ABSTRACT: Most of mathematic forgetting curve models fit well with the forgetting data under the learning condition of one time rather than repeated. In the paper, a convolution model of forgetting curve is proposed to simulate the memory process during learning. In this model, the memory ability (i.e. the central procedure in the working memory model) and learning material (i.e. the input in the working memory model) is regarded as the system function and the input function, respectively. The status of forgetting (i.e. the output in the working memory model) is regarded as output function or the convolution result of the memory ability and learning material. The model is applied to simulate the forgetting curves in different situations. The results show that the model is able to simulate the forgetting curves not only in one time learning condition but also in multi-times condition. The model is further verified in the experiments of Mandarin tone learning for Japanese learners. And the predicted curve fits well on the test points. Keywords: Memory forgetting curves; Convolution; Mathematical modeling 1.Introduction Since Ebbinghaus proposed the eminent'forgetting curve' to quantitatively describe the procedure of memory [1], researchers have made great effort to find out the exactly form of the models for forgetting curve. The problem is still being considered as'central theoretical importance' [2].

In this study we present a kernel based convolution model to characterize neural responses to natural sounds by decoding their time-varying acoustic features. The model allows to decode natural sounds from high-dimensional neural recordings, such as magnetoencephalography (MEG), that track timing and location of human cortical signalling noninvasively across multiple channels. We used the MEG responses recorded from subjects listening to acoustically different environmental sounds. By decoding the stimulus frequencies from the responses, our model was able to accurately distinguish between two different sounds that it had never encountered before with 70% accuracy. Convolution models typically decode frequencies that appear at a certain time point in the sound signal by using neural responses from that time point until a certain fixed duration of the response. Using our model, we evaluated several fixed durations (time-lags) of the neural responses and observed auditory MEG responses to be most sensitive to spectral content of the sounds at time-lags of 250 ms to 500 ms. The proposed model should be useful for determining what aspects of natural sounds are represented by high-dimensional neural responses and may reveal novel properties of neural signals.

We present a new neural network model for processing of temporal patterns. This model, the gamma neural model, is as general as a convolution delay model with arbitrary weight kernels w(t). We show that the gamma model can be formulated as a (partially prewired) additive model. A temporal hebbian learning rule is derived and we establish links to related existing models for temporal processing. 1 INTRODUCTION In this paper, we are concerned with developing neural nets with short term memory for processing of temporal patterns. In the literature, basically two ways have been reported to incorporate short-term memory in the neural system equations.

We present a new neural network model for processing of temporal patterns. This model, the gamma neural model, is as general as a convolution delay model with arbitrary weight kernels w(t). We show that the gamma model can be formulated as a (partially prewired) additive model. A temporal hebbian learning rule is derived and we establish links to related existing models for temporal processing. 1 INTRODUCTION In this paper, we are concerned with developing neural nets with short term memory for processing of temporal patterns. In the literature, basically two ways have been reported to incorporate short-term memory in the neural system equations.

We present a new neural network model for processing of temporal patterns. This model, the gamma neural model, is as general as a convolution delay model with arbitrary weight kernels w(t). We show that the gamma model can be formulated as a (partially prewired) additive model. A temporal hebbian learning rule is derived and we establish links to related existing models for temporal processing. 1 INTRODUCTION In this paper, we are concerned with developing neural nets with short term memory for processing of temporal patterns. In the literature, basically two ways have been reported to incorporate short-term memory in the neural system equations.