This paper presents an analysis of random number generators based on continuous-time chaotic oscillators. Two different methods for random number generation have been studied: 1) Regular sampling of a chaotic waveform, and 2) Chaotic sampling of a regular waveform. Kernel density estimation is used to analytically describe the distribution of chaotic state variables and the probability density function corresponding to the output bit stream. Random bit sequences are generated using analytical equations and results from numerical simulations. Applying the concepts of autocorrelation and approximate entropy, randomness quality of the generated bit sequences are assessed to analyze relationships between the frequencies of the regular and chaotic waveforms used in both random number generation methods. It is demonstrated that in both methods, there exists certain ratios between the frequencies of regular and chaotic signal at which the randomness of the output bit stream changes abruptly. Furthermore, both random number generation methods have been compared against their immunity to interference from external signals. Analysis shows that chaotic sampling of regular waveform method provides more robustness against interference compared to regular sampling of chaotic waveform method.

Software defect prediction (SDP) plays a significant part in allocating testing resources reasonably, reducing testing costs, and ensuring software quality. One of the most widely used algorithms of SDP models is Naive Bayes (NB) because of its simplicity, effectiveness and robustness. In NB, when a data set has continuous or numeric attributes, they are generally assumed to follow normal distributions and incorporate the probability density function of normal distribution into their conditional probabilities estimates. However, after conducting a Kolmogorov-Smirnov test, we find that the 21 main software metrics follow non-normal distribution at the 5% significance level. Therefore, this paper proposes an improved NB approach, which estimates the conditional probabilities of NB with kernel density estimation of training data sets, to help improve the prediction accuracy of NB for SDP. To evaluate the proposed method, we carry out experiments on 34 software releases obtained from 10 open source projects provided by PROMISE repository. Four well-known classification algorithms are included for comparison, namely Naive Bayes, Support Vector Machine, Logistic Regression and Random Tree. The obtained results show that this new method is more successful than the four well-known classification algorithms in the most software releases.

We propose a novel saliency detection model based on Bayes' theorem. The model integrates the two parts of Bayes' equation to measure saliency, each part of which was considered separately in the previous models. The proposed model measures saliency by computing local kernel density estimation of features in the center-surround region and global kernel density estimation of features at each pixel across the whole image. Under the proposed model, a saliency detection method is presented that extracts DCT (Discrete Cosine Transform) magnitude of local region around each pixel as the feature. Experiments show that the proposed model not only performs competitively on psychological patterns and better than the current state-of-the-art models on human visual fixation data, but also is robust against signal uncertainty.