A Mathematical Method for Determining the Parameters of Functional Dependencies Using Multiscale Probability Distribution Functions

This article discusses the application of the method of approximation of experimental data by functional dependencies, which uses a probabilistic assessment of the deviation of the assumed dependence from experimental data. The application of this method involves the introduction of an independent parameter “scale of the error probability distribution function” and allows one to synthesize the deviation functions, forming spaces with a nonlinear metric, based on the existing assumptions about the sources of errors and noise. The existing method of regression analysis can be obtained from the considered method as a special case. The article examines examples of analysis of experimental data and shows the high resistance of the method to the appearance of single outliers in the sample under study. Since the introduction of an independent parameter increases the number of computations, for the practical application of the method in measuring and information systems, the architecture of a specialized computing device of the “system on a chip” class and practical approaches to its implementation based on programmable logic integrated circuits are considered.

Sustainable Development with Schumpeter Extended Endogenous Type of Innovation and Statistics in European Countries

In the economic growth models, technological progress is either exogenous or endogenous. The endogenized theory is based on analytical modeling of the economic process in order to include the event of innovating. Theory around the subject innovation and economic growth also includes several independent parameters that have a strong impact over innovation. However, few of them established creativity as an independent parameter of innovation. The present paper aims to extend the endogenized theory in order to include creativity as an independent parameter of innovation, based on the evidence of a panel data of 28 countries, through 8 years. A theoretical model, a multiple linear regression, an ANOVA analysis and correlational matrixes were used in order to fulfill our purpose. Results show that innovation is determined by the level of knowledge twice as much as the level of creativity. A conceptual framework for an extension of endogenous growth models, in order to include creativity, is presented in the paper. The model can enhance economic growth by fostering creativity or knowledge and thus, the size of innovation, which is the main driver for economic growth in the model presented.

bootComb - An R Package to Derive Confidence Intervals for Combinations of Independent Parameter Estimates

MotivationThe epidemiologist sometimes needs to combine several independent parameter estimates: e.g. (i) adjust an incidence rate for healthcare utilisation, (ii) derive a disease prevalence from the conditional prevalence on another condition and the prevalence of that condition, (iii) adjust a seroprevalence for test sensitivity and specificity. While obtaining the combined parameter estimate is usually straightforward, deriving a corresponding confidence interval often is not. bootComb is an R package using parametric bootstrap sampling to derive such confidence intervals.ImplementationbootComb is a package for the statistical computation environment R.General featuresAs well as a function that returns confidence intervals for parameters combined from several independent estimates, bootComb provides auxiliary functions for 6 common distributions (beta, normal, exponential, gamma, Poisson and negative binomial) to derive best-fit distributions (and their sampling functions) for parameters given their reported confidence intervals.AvailabilitybootComb is available from the Comprehensive R Archive Network (https://CRAN.R-project.org/package=bootComb).Key FeaturesbootComb derives confidence intervals with the required coverage for parameters that are computed from independent parameter estimates for which confidence intervals are reported.Includes auxilliary functions for 6 common distributions (beta, normal, exponential, gamma, Poisson and negative binomial) to derive best-fit distributions (and their sampling functions) for parameters given their reported confidence intervals.R package: open-source, easy-to-use, platform independent.Stable version hosted on CRAN: https://CRAN.R-project.org/package=bootCombLatest development version available from GitHub: https://github.com/gitMarcH/bootComb

Surfaces of congruent sections on cylinders

Introduction. The definition of surfaces of congruent sections was first formulated in the work written by I.I. Kotov. These and several other types of surfaces, generated by the motion of a curve, belonged to the class of kinematic surfaces. Such kinematic surfaces as those of plane parallel displacement, surfaces of rotation, Monge surfaces, cyclic surfaces with ge-nerating circles having constant radius, rotative and spiroidal surfaces, helical some helix-shaped surfaces can be included into the class of surfaces that have congruent sections. Materials and methods. Using I.I. Kotov’s methodology, the authors first derived parametrical and vector equations for eight surfaces of congruent pendulum type cross sections of circular, elliptic, and parabolic cylinders and several helix-shaped surfaces. Circles, ellipses, and parabolas, located in the plane of the generating curve of a guiding cylinder or in the planes of a bundle that passes through the longitudinal axis of a cylinder, generate plane curves. Ellipses, analyzed in the article, can be easily converted into circles and this procedure can increase the number of shapes analyzed here. Results. Formulas are provided in the generalized form, so the shape of a plane generating curve can be arbitrary. Some surfaces of congruent sections are determined by two varieties of parametric equations. In one case, the central angle of the guiding cylindrical surface was used as an independent parameter, but in the other case, one of rectangular coordinates of the cylinder’s guiding curve served as an independent parameter. Two types of surfaces are analyzed: 1) when local axes of generating curves remain parallel in motion; 2) when these axes rotate. Conclusions. The analysis of the sources and the results, recommendations and proposals for application of surfaces, having congruent sections, is made with a view to their use in architecture and technology. The list of references has 27 positions, and it shows that the surfaces considered in this paper are being analyzed by architects, engineers, and geometricians both in Russia and abroad.

Cervical effacement, as an independent parameter versus modified bishop score, for predicting the favorability of vaginal delivery in a primigravida at 40 weeks gestation and beyond

Background: Dr. Edward Bishop developed the original bishop score. He concluded that elective induction in multiparous women was successful with a score > 8. Calder introduced the modified bishop score in which he replaced cervical effacement with cervical length in cms. Score of 6-12 is favourable. In this study, studied the cervical effacement/ length as an independent predictor of vaginal delivery in a primigravida.Methods: A retrospective observational study was conducted from May 2018 to January 2019. Total participants were divided into two groups on the basis of spontaneous labor and induced labor. Both the groups were assessed individually and collectively in terms of cervical effacement/length and modified bishop score. Study primary outcome was vaginal delivery. The results were reflected in terms of sensitivity, specificity, PPV and NPV. These values were compared for cervical effacement/ length as well as modified bishop score and p value calculated. Also, association between modified bishop score and cervical effacement/length was established.Results: Total number of participants included was n = 91. Those with modified bishop score > 6, 78.16% had vaginal delivery. This gave a sensitivity of 78.16%, specificity of 50%, PPV of 97.14%. Those with cervical effacement of >/=50% or cervical length of </= 2 cms, 78.82% had vaginal delivery. This gave a sensitivity of 78.82%, specificity of 55%, PPV of 95.71%. Thus, it had similar sensitivity, specificity, PPV to that of modified bishop score, and therefore has the same accuracy in predicting vaginal delivery. Also, 89.01% participants who had cervical effacement >/= 50% had modified bishop score >/= 6, reflecting the association between them.Conclusions: Cervical effacement of >/= 50% or cervical length </= 2 cms yielded an equivalently high predictive ability similar to modified bishop score, for spontaneous as well as induced labor. Hence, cervical effacement can be taken as an independent parameter to assess the favorability of successful vaginal delivery in a primigravida.