We use dense variable-ordering to define HRD (Hybrid-Restriction Diagram), a new BDD-like datastructure for the representation and manipulation of state-spaces of linear hybrid automata. We present and discuss various manipulation algorithms for HRD, including the basic set-oriented operations, weakest precondition calculation, and normalization. We implemented the ideas and experimented to see...

Consider a problem of predicting a response variable using a set of covariates in a linear regression model. If it is a priori known or suspected that a subset of the covariates do not significantly contribute to the overall fit of the model, a restricted model that excludes these covariates, may be sufficient. If, on the other hand, the subset provides useful information, shrinkage meth...

We propose a new nonparametric test of affiliation, a strong form of positive dependence with independence as a special, knife–edge, case. The test is consistent against all departures from the null of affiliation, and its null distribution is standard normal. Like most nonparametric tests, a sample–size dependent input parameter is needed. We provide an informal procedure for choosing the inpu...

We describe a mechanism for theory interpretations in PVS. The mechanization makes it possible to show that one collection of theories is correctly interpreted by another collection of theories under a user-specified interpretation for the uninterpreted types and constants. A theory instance is generated and imported, while the axiom instances are generated as proof obligations to ensure that t...

This paper discusses robust function approximation when the Takagi-Sugeno type model is used for the consequent part of fuzzy rules. With this model, the parameters of the liner equation that defines the output value of the fuzzy rule are determined by the least-squares method. Therefore, if the training data include outliers, the method fails to determine the parameter values correctly. To ove...

This paper introduces a method for predicting the likely behaviors of continuous nonlinear systems in equilibrium in which the input values can vary. The method uses a parameterized equation model and a lower bound on the input joint density to bound the likelihood that some behavior will occur, such as a state variable being inside a given numeric range. Using a bound on the density instead of...