We thank all reviewers for their careful reviews and many positive comments. We feel that the typos and minor issues are easily addressable and will be corrected. We will incorporate this analysis into a revision of the paper. We thank R1 for bringing this highly related work to our attention. That work focuses on environments for which mice have previously developed spatial maps.

We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet distributions, Negative binomial regression, Poisson-Gamma hierarchical models, Extreme value models, to name but a few. All of those models include a gamma function which does not admit a natural conjugate prior distribution providing a significant challenge to inference and prediction. To provide a data augmentation strategy, we construct and develop the theory of the class of Exponential Reciprocal Gamma distributions. This allows scalable EM and MCMC algorithms to be developed. We illustrate our methodology on a number of examples, including gamma shape inference, negative binomial regression and Dirichlet allocation. Finally, we conclude with directions for future research.

We present a unifying view of discrete-time operator models used in the context of finite word length linear signal processing. Comparisons are made between the recently presented gamma operator model, and the delta and rho operator models for performing nonlinear system identification and prediction using neural networks. A new model based on an adaptive bilinear transformation which generalizes all of the above models is presented.

We present a unifying view of discrete-time operator models used in the context of finite word length linear signal processing. Comparisons are made between the recently presented gamma operator model, and the delta and rho operator models for performing nonlinear system identification and prediction using neural networks. A new model based on an adaptive bilinear transformation which generalizes all of the above models is presented.

We present a unifying view of discrete-time operator models used in the context of finite word length linear signal processing. Comparisons are made between the recently presented gamma operator model, and the delta and rho operator models for performing nonlinear system identification and prediction using neural networks. A new model based on an adaptive bilinear transformation which generalizes all of the above models is presented.

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.