NME 130
NME 130 is a new class on "information systems" that we are planning. This web page collects together some of the information from discussions during the spring term 2009 between faculty, postdocs and students about what might be part of this course.
Participants: John Doyle (CDS/BE/EE), Steven Low (CS/EE), Michelle Effros (EE), Tracey Ho (EE/CS), Joel Tropp (ACM), Andreas Krause (CS), Pablo Parrilo (MIT), Richard Murray (CDS/BE).
Background information
(The information below is pulled from a planning document put together by Emmanuel Candes, John Doyle, Steven Low, Richard Murray and Pablo Parrilo, based on discussions in 200809.)
Many cutting edge problems in the natural sciences involve understanding aggregate behavior in complex largescale systems. This behavior "emerges" from the interaction of multitudinous simpler systems, with intricate patterns of information flow. Representative examples can be found in fields ranging from embryology to seismology to global climate change. Key features of these new challenges include the (sometimes bewildering) complexity of the underlying phenomena of interest, the increasing ability to collect large amounts of data from sophisticated instruments, and the desire to develop principles that aid in our understanding and allow us to predict future behavior and/or design systems that behave reliably in the presence of large amounts of uncertainty.
While sophisticated theories have been developed by domain experts for the analysis of various complex systems, the development of rigorous methodology that can discover and exploit common features and essential mathematical structure remains a major challenge to the research community; we need new approaches and techniques.
To address this opportunity, we believe that a new PhD program in Network Mathematics and Engineering (working title) is timely and would keep Caltech in a leadership position in fundamental research on complex, networked systems across several areas of applied science and mathematics in which Caltech is already active, as well as enable potentially new thrusts within the sciences. The long term goals of this PhD program are:
 Develop new approaches for understanding and building complex systems, with an emphasis on the underlying theory and application across a broad variety of the sciences and engineering.
 Recruit students, postdocs and faculty to Caltech who will serve as leaders in their respective fields around the world, and who will help develop the theoretical frameworks required to tackle new problems in complex, networked systems.
 Develop a curriculum and educational culture that supports the education of broadlytrained scientists, applied mathematician and engineers who work in and across multiple disciplines over the course of their careers. careers and
A key theme of the program is to help facilitate interaction between a broad variety of application areas in which in a common set of mathematical problems arise. This will be accomplished in part by keeping the program very open and encouraging students to work with faculty from around the campus.
The following nominal course sequences will make up the core courses in the PhD program (taken by all students):
 NME 110ab. Stochastic systems} (2 quarters)  random processes, Markov chains
 NME 120. Optimization} (1 quarter)  convex optimization
 NME 121. Algorithms} (1 quarter)  TBD. Could range from numerical algorithms to computational complexity.
 NME 130ab. Information systems} 9 units (306); first and second terms. Prerequisites: CS 21 (or equivalent), EE 111 (or equivalent), Ma 2, \phdabbv 110 (may be taken concurrently). This course covers the fundamental mathematics of information systems, including key concepts and theories from communications, computer science, control theory, information theory and networking. Topics include: mathematical representations of information, signals and systems, computational complexity, fundamental limits of feedforward and feedback systems (Bode/Shannon), applications of graph theory to distributed systems.
 NME 140ab. Datadriven modeling and analysis} (2 quarters)  statistics, machine learning, model reduction
Discussion sessions
To help understand the contents of the courses and the interactions between the different topics, a series of discussions sections were held. The focus of these sessions was on topics related to the "information systems" course (NME 130). The links for each topic contain notes for the discussion.
Date  Topics  Discussion leaders  Unavailable 
15 May (Fri) @ 3 pm, 110 Steele  Optimization

John, Ben  Nader, Michelle, Tracy, Pablo, Ufuk 
20 May (Wed) @ 12 pm  Distributed/networked systems

Steven, Javad  Richard (phone?), Nader 
28 May (Thu) @ 12 pm  Information theory

Tracey, Michelle  Richard, Ufuk, Nader 
3 Jun (Wed) @ 12 pm  Uncertainty

Ufuk, Nader  Richard 
16 Jun (Tue) @ 3 pm  Dynamical Systems

Nader, Andy  Michelle, John, Tracey 
19 Jun (Fri) @ 11 am  Graphical models  Andreas  John (phone?) 
24 Jun (Wed) @ 4 pm  Synthesis theory

TBD  
26 Jun (Fri) @ 11 am  Course planning  Richard 
200910 course plan
Based on the discussions over the term, the following rough curriculum was sketched out as a possible starting point for the program. This curriculum attempts to make maximal use of courses that are already taught, so that we don't have to create too many new courses at once. The top set of courses are the core program, followed by a list of courses offered through the various options whose students faculty might eventually participate in the program:
Track  Fall  Winter  Spring 
Stochastic systems 
ACM/EE 116 (Owhadi)Introduction to Stochastic Processes and Modeling 
ACM 216 (Tropp)Markov Chains, Discrete Stochastic Processes and Applications 
NME 130

Optimization and algorithms 

ACM 113/CDS 203 (Owhadi)
 
Information systems 
CS/EE/Ma 129a (Winfree)Information and complexity

CS/EE/Ma 129b (Winfree)Information and complexity
 
Datadriven modeling 
CS/CNS/EE 156 (AbuMostafa)
CS 155 (Krause)


ACM 



CS 



CDS 
CDS 210a  Control theory (MacMynowski)

CDS 110b  Optimizationbased control (MacMynowski)
CDS 212 Modern control theory (Doyle)


EE 


