Point Processes and Time Series: Networks and Wavelets

拟议的研究涉及两个基本课题：a）在节点和B）涉及时间和空间点过程的小波分析的变体的时间过程的网络的研究。应用程序的基础上记录的尖峰列车，以了解大脑的听觉系统的互连和创建地震的等震线图的破坏性事件的后果。网络的努力涉及到图形建模，而小波工作可以被看作是一个竞争对手的本地加权程序，处理非平稳性。 这些主题集中在评估生物神经元网络中是否发生学习的问题上，在网络研究中，主要应用是从猫和大鼠死后确定的位置上的生物神经元获得的同期尖峰序列，其目的是推断潜在的布线图。 在小波研究的情况下，应用地震学和神经生理学抓住小波方法处理非平稳性的能力。时间和空间的情况下，被认为是提出的研究的动机所产生的问题，例如，在生物学和地震学领域，并相信他们可能会很好地解决当代研究工作涉及网络的概念。 涉及新颖的数学表达式的工作，允许在时间或空间上发生一些变化，也与研究有关。 本研究既包括理论的发展，也包括实证模型的拟合与验证。 可能存在对生物技术（毕奥）领域具有联邦战略利益的应用。 在生物学和地震学等不同领域工作的价值在于，为一个领域考虑的分析技术可以抽象并应用于另一个领域。

The proposed research concerns two basic topics: a) the study of networks with temporal processes at the nodes and b) variants of wavelet analysis involving temporal and spatial point processes. Applications are made to understanding the interconnections of the auditory system of the brain on the basis of recorded spike trains and to creating isoseismal maps of earthquakes in the aftermath of a destructive event. The network effort relates to graphical modeling while the wavelet work may be seen as a competitor to local weighting procedures, for handling nonstationarity. The topics come together in the problem of assessing whether learning is taking place in a biological neuron network.In the case of the network study, principal applications are to contemporaneous spike trains obtained from biological neurons at locations, determined post mortem in cats and rats, having in mind the goal of inferring a latent wiring diagram. In the case of the wavelet research, applications are made to both seismology and neurophysiology seizing on the ability of the wavelet approach to handle nonstationarity. Both the temporal and the spatial cases are considered.The research proposed is motivated by problems arising in the fields of biology and seismology, for example, and the belief that they may be well-addressed by contemporary research work involving the concept of networks. Work involving novel mathematical expressions, which allow some change in time or space to take place in a situation, also relates to the research. Both theoretical development and empirical model fitting and verification will be involved. There may be applications to the Biotechnology (BIOT) area of Federal strategic interest. The value of working in fields as diverse as biology and seismology is that analytical techniques thought of for one may be abstracted and applied in the other.