Inferring core processes using stochastic models of the geodynamo

Summary Recent studies have represented time variations in the Earth’s axial magnetic dipole field as a stochastic process, which comprise both deterministic and random elements. To explore how these elements are affected by the style and vigour of convection in the core, as well as the core-mantle boundary conditions, we construct stochastic models from a set of numerical dynamo simulations at low Ekman numbers. The deterministic part of the stochastic model, the drift term, characterises the slow relaxation of the dipole back to its time-average. We find that these variations are predominantly accommodated by the slowest decay mode, enhanced by turbulent diffusion to enable a faster relaxation. The random part—the noise term—is set by the amplitude and timescale of variations in dipole field generation, including contributions from both velocity and internal magnetic field variations. Applying these interpretations to the paleomagnetic field suggest that reversal rates are very sensitive to rms variations in the field generation. Less than a 50 per cent reduction in rms field generation variations is sufficient to prevent reversals for the recent magnetic field.

Random Perturbation of Sparse Graphs

In the model of randomly perturbed graphs we consider the union of a deterministic graph $\mathcal{G}_\alpha$ with minimum degree $\alpha n$ and the binomial random graph $\mathbb{G}(n,p)$. This model was introduced by Bohman, Frieze, and Martin and for Hamilton cycles their result bridges the gap between Dirac's theorem and the results by Pósa and Korshunov on the threshold in $\mathbb{G}(n,p)$. In this note we extend this result in $\mathcal{G}_\alpha\cup\mathbb{G}(n,p)$ to sparser graphs with $\alpha=o(1)$. More precisely, for any $\varepsilon>0$ and $\alpha \colon \mathbb{N} \mapsto (0,1)$ we show that a.a.s. $\mathcal{G}_\alpha\cup \mathbb{G}(n,\beta /n)$ is Hamiltonian, where $\beta = -(6 + \varepsilon) \log(\alpha)$. If $\alpha>0$ is a fixed constant this gives the aforementioned result by Bohman, Frieze, and Martin and if $\alpha=O(1/n)$ the random part $\mathbb{G}(n,p)$ is sufficient for a Hamilton cycle. We also discuss embeddings of bounded degree trees and other spanning structures in this model, which lead to interesting questions on almost spanning embeddings into $\mathbb{G}(n,p)$.

Bond and Option Prices under Skew Vasicek Model with Transaction Cost

This paper studies the European option pricing on the zero-coupon bond in which the Skew Vasicek model uses to predict the interest rate amount. To do this, we apply the skew Brownian motion as the random part of the model and show that results of the model predictions are better than other types of the model. Besides, we obtain an analytical formula for pricing the zero-coupon bond and find the European option price by constructing a portfolio that contains the option and a share of the bond. Since the skew Brownian motion is not a martingale, thus we add transaction costs to the portfolio, where the time between trades follows the exponential distribution. Finally, some numerical results are presented to show the efficiency of the proposed model.

Analysis of longitudinal vibration acceleration based on continuous time-varying model of high-speed elevator lifting system with random parameters

In this paper, for studying the influence of the randomness of structural parameters of high-speed elevator lifting system (HELS) caused by manufacturing error and installation error, a continuous time-varying model of HELS was constructed, considering the compensation rope mass and the tension of the tensioning system. The Galerkin weighted residual method is employed to transform the partial differential equation with infinite degrees of freedom (DOF) into the ordinary differential equation. The five-order polynomial is used to fit the actual operation state curve of elevator, and input as operation parameters. The precise integration method of time-varying model of HELS is proposed. The determination part and the random part response expression of the longitudinal dynamic response of HELS are derived by the random perturbation method. Using the precise integration method, the sensitivity of random parameters is determined by solving the random part response expression of time-varying model of HELS, and the digital characteristics of the acceleration response are analyzed. It is found that the line density of the hoisting wire rope has the maximum sensitivity on longitudinal vibration velocity response, displacement response and acceleration response, and the sensitivity of the elastic modulus of the wire rope is smallest.

Periodic Numerical Rough Surface Filtered Generation

Numerical surface filtered generation is one of the main methods for generating numerical rough surfaces, but when faced with rough surfaces with waviness or large periodicity, traditional filtering methods cannot be implemented well. Because of this, the paper adopts the method of decomposing and synthesizing the maximum period and random part of the periodic rough surface. By decomposing the statistical parameters of the target surface, the statistical parameters of the ideal periodic surface and the random surface are generated, respectively, and then according to the surface parameters generate the surfaces and synthesize them. By comparing the statistical parameters and morphology of the synthesized surface with its actual surface, it can be found that this method can well achieve the generation of periodic rough surfaces, which is a good improvement to the original filter generation method.

Classification of Unbalanced Data Based on RSM and Binomial Distribution

In the case of extremely unbalanced data, the results of the traditional classification algorithm are very unbalanced, and most samples are often divided into the categories of majority samples, so the accuracy of judgment of the minority classes will be reduced. In this paper, we propose a classification algorithm for unbalanced data based on RSM and binomial undersampling. We use RSM’s random part features rather than all each classifier to make each training classifier reduce the dimensions, and dimension reduction makes relatively minority class samples indirectly lift. Using the above characteristics of the RSM to reduce dimension can solve the problem that unbalanced data classification in the minority class samples is too little, and it can also find the important attribute of variables to make the model have the ability of explanation. Experiments show that our algorithm has high classification accuracy and model interpretation ability when classifying unbalanced data.

The effects of misspecifying the random part of multilevel models

This paper examined the amount bias in standard errors for fixed effects when the random part of a multilevel model is misspecified. Study 1 examined the effects of misspecification for a model with one Level 1 predictor. Results indicated that misspecifying random slope variance as fixed had a moderate effect size on the standard errors of the fixed effects and had a greater effect than misspecifying fixed slopes as random. In Study 2, a second Level 1 predictor was added and allowed for the examination of the effects of misspecifying the slope variance of one predictor on the standard errors for the fixed effects of the other predictor. Results indicated that only the standard errors of coefficient relevant to that predictor were impacted and that the effect size for the bias could be considered moderate to large. These results suggest that researchers can use a piecemeal approach to testing multilevel models with random effects.

Changing attitudes to secularization processes within the theory of modernization of religion

The article considers the key factors in development of the religious situation in the second half of the twentieth century, which caused a radical change in the attitude to the theory of secularization by sociologists of religion. From the beginning, the theory of secularization was a core part of the general theory of modernization and marked the specifics of modernization`s impact on religious life. However, the inability to explain such phenomena as the sharp rise in religiosity in post-socialist countries, as well as the consistently high level of religiosity in the typically modernist United States, led researchers to abandon the classical theory of secularization. Another reason for the change in the attitude to secularization was the presence of a religious component in numerous political conflicts in the late twentieth and early twenty-first centuries. The religious factor in the conflicts was so unusual and decisive that under its influence the theory of “clash of civilizations” by S. Huntington was born at the end of the twentieth century. Even though the general theory of modernization has not disappeared and still remains popular among sociologists of religion, there is no clear reference to the theory of secularization. Secularization is considered either a random part of modernization processes at certain stages, or one of the options for the development of the religious situation along with counter-secularization, or even completely rejected as a false positivist construct that has not been validated with the real state of affairs.

Estimation of genetic parameters for dairy traits using repeatability animal models based on test-day data for Alpine goat in Croatia

The objective of this study was to estimate genetic parameters for daily milk yield (DMY), fat (FC), and protein content (PC) using 329.022 test-day records of 23.756 Alpine does. Single trait repeatability animal model was applied. Parity, litter size, season, and lactation stage (Ali-Schaeffer’s curve) were fitted in the fixed, while herd, herd-test-day, permanent environment (within lactations) and additive genetic effect in the random part of the model. Variance components were estimated using Residual Maximum Likelihood Method in the VCE-6 program. Additive genetic effect explained 23 %, 16 % and 25 % of DMY, FC and PC variability which is in general agreement with numerous previous reports for dairy goat breeds. Among the non-genetic effects, herd explained 24 %, 12 %, and 9 %, herd-test-day 17 %, 29 %, and 30 %, and permanent environment 16 %, 3 %, and 5 % of DMY, FC and PC variability, respectively. The estimated parameters and developed single trait repeatability test-day models will serve as a basic tool in BLUP based genetic evaluation of Alpine breed in Croatia.