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Pain is a complex, multidimensional experience that involves dynamic interactions between sensory-discriminative and affective-emotional processes. Pain experiences have a high degree of variability depending on their context and prior anticipation. Viewing pain perception as a perceptual inference problem, we use a predictive coding paradigm to characterize both evoked and spontaneous pain. We record the local field potentials (LFPs) from the primary somatosensory cortex (S1) and the anterior cingulate cortex (ACC) of freely behaving rats-two regions known to encode the sensory-discriminative and affective-emotional aspects of pain, respectively. We further propose a framework of predictive coding to investigate the temporal coordination of oscillatory activity between the S1 and ACC. Specifically, we develop a high-level, empirical and phenomenological model to describe the macroscopic dynamics of bottom-up and top-down activity. Supported by recent experimental data, we also develop a mechanistic mean-field model to describe the mesoscopic population neuronal dynamics in the S1 and ACC populations, in both naive and chronic pain-treated animals. Our proposed predictive coding models not only replicate important experimental findings, but also provide new mechanistic insight into the uncertainty of expectation, placebo or nocebo effect, and chronic pain. Author SummaryPain perception in the mammalian brain is encoded through multiple brain circuits.The experience of pain is often associated with brain rhythms or neuronal oscillations at different frequencies. Understanding the temporal coordination of neural oscillatory activity from different brain regions is important for dissecting pain circuit mechanisms and revealing differences between distinct pain conditions. Predictive coding is a general computational framework to understand perceptual inference by integrating bottom-up sensory information and top-down expectation. Supported by experimental data, we propose a predictive coding framework for pain perception, and develop empirical and biologically-constrained computational models to characterize oscillatory dynamics of neuronal populations from two cortical circuits-one for the sensory-discriminative PLOS 2/49 experience and the other for affective-emotional experience, and further characterize their temporal coordination under various pain conditions. Our computational study of biologically-constrained neuronal population model reveals important mechanistic insight on pain perception, placebo analgesia, and chronic pain. Introduction 1Pain is a basic experience that is subjective and multidimensional. Pain processing 2 involves sensory, affective, and cognitive processing across distributed neural 3 circuits [1-5]. However, a complete understanding of pain perception and cortical pain 4 processing has remained elusive. Given the same nociceptive stimuli, the context 5 matters for pain percept. Human neuroimaging studies have shown that among many 6 brain regions, the primary somatosensory cortex (S1) a...

In this brief, we consider an online gradient method with penalty for training feedforward neural networks. Specifically, the penalty is a term proportional to the norm of the weights. Its roles in the method are to control the magnitude of the weights and to improve the generalization performance of the network. By proving that the weights are automatically bounded in the network training with penalty, we simplify the conditions that are required for convergence of online gradient method in literature. A numerical example is given to support the theoretical analysis.

This paper is concerned with the sparsification of the input-hidden weights of ELM (Extreme Learning Machine). For ordinary feedforward neural networks, the sparsification is usually done by introducing certain regularization technique into the learning process of the network. But this strategy can not be applied for ELM, since the input-hidden weights of ELM are supposed to be randomly chosen rather than to be learned. To this end, we propose a modified ELM, called ELM-LC (ELM with local connections), which is designed for the sparsification of the input-hidden weights as follows: The hidden nodes and the input nodes are divided respectively into several corresponding groups, and an input node group is fully connected with its corresponding hidden node group, but is not connected with any other hidden node group. As in the usual ELM, the hiddeninput weights are randomly given, and the hidden-output weights are obtained through a least square learning. In the numerical simulations on some benchmark problems, the new ELM-CL behaves better than the traditional ELM.Index Terms-Extreme learning machine (ELM), local connections, sparsification of input-hidden weights, high dimensional input data.

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