Inverse Function Research Articles

Different ecological demands shape differences in population structure and behaviour among the two generations of the small pearl-bordered fritillary.

The population structure and behaviour of univoltine butterfly species have been studied intensively. However, much less is known about bivoltine species. In particular, in-depth studies of the differences in population structure, behaviour, and ecology between these two generations are largely lacking. Therefore, we here present a mark-release-recapture study of two successive generations of the fritillary butterfly Boloria selene performed in eastern Brandenburg (Germany). We revealed intersexual and intergenerational differences regarding behaviour, dispersal, population characteristics, and protandry. The observed population densities were higher in the second generation. The flight activity of females decreased in the second generation, but remained unchanged in males. This was further supported by the rate of wing decay. The first generation displayed a linear correlation between wing decay and passed time in both sexes, whereas the linear correlation was lost in second-generation females. The proportion of resting individuals in both sexes increased in the second generation, as well as the number of nectaring females. The choice of plant genera used for nectaring seems to be more specialised in the first and more opportunistic in the second generation. The average flight distances were generally higher for females than for males and overall higher in the first generation. Predictions of long-distance movements based on the inverse power function were also generally higher in females than in males but lower in the first generation. Additionally, we found protandry only in the first but not in the second generation, which might correlate with the different developmental pathways of the two generations. These remarkable differences between both generations might reflect an adaptation to the different ecological demands during the flight season and the different tasks they have, i.e., growth in the spring season; dispersal and colonisation of new habitats during the summer season.

Generation of normal distributions revisited

AbstractNormally distributed random numbers are commonly used in scientific computing in various fields. It is important to generate a set of random numbers as close to a normal distribution as possible for reducing initial fluctuations. Two types of samples from a uniform distribution are examined as source samples for inverse transform sampling methods. Three types of inverse transform sampling methods with new approximations of inverse cumulative distribution functions are also discussed for converting uniformly distributed source samples to normally distributed samples.

Adaptive fast finite‐time control for nonlinear systems subject to output hysteresis by fuzzy approach

SummaryThis article investigates an adaptive fast finite‐time tracking control problem for a class of uncertain nonlinear systems with output hysteresis. The idea of output hysteresis compensation is skillfully extended to adaptive design by employing a hysteresis inverse transformation and barrier Lyapunov function. The backstepping technique is adopted to establish the fast finite‐time control strategy, which can realize finite‐time convergence of the closed‐loop system. A rigorous theoretical analysis is performed to illustrate that the signals in the closed‐loop systems are bounded in finite time, and the tracking error can converge into a compact set with sufficient accuracy. Finally, a numerical simulation is given to confirm the effectiveness of the presented strategy.

Minimax Regret Robust Screening with Moment Information

Problem definition: We study a robust screening problem where a seller attempts to sell a product to a buyer knowing only the moment and support information of the buyer’s valuation distribution. The objective is to maximize the competitive ratio relative to an optimal hindsight policy equipped with full valuation information. Methodology/results: We formulate the robust screening problem as a linear programming problem, which can be solved efficiently if the support of the buyer’s valuation is finite. When the support of the buyer’s valuation is continuous and the seller knows the mean and the upper and lower bounds of the support for the buyer’s valuation, we show that the optimal payment is a piecewise polynomial function of the valuation with a degree of at most two. Moreover, we derive the closed-form competitive ratio corresponding to the optimal mechanism. The optimal mechanism can be implemented by a randomized pricing mechanism whose price density function is a piecewise inverse function adjusted by a constant. When the mean and variance are known to the seller, we propose a feasible piecewise polynomial approximation of the optimal payment function with a degree of at most three. We also demonstrate that the optimal competitive ratio exhibits a logarithmic decay with respect to the coefficient of variation of the buyer’s valuation distribution. Managerial implications: Our general framework provides an approach to investigating the value of moment information in the robust screening problem. We establish that even a loose upper bound of support or a large variance can guarantee a good competitive ratio. Funding: The research of S. Wang is partially supported by the National Natural Science Foundation of China [Grant 72394395]. The research of S. Liu is partly supported by the National Natural Science Foundation of China [Grant NSFC-72072117]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0072 .

Revisiting the Dynamics of Two-Body Problem in the Framework of the Continued Fraction Potential

In this analytical study, a novel solving method for determining the precise coordinates of a mass point in orbit around a significantly more massive primary body, operating within the confines of the restricted two-body problem (R2BP), has been introduced. Such an approach entails the utilization of a continued fraction potential diverging from the conventional potential function used in Kepler’s formulation of the R2BP. Furthermore, a system of equations of motion has been successfully explored to identify an analytical means of representing the solution in polar coordinates. An analytical approach for obtaining the function t = t(r), incorporating an elliptic integral, is developed. Additionally, by establishing the inverse function r = r(t), further solutions can be extrapolated through quasi-periodic cycles. Consequently, the previously elusive restricted two-body problem (R2BP) with a continued fraction potential stands fully and analytically solved.

Examining the relationship between brain activation and proxies of disease severity using quantile regression in individuals at risk of Alzheimer's disease

Previous studies have reported a pattern of hyperactivation in the pre-dementia phase of Alzheimer's disease (AD), followed by hypoactivation in later stages of the disease. This pattern was modeled as an inverse U-shape function between activation and markers of disease severity. In this study, we used quantile regression to model the association between task-related brain activation in AD signature regions and three markers of disease severity (hippocampal volume, cortical thickness, and associative memory). This approach offers distinct advantages over standard regression models as it analyzes the relationship between brain activation and disease severity across various levels of brain activation. Participants were 54 older adults with subjective cognitive decline+ (SCD+) or mild cognitive impairment (MCI) from the CIMA-Q cohort. The analysis revealed an inverse U-shape quadratic function depicting the relationship between disease severity markers and the activation of the left superior parietal region, while a linear relationship was observed for activation of the hippocampal and temporal regions. Quantile differences were observed for temporal and parietal activation, with more pronounced effects observed in the higher quantiles of activation. When comparing quantiles, we found that higher quantile of activation featured a greater number of individuals with SCD+ compared to mild cognitive impairment (MCI). Results are globally consistent with the presence of an inverse-U shape function of activation in relation to disease severity. They study also underscores the utility of employing quantile regression modeling as the modeling approach revealed the presence of non-homogeneous effects across various quantiles.

Memory type Max-EWMA control chart for the Weibull process under the Bayesian theory

The simultaneous monitoring of both process mean and dispersion, particularly in normal processes, has garnered significant attention within the field. In this article, we present a new Bayesian Max-EWMA control chart that is intended to track a non-normal process mean and dispersion simultaneously. This is accomplished through the utilization of the inverse response function, especially in cases where the procedure follows a Weibull distribution. We used the average run length (ARL) and the standard deviation of run length (SDRL) to assess the efficacy of our suggested control chart. Next, we contrast our suggested control chart's performance with an already-existing Max-EWMA control chart. Our results show that compared to the control chart under consideration, the proposed control chart exhibits a higher degree of sensitivity. Finally, we present a useful case study centered around the hard-bake process in the semiconductor manufacturing sector to demonstrate the performance of our Bayesian Max-EWMA control chart under different Loss Functions (LFs) for a Weibull process. The case study highlights how flexible the chart is to various situations. Our results offer strong proof of the outstanding ability of the Bayesian Max-EWMA control chart to quickly identify out-of-control signals during the hard-bake procedure. This in turn significantly contributes to the enhancement of process monitoring and quality control.

Improved Synchronous Sampling and Its Application in High-Speed Railway Bearing Damage Detection

Synchronous analysis is one of the most effective and practical techniques in rotating machinery diagnostics, especially in cases with variable speed operations. A modern analog-to-digital convertor (ADC) usually digitizes an analog signal to an equal time interval data series. Synchronous resampling converts the data series from an equal time interval data series to an equal shaft rotation angle interval data series. This conversion is usually achieved in the digital domain with the aid of shaft speed information, through either direct measurement or identification from a measured vibration signal, which is a time-consuming process. In order to improve the computational efficiency as well as the data processing accuracy, in this paper, a fast synchronous time-point calculation method based on an inverse function interpolation procedure is proposed. By identifying the inverse function of the instantaneous phase with respect to time, the calculation process of synchronous time points is optimized, which results in improved calculation efficiency and accuracy. These advantages are demonstrated by numerical simulations as well as experimental verifications. The numerical simulation results show that the proposed method can improve calculation speed by about five times. The synchronous analysis based on the proposed method was applied to a bearing fault detection in a high-speed rail carriage, which demonstrated the advantages of the proposed algorithm in improving the signal-to-noise ratio (SNR) for bearing damage feature extraction.

Licensing Scheme in the Green Industry Sector: The Case of Georgia Tree Care Service Providers

AbstractTree care license requirements are expected to improve service quality and provider competencies. The study elicits the licensing fee Georgia firms would pay using survey data from 153 tree care firms. An empirical relationship identifies firm characteristics that influence the fee size using the inverse hyperbolic sine transformation function. Results show that respondents who propose higher annual licensing fees are on average younger, more educated, male, and likely to agree that mandatory licensing is necessary to establish professionalism in the tree care industry. Also, those often engaged in tree trimming services and firms with higher annual revenues contemplate paying higher licensing fees.

Inverse logarithmic coefficient bounds for starlike functions subordinated to the exponential functions

In recent years, many subclasses of univalent functions, directly or not directly related to the exponential functions, have been introduced and studied. In this paper, we consider the class of Se∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{S}^{\\ast}_{e}$\\end{document} for which zf′(z)/f(z)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$zf^{\\prime}(z)/f(z)$\\end{document} is subordinate to ez\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$e^{z}$\\end{document} in the open unit disk. The classic concept of Hankel determinant is generalized by replacing the inverse logarithmic coefficient of functions belonging to certain subclasses of univalent functions. In particular, we obtain the best possible bounds for the second Hankel determinant of logarithmic coefficients of inverse starlike functions subordinated to exponential functions. This work may inspire to pay more attention to the coefficient properties with respect to the inverse functions of various classes of univalent functions.

Arctic Sea Ice Surface Temperature Inversion Using FY-3D/MWRI Brightness Temperature Data

The Arctic plays a crucial role in the intricate workings of the global climate system. With the rapid development of information technology, satellite remote sensing technology has emerged as the main method for sea ice surface temperature (IST) observation. To obtain Arctic IST, we used the FengYun-3D Microwave Radiation Imager (FY-3D/MWRI) brightness temperature (Tb) data for IST inversion using multiple linear regressions. Measured data on IST parameters in the Arctic are difficult to obtain. We used the Moderate-Resolution Imaging Spectroradiometer (MODIS) MYD29 IST data as the baseline to obtain the coefficients for the MWRI IST inversion function. The relation between MWRI Tb data and MODIS MYD29 IST product was established and the microwave IST inversion equation was obtained for the months of January to December 2019. Based on the R2 results and the IST inversion results, we compared and analyzed the MWRI IST data from the months of January to April, November, and December with the Operation IceBridge KT19 IR Surface Temperature data and the Northern High Latitude Level 3 Sea and Sea Ice Surface Temperature (NHL L3 SST/IST). We found that compared MWRI IST with NHL L3 IST, the correlation coefficients (Corr) > 0.72, mean bias ranged from −1.82°C to −0.67 °C, and the standard deviation (Std) ranged from 3.61 °C to 4.54 °C; comparing MWRI IST with KT19 IST, the Corr was 0.69, the bias was 0.51 °C, and the Std was 4.34 °C. The obtained error conforms to the precision requirement. From these results, we conclude that the FY-3D/MWRI Tb data are suitable for IST retrieval in the Arctic using multiple linear regressions.

New Applications of Fractional q-Calculus Operator for a New Subclass of q-Starlike Functions Related with the Cardioid Domain

Recently, a number of researchers from different fields have taken a keen interest in the domain of fractional q-calculus on the basis of fractional integrals and derivative operators. This has been used in various scientific research and technology fields, including optics, mathematical biology, plasma physics, electromagnetic theory, and many more. This article explores some mathematical applications of the fractional q-differential and integral operator in the field of geometric function theory. By using the linear multiplier fractional q-differintegral operator Dq,λmρ,σ and subordination, we define and develop a collection of q-starlike functions that are linked to the cardioid domain. This study also investigates sharp inequality problems like initial coefficient bounds, the Fekete–Szego problems, and the coefficient inequalities for a new class of q-starlike functions in the open unit disc U. Furthermore, we analyze novel findings with respect to the inverse function (μ−1) within the class of q-starlike functions in U. The findings in this paper are easy to understand and show a connection between present and past studies.

Estimation and inference for multi-kink expectile regression with nonignorable dropout

In this paper, we consider parameter estimation, kink points testing and statistical inference for a longitudinal multi-kink expectile regression model with nonignorable dropout. In order to accommodate both within-subject correlations and nonignorable dropout, the bias-corrected generalized estimating equations are constructed by combining the inverse probability weighting and quadratic inference function approaches. The estimators for the kink locations and regression coefficients are obtained by using the generalized method of moments. A selection procedure based on a modified BIC is applied to estimate the number of kink points. We theoretically demonstrate the number selection consistency of kink points and the asymptotic normality of all estimators. A weighted cumulative sum type statistic is proposed to test the existence of kink effects at a given expectile, and its limiting distributions are derived under both the null and the local alternative hypotheses. Simulation studies show that the proposed estimators and test have desirable finite sample performance in both homoscedastic and heteroscedastic errors. An application to the Nation Growth, Lung and Health Study dataset is also presented.

Spherical interpolation of scattered data using least squares thin-plate spline and inverse multiquadric functions

Spherical interpolation of scattered data using least squares thin-plate spline and inverse multiquadric functions

Quantile Regression in Survival Analysis: Comparing Check-Based Modeling and the Minimum Distance Approach

Introduction: Quantile regression is a valuable alternative for survival data analysis, enabling flexible evaluations of covariate effects on survival outcomes with intuitive interpretations. It offers practical computation and reliability. However, challenges arise when applying quantile regression to censored data, particularly for upper quantiles. The minimum distance approach, utilizing dual-kernel estimation and the inverse cumulative distribution function, shows promise in addressing these challenges, especially with higher-dimensional covariates.
 Methods: This study contrasts two methods within the realm of quantile linear regression for survival analysis: check-based modeling and the minimum distance approach. Effectiveness is assessed across various scenarios through comprehensive simulation.
 Results: The simulation results showed that using the quantile regression model with the minimum distance approach reduces the percentage of root mean square error in parameter estimation compared to the quantile regression models based on the check loss function. Additionally, a larger sample size and reduced censoring percentage led to decreased root mean square error in parameter estimation.
 Conclusion: The research highlights the benefits of using the minimum distance approach for quantile regression. It reduces errors, improves model predictions, captures patterns, and optimizes parameters even with complete data. However, this approach has limitations. The accuracy of estimated quantiles can be influenced by the choice of distance metric and weighting scheme. The assumption of independence between censoring mechanism and survival time may not hold in real-world scenarios. Additionally, dealing with large datasets can be computationally complex.
 

Rapid inverse radiative transfer solver for multiparameter spectrophotometry without integrating sphere.

Multiparameter spectrophotometry (MPS) provides a powerful tool for accurate characterization of turbid materials in applications such as analysis of material compositions, assay of biological tissues for clinical diagnosis and food safety monitoring. This work is aimed at development and validation of a rapid inverse solver based on a particle swarm optimization (PSO) algorithm to retrieve the radiative transfer (RT) parameters of absorption coefficient, scattering coefficient and anisotropy factor of a turbid sample. Monte Carlo (MC) simulations were performed to obtain calculated signals for comparison to the measured ones of diffuse reflectance, diffuse transmittance and forward transmittance. An objective function has been derived and combined with the PSO algorithm to iterate MC simulations for MPS. We have shown that the objective function can significantly reduce the variance in calculated signals by local averaging of an inverse squared error sum function between measured and calculated signals in RT parameter space. For validation of the new objective function for PSO based inverse solver, the RT parameters of 20% Intralipid solutions have been determined from 520 to 1000nm which took about 2.7 minutes on average to complete signal measurement and inverse calculation per wavelength. The rapid solver enables MPS to be translated into easy-to-use and cost-effective instruments without integrating sphere for material characterization by separating and revealing compositional profiles at the molecular and particulate scales.

Hankel determinants, Fekete-Szegö inequality, and estimates of initial coefficients for certain subclasses of analytic functions

<abstract><p>In this paper, we define new subclasses of analytic functions related to a modified sigmoid function and analytic univalent function. Then, we attempt to investigate the upper bounds of the third and fourth Hankel determinant in the special case. Further, bound on third Hankel determinant of its inverse function is also investigated. In addition, we attempt to obtain the Fekete-Szegö inequality for the classes. Then, we estimate the bounds of initial coefficients for the function belongs to some kind of new subclasses when its inverse function also belongs to these new subclasses.</p></abstract>

Sharp Shafer-Fink, Lazarevic and Cusa type inequalities for the Gudermannian and inverse Gudermannian functions

In this paper, we present sharp Shafer-Fink, Lazarevic and Cusa type inequalities for the Gudermannian and inverse Gudermannian functions.

A Systems Biology Approach to the Pathogenesis of Celiac Disease: Identification of Potential Protective and Promoting Mechanisms.

Celiac disease (CeD) is an autoimmune enteropathy triggered by dietary gluten. Almost 90% of CeD patients have HLA-DQ2 or -DQ8 haplotypes. As a high proportion of first-degree relatives (FDRs) of CeD patients have the same haplotype, it is assumed that they are at a higher risk of disease development than the general population. Nevertheless, the prevalence of CeD among FDRs is considerably low (7.5%). In order to figure out this discrepancy, a microarray dataset of intestinal mucosal biopsies of CeD patients, FDRs, and control groups was reanalyzed, and a protein-protein interaction network was constructed. Principal component analysis showed that CeD and FDR groups are far away in terms of gene expression. Comparing differentially expressed genes of both networks demonstrated inverse expression of some genes mainly related to cell cycle mechanisms. Moreover, analysis of the modular structures of up- and downregulated gene networks determined activation of protein degradation mechanisms and inhibition of ribosome-related protein synthesis in celiac patients with an upside-down pattern in FDRs. The top-down systems biology approach determined some regulatory pathways with inverse function in CeD and FDR groups. These genes and molecular mechanisms could be a matter of investigation as potential druggable targets or prognostic markers in CeD.

An improved error cancellation method for high speed FMCW radar based on FPGA platform

AbstractTarget detection of frequency‐modulated continuous wave radar has the problems of high noise and low detection accuracy. The reason is due to the influence of internal hardware and external environment. In response to this issue, this article uses the field programmable gate array platform to perform frequency modulation on the radar module, time‐frequency conversion, autoregression moving average model, inverse proportion function compensation, and frequency domain selection processing on the intermediate frequency in‐phase signals collected by the oscilloscope. The algorithm proposed in this article could effectively reduce noise and system errors. Compared with traditional methods before filtering and variational mode decomposition Hilbert–Huang Transform algorithm, the effective target detection rate of this method is improved by 50%.