Weighted nearest-neighbor classification is analyzed in terms of squared error of class probability estimates. Two classes of algorithms for calculating weights are studied with respect to their ability to minimize the first-order term of the squared error: local linear regression and a new class termed regularized linear interpolation. A number of variants of each class are considered or propo...

New developments are presented in the area of grid convergence error analysis for mixed-order numerical schemes. A mixed-order scheme is deŽ ned as a numerical method where the formal order of the truncation error varies either spatially, for example, at a shock wave, or for different terms in the governing equations, for example, third-order convection with second-order diffusion. The case exa...

We address the problem of detecting English language learner errors by using a discriminative high-order sequence model. Unlike most work in error-detection, this method is agnostic as to specific error types, thus potentially allowing for higher recall across different error types. The approach integrates features from many sources into the error-detection model, ranging from language model-ba...

The use of reduced order models to describe a dynamical system is pervasive in science and engineering. Often these models are used without an estimate of their error or range of validity. In this paper we consider dynamical systems and reduced models built using proper orthogonal decomposition. We show how to compute estimates and bounds for these errors, by a combination of small sample stati...

In this paper a new approach is developed for analyzing the discontinuous Galerkin method for hyperbolic equations. For a model problem in R2, the method is shown to converge at a rate 0(hn+l) when applied with nth degree polynomial approximations over a semiuniform triangulation, assuming sufficient regularity in the solution.

Power systems should have acceptable reliability in order to operate properly. Highly available and dependable protective relays help to obtain the desirable reliability. The relays should be periodically evaluated during specific intervals to achieve the mentioned characteristics. The Routine Test Interval (RTI) should be optimized in order to economically maximize the reliability of the prote...

Error propagation on the Euclidean motion group arises in a number of areas such as and in dead reckoning errors in mobile robot navigation and joint errors that accumulate from the base to the distal end of manipulators. We address error propagation in rigid-body poses in a coordinate-free way. In this paper we show how errors propagated by convolution on the Euclidean motion group, SE(3), can...

Previous methods have generally identified the location of a type error as a particular program point or the program subtree rooted at that point. We present a new approach that identifies the location of a type error as a set of program points (a slice) all of which are necessary for the type error. We describe algorithms for finding minimal type error slices for implicitly typed higher-order ...

The aim of the paper is to employ the dual numbers in the multi axes machine error modelling in order to apply the algebraic methods in computations. The calculus of higher order dual numbers allows us to calculate with the appropriate geometric parametrization effectively. We test the model on the phantom data based on the real machine tool. The results of our analysis are used for the geometr...

AbstructWe consider the problem of estimating the order of a stationary ergodic Markov chain. Our focus is on estimators which satisfy a generalized Neyman-Pearson criterion of optimality. Specifically, the optimal estimator minimizes the probability of underestimation among all estimators with probability of overestimation not exceeding a given value. Our main result identifies the best expone...