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In this article, we introduce the multifractal conditional diffusion entropy method for analyzing the volatility of financial time series. This method utilizes a q-order diffusion entropy based on a q-weighted time lag scale. The technique of conditional diffusion entropy proves valuable for examining bull and bear behaviors in stock markets across various time scales. Empirical findings from analyzing the Dow Jones Industrial Average (DJI) indicate that employing multi-time lag scales offers greater insight into the complex dynamics of highly fluctuating time series, often characterized by multifractal behavior. A smaller time scale like t = 2 to t = 256 coincides more with the state of the DJI index than larger time scales like t = 256 to t = 1024 . We observe extreme fluctuations in the conditional diffusion entropy for DJI for a short time lag, while smoother or averaged fluctuations occur over larger time lags. [ABSTRACT FROM AUTHOR]

This work is devoted to the generalization of previous results on Gleason measures to complex Gleason measures. We develop a functional calculus for complex measures in relation to the Nemytsky operator. Furthermore we present and discuss the interpretation of our results with applications in the field of quantum mechanics. Some concrete examples and further extensions of several theorems are also presented.

In this work, we have analyzed data sets from various fields using a coupled Ornstein–Uhlenbeck (OU) system of equations driven by Lévy processes. The Ornstein–Uhlenbeck model is well known for its ability to capture stochastic behaviors when used as a predictive model. There's empirical evidence showing that there exist dependencies or correlations between events; thus, we may be able to model them together. Here we show such correlation between data from finance, geophysics and health as well as show the predictive performance when they are modeled with a coupled Ornstein–Uhlenbeck system of equations. The results show that the solution to the stochastic system provides a good fit to the data sets analyzed. In addition by comparing the results obtained when the BDLP is a Γ (a , b) process or an IG(a,b) process, we are able to deduce the best choice out of the two to model our data sets. [ABSTRACT FROM AUTHOR]

This work analyses the diagnosis and prognosis of cancer and heart disease data using five Machine Learning (ML) algorithms. We compare the predictive ability of all the ML algorithms to breast cancer and heart disease. The important variables that causes cancer and heart disease are also studied. We predict the test data based on the important variables and compute the prediction accuracy using the Receiver Operating Characteristic (ROC) curve. The Random Forest (RF) and Principal Component Regression (PCR) provides the best performance in analyzing the breast cancer and heart disease data respectively. [ABSTRACT FROM AUTHOR]