Thermodynamic analysis of the cracking of hexane has been conducted by the Gibbs free energy minimization method and second law analysis of overall reactions. By-products have been divided into three groups of methane, alkynes and aromatics and their possible production paths have been discussed. Effect of operating conditions such as temperature and steam-to-hexane ratio on the cracking perfor...

Principal subspace theorems deal with the problem of finding subspaces supporting optimal approximations of multivariate distributions. The optimality criterion considered in this paper is the minimization of the mean squared distance between the given distribution and an approximating distribution, subject to some constraints. Statistical applications include, but are not limited to, cluster a...

We consider the problem of foreground and background extraction from compressed-sensed (CS) surveillance video. We propose, for the first time in the literature, a principal component analysis (PCA) approach that computes the low-rank subspace of the background scene directly in the CS domain. Rather than computing the conventional L2-norm-based principal components, which are simply the domina...

Many settings of unsupervised learning can be viewed as quantization problems, namely of minimizing the expected quantization error subject to some restrictions. This has the advantage that tools known from the theory of (supervised) risk minimization like regularization can be readily applied to unsupervised settings. Moreover, one may show that this setting is very closely related to both, pr...

We consider concave minimization problems over nonconvex sets. Optimization problems with this structure arise in sparse principal component analysis. We analyze both a gradient projection algorithm and an approximate Newton algorithm where the Hessian approximation is a multiple of the identity. Convergence results are established. In numerical experiments arising in sparse principal component...

Functional Data Analysis (FDA) is used for datasets that are more meaningfully represented in the functional form. Functional principal component analysis, for instance, is used to extract a set of functions of maximum variance that can represent the data. In this paper, a method of Mutual Interdependence Analysis (MIA) is proposed that can extract an equally correlated function with a set of i...

This paper examines the effects of liability-sharing rules on social welfare and risk reduction when one firm (the principal) delegates indivisible hazardous activities to one of the potential firms (the agents). The problem is posed as providing incentives from the principal to the agents, through the contract, to reduce the level of accident probability under a liability rule in force. Our ma...

We derive bounds on the sample complexity of empirical risk minimization (ERM) in the context of minimizing non-convex risks that admit the strict saddle property. Recent progress in non-convex optimization has yielded efficient algorithms for minimizing such functions. Our results imply that these efficient algorithms are statistically stable and also generalize well. In particular, we derive ...

The aim of this study is to develop the Bayesian Least Squares Support Vector Machine (LS-SVM) classifiers, for preoperatively predicting the malignancy of ovarian tumors. We describe how to perform parameter estimation, input variable selection for LS-SVM within the evidence framework. The issue of computing the posterior class probability for risk minimization decision making is addressed. Th...

In this paper, we proposed algorithms interior proximal methods based on entropylike distance for the minimization of the quasiconvex function subjected to nonnegativity constraints. Under the assumptions that the objective function is bounded below and continuously differentiable, we established the well definedness of the sequence generated by the algorithms and obtained two important converg...