Posts Tagged ‘applied math’

The Truth Behind the ‘Summer Rally’

June 6, 2016

Statistics students should read The Wall Street Journal article about the myth of the summer stock market rally (WSJ, June 6, 2016).  By examining the data the author shows that the summer historically had less rallies than other times of the year, and yet the name, the concept and the belief persists.  The author suggests that the name might go back to the Depression when in the summer of 1932 the Dow Jones Industrial Average gained 76.5% from the low close of June to the high close of August.

Sometimes we see what we expect to see, and no one is immune from the perception bias, but being aware of the tendency makes you better prepared to deal with it in an intelligent manner.

For the full article, click here: The Market’s Summer-Rally Myth – WSJ

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MBAs Need Data Comprehension and Communication With Geeks

May 5, 2016

The Wharton School has come to realize that in a data filled world, understanding how data can drive good decision making is key to tomorrow’s (and today’s) executives.  Case studies, which have long dominated MBA education, is no match for a deep understanding of analytics.  Being able to communicate with the data handlers and being knowledgeable about what one can expect from them in now a key skill.  The Wharton School of the University of Pennsylvania, in now pushing analytics in their MBA programs.  See the attached article.

Wharton M.B.A

Percent by weight or volume? Big difference!

March 27, 2016

When researching quartz counter tops, I discovered that this man made material is made from ground up quartz with a polyester resin binder material.  Wanting to know how much stone and how much resin, I read further to find out that the material is approximately 93% stone and 7% resin.  I was having a hard time visualizing how such a small amount of binder could work.

Reading further I discovered that the  93% and 7% is based on the weight of the components, but since the stone is much heavier per volume than the polyester resin binder, the percentages by volume should be different, and indeed they are.

By volume, it turns out that the same material calculates to 66% quartz and 34% resin binder.  Big difference.

 

Using Big Data to Predict Worker Illness and Pregnancies

February 29, 2016

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.”

How to measure the flow rate of a stream

January 31, 2016

Calculating the flow in a stream could be a design consideration, and sometimes it is just for the sake of the record, but the attached link describes how it is done.

http://water.usgs.gov/edu/streamflow2.html

Zack Greinke: Baseball’s Big-Data Pitcher

October 10, 2015

Greinke might be the perfect pitcher for baseball’s era of big data. There are other pitchers who study hitters as extensively, combing through statistics and video clips for revelations of their vulnerabilities. But few of them can match that understanding with the precision Greinke uses to turn game theory into results.

For the full story from the Wall Street Journal, Oct. 10-11, 2015:

Zack Greinke_ Baseball’s Most Obsessively Prepared Pitcher – WSJ

Math Being Used by Cancer Researchers

July 4, 2013

The following article from the NY Times discusses how mathematical models are being used to understand how different cancer drug therapies can be used for optimal results.

Math in cancer research

Calculation of Eigen Values and Eigen Vectors

May 29, 2013

Well done.  Dr. Chris Tisdell shows how to calculate the Eigen Values and Eigen Vectors for a basic problem and invokes the Principle Axis Theorem.

Bad things can happen when you miscalculate.

September 4, 2012

The attached link will take you to a YouTube that shows a crane collapse because of miscalculation, or misjudgment or both.

An Ancient Math Problem Could Improve Medicine and Microelectronics

May 15, 2012

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.