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Difference between revisions of "Research Experiences for Undergraduates 2015-Potential Mentors"

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(Josh Grochow, Santa Fe Institute, Omidyar Fellow)
(Josh Grochow, Santa Fe Institute, Omidyar Fellow)
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==[http://www.santafe.edu/about/people/profile/Josh%20Grochow Josh Grochow], Santa Fe Institute, Omidyar Fellow ==
 
==[http://www.santafe.edu/about/people/profile/Josh%20Grochow Josh Grochow], Santa Fe Institute, Omidyar Fellow ==
 
Title: Exploring the space of algorithms, or, finding novel algorithms for hard and easy problems using genetic algorithms
 
Title: Exploring the space of algorithms, or, finding novel algorithms for hard and easy problems using genetic algorithms
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Mentor(s): Josh Grochow  
 
Mentor(s): Josh Grochow  
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Despite nearly half a century of algorithm development, our understanding of algorithms is still shockingly poor. For example, how long does it take to multiply two n-digit numbers? The state of the art is nearly O(n log(n)) steps, much better than the standard way we are taught in elementary school. Yet it's consistent with current knowledge that this could be done in only O(n) steps - i.e., that multiplying two numbers is just about as easy as adding them! No one knows the right answer. Such issues are even worse for the famous P versus NP problem, which essentially asks whether brute-force search can always be improved upon. Unlike multiplying numbers, virtually no progress has been made on this problem in the half-century that it's been around.
 
Despite nearly half a century of algorithm development, our understanding of algorithms is still shockingly poor. For example, how long does it take to multiply two n-digit numbers? The state of the art is nearly O(n log(n)) steps, much better than the standard way we are taught in elementary school. Yet it's consistent with current knowledge that this could be done in only O(n) steps - i.e., that multiplying two numbers is just about as easy as adding them! No one knows the right answer. Such issues are even worse for the famous P versus NP problem, which essentially asks whether brute-force search can always be improved upon. Unlike multiplying numbers, virtually no progress has been made on this problem in the half-century that it's been around.
 
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Revision as of 14:36, 6 April 2015

Research Experiences for Undergraduates 2015

A complete list of resident faculty list and our postdoctoral fellows can be found here


Potential Mentors and Projects

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Cristopher Moore, SFI REU PI, Santa Fe Institute, Resident Faculty


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Nihat Ay, Santa Fe Institute, Resident Faculty


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Andrew Berdahl, Santa Fe Institute, Omidyar Fellow


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Tanmoy Bhattacharya, Santa Fe Institute, Resident Faculty


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Vanessa Ferdinand, Santa Fe Institute, Omidyar Fellow


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Stephanie Forrest, Santa Fe Institute, External Professor

1. Understanding and evolving software diversity:

Neutral landscapes and mutational robustness are believed to be important enablers of evolvability in biology. We apply these concepts to software, defining mutational robustness to be the fraction of random mutations to program code that leave a program’s behavior unchanged. Test cases are used to measure program behavior and mutation operators are taken from earlier work on genetic programming. Although software is often viewed as brittle, with small changes leading to catastrophic changes in behavior, our results show surprising robustness in the face of random software mutations. Depending on the student's interest, the REU project could either involve learning to use the GenProg software and running new experiments, or it could involve developing theoretical models based on earlier work in the biological literature.

2. Understanding and modeling large-scale cybersecurity threats:

Cyber security research has traditionally focused on technical solutions to specific threats such as how to protect desktops and mobile devices against the latest malware. This approach has greatly enhanced our ability to defend against specific attacks, but technical improvements will not be sufficient on their own. Today’s cyber issues involve social, economic, organizational, and political components, which are often pursued in isolation from technical reality. Forrest and Prof. Robert Axelrod (Univ. of Michigan) are collaborating on project that aims to address that gap by focusing on the problem of reducing risks arising from cyber conflicts, especially those among state actors. Our current plan is to focus on the attribution problem, that is, once a cyberattack has been discovered, what does it take to hold a particular actor responsible? Depending on the student's interest and background, this project could entail statistical modeling, developing game-theoretic or decision-theoretic models (e.g., when is it advantageous to plant false flags), to researching the current (public) state of the art for attributing cyberattacks.

3. Forrest and Moses are collaborating on a project to examine how ant colonies and immune systems form distributed information exchange networks to search, adapt and respond to their environments. The is characterizing search strategies quantitatively in terms of how information flows over networks of communicating components, in this case, ants or immune cells. It will measure how information improves performance, measured in terms of how quickly a colony finds seeds or the immune system neutralizes pathogens. By studying in detail how distributed interaction networks guide search in two distinct systems, this project aspires to formulate a general theory describing how decentralized biological networks are organized to search, respond and adapt to different environments, and how they effectively scale up to large sizes. As the research has progressed we have begun to test our theoretical understanding of distributed search strategies by implementing them as search algorithms in robotic swarms. This demonstrates practical applications as well as providing a controlled experimental system in which to test theoretical predictions.



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Mirta Galesic, Santa Fe Institute, Professor


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Josh Grochow, Santa Fe Institute, Omidyar Fellow

Title: Exploring the space of algorithms, or, finding novel algorithms for hard and easy problems using genetic algorithms

Mentor(s): Josh Grochow

Despite nearly half a century of algorithm development, our understanding of algorithms is still shockingly poor. For example, how long does it take to multiply two n-digit numbers? The state of the art is nearly O(n log(n)) steps, much better than the standard way we are taught in elementary school. Yet it's consistent with current knowledge that this could be done in only O(n) steps - i.e., that multiplying two numbers is just about as easy as adding them! No one knows the right answer. Such issues are even worse for the famous P versus NP problem, which essentially asks whether brute-force search can always be improved upon. Unlike multiplying numbers, virtually no progress has been made on this problem in the half-century that it's been around.

Part of the reason for our paltry understanding of these questions is that, despite thousands of new algorithms, we've actually only explored a tiny corner of the space of all possible algorithms. This was brought home with the discovery in the early 2000's of so-called holographic algorithms - classical algorithms, inspired by quantum computing, that take advantage of surprising cancellations to efficiently solve problems that no one would have thought could be efficiently solved.

In this project we propose to explore more of the space of algorithms by several methods. We'll mention one such method here, and can discuss others in person if you're interested.

We propose to use novelty-seeking genetic algorithms to help find examples of truly new classes of algorithms. Given that genetic algorithms have long been used to search for new and better algorithms, what's special here? At least three things: (1) in the last decade or so there have been great advances in using genetic algorithms to search for novel solutions, rather than to directly search for better solutions; whether or not this finds better algorithms, in looking to further explore the space of algorithms, novelty is a key aspect; (2) the methods used in these novelty-seeking algorithms, such as indirect encoding, match up well with frontier problems in computational complexity, and (3) we propose to apply genetic algorithms to problems that we think may not have efficient solutions, such as NP-hard problems. If the genetic algorithm fails to find a good algorithm, we hope to still extract some insight from the bad algorithms it finds. Our hope is that we'll either find genuinely new algorithms for these problems, or that we'll gain theoretical insight into how hard these problems truly are.

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Laurent Hebert-Dufresne, Santa Fe Institute, Postdoctoral Fellow


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Alfred Hubler, Santa Fe Institute, External Professor


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Eric Libby, Santa Fe Institute, Omidyar Fellow


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John Miller, Santa Fe Institute, External Professor


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John Pepper, Santa Fe Institute, External Professor


Project Proposal:

This project is to refine and implement a new evolutionary heuristic algorithm for a classic NP-hard spatial optimization problem called the “Traveling Salesman Problem” The implementation could be done in any object-oriented programming platform with good spatial graphics, so we could decide that part together if you’re interested. -Faculty mentor: Dr. John W Pepper, external faculty

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John Rundle, Santa Fe Institute, External Professor



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Sam Scarpino, Santa Fe Institute, Omidyar Fellow


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Markus Schlapfer, Santa Fe Institute, Postdoctoral Fellow


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Caitlin Stern, Santa Fe Institute, Omidyar Fellow


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Pan Zhang, Santa Fe Institute, Postdoctoral Fellow