A consistent description of kinetic equation with triangle anomaly

We provide a consistent description of the kinetic equation with triangle anomaly which is compatible with the entropy principle of the second law of thermodynamics and the charge/energy-momentum conservation equations. In general an anomalous source term is necessary to ensure that the equations for the charge and energy-momentum conservation are satisfied and that the correction terms of distribution functions are compatible to these equations. The constraining equations from the entropy principle are derived for the anomaly-induced leading order corrections to the particle distribution functions. The correction terms can be determined for minimum number of unknown coefficients in one charge and two charge cases by solving the constraining equations.Comment: RevTex 4, 11 pages; With minor changes: typos are corrected and one reference is added. Accepted version to PR

A Study on the Effect of Metaphor Awareness Raising on Chinese EFL Learners’ Vocabulary Acquisition and Retention

The research investigates the vocabulary acquisition and retention effect of raising learners’ metaphor awareness on EFL learners (non-English majors) of intermediate-low English proficiency level. The subjects are first-year non-English college students in a vocational college. The pre-test, immediate post-test and delayed post-test experiment lasted for a whole semester and the data collected at the tests were processed with SPSS Windows 13.0. The result shows that in EFL class, organizing metaphorical expressions along their metaphorical theme is more effective in enhancing EFL learners’ vocabulary retention. Accordingly, efforts to raise learners’ metaphor awareness should be made in classroom-based EFL teaching and the considerations should be given in teaching treatment to achieve a better effect in EFL vocabulary teaching and learning.Keywords: metaphorical theme/source; domain metaphor awareness; Vocabulary acquisition; vocabulary retention   Résumé:  La recherche étudie l'effet  de la sensibilisation à la métaphore sur l'acquisition et la mémorisation de vocabulaire chez les étudiants chinois EFL (spécialité non-anglais) qui ont un niveau d'anglais intermédiaire-faible. Les sujets d'études sont des étudiants en première année dans une école professionnelle non-anglaise. Le pré-test, le post-test immédiat et le post-test différé ont duré un semestre entier et les données recueillies lors des tests ont été traitées avec SPSS Windows 13.0. Le résultat montre que dans la classe EFL, l'organisation des expressions métaphoriques le long de leur thème métaphorique est plus efficace dans l'amélioration de la mémorisation de vocabulaire chez les apprenants EFL. En conséquence, les efforts visant à sensibiliser la conscience des apprenants sur la métaphore doivent être réalisés dans l'enseignement EFL basé sur des cours en salle de classe et les considérations devraient être y accordées pour atteindre un meilleur effet dans l'enseignement et dans l'apprentissage de vocabulaire anglais .Mots-Clés:  Thème métaphorique ; sensibilisation à la métaphore ; domaine source; acquisition de vocabulaire; mémorisation de vocabulair

A Method for Filling up the Missed Data in Information Table

Almost algorithms based on the rough sets, such as mean value method, maximum frequency method, mode method are week in supporting the hidden rules in the information tablel. By the breaking point sets in the information system, a new method for packing the missed attribute value is provided in the paper,. The method is more efficient for indicating the decision rules

On the Approximation and Complexity of Deep Neural Networks to Invariant Functions

Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and complexity, i.e., showing which architecture and size are sufficient to handle the concerned tasks. This work takes one step on this direction by theoretically studying the approximation and complexity of deep neural networks to invariant functions. We first prove that the invariant functions can be universally approximated by deep neural networks. Then we show that a broad range of invariant functions can be asymptotically approximated by various types of neural network models that includes the complex-valued neural networks, convolutional neural networks, and Bayesian neural networks using a polynomial number of parameters or optimization iterations. We also provide a feasible application that connects the parameter estimation and forecasting of high-resolution signals with our theoretical conclusions. The empirical results obtained on simulation experiments demonstrate the effectiveness of our method