A Search for A Stochastic Archetype of Quantum Probability

Superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into a probability density, which has long been a puzzle because interference between probability densities exists nowhere else in probability theory. In recent years, Man’ko and coauthors have successfully reconciled quantum and classic probability using a symplectic tomographic model. Nevertheless, there remains an unexplained coincidence in quantum mechanics, namely, that mathematically, the interference term in the squared amplitude of superposed wavefunctions gives the squared amplitude the form of a variance of a sum of correlated random variables, and we examine whether there could be an archetypical variable behind quantum probability that provides a mathematical foundation that observes both quantum and classic probability directly. The properties that would need to be satisfied for this to be the case are identified, and a generic hidden variable that satisfies them is found that would be present everywhere, transforming into a process-specific variable wherever a quantum process is active. Uncovering this variable confirms the possibility that it could be the stochastic archetype of quantum probability

A search for a stochastic archetype of quantum probability

Superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into a probability density, which has long been a puzzle because interference between probability densities exists nowhere else in probability theory. In recent years, Man’ko and coauthors have successfully reconciled quantum and classic probability using a symplectic tomographic model. Nevertheless, there remains an unexplained coincidence in quantum mechanics, namely, that mathematically, the interference term in the squared amplitude of superposed wavefunctions gives the squared amplitude the form of a variance of a sum of correlated random variables, and we examine whether there could be an archetypical variable behind quantum probability that provides a mathematical foundation that observes both quantum and classic probability directly. The properties that would need to be satisfied for this to be the case are identified, and a generic hidden variable that satisfies them is found that would be present everywhere, transforming into a process-specific variable wherever a quantum process is active. Uncovering this variable confirms the possibility that it could be the stochastic archetype of quantum probability.

Complex Numbers Related to Semi-Antinorms, Ellipses or Matrix Homogeneous Functionals

We generalize the property of complex numbers to be closely related to Euclidean circles by constructing new classes of complex numbers which in an analogous sense are closely related to semi-antinorm circles, ellipses, or functionals which are homogeneous with respect to certain diagonal matrix multiplication. We also extend Euler’s formula and discuss solutions of quadratic equations for the p-norm-antinorm realization of the abstract complex algebraic structure. In addition, we prove an advanced invariance property of certain probability densities.

Enterprise Compensation System Statistical Modeling for Decision Support System Development

This article raises the issue of decision support system (DSS) development in enterprises concerning the compensation system (CS). The topic is relevant as the CS is one of the main components in human resource management in business. A key element of such DSSs is CS models that provide predictive analytics. Such models are able to give information about how a particular CS affects output, product quality, employee satisfaction, and wage fund. Thus, the main goal of this article is to obtain a CS statistical model and its formulas for determining the probability densities of resultant indicators. To achieve this goal, the authors conducted several blocks of research. Firstly, mathematical formalization of CS functionality was described. Secondly, a statistical model of CS was built. Thirdly, calculations of CS result indicators were made. Reliable scientific methods were used: black box modeling and statistical modeling. This article proposes a statistical and analytical model. As an example, a piecework-bonus system statistical model is demonstrated. The discussion derives formulas of integral estimations showing the probability density of the resulting CS indicators and the related statistical characteristics. These results can be used to predict the behavior of the workforce. This constitutes the scientific novelty of the study, which will establish significant advances in the development of DSSs in the field of labor economics and HR management.

A search for a stochastic archetype of quantum probability

Superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into a probability density, which has long been a puzzle because interference between probability densities exists nowhere else in probability theory. In recent years, Man’ko and coauthors have successfully reconciled quantum and classic probability using a symplectic tomographic model. Nevertheless, there remains an unexplained coincidence in quantum mechanics, namely, that mathematically, the interference term in the squared amplitude of superposed wavefunctions gives the squared amplitude the form of a variance of a sum of correlated random variables, and we examine whether there could be an archetypical variable behind quantum probability that provides a mathematical foundation that observes both quantum and classic probability directly. The properties that would need to be satisfied for this to be the case are identified, and a generic hidden variable that satisfies them is found that would be present everywhere, transforming into a process-specific variable wherever a quantum process is active. Uncovering this variable confirms the possibility that it could be the stochastic archetype of quantum probability.

Mathematical modeling of equivalent ellipse radii of Raman spectra for identification of gold nanoparticles

To ensure the biomedical, therapeutic and protective properties of textile materials using gold nanoparticles, there is a need to apply the convergence of nano-, bio-, info -, cognitive sciences and technology. It is proposed to evaluate the accuracy of identification of colloidal gold nanoparticles on organic fibers based on the multidimensional correlation components of the Raman spectra under control by the polarization characteristics. The aim of the work is to improve the accuracy of identification of gold nanoparticles in nanostructured biological objects during mathematical modeling based on the components of Raman spectrograms.The paper analyzes the Raman spectra of polyester fibers with and without gold nanoparticles in different ranges. A method for solving a system of multidimensional equations with differentiation in X and Y is proposed, according to which the coordinates of the intersection points of ellipses are determined under conditions of equality of equivalent radii and probability densities of two-dimensional distributions. The sensitivity to the concentration of gold nanoparticles of the developed method under various conditions is estimated. The research carried out in this work will improve the accuracy of identification of gold nanoparticles on various biological objects, as well as solve a wide range of problems related to increasing the reliability of control of metal nanoparticles

Weighted Means of Likelihood Ratio as Indices Measuring Similarity Between Densities

Criteria for similarity between probability density functions are important in the field of statistics such as density estimation. In this short paper, a set of indices measuring similarity between probability densities is proposed using the weighted means of the likelihood ratio function. Numerical simulations demonstrate that the estimates of these indices are easily obtained from observations and could be useful for both parametric and nonparametric density estimation with numerical optimization.

Temperature and relative humidity trends in the northernmost region of South Africa, 1950–2016

The northernmost Limpopo Province is located in one of the warmest regions of South Africa, where the agricultural sector is prone to heat stress. The aim of this study was to explore air temperature and relative humidity trends for the region, which have implications for agricultural adaptation and management (amongst other sectors). In particular, we investigated seasonal, annual and decadal scale air temperature and relative humidity changes for the period 1950–2016. Positive temperature trends were recorded for this period, averaging +0.02 °C/year, with the strongest changes observed in mean maximum summer temperatures (+0.03 °C/year). Interannual temperature variability also increased over time, especially for the period 2010–2016, which presents probability densities of <50% for minimum temperatures. Positive relative humidity trends (+0.06%/year) were also recorded for the period 1980– 2016, but proved to be the least predictable weather parameter, with probability densities of <0.5% across seasons for the study period. Considering the substantial interannual variability in temperature and relative humidity, there is clear increased risk for the agricultural sector, particularly for small-scale farmers who generally have limited capacity to adapt. Climate science focusing on the southern African region should continue to establish the impact of climate change and variability on specific small-scale farming systems and enterprises, with recommendations for strategic adaptation based on up-to-date evidence.