In this paper, an effective procedure based on coordinate stretching and radial basis functions (RBFs) collocation method is applied to solve singularly perturbed differential-difference equations with layer behavior. It is well known that if the boundary layer is very small, for good resolution of the numerical solution at least one of the collocation points must lie in the boundary layer. In ...

Calibration and validation of geophysical measurement systems typically requires knowledge of the “true” value of the target variable. However, the “true” values often include their own measurement errors, calibration biases, and validation results. Triple collocation (TC) can be used to estimate the root-mean-square-error (RMSE), using observations from three mutuallyindependent, error-prone m...

We present a collocatIon method based on piecewise cubic polynomials I In C for solving various Integral and differential equatIons. Two new methods for handling curved boundaries are discussed based on collocation and discrete least-squares. Finally, a summary of the properties of the collocation method Is given which IndIcates the simplicity, flexlbl1fty, efficiency, and generality of the met...

This paper proposes a novel method of learning probabilistic subcategorization preference. In the method, for the purpose of coping with the ambiguities of case dependencies and noun class generalization of argument/adjunct nouns, we introduce a data structure which represents a tuple of independent partial subcategorization frames. Each collocation of a verb and argument/adjunct nouns is assum...

Collocation extraction systems based on pure statistical methods suffer from two major problems. The first problem is their relatively low precision and recall rates. The second problem is their difficulty in dealing with sparse collocations. In order to improve performance, both statistical and lexicographic approaches should be considered. This paper presents a new method to extract synonymou...

This study investigates the relationship among working memory (WM), first language (L1), second language (L2), and mathematics; with an aim to understand whether achievement in mathematics and L1 is related to performance in later L2 learning; and if so, whether WM components (i.e. phonological loop and central executive) play a role in this relationship between mathematics and language. A seco...

The use of L1 regularisation for sparse learning has generated immense research interest, with many successful applications in diverse areas such as signal acquisition, image coding, genomics and collaborative filtering. While existing work highlights the many advantages of L1 methods, in this paper we find that L1 regularisation often dramatically under-performs in terms of predictive performa...

In recent years, collocation has been widely acknowledged as an essential characteristic to distinguish native speakers from non-native speakers. Research on academic writing has also shown that collocations are not only common but serve a particularly important discourse function within the academic community. In our study, we propose a machine learning approach to implementing an online collo...