Interactions between Stimuli and Spatiotemporal Activity

神经系统中正在进行的活动以及它如何影响感觉和其他输入是最近许多实验活动的主题。特别是，很明显，在没有输入的情况下，神经元电路之间的内在相互作用可以对系统如何对传入的刺激做出反应产生强烈的影响，即使在大规模认知水平上也是如此。因此，非线性动力学方法将被应用于理论神经科学中处理这一问题的问题。在实验中观察到了各种形式的时空活动，包括空间局域活动、振荡和传播波。微扰和数值方法将被用来分析这些图案在受到各种刺激时的动力学，例如空间局部短暂的扰动、相关的宽带输入以及运动或振荡刺激。在表现良好的动物和减少的实验准备中观察到的一种类型的持续活动是大脑皮层上状态。我们将为这种状态研究一个新的模型，以了解它是如何在大脑皮层传播的，以及它诱导自发模式形成的能力。为了研究扰动如何影响耦合神经元的大型网络，将发展一类新的平均场模型来研究尖峰神经活动。我们感知世界的方式既受我们不断受到轰炸的感官输入的支配，也受我们大脑中正在进行的活动和我们以前的经验的支配。这种活动以及神经系统的自然连接塑造了我们大脑的自发行为，这种自发活动强烈地调节了感觉输入。在这里，我们使用神经元(组成大脑的细胞)的计算和数学模型来了解哪些类型的自发行为是可能的，这如何依赖于连接，以及这种活动如何与感觉输入相互作用。正在进行的和诱发的行为受到积极(兴奋)和消极(抑制)影响的平衡控制。这种平衡的丧失可能会扰乱正常行为，并导致癫痫和精神分裂症等疾病。神经系统的数学模型提供了一种方法来检验实验者提出的假设，并根据这些模型的预测提出新的实验建议。

Ongoing activity in the nervous system and how it impacts sensory and other inputs is the subject of much recent experimental activity. In particular, it is clear that the intrinsic interactions between neuronal circuits in absence of inputs can have a strong impact on how the system responds to incoming stimuli even at the large scale cognitive level. Thus, nonlinear dynamics methods will be applied to problems in theoretical neuroscience dealing with this question. Various forms of spatiotemporal activity are observed in experiments which include spatially localized activity, oscillations, and propagating waves. Perturbation and numerical methods will be used to analyze the dynamics of these patterns when subjected to various stimuli such as spatially local short lasting perturbations, correlated broad-band inputs, and moving or oscillatory stimuli. One type of persistent activity observed both in behaving animals and in reduced experimental preparations is the cortical up-state. We will study a new model for this state in order to understand how it propagates across the cortex as well as its ability to induce spontaneous pattern formation. A new class of mean field models for spiking neural activity will be developed in order to study how perturbations affect large networks of coupled neurons. How we perceive the world is governed both by the sensory inputs with which we are constantly bombarded, by ongoing activity in the brain, and by our previous experience. This activity as well as the natural wiring of the nervous system shapes the spontaneous behavior of our brains and this spontaneous activity strongly modulates the sensory inputs. Here we use computational and mathematical models of neurons (the cells that make up the brain) to understand what kinds of spontaneous behavior are possible, how this depends on the wiring and how this activity interacts with sensory inputs. The ongoing and evoked behavior is carefully controlled by a balance of positive (excitatory) and negative (inhibitory) influences. The loss of this balance can disrupt normal behavior and lead to diseases such as epilepsy and schizophrenia. Mathematical models of the nervous system provide a way to test hypotheses put forth by experimentalists and to also suggest new experiments based on the predictions of these models.