CAREER: Mathematical Questions Arising from Neural Systems - Research and Education

大脑的神经回路是人类行为、思想和情感的中枢。因为这些回路非常复杂，而且回路的细节因人而异，所以我们对大脑的了解仍然有限。在这个项目中，首席研究员将研究大脑中有关电路结构和动力学的基本问题。关于大脑，我们知道的一件事是，从婴儿期到成年期，再到我们的晚年，神经回路是会发生变化的。其中一些变化是健康发展转变的一部分，例如婴儿能够整夜睡觉或青少年进入青春期；其他的变化是病理性的，比如睡眠障碍发作性睡症中一组特定神经元的丢失。在与实验室科学家的密切合作中，首席研究员寻求描述这些神经变化并确定潜在的神经机制。她将专注于三个领域：(1)青春期；(2)睡眠-觉醒调节；(3)神经递质系统，如多巴胺和血清素。神经回路细胞的变化可以改变这些神经递质的活动，有时会对进食、情绪和社会互动等重要的人类行为产生深远的影响。首席研究员将通过研究不同大脑回路的数学模型来开展这些调查，使用她为此目的而开发的数学。数学研究将包括发展混合模式振荡理论，研究图上的随机动力学如何随着图的变化而变化，使用谱分析来理解图结构如何决定马尔可夫过程吸收时间分布的一般特征，以及发展双随机过程理论。这些研究将有助于理解特定神经回路的正常功能，也有助于解释神经精神疾病和神经退行性疾病的问题。调查员将利用她在教学、招聘和指导学生方面的丰富经验，在俄亥俄州设计一个新的管道项目，鼓励学生选择科学领域的职业。

The neural circuits of the brain are central to human actions, human thoughts, and human feelings. Because these circuits are so complicated and the details of the circuitry vary from person to person, our understanding of the brain remains limited. In this project the Principal Investigator will study fundamental questions relating circuit structure and dynamics in the brain. One thing we do know about the brain is that neural circuits change, from infancy through young adulthood and into our later years. Some of these changes are part of healthy developmental transitions, such as an infant becoming able to sleep through the night or an adolescent entering puberty; other changes are pathological, such as the loss of a particular group of neurons in the sleep disorder narcolepsy. In close collaboration with laboratory scientists, the Principal Investigator seeks both to characterize these neural changes and to determine the underlying neural mechanisms. She will focus on three areas: (1) puberty, (2) sleep-wake regulation, and (3) systems of neurotransmitters such as dopamine and serotonin. Changes in the cells of neural circuits can alter the activity of these neurotransmitters, with sometimes profound effects on important human behaviors such as feeding, mood, and social interactions. The Principal Investigator will carry out these investigations by studying mathematical models of different brain circuits, using mathematics that she is developing for this purpose.Mathematical investigations will include developing the theory of mixed mode oscillations, studying how stochastic dynamics on graphs change as the graph changes, using spectral analysis to understand how graph structure determines the general character of the distribution of absorption times of Markov processes, and developing the theory of doubly stochastic processes. These investigations will give understanding of the normal functioning of particular neural circuits and also help to explain what goes wrong in neuropsychiatric illnesses and neurodegenerative diseases. The Investigator will use her extensive experience in teaching, recruiting, and mentoring students to design a new pipeline program in Ohio that will encourage students to choose careers in science.