April 20th Math Club – Directed Reading Program

This Wednesday, April 20th, come hear about the experiences of the first cohort of students in the Directed Reading Program. In this program undergraduate students team up with math graduate student mentors to read about some cool topic in math.

Plus, if that is not already enough, there will be pizza.  Hope to see you all there!

Here are the details:

When: Wednesday, April 20, at 5:30

Where: PHSC1105

April20_2016

Math Club meeting this week.

This is perhaps the last Math Club meeting for the calendar year 2013. Come one, come all!

Untitled

Where: Physical Sciences, Room 1105

When: Wednesday, December 4th, 5:00 pm

Who: Dr. Hansmann from the Chemistry Department will talk about, “Computational Tools in Protein Folding”. Here is a link to the flyer:

mathclubDec4_2013

As always, FREE PIZZA!

OU Citizen Science Club

We’re happy to spread the word about OU’s Citizen Science Club.They are meeting this

Monday, October 7th at 7pm in Dale Hall Room 107.

What is citizen science?

Back in the old days science was learned about and done by amateurs as well as professionals.  Heck, Fermat was a lawyer and government official during the day and came up with Fermat’s Little Theorem, Fermat’s Last Theorem, etc. at night (like Batman!).

stand_back_i__m_going_to_try_science__fb_cover_by_ahandgesture-d5fh4c8

But it’s not just in the good old days!  It’s even easier with the Internet, crowd sourcing, smartphones, etc. for people to get involved with science reearch!  One example we told you about two years ago was FolditThis page has more good examples!

Or you could just go to the meeting!

Dr. Martin on Amazon.com!

51ZcS808FCL._SY300_Of course everybody thinks about the teaching when they think of professors, but profs also do  cutting edge research!

This is another installment of our very occasional series on the research being done by the faculty of the OU Math department.  This time we’re talking about our own Kimball Martin.  He recently published a book entitled “On Central Critical Values of the Degree Four $l$-functions for Gsp (4): The Fundamental Lemma. III”.  It was written by Dr. Martin, Masaaki Furusawa, and Joseph Shalika*.

If you’d like a copy, you can get it from amazon.com for the low, low price of $74 (free shipping!), or you can just download the preprint version from Dr. Martin’s webpage.  So far there’s no reviews on amazon, so you’ll have to read it yourself to see if it’s as gripping as parts I and II :-).

* Fun fact about Dr. Shalika — he was the mathematical grandfather of both OU’s Luis Lomeli and OSU’s Mahdhi Asgari!

Robots vs. Math

Earlier this semester an OU math professor, Dr. Murad Özaydin, and a former OU grad student, Dr. James Dover (now at Cameron University in Lawton), posted their most recent paper on the ArXiv.

It is entitled “Homeomorphism and Homotopy Types of Restricted Configuration Spaces of Metric Graphs”.  But really, as Dr. Özaydin explained in the topology seminar, it’s about Robots on Rails.

As part of our very occasional postings on research in the OU Math department, we wanted to tell you about their very cool theorem.  Before we do that, let’s talk robots.

robot_vs_human_post_card-raccc52d4f8bb4dfea19ea6c283ec22a0_vgbaq_8byvr_512

In real life, robots which can move are often only allowed to move along certain paths.  They might actually move along rails; or, even if they just drive along on wheels in a factory their programming steers them along certain fixed paths so they don’t accidentally run into walls, expensive machines, people, etc.

And even non-robots often travel on real or virtual rails.  Trains, of course.  But cars on the freeway system, planes flying through the air (commercial planes can’t go any which way, air traffic control routes planes around the US on “highways in the sky”).

A typical problem, then, is to route multiple robots around a fixed set of paths on a factory floor so that they all get place to place without running into each other.  To a mathematician, this is a problem about moving around on a graph.  Each vertex is a destination, and each edge from one vertex to another is a path from one place to another.  So it might look like this (the numbers on each edge is the length of that edge):

master_graph

We can then think of robots in this picture as little disks moving along these paths. Of course, the whole problem is that you don’t want the robots running in to each other. This means each robot’s disk should bigger or smaller as needed to represent the size of the robot.  A graph with distances is called a metric graph and moving robots of various sizes around on such a graph is sometimes called “Pebble Motion on Graphs Problems”.

Actually developing a routing algorithm for moving the robots around is a very challenging problem. It is already interesting and difficult to understand which routings are even possible.

How do we tackle such a problem?  Mathematicians (like Drs. Dover and Özaydın) do something bold which actually simplifies the problem (once you get your mind around it).  They consider the set of all possible configurations of robot positions on the graph.

On the one hand, this a a much bigger and more complicated gadget, but on the other hand it is topological space called a configuration space.  This means you can unleash all the tools we have from topology to study the possible configurations of robots.

image_preview

For example, a path in the configuration space translates into the simultaneous motion of the robots around the graph.  So knowing that there is a path between any two configurations in the configuration space tells you that it is possible to move the robots into any positions you like.

The first question, then, is how many different configuration spaces are there for a fixed graph if you vary the size of the robots.  To go back to our example of the factory, if you you replace your robots with new and improved models which are half the size of the old ones, does your old software still work, or are their new paths and configurations possible?  For example, if you have a single track of length 1 meter:

line segment

If you have a two gigantic robots which are each 3/4 meter across, then they can’t both fit on this track.  So there is zero possible configuration spaces for two big robots on this graph.  But if you replace them with two small robots (say of size 1 cm), then they now both fit on the graph and so you have at least one space of possible configurations.

As a topological space, you count spaces the same if they are homeomorphic.  So the first problem to ask (and which Drs. Dover and Özaydın answer) is how many non-homeomorphic configuration spaces are there?

You might think that there is infinitely many.  Or at least many, many, many.  In his 2011 PhD thesis at the University of Durham, Ken Deeley proved* that if you consider the first interesting case of two robots (one robot is easy!), then the number of possible configurations is actually finite.

Dr. Deeley gave an upper bound which is an exponential function in the number of edges on the graph.  The good news is that it only depends on the number of edges, not how they are connected or how long they are or anything else.  The bad news — as we all know — is that exponential functions get very big very fast.  So if it really is an exponential number of configuration spaces, then it is surely impractical to handle them on a case by case base.

Drs. Dover and Özaydın took on the challenge.  They prove the following amazing result:

Theorem:  If you have n robots traveling around a graph, then the number of possible configuration spaces is bounded by a polynomial of degree n in the number of edges in the graph.

For example, in Deeley’s case of two robots, the bound is a quadratic polynomial!  In fact, they even compute the bound for two robots on a graph with E edges in their paper and get that the number of configuration spaces is no more than:

9 E^{2}-5E-1

That’s a heck of a lot less than an exponential bound!

A couple of notes before we go:

  • They give an example with two robots where the number of configurations is bounded below by a quadratic polynomial.  This shows that you can’t get it down to a linear function.
  • They also consider the case when the robots have various sizes.  In fact, they even allow you to set how close each pair of robots can get to each other.  Let’s say robots A, B, and C are all small, but A is carrying radioactive material.  If robot B is  sensitive and robot C is not sensitive to radioactivity, you can set the distance between A and B to be larger than the distance between A and C and B and C.  Their theorem still applies!

Very nice result!

"Imagine if all these fish were mathematical theorems..." -- James Dover

“Imagine if all these fish were mathematical theorems…” — James Dover

* To be 100% mathematically honest, Deeley considered spaces up to homotopy, not homeomorphism.  There are fewer homotopy types, so a bound on homotopy types is not quite as strong a result as on homeomorphism types.  That is, Drs. Dover and Özaydın result implies Dr. Deeley’s but not vice versa.

Work on the OU supercomputer!

Henry Neeman passed along this great opportunity for OU students only:

The OU Norman campus opportunity below is available to OU students only.

Henry

==================================================================

Student Employee – Supercomputing Internship (FALL)

http://jobs.ou.edu/

Requisition Number: 15162
Position #: 00022344

Job Search Category: Student or Work Study
Job Type: Part-Time
Number Needed: 1
Listing Category: Technical and Paraprofessional

Department: Information Technology (IT)
Campus: Norman

Application Deadline: Open Until Filled

Work Schedule: Normal working hours are M-F 8-5. Will depend on
class schedule.
Hours per week: 15-20

Are you interested in an Opportunity to gain real-world IT
experience?

Information Technology is offering a one-year paid Internship
that will emphasize the prevalence of Supercomputing Technology.

As an OU IT Intern, you will have an opportunity to work as a
member of a team of IT Professionals specializing in
Supercomputing technology.

You will be assigned a mentor and will learn the following
development concepts as well as apply them in real-life IT
projects:

* Account management
* Batch system/queue management
* Software management
* File system management
* Network management and troubleshooting
* User application support
* Hardware maintenance
* Backups/Restores

Note: This internship may also be eligible for college credit.

Required Education and Experience: High School diploma or GED as
well as some formal college training.

***Must have completed intro programming classes or equivalent
experience.

Must be currently enrolled in the FALL 2012 term as a student at
the University of Oklahoma. Hiring contingent upon verification of
current student status.

Required Skills and Proficiencies:

The ideal candidate demonstrates a strong work ethic, is
self-directed and is productive working independently as well as
collaboratively; Must be an analytical thinker with the ability to
identify, define, interpret, and resolve both technical and human
issues.

Must have completed intro programming classes or equivalent
experience.

* Computer Skills
* Excellent Communication Skills

Department Preferences:

* Undergraduate study in MIS, Computer Science, Engineering or
other computer related field.
* Experience in Unix system administration.
* Experience with C programming language.
* Experience with Perl programming language.

You’ll be working with OSCER not Oscar!

It’s Alive!

As promised, Boomer is up and running!

A picture of Boomer (but where’s the blinking lights?)

Henry Neeman sent us the announcement:

OU Deploys Fastest Academic Supercomputer in Oklahoma History

May 24, 2012

NORMAN — “Boomer,” the fastest academic supercomputer in state history, was deployed today at the University of Oklahoma.

“The deployment of the state’s fastest supercomputer in state history will further enhance OU’s academic excellence,” said OU President David L. Boren.

The supercomputer clocks in at a peak speed of roughly 109
trillion calculations per second and supports OU’s research
initiatives.

“This new supercomputer represents an incredible opportunity for OU,” said Loretta Early, OU’s Chief Information Officer and University Vice President for Information Technology. “Boomer will substantially expand OU’s ability to engage in cutting-edge,
computing-intensive research — to do more, and to do it faster and better, at a lower cost.”

Researchers will employ Boomer to compute large amounts of data for a broad variety of research with emphasis on weather forecasting, molecular dynamics and high-energy physics, which explores the fundamental nature of matter and energy. Boomer also will support research in astronomy, coastal flooding, biomedical
engineering, data encoding for disk drives, petroleum engineering, nanotechnology, groundwater contamination, biofuels, and wireless networks, among many other areas.

Henry Neeman, Director of the OU Supercomputing Center for Education and Research, a division of OU Information Technology, said that OU IT focuses on the needs of researchers at a level that is almost unprecedented nationally even among top research universities.

“For the past decade, OU has been a national leader in supporting the computational research and education needs of local students, faculty and staff,” Neeman said. “We’re extremely proud to expand a great tradition with this fourth generation OU IT supercomputer,
which will enhance research capabilities by connecting scientific collaborators throughout the state and nation.”

Boomer is three times as fast as the previous fastest academic supercomputer in the state, OU’s “Sooner,” which served hundreds of undergraduates, graduate students, staff and faculty from 2008 to early 2012. It’s also 100 times as fast as OU IT’s first supercomputer, built in 2002.

OneNet, Oklahoma’s statewide research, education and government network, will deliver Boomer’s capabilities from OU IT’s high-speed campus network to OU research teams, and 24 other Oklahoma institutions and more than 150 out-of-state and international collaborators will also be connected through OneNet.

“We’re very proud of our role in facilitating research, one of
OU’s key missions and a crucial engine for statewide economic development,” Early said. “With this new resource, we improve our potential to attract a growing number of research projects and increase external funding, and therefore attract and retain the best and brightest researchers, both faculty and students. Boomer
is both a logical next step and a major breakthrough for
researchers on campus.”

In addition, Boomer will connect to the Oklahoma PetaStore, which has the capacity to store multiple Petabytes (millions of Gigabytes) of research data, allowing OU researchers to create and maintain very large research data collections. Keith Brewster, acting Director of the Center for Analysis and Prediction of Storms, is looking forward to improving forecasting models with Boomer’s capabilities. “Severe weather, including tornadoes and hurricanes, kills hundreds of people and destroys billions of dollars of property every year. OU’s new supercomputer will help us to improve forecasts of these events, allowing us to resolve features half the size we could resolve previously.” Making large-scale, accessible and professionally managed advanced computing capability available to OU’s researchers also ensures that investigators will meet the requirements of federal research funding programs. Through deployment of Boomer, the University’s goal is to strengthen OU’s grant applications, leading to improved outcomes for researchers, students and Oklahoma’s economy.

To paraphrase Dr. Boren when approving the construction of Boomer: “But the deciding factor was when we learned that Texas was working along similar lines, and we were afraid of a doomsday gap.”