NeTS: Medium: A Sparse Decomposition Framework for Complex System Design and Analysis

大规模、无处不在的通信系统是日常生活的重要组成部分，随着万物互联技术的出现，正在成为我们基础设施的重要组成部分。未来的通信系统需要非常新的设计范例，因为它们是大规模的，涉及通信、“自然”(环境)网络以及控制的复杂交互作用。这种复杂性、互联性和规模的系统的无缝管理是令人望而生畏的。需要一种全新的方法来解决规模和复杂性问题。研究人员正在研究用于网络设计和优化的新数学模型，这些模型适用于规模比目前方法容易处理的系统要大得多的系统。他们计划在认知无线电、无线身体区域传感网络和潜在的细菌种群模型等应用上展示它们的实用性。这项研究通过分析、跟踪和控制复杂系统图上的马尔可夫过程，提出了一种新的理论框架来应对大规模系统设计的挑战。利用稀疏逼近理论，利用图小波来表示这些大的马尔可夫链中的相关性。典型的复杂系统引入了一种潜在的稀疏性，这使得能够通过类似压缩传感的方案来降维。该研究通过为有向图设计新的图小波，结合新的稀疏近似算法和针对复杂系统的估计、通信和控制的控制方法，开发了新的稀疏技术，用于时间演化的大系统的形式化建模、分析和优化。

Large scale, pervasive communication systems are an important part of everyday life and, with the emergence of the Internet of Everything technology, are becoming an essential part of our infrastructure. Future communication systems necessitate significantly new design paradigms because they are large scale and involve a complex interaction of communications, "natural" (environmental) networks as well as control. The seamless management of a system of this complexity, interconnection, and scale is daunting. A fundamentally new approach is needed to tackle the issues of scale and complexity. The investigators are studying novel mathematical models for network design and optimization for systems of much larger size than those that are tractable with current methods. They are planning to demonstrate their utility on applications such as cognitive radio, wireless body area sensing networks and potentially models for bacterial populations. The new methods have the potential to impact the design and control of very general, large-scale networks such as biological, social networks and the SmartGrid.This research develops a novel theoretical framework to address the challenges of large scale system design by analyzing, tracking, and controlling Markov processes over graphs associated with complex systems. The correlation induced in these large Markov chains is exploited via sparse approximation theory employing graph wavelets for representation. Typical complex systems induce an underlying sparsity that enables dimensionality reduction via compressed sensing-like schemes. This research develops new sparse techniques for formal modeling, analysis and optimization of large-scale systems that evolve temporally, by designing novel graph wavelets for directed graphs, in combination with new sparse approximation algorithms and control methods tailored to the complex systems for estimation, communication and control.