-ray tube settings regardless of the optimization starting point. Common collimator geometries were re-derived using this algorithm while simultaneously optimizing geometry-specific parameters. The advantages of this strategy over iterative Monte Carlo-based techniques, including computational efficiency, radiation source-specificity, and solution flexibility, make it a desirable optimization method for complex irradiation geometries.

METHODS FOR 3D INVERSION OF GRAVITY DATA IN INDENTIFYING TECTONIC FACTORS CONTROLLING HYDROCARBON ACCUMULATIONS IN THE EL ZEIT BASIN AREA, SOUTHWESTERN GULF OF SUEZ, EGYPT

The Gebel EL-Zeit area in the southwestern Gulf of Suez, Egypt, is an area with a significant hydrocarbon potential in sedimentary basins, so that the three-stage inversion method was proposed for the Bouguer anomalies observed therein. Salt diapirs obscured the deep structure of the main central El-Zeit basin; hence, this method was implemented to overcome challenges in 3D seismic modeling. Our study included direct and inverse parameterization sequences that involved analyzing the inputs and outputs within trial-and-error initiations and inverse estimations to assess whether and how much the constraining parameters used in the calculations could achieve the intended aim. Data reduction, filtering, optimization, and constraint assumptions were used to determine the minimal set of density model parameters needed to set limits on the acceptable range of density contrasts that are required to study the basement depths, swells, troughs, faulting/folding and intra-sedimentary structures, and for direct modeling aimed at creating a simple model to save time. The thirteen constrained wells with a total depth ranging from shallow to deep were not involved in direct modeling but provided quality control over the graphical display of the inverse results for the entire study area. Moreover, many parameter constraints were inverted to regulate the way the calculated data are related to the model’s solution that allowed us to determine which inversion trial provided the best parameterization sequence and, therefore, yielded the most appropriate solution for the depth-density model which is approximating reality with a minimal computation error in the study area.

Quantification of crack tip constraint effect based on the critical distance

AbstractThe effect of crack tip constraint on the fracture properties of flawed components is a critical consideration in the safety assessment of engineering structures. In this work, an approximate expression of three‐dimensional von Mises stress fields ahead of the crack tip has been derived by referring to the classic Hutchinson‐Rice‐Rosengren (HRR) solution. The critical distance rc is chosen as the constraint parameter to quantify the level of the crack tip constraint. A theoretical relationship between the parameter rc and fracture toughness JQ has been proposed. The critical constraint parameter rc can be experimentally determined by using the critical fracture toughness JQ. The experimental results of compact tension (CT) and single edge‐notched bending (SENB) specimens with different crack tip constraint levels for SA‐508 and Q345B steels successfully validate the relationship between the critical fracture toughness JQ and the constraint parameter rc. According to the test results, the critical distance rc is feasible to quantify the crack tip constraint of CT and SENB specimens with different crack tip constraint levels.

Simulation-based process parameter optimization for wire arc additive manufacturing

AbstractDuring manufacturing of components using wire arc additive manufacturing, specific cooling times are required to prevent overheating of the structure and geometrical distortions. Currently, these cooling times are inserted based on experience at certain interlayer temperatures — which reduces the reproducibility, leads to unwanted component properties, and increases the process time. In this contribution, instationary thermal finite element simulations are applied to compute the temperature evolution of additively manufactured components using the inactive element method. This allows to optimize the process parameters, which are — in our considerations here — the welding velocity and the cooling time of each layer, to reduce the total process time while achieving sufficient component properties. The optimization is carried out with the gradient-free Nelder–Mead simplex algorithm, where certain constraints of the process parameters are considered via penalty functions. To obtain reasonable simulation results, the temperature-dependent heat transfer of the experimental setup is modeled and calibrated with experimental data beforehand. It becomes apparent that thermal finite element simulations combined with a gradient-free optimization procedure are a suitable numerical tool to perform the optimization of process parameters for wire arc additive manufacturing. The optimized process parameters fulfill certain requirements regarding the cooling of the manufactured component. Moreover, the optimized parameters can significantly reduce the process time compared to manually chosen parameters. In our example, this is around 48 %.

Dynamical system analysis of scalar field cosmology in coincident f(Q) gravity

In this article, we investigate scalar field cosmology in the coincident f(Q) gravity formalism. We calculate the motion equations of f(Q) gravity under the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a scalar field. We consider a non-linear f(Q) model, particularly f(Q) = − Q + α Q n , which is nothing but a polynomial correction to the Symmetric Teleparallel Equivalent to General Relativity (STEGR) case. Further, we assumed two well-known specific forms of the potential function, specifically the exponential from V(ϕ) = V 0 e −β ϕ and the power-law form V(ϕ) = V 0 ϕ −k . We employ some phase-space variables and transform the cosmological field equations into an autonomous system. We calculate the critical points of the corresponding autonomous systems and examine their stability behaviors. We discuss the physical significance corresponding to the exponential case for parameter values n = 2 and n = − 1 with β = 1, and n = − 1 with β=3 . Moreover, we discuss the same corresponding to the power-law case for the parameter value n = − 2 and k = 0.16. We also analyze the behavior of corresponding cosmological parameters such as scalar field and dark energy density, deceleration, and the effective equation of state parameter. Corresponding to the exponential case, we find that the results obtained for the parameter constraints in Case III is better among all three cases, and that represents the evolution of the Universe from a decelerated stiff era to an accelerated de-Sitter era via matter-dominated epoch. Further, in the power-law case, we find that all trajectories exhibit identical behavior, representing the evolution of the Universe from a decelerated stiff era to an accelerated de-Sitter era. Lastly, we conclude that the exponential case shows better evolution as compared to the power-law case.

Feed optimization based on force modelling and TLBO algorithm in milling Al 7075

Aluminium alloys find wide applications in structural industries. They are only second to steel when it comes to their applications. Their wide application is due to their numerous good properties. They have a high resistance to corrosion and high fatigue strength. Their specific density, electrical and thermal properties make them stand out amongst many structural metals. Al 7075 is an alloy of aluminium in which zinc is the dominant alloying element. This alloy is in the 7xxx series of aluminium alloys, a series considered to be the strongest with yield strengths greater or equal to 500 Mpa. It, therefore, finds a wide application in aircraft structural components manufacturing and other areas where high strength is a critical property. Therefore, this paper focuses on the CNC milling process of aluminium 7075 to establish force components models and the optimal values for the critical process parameters. The work reported in this paper involved designing experiments and the development of force components and resultant force models from the experimentally acquired data. The models were validated, and their prediction ability was within the accepted range. The validated force component models were used to investigate the interaction effects of the process parameters on the respective force components. The resultant force model was eventually used as the objective function in the TLBO algorithm to acquire the optimal force and control parameters. After that, the optimal resultant force was used as a constraint parameter to demonstrate feed optimization relative to the other parameters.

Certain analytical solutions of the concatenation model with a multiplicative white noise in optical fibers

In the presence of spatio-temporal dispersion, perturbation terms of the Hamiltonian type as well as multiplicative white noise, analytical investigation of the concatenation model having the Kerr law of nonlinearity is carried out in this work. The Cole–Hopf transformation and direct assumptions with arbitrary functions are utilized to determine several analytic solutions to the governing equation, including multi-wave, two solitary wave, breather, periodic cross kink, Peregrine-like rational, and three-wave solutions. The parameter constraints that serve as the requisite condition for the existence of these wave solutions are also identified. In order to explore and illustrate the propagation and dynamical behaviors of some solutions reported in this research, 3D graphics and their corresponding contour plots are included. Results of this paper may be useful for the experimental realization of certain nonlinear waves in optical fibers and further understanding of their propagation dynamics.

Extraction of Solar Module Parameters using a Novel Optimization Technique

The parameters of a Photovoltaic (PV) model are pivotal in gauging its efficiency under varying sunlight irradiances, temperatures, and different load scenarios. Determining these PV model parameters poses a complex non-linear optimization challenge. This study is based on a new metaheuristic optimization algorithm called the Pelican Optimization Algorithm (POA) to discern the unknown parameters of the PV model. The suggested POA algorithm underwent testing using a monocrystalline panel, encompassing its single-diode configuration. The objective function is designed to minimize the root of the mean squared errors between the predicted and actual current values, adhering to specific parameter constraints. Various statistical error metrics were utilized to emphasize the performance of the proposed algorithm. A comparative analysis with other well-established algorithms was conducted, indicating that POA stands out as highly competitive since it showcases superior efficiency in parameter identification compared to its counterparts.

Optical Soliton Perturbation with the Concatenation Model: Semi-inverse Variation

This paper retrieves bright 1-soliton solution to the perturbed concatenation model by the application of the semi-inverse variational principle. The perturbation terms are from inter-modal dispersion and self-steepening effect that is considered with maximum allowable intensity. The parameter constraints that naturally emerged from the integration scheme are enumerated.

An intelligent recommendation system for personalised parametric garment patterns by integrating designer’s knowledge and 3D body measurements

Garment pattern-making is one of the most important parts of the apparel industry. However, traditional pattern-making is an experience-based work, very time-consuming and ignores the body shape difference. This paper proposes a parametric design method for garment pattern based on body dimensions acquired from a body scanner and body features (body feature points and three segmented body part shape classification) identified by designers according to their professional knowledge. By using this method, we construct a men’s shirt pattern recommendation system oriented to personalised fit. The system consists of two databases and three models. The two databases include a relational database (Database I) and a personalised basic pattern (PBP) database (Database II). The Database I is based on manual and three-dimensional (3D) measurements of human bodies by using designer’s knowledge. And Database I is a relational database, which is organised in terms of the relational model of the body part shape and its key body feature dimensions. After a deep analysis of measured data, the irrelevant measured dimensions to human body shape have been excluded by designers and extract representative human body feature dimensions. In addition, the relations between body shapes and previously identified body feature dimensions have been modelled. From the above relational model, we label key feature point positions on the corresponding 3D body model obtained from 3D body scanning and correct the whole 3D human upper body model into the semantically interpretable one. The 3D personalised basic pattern is drawn on the corrected model based on these key feature points. By using three-dimensional to two-dimensional (3D-to-2D) flattening technology, a 2D flatten graph of the 3D personalised basic pattern of the interpretable model is obtained and slightly adjusted to the form suitable for industrial production, i.e., PBP and the PBP database (Database II) is built. In addition, the three models include a basic pattern parametric model (Model I) (characterizing the relations between the basic pattern and its key influencing human dimensions (chest girth and back length)), a regression model (Model II) which enables to infer from basic pattern to PBP for three body parts based on the one-to-one correspondence of key points between the PBPs and the basic patterns and a personalised shirt pattern parametric model (Model III) (characterizing the structural relations between the personalised shirt pattern (PBPshirt) and PBP). The initial input items of the recommendation system are the body dimension constraint parameters, including chest girth, back length and the body feature dimensions used to determine each body part shape as well as three shirt style constraint parameters (slim, regular and loose). By using Model I, the corresponding basic pattern can be generated through the user’s chest girth and back length. Body feature dimensions determine the three body parts’ shapes. Then, Model II is used to generate the PBP for the corresponding body parts shape. Based on the shirt style chosen by the user, Mode III is used to generate the PBPshirt from the PBP. The output of the recommendation system is a fit-oriented PBPshirt. Moreover, if the PBPshirt is unsatisfactory after a virtual try-on, four adjustable parameters (front side-seam dart, back side-seam dart, waist dart and garment bodice length) are designed to adjust the PBPshirt generated by the proposed recommendation system.

A novel global calibration method for vision measurement system based on mirror-image stereo target

Using three-dimensional (3D) targets to solve the transformation relationship between the local and global coordinate systems is a common global calibration method. However, 3D targets have complex structures and high costs. And multiple coordinate transformations during global calibration can cause significant cumulative errors. Therefore, based on reflection imaging, this paper designs a new mirror-image stereo target (MST) and analyzes its view area and three structural parameter constraints. A new global calibration method is proposed, as well as three optimization algorithms for pose solution between MST, optical 3D sensor and global camera to improve the global calibration accuracy. The experimental results show that the registration errors of two workpieces are 0.086 mm and 0.114 mm, respectively, confirming the feasibility and precision of the proposed method. Our method is flexible, requiring only a planar target and a mirror, rather than complex 3D targets, to achieve global calibration with non-overlapping field of view.

Effect of constraint on creep fracture toughness of a Cr-Mo-V steel

The creep fracture toughness of materials is required for the assessment of defective components at high-temperatures. Existing evidence indicates that creep crack-tip constraint state has a great influence on the fracture behavior of materials. In this work, the effect of constraint on creep fracture toughness was explored by conducting a series of creep crack growth tests on specimens with various thicknesses and loading modes. Results showed that the curves of creep fracture toughness with creep crack initiation time on the logarithmic scale for different groups of specimens were almost parallel with one another. Through the characterization of crack-tip constraint level for different groups of specimens in terms of a load-independent creep fracture constraint parameter, R*, the creep fracture toughness was found to increase with the decrease in the crack-tip constraint level. Moreover, evident effect of specimen geometry on creep fracture toughness was observed. Of all types of specimens, the CCT2 and CT10-SG exhibited the highest and lowest values of Kcmat at the same ti, respectively. In addition, the Kcmat was found to increase following a specimen group order of CT10-SG, CT10, CT5, SENT5, CT2, SENT2 and CCT2 at a given ti. Finally, a constraint-dependent creep fracture toughness equation was established for the Cr-Mo-V steel, which is expected for practical applications to improve accuracy of life assessment methods. Follow-up work on life assessment methods incorporating the constraint parameter R* is still necessary.

UAV building point cloud contour extraction based on the feature recognition of adjacent points distribution

Building point cloud contour is widely used in urban planning and building identification. The existing method cannot work well in the extraction of UAV building point cloud contour points because the low point cloud accuracy of UAV, and effect of noise. In this paper we propose extraction method of UAV building point cloud contour based on the adjacent points distribution. Firstly, we construct an information entropy model for determining optimal neighborhood points, and then use the eigenvectors corresponding to the maximum and minimum eigenvalues obtained by PCA to construct initial projection plane Π1 and Π2. Secondly, we propose the fine-tuning model of the projection plane Π2 by using the aggregation characteristics of neighborhood points, and construct the extraction model of fold points with three parameter constraints. Finally, we propose the information entropy model of points probabilities in different quadrants on the plane Π1 to extract boundary points. Real UAV point cloud data is used to test the performance and parameters of the proposed method, experiment results show that the proposed method is superior to OPAHT, 2D line detection and region clustering segmentation methods in the performance of UAV building point cloud contour extraction. The proposed method can accurately extract the point cloud contour points of UAV buildings.

SIR epidemic model with non-Lipschitz stochastic perturbations

This paper investigates a stochastic SIR epidemic model with non-Lipschitz coefficients in the diffusion term. Firstly, we study the existence and uniqueness of the global positive solution of this model. Then, we prove that the stochastic process has a stationary distribution, and we also establish an exact expression of the density function of the stationary distribution under certain parameter constraints. Finally, we discuss the extinction of the epidemic and the asymptotic properties around the equilibrium points of the deterministic SIR model.

Constrained Reweighting of Distributions: An Optimal Transport Approach.

We commonly encounter the problem of identifying an optimally weight-adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the moments, tail behavior, shapes, number of modes, etc., of the resulting weight-adjusted empirical distribution. In this article, we substantially enhance the flexibility of such a methodology by introducing a nonparametrically imbued distributional constraint on the weights and developing a general framework leveraging the maximum entropy principle and tools from optimal transport. The key idea is to ensure that the maximum entropy weight-adjusted empirical distribution of the observed data is close to a pre-specified probability distribution in terms of the optimal transport metric, while allowing for subtle departures. The proposed scheme for the re-weighting of observations subject to constraints is reminiscent of the empirical likelihood and related ideas, but offers greater flexibility in applications where parametric distribution-guided constraints arise naturally. The versatility of the proposed framework is demonstrated in the context of three disparate applications where data re-weighting is warranted to satisfy side constraints on the optimization problem at the heart of the statistical task-namely, portfolio allocation, semi-parametric inference for complex surveys, and ensuring algorithmic fairness in machine learning algorithms.