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Register a new userNeural Field Models: historical perspectives and recent advances
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Rhythmic electrical activity in the brain emerges from regular non-trivial interactions between millions of neurons. Neurons are intricate cellular structures that transmit excitatory (or inhibitory) signals to other neurons, often non-locally, depending on the graded input from other neurons. Often this requires extensive detail to model mathematically, which poses several issues in modelling large systems beyond clusters of neurons, such as the whole brain. Approaching large populations of neurons with interconnected constituent single-neuron models results in an accumulation of exponentially many complexities, rendering a realistic simulation that does not permit mathematical tractability and obfuscates the primary interactions required for emergent electrodynamical patterns in brain rhythms. A statistical mechanics approach with non-local interactions may circumvent these issues while maintaining mathematically tractability. Neural field theory is a population-level approach to modelling large sections of neural tissue based on these principles. Herein we provide a review of key stages of the history and development of neural field theory and contemporary uses of this branch of mathematical neuroscience. We elucidate a mathematical framework in which neural field models can be derived, highlighting the many significant inherited assumptions that exist in the current literature, so that their validity may be considered in light of further developments in both mathematical and experimental neuroscience.
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Topographic maps are a brain structure connecting pre-synpatic and post-synaptic brain regions. Topographic development is dependent on Hebbian-based plasticity mechanisms working in conjunction with spontaneous patterns of neural activity generated in the pre-synaptic regions. Studies performed in mouse have shown that these spontaneous patterns can exhibit complex spatial-temporal structures which existing models cannot incorporate. Neural field theories are appropriate modelling paradigms for topographic systems due to the dense nature of the connections between regions and can be augmented with a plasticity rule general enough to capture complex time-varying structures. We propose a theoretical framework for studying the development of topography in the context of complex spatial-temporal activity fed-forward from the pre-synaptic to post-synaptic regions. Analysis of the model leads to an analytic solution corroborating the conclusion that activity can drive the refinement of topographic projections. The analysis also suggests that biological noise is used in the development of topography to stabilise the dynamics. MCMC simulations are used to analyse and understand the differences in topographic refinement between wild-type and the $beta2$ knock-out mutant in mice. The time scale of the synaptic plasticity window is estimated as $0.56$ seconds in this context with a model fit of $R^2 = 0.81$.
The theory of communication through coherence (CTC) proposes that brain oscillations reflect changes in the excitability of neurons, and therefore the successful communication between two oscillating neural populations depends not only on the strength of the signal emitted but also on the relative phases between them. More precisely, effective communication occurs when the emitting and receiving populations are properly phase locked so the inputs sent by the emitting population arrive at the phases of maximal excitability of the receiving population. To study this setting, we consider a population rate model consisting of excitatory and inhibitory cells modelling the receiving population, and we perturb it with a time-dependent periodic function modelling the input from the emitting population. We consider the stroboscopic map for this system and compute numerically the fixed and periodic points of this map and their bifurcations as the amplitude and the frequency of the perturbation are varied. From the bifurcation diagram, we identify the phase-locked states as well as different regions of bistability. We explore carefully the dynamics emphasizing its implications for the CTC theory. In particular, we study how the input gain depends on the timing between the input and the inhibitory action of the receiving population. Our results show that naturally an optimal phase locking for CTC emerges, and provide a mechanism by which the receiving population can implement selective communication. Moreover, the presence of bistable regions, suggests a mechanism by which different communication regimes between brain areas can be established without changing the structure of the network
In the last few years, deep learning has led to very good performance on a variety of problems, such as visual recognition, speech recognition and natural language processing. Among different types of deep neural networks, convolutional neural networks have been most extensively studied. Leveraging on the rapid growth in the amount of the annotated data and the great improvements in the strengths of graphics processor units, the research on convolutional neural networks has been emerged swiftly and achieved state-of-the-art results on various tasks. In this paper, we provide a broad survey of the recent advances in convolutional neural networks. We detailize the improvements of CNN on different aspects, including layer design, activation function, loss function, regularization, optimization and fast computation. Besides, we also introduce various applications of convolutional neural networks in computer vision, speech and natural language processing.
Over the past few years, adversarial training has become an extremely active research topic and has been successfully applied to various Artificial Intelligence (AI) domains. As a potentially crucial technique for the development of the next generation of emotional AI systems, we herein provide a comprehensive overview of the application of adversarial training to affective computing and sentiment analysis. Various representative adversarial training algorithms are explained and discussed accordingly, aimed at tackling diverse challenges associated with emotional AI systems. Further, we highlight a range of potential future research directions. We expect that this overview will help facilitate the development of adversarial training for affective computing and sentiment analysis in both the academic and industrial communities.
Noise-induced population bursting has been widely identified to play important roles in the information process. We constructed a mathematical model for a random and sparse neural network where bursting can be induced from the resting state by the global stochastic stimulus. Importantly, the noise-induced bursting dynamics of this network are mediated by calcium conductance. We use two spectral measures to evaluate the network coherence in the context of network bursts, the spike trains of all neurons and the individual bursts of all neurons. Our results show that the coherence of the network is optimized by an optimal level of stochastic stimulus, which is known as coherence resonance (CR). We also demonstrate that the interplay of calcium conductance and noise intensity can modify the degree of CR.
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