In this paper, we provide theoretical and numerical analysis of a geometric activity flow network model which is aimed at explaining mathematically the scale-free functional graph self-organization phenomena emerging in complex nervous systems at a mesoscale level. In our model, each unit corresponds to a large number of neurons and may be roughly seen as abstracting the functional behavior exhibited by a single voxel under functional magnetic resonance imaging (fMRI). In the course of the dynamics, the units exchange portions of formal charge, which correspond to waves of activity in the underlying microscale neuronal circuit. The geometric model abstracts away the neuronal complexity and is mathematically tractable, which allows us to establish explicit results on its ground states and the resulting charge transfer graph modeling functional graph of the network. We show that, for a wide choice of parameters and geometrical setups, our model yields a scale-free functional connectivity with the exponent approaching 2, which is in agreement with previous empirical studies based on fMRI. The level of universality of the presented theory allows us to claim that the model does shed light on mesoscale functional self-organization phenomena of the nervous system, even without resorting to closer details of brain connectivity geometry which often remain unknown. The material presented here significantly extends our previous work where a simplified mean-field model in a similar spirit was constructed, ignoring the underlying network geometry.

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The topic of this paper is neural multi-task training for text style transfer. We present an efficient method for neutral-to-style transformation using the transformer framework. We demonstrate how to prepare a robust model utilizing large paraphrases corpora together with a small parallel style transfer corpus. We study how much style transfer data is needed for a model on the example of two transformations: neutral-to-cute on internal corpus and modern-to-antique on publicly available Bible corpora. Additionally, we propose a synthetic measure for the automatic evaluation of style transfer models. We hope our research is a step towards replacing common but limited rule-based style transfer systems by more flexible machine learning models for both public and commercial usage.

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