CARGO: Approximation and Simulation of Neurons

DMS-0138065朱滨海在这个项目中，我们研究了一个起源于神经映射的三维几何问题，神经映射模拟了神经元的运动，从而理解了人类的行为。该问题定义如下：给定一个神经元，它被建模为多面体，计算一个最小的（最小）圆柱段集来近似神经元。我们计划为这个问题设计一个很好的近似（即，圆柱段和神经元之间的误差很小）。我们还计划有一个很好的实现，建立一个原型系统，并进行广泛的实证研究。实际上，这个问题的解决方案将对计算生物学产生重大影响。 从理论上讲，这个问题可以概括为在3D空间中找到一条线刺穿一组球的问题（据我们所知，这一问题从未得到过认真的研究）。对人类神经元的运动建模是生物学中的一个重要问题，特别是在理解人类在不同情况下的行为方面。 要做到这一点，我们首先需要使用一组圆柱段来建模单个神经元，它非常像一个树形多面体。不同半径的不同圆柱段具有不同的功能，因此圆柱段的联合应尽可能靠近神经元。在实践中，这个问题是由计算生物学社区的技术人员手动估计的。这个过程既费时又容易出错。我们的研究将集中在用计算机自动化这个过程，成功的解决方案将在计算生物学界产生深远的影响。我们将在整个项目中培养两名研究生。

DMS-0138065Binhai ZhuIn this project, we investigate a three-dimensional geometric problem that originated in neural maps, which model the motions of neurons so as to understand the human behavior. The problem is defined as follows: given a neuron, which is modeled as a polyhedron, compute a minimum set of (minimal) cylindrical segments to approximate the neuron. We plan to design a good approximation for this problem (i.e., the error between the cylindrical segments and the neuron is small).We also plan to have a good implementation, build a prototype system, and perform extensive empirical studies. Practically, a solution to this problem will have a great impact in computational biology. Theoretically, this problem generalizes the problem of finding a single line stabbing a set of balls in 3D (and has never been seriously studied to the best of our knowledge).Modeling the motions of human neurons is an important problem in biology, especially in understanding human behavior under different circumstances. To do that, we first need to model a single neuron, which is very much like a tree-shaped polyhedron, using a set of cylindrical segments. Differentcylindrical segments of different radii have different functionality, so the union of the cylindrical segments should be as close to the neuron as possible. In practice this problem is estimated manually by technicians inthe computational biology community. The process is time-consuming and error-prone. Our research will focus on automating this process with computers and a successful solution will have deep influence in the computational biology community. We will train two graduate studentsthroughout this project.