In this paper, we proposed a sentence encoding-based model for recognizing text entailment. In our approach, the encoding of sentence is a two-stage process. Firstly, average pooling was used over word-level bidirectional LSTM (biLSTM) to generate a firststage sentence representation. Secondly, attention mechanism was employed to replace average pooling on the same sentence for better represent...

In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if φ is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition φ , is given by the convolution of φ with the heat kernel (Gaussian density). Our results also extend the probabilistic representation of solutions of the heat equation...

Erraticity analysis of multiparticle production data is introduced as a way of extracting the maximum amount of information on self-similar fluctuations. It is presented as the next logical step to take beyond the intermittency analysis. An erraticity spectrum e(α) can be determined analogous to the multifractal spectrum f(α). An analytical example is presented to elucidate the method of analys...

In this paper, we present a deeper analysis of linear regression as an efficient method for face alignment. Linear regression for face alignment [2] consists of learning a mapping matrix between image features and shape parameters displacements. Typically, shape parameters are projections of a set of points which follow a Point Distribution Model onto the subspace generated by applying Principa...

A link in production network is usually a creditordebtor relationship. If a firm goes into financial insolvency state or bankruptcy, then firms on its upstream can have secondary effect from the bankruptcy. By using the recent 10 years data of bankruptcy in japan, we show that these causes of “link effect” are by no means negligible. Indeed, nearly 20% of total debt (a few percent of GDP) is du...