Liberal Arts Become Mathematical

“Adding Math To Save Humanities” is the title of a sidebar article in the Wall Street Journal, April 25, 2017, about liberal arts colleges trying to add more mathematical contents to traditional liberal arts courses to better prepare their graduates for the work world.  Along with the Big Data revolution comes the need for employees in many diverse fields to be able to analyze data and to “rigorously and effectively” use data to answer questions.  “Emory University in Atlanta has created a degree that marries traditionally qualitative disciplines such as anthropology and English with math and statistics.”  This shift is in part to due students enrolling in liberal arts programs in smaller numbers.  Click below for the full article.

saving liberal arts

Using a Computer Simulator to Improve Place Kicker Performance

This 2 minute video explains how computer simulators in a lab can help a kicker improve his form.

Using Big Data to Predict Worker Illness and Pregnancies

Not a typographical error!  Companies who hire outside consultants are able to get data about their workforce that borders on a serious intrusion of privacy.  Click below for the whole WSJ article, but just a few quotes might give the sense of what I am talking about.

Bosses Tap Outside Firms to Predict Which Workers Might Get Sick – WSJ

“Trying to stem rising health-care costs, some companies, including retailer Wal-Mart Stores Inc., are paying firms like Castlight Healthcare Inc. to collect and crunch employee data to identify, for example, which workers are at risk for diabetes, and target them with personalized messages nudging them toward a doctor or services such as weight-loss programs.”

“To determine which employees might soon get pregnant, Castlight recently launched a new product that scans insurance claims to find women who have stopped filling birth-control prescriptions, as well as women who have made fertility-related searches on Castlight’s health app.”

“Privacy advocates have raised concerns about such practices. Employees generally have a choice in whether to participate in the programs. The services are new enough that relatively few workers are aware of them.”

“Federal health-privacy laws generally bar employers from viewing workers’ personal health information, though self-insured employers have more leeway, says Careen Martin, a health-care and cybersecurity lawyer at Nilan Johnson Lewis PA. Instead, employers contract with wellness firms who have access to workers’ health data.”

A New Biggest Prime Found

A new biggest prime number has been found.  It is called a Mersenne Prime because it can be written as 2^(74,207,281)-1.  It is so large that it defies comprehension.

As written in the New York Times http://www.nytimes.com/2016/01/22/science/new-biggest-prime-number-mersenne-primes.html?emc=edit_tnt_20160121&nlid=56749405&tntemail0=y

“How big is this big prime number?

I timed how quickly I could write down a number: about four seconds for 10 digits. If I had enough paper and ink — and made the impossible assumption that my hand could maintain this pace — it would take me more than three months to write down the 22,338,618 digits of 2^74,207,281− 1.”

An Ancient Math Problem Could Improve Medicine and Microelectronics

New Twist On Ancient Math Problem Could Improve Medicine, Microelectronics

ScienceDaily (May 10, 2012) — A hidden facet of a math problem that goes back to Sanskrit scrolls has just been exposed by nanotechnology researchers at the University of Michigan and the University of Connecticut.

It turns out we’ve been missing a version of the famous “packing problem,” and its new guise could have implications for cancer treatment, secure wireless networks, microelectronics and demolitions, the researchers say.

Called the “filling problem,” it seeks the best way to cover the inside of an object with a particular shape, such as filling a triangle with discs of varying sizes. Unlike the traditional packing problem, the discs can overlap. It also differs from the “covering problem” because the discs can’t extend beyond the triangle’s boundaries.

“Besides introducing the problem, we also provided a solution in two dimensions,” said Sharon Glotzer, U-M professor of chemical engineering.

That solution makes it immediately applicable to treating tumors using fewer shots with radiation beams or speeding up the manufacturing of silicon chips for microprocessors.

The key to solutions in any dimension is to find a shape’s “skeleton,” said Carolyn Phillips, a postdoctoral fellow at Argonne National Laboratory who recently completed her Ph.D. in Glotzer’s group and solved the problem as part of her dissertation.

“Every shape you want to fill has a backbone that goes through the center of the shape, like a spine,” she said.

For a pentagon, the skeleton looks like a stick-drawing of a starfish. The discs that fill the pentagon best will always have their centers on one of those lines.

Junctions between lines in the skeleton are special points that Glotzer’s team refers to as “traps.” The pentagon only has one trap, right at its center, but more complicated shapes can contain multiple traps. In most optimal solutions, each trap has a disc centered over it, Phillips said.

Other discs in the pattern change size and move around, depending on how many discs are allowed, but those over the traps are always the same. Phillips suspects that if a design uses enough discs, every trap will have a disc centered over it.

In their paper, published online May 10 in Physical Review Letters, the researchers report the rules for how to find the ideal size and spacing of the discs that fill a shape. In the future, they expect to reveal an algorithm that can take the desired shape and the number of discs, or the shape and percentage of the area to be filled, and spit out the best pattern to fill it.

Extending the approach into three dimensions, Glotzer proposes that it could decide the placement of wireless routers in a building where the signal must not be available to a potential hacker in the parking lot. Alternatively, it could help demolition workers to set off precision explosions, ensuring that the blast covers the desired region but doesn’t extend beyond a building’s outer walls.

Phillips expects filling solutions to be scientifically useful as well. Glotzer’s team developed the new problem by trying to find a way to represent many-sided shapes for their computer models of nanoparticles. In addition to nanotechnology, biology and medicine often need models for complex shapes, such as those of proteins.

“You don’t want to model every single one of the thousands of atoms that make up this protein,” Phillips said. “You want a minimal model that gives the shape, allowing the proteins to interact in a lock-and-key way, as they do in nature.”

The filling approach may prove a perfect fit for a variety of fields.

Actuary Gets a Patent for Method of Statistical Sampling

May 12, 2012

From the New York Times

Patents Aren’t Only for Engineers

By JAY VADIVELOO

I NEVER considered that I might obtain a patent one day. To me, patents were mostly for engineers, not for actuaries like me.

At Towers Watson, I advise insurance companies on risks associated with their businesses. I’m also a mathematics professor in residence at the University of Connecticut. I oversee several graduate students at an actuarial research center there and am always looking for real-world examples for them to work on.

A few years ago, I started thinking about statistical sampling in the insurance industry as something for students to test. I threw out some ideas to them that were based on concepts in consumer polling. We started with simple calculations and moved on to more involved ones. To me, the results were astounding: statistical sampling worked.

Generally when an insurer performs certain calculations, it includes data from all its policies. If it has a million policies, that means a lot of processing as various scenarios are considered. Sometimes, the work can take days.

I believed I had a solution to this cumbersome and costly process: create subgroups from the database, sample policies from each, repeat the process several times, then combine the results.

My technique provides results similar to those from studying all policies, and saves time and money. And unlike consumer polling, which requires finding participants, insurance databases contain ready-made samples.

As far as I knew, no one had proposed this model. I developed and tested it for several months before I told my boss, Craig Buck, head of United States life insurance consulting. We agreed that it should be patented, and that Towers Watson could license it to clients.

I worked with an outside patent firm to translate technical information into layman’s terms for the application. There is an art to that. The description had to be specific, yet  generic enough so as not to limit it too severely.

The lawyer I worked with — who later left the firm — said the first step was to search the database of existing patents to see if any were similar to mine. She had me check about 12, and they weren’t similar. She submitted the application to the United States Patent and Trademark Office in September 2009, and I hoped for the best.

Now I was excited, and after not hearing anything for months, I called the law firm and worked with another lawyer, Michael V. Young Sr. The patent office had a backlog of applications, but he said he could submit a second application with a request for an accelerated review that would require a special filing fee. Craig and I jumped at the offer.

By then, more than a year had passed since the first application was filed, so Michael did another search. For each new patent that might be similar, I again had to document why it differed from my idea. That was painful and tedious.

In January 2011, Michael filed a second, revised application for accelerated review. He also modified the first application, so both could still be considered. Several months later, the patent office granted the accelerated review.

Our Towers Watson colleagues in Britain, meanwhile, heard about my technique. They came to Connecticut, tested the model and confirmed that it performed as I had described.

Because of our request, a patent examiner picked up the second application first. I was awarded that patent this February and the first one a month later. The original took more than two and a half years from filing to approval, and the second one just over a year.

In February, when Michael e-mailed me that I would soon receive the patents, I probably screamed. First I called my wife, then asked my administrative assistant to read it on the screen.

EVEN before either patent came through, I was nominated for a company leadership award for the technique I developed. I received a plaque, and then $2,000 when I was awarded the patents. I won’t share in any profits, but the feedback I’ve received has been outstanding.

So if you think you’ve come up with an elementary idea, remember that anything is possible. I still believe that what I developed is so elegantly simple that others could have discovered it and received a patent. But they didn’t — I did.

The Sounds of Silence Yield the Fastest Random Number Generator

From Science Daily April 13, 2012

Researchers at The Australian National University have developed the fastest random number generator in the world by listening to the ‘sounds of silence’.

“While it has always been thought to be an annoyance that engineers and scientists would like to circumvent, we instead exploited this vacuum noise and used it to generate random numbers,” Professor Lam said.

“Random number generation has many uses in information technology. Global climate prediction, air traffic control, electronic gaming, encryption, and various types of computer modeling all rely on the availability of unbiased, truly random numbers.

“To date, most random number generators are based on computer algorithms. Although computer generated random numbers can be useful, knowing the input conditions to the algorithm will lead to predictable and reproducible output, thus making the numbers not truly random. To overcome this issue, random number generators relying on inherently random physical processes, such as radioactive decay and chaotic behaviour in circuits, have been developed.”

Dr Thomas Symul added: “Vacuum noise is one of the ultimate sources of randomness because it is intrinsically broadband and its unpredictability is guaranteed by quantum theory. Because of this, we are able to generate billions of random numbers every second.”

Dr Syed Assad said the team has linked their table-top laser experiment directly to the internet. “We can easily push this technology even faster but currently we have already reached the capacity of our Internet connection,” he said.

The random number generator is online and can be accessed from anywhere, anytime around the world at http://photonics.anu.edu.au/qoptics/Research/qrng.php Moreover, anyone who downloaded live random numbers from the ANU website will get a fresh and unique sequence of numbers that is different from all other users.

In collaboration with QuintessenceLabs, an Australian quantum technology company, the ANU team is now looking into commercialising this device. The team hopes to have this technology miniaturised down to the size of a thumb drive.