Contributions of Areas LIP and VIP to Numerical Behavior

目前的证据确定了两个相互关联的系统，用于表示和操纵 人类：1）用于精确数学运算的符号中介精确数值系统; 2） 一种非语言的近似的数量感，在进化上是原始的， 人类个体发育神经生物学和行为学数据强烈表明， 精确的数值系统利用了近似的数值意义。对数字的敏感性，一个模糊的 物体或事件的数量感，预测整个过程中的数字和数学表现 发展此外，对人类大脑成像和病变的研究表明，顶叶皮层在这两个确切的 数值处理和近似数感。灵长类动物腹侧的单个神经元 顶叶内区（VIP）以及前额叶皮层（dlPFC）选择性地对特定数量的 一个视觉数组中的元素。相比之下，外侧顶内区（LIP）的神经元以较低的频率响应。 单调的方式，在位于神经元感受野内的视觉阵列中的元素的数量。 这些观察结果表明，LIP神经元整合视觉信息，形成一个神经元的假设。 表示累积的数量，由VIP和dlPFC中的神经元读出，以发出信号。 具体数值。这一假设是一致的几个计算模型的数值 表示，其中表示特定基数值（例如3或5）的数量单位接收 来自求和单元的输入，其对在其感受野内的元素的数量进行编码。尽管 尽管这一假设很有吸引力，但仍存在几个重要问题。首先，代表基数的神经元 在被训练做出明确的相同/不同判断的猴子中， 代表累积的数值大小的猴子， 任何明确的数字判断。因此，用于表示数字的神经元编码方案可以 反映了训练或任务的需求，而不是神经元内在的数字编码特性， 数字敏感区。由于数学成绩可以通过简单数字训练来提高， 空间操作任务，理解外显训练对数字编码的影响， 顶叶皮层的神经元尤为重要。第二，假设LIP中的求和单元 为VIP（或dlPFC）中的数值单位提供输入，并且这些连接在功能上相关 数字的辨别力，还有待检验。拟议项目的目标是解决这些问题 问题使用行为，神经生理学，药理学和计算技术。 理解将视觉空间信息处理与表征联系起来的神经机制 数字的重要性可能表明在幼儿数学教育中的重要改进， 这一补救措施将使所有儿童受益，特别是那些数量能力受损的儿童。

Current evidence identifies two inter-related systems for representing and manipulating quantities in humans: 1) a symbolically-mediated exact numerical system used in precise mathematical operations; 2) a nonverbal approximate sense of numerosity that is evolutionarily primitive and which is present early in human ontogeny. Neurobiological and behavioral data strongly suggest that the symbolically-mediated exact numerical system taps into the approximate numerosity sense. Sensitivity to numerosity, a fuzzy sense of the number of objects or events, predicts numerical and mathematical performance throughout development. Moreover, brain imaging and lesion studies in humans implicate parietal cortex in both exact numerical processing and the approximate numerosity sense. Single neurons in the primate ventral intraparietal area (VIP), as well as in prefrontal cortex (dlPFC), respond selectively to a specific number of elements in a visual array. By contrast, neurons in the lateral intraparietal area (LIP) respond in a monotonic fashion to the number of elements in a visual array located within the neuronal receptive field. These observations suggest the hypothesis that LIP neurons integrate visual information to form a representation of accumulated numerosity, which is read out by neurons in VIP and dlPFC to signal a specific numerical value. This hypothesis is consistent with several computational models of numerical representation, in which numerosity units representing a specific cardinal value, such as 3 or 5, receive input from summation units encoding the quantity of elements within their receptive fields. Despite the attractiveness of this hypothesis, several important questions remain. First, neurons representing cardinal numerosity were described in monkeys trained to make explicit same/different judgments, while neurons representing accumulated numerical magnitude were described in monkeys that were not trained to make any explicit numerosity judgments. Thus, the neuronal coding scheme used to represent number may reflect training or task demands, rather than the intrinsic numerical coding properties of neurons in number-sensitive areas. Since math performance can be improved by training on simple numerosity and spatial manipulation tasks, understanding the effects of explicit training on numerosity encoding by neurons in parietal cortex is particularly important. Second, the assumption that summation units in LIP provide inputs to numerosity units in VIP (or dlPFC), and that these connections are functionally relevant for numerosity discrimination, remains to be tested. The goal of the proposed project is to address these questions using behavioral, neurophysiological, pharmacological, and computational techniques. Understanding the neural mechanisms that relate visuospatial information-processing to representations of numerosity may suggest important improvements in early childhood mathematical education and remediation that will benefit all children, particularly those suffering from impaired quantitative abilities.