The Pearson Correlation Model – Work of the Devil?

While by far the most applied correlation model in finance, the Pearson correlation model is – due to its simplicity and linearity – also the most heavily criticised: “Anything that relies on correlation is charlatanism” (Nassim Taleb) and “Instruments whose pricing requires the input of correlation … are accidents waiting to happen” (Paul Wilmott). In this chapter we address this contradiction and evaluate whether the Pearson correlation approach is rigorous and suitable for modelling associations in finance.

Forecasting currency covariances using machine learning tree-based algorithms with low and high prices

We combine machine learning tree-based algorithms with the usage of low and high prices and suggest a new approach to forecasting currency covariances. We apply three algorithms: Random Forest Regression, Gradient Boosting Regression Trees and Extreme Gradient Boosting with a tree learner. We conduct an empirical evaluation of this procedure on the three most heavily traded currency pairs in the Forex market: EUR/USD, USD/JPY and GBP/USD. The forecasts of covariances formulated on the three applied algorithms are predominantly more accurate than the Dynamic Conditional Correlation model based on closing prices. The results of the analyses indicate that the GBRT algorithm is the bestperforming method.

First-principles calculations for Gilbert damping constant at finite temperature

We propose a first-principles calculation method for the Gilbert damping constants α at finite temperatures. α is described by the torque correlation model in which the electronic structure is computed by the tight-binding linear muffin-tin orbital method. We include the finite-temperature effect as the transverse spin fluctuation in the disordered local moment picture within the coherent potential approximation. Applying the present method to bcc-Fe and L10-FePt, we demonstrate these temperature-dependent α. By comparing our calculated results with experimental results, we find the calculated values are less than half of the experimental values, reflecting the characteristics of the torque correlation model.

Nonlinear Hyperparameter Optimization of a Neural Network in Image Processing for Micromachines

Deep neural networks are widely used in the field of image processing for micromachines, such as in 3D shape detection in microelectronic high-speed dispensing and object detection in microrobots. It is already known that hyperparameters and their interactions impact neural network model performance. Taking advantage of the mathematical correlations between hyperparameters and the corresponding deep learning model to adjust hyperparameters intelligently is the key to obtaining an optimal solution from a deep neural network model. Leveraging these correlations is also significant for unlocking the “black box” of deep learning by revealing the mechanism of its mathematical principle. However, there is no complete system for studying the combination of mathematical derivation and experimental verification methods to quantify the impacts of hyperparameters on the performances of deep learning models. Therefore, in this paper, the authors analyzed the mathematical relationships among four hyperparameters: the learning rate, batch size, dropout rate, and convolution kernel size. A generalized multiparameter mathematical correlation model was also established, which showed that the interaction between these hyperparameters played an important role in the neural network’s performance. Different experiments were verified by running convolutional neural network algorithms to validate the proposal on the MNIST dataset. Notably, this research can help establish a universal multiparameter mathematical correlation model to guide the deep learning parameter adjustment process.

Multiple Analytical Models to Evaluate the Impact of Carbon Nanotubes on the Electrical Resistivity and Compressive Strength of the Cement Paste

Cement paste is the most common construction material being used in the construction industry. Nanomaterials are the hottest topic worldwide, which affect the mechanical properties of construction materials such as cement paste. Cement pastes containing carbon nanotubes (CNTs) are piezoresistive intelligent materials. The electrical resistivity of cementitious composites varies with the stress conditions under static and dynamic loads as carbon nanotubes are added to the cement paste. In cement paste, electrical resistivity is one of the most critical criteria for structural health control. Therefore, it is essential to develop a reliable mathematical model for predicting electrical resistivity. In this study, four different models—including the nonlinear regression model (NLR), linear regression model (LR), multilinear regression model (MLR), and artificial neural network model (ANN)—were proposed to predict the electrical resistivity of cement paste modified with carbon nanotube. Furthermore, the correlation between the compressive strength of cement paste and the electrical resistivity model has also been proposed in this study and compared with models in the literature. In this respect, 116 data points were gathered and examined to develop the models, and 56 data points were collected for the proposed correlation model. Most critical parameters influencing the electrical resistivity of cement paste were considered during the modeling process—i.e., water to cement ratio ranged from 0.2 to 0.485, carbon nanotube percentage varied from 0 to 1.5%, and curing time ranged from 1 to 180 days. The electrical resistivity of cement paste with a very large number ranging from 0.798–1252.23 Ω.m was reported in this study. Furthermore, various statistical assessments such as coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), scatter index (SI), and OBJ were used to investigate the performance of different models. Based on statistical assessments—such as SI, OBJ, and R2—the output results concluded that the artificial neural network ANN model performed better at predicting electrical resistivity for cement paste than the LR, NLR, and MLR models. In addition, the proposed correlation model gives better performance based on R2, RMSE, MAE, and SI for predicting compressive strength as a function of electrical resistivity compared to the models proposed in the literature.

ANALYTICAL MODEL OF INCREASING THE COEFFICIENT FOR THE EXTRACTION OF OIL OF HYDROCARBON DEPOSITS

The article considers the main causes and factors affecting the oper¬ation of wells in oil fields, the coefficients of rank correlation and the frequency of well oscillations are determined to compile an analytical model describing the formation of a field in the formation with a joint inflow of formation water and carbonated oil to the well in order to inject wells into optimal regimes work. Keyword: correlation, model, formation, pres¬sure, radius.

Testability Analysis Method of Radar Equipment Based on Dependency Model

In order to improve the testability design level of radar equipment, achieve rapid detection and isolation of faults, and reduce the life cycle cost of the system, a testability analysis method of radar equipment based on correlation model is proposed. The basic process of correlation model modeling is introduced. On this basis, the optimization method of test points for fault detection and isolation and the generation method of fault diagnosis strategy are analyzed. The effectiveness of the proposed method is verified by applying it to radar transmitting subsystem.

Correlated Damage Probabilities of Bridges In Seismic Risk Assessment of Transportation Networks

This paper aims to identify and use a logistic regression approach to model the spatial correlation of damage probabilities in expanded transportation networks. This paper uses Bayesian theory and the multinomial logistic model to analyze the different damage states and damage probabilities of bridges by considering the damage correlation. The correlation of the damage probabilities is considered both in different bridges of a network and in the different damage states of each bridge. The correlation model of the damage probabilities is considered in the seismic assessment of a part of the Tehran transportation network with 26 bridges. Moreover, the extra daily traffic time (EDTT) is selected as an operational parameter of the transportation network, and the shortest path algorithm is considered to select the path between two nodes. The results show that including the correlation of the damage probabilities decreases the travel time of the selected network. The average decreasing in the correlated case compared to the uncorrelated case, using two selected EDTT models are 53% and 71%, respectively.