This section was written by Associate Editor Jean Thilmany.

STUFFING SPACE

As anyone who has tried to ready a box of books for shipping can attest, finding the best way to pack the greatest number of specifically shaped objects into a confined space is no simple task. But the problem is also a subject of intense study; a greater understanding of packing problems could result in better ways to store data on compact discs as well as a better understanding of matter itself.

That’s why a recent paper by two Princeton University researchers made headlines. They reported that they’ve jammed more tetrahedra—solid figures with four triangular faces—and other polyhedral solid objects than ever before into a space.

Their work appeared in the Aug. 13 issue of the journal Nature.

The researchers—Salvatore Torquato, a Princeton professor of chemistry, and Yang Jiao, a graduate student in the school’s department of mechanical and aerospace engineering—report that they have bested the world record for packing, set last year by Elizabeth Chen, a graduate student at the University of Michigan.

Using computer simulations, Torquato and Jiao were able to fill a volume to 78.2 percent of capacity with tetrahedra. Chen, before them, had filled 77.8 percent of the space.


Princeton researchers have beaten the present world record for packing the most tetrahedra, pictured, and other shapes into a volume. Research into these so-called packing problems have produced mathematical ideas and led to practical computing applications.

The Princeton scientists developed a complex computer program and married it to a theoretical analysis to achieve their results, Torquato said. Previous computer simulations had taken virtual piles of polyhedra and stuffed them in a virtual box and allowed them to grow. But Torquato and Jiao designed an algorithm—called an adaptive shrinking cell optimization technique—that did it the other way. Their simulation placed virtual polyhedra of a fixed size in a box and then made the box shrink and change shape, Torquato said.

The Princeton researchers placed pairs of tetrahedra face-to-face, forming a kissing pattern that, viewed from the outside of the container, looks strangely jumbled and irregular, Torquato said.

Efficient packing of solids lies behind the error-detecting and error-correcting codes widely used to store information on compact discs and to compress information for efficient transmission around the world, he added. Torquato and Jiao’s packing solution may help researchers searching for ways to improve error-detecting and error-correcting, Torquato said.

COMPOSITE AID

The Ares V is NASA’s next generation space launch vehicle. In order to streamline the design process, NASA engineers paired finite element analysis software with special software that can verify the vehicle’s structural integrity.

According to the vehicle specifications, the shroud of the Ares V will separate into four petals during flight, to release the lunar lander, said Craig Collier, president of Collier Research of Hampton, Va. His company makes the structural integrity software, called HyperSizer, used for the Ares simulation.

One factor that designers must account for is that, during flight, the aerodynamic pressure on the shroud is resolved into internally distributed forces, Collier said.


NASA engineers recently analyzed the composite shroud that's part of its Ares V space launch vehicle. The simulation is pictured. The engineers paired FEA and composite-analysis software to find the best dimensions and composite materials for the shroud.

The NASA designers first used the finite element analysis software Abaqus from Simulia of Providence, R.I., to determine the load path, load direction, and also to determine how much load is in the stiffened panel and the ringframe, said Tom Battisti, Simulia director of alliances.

They then used HyperSizer to size the panels’ cross-sectional dimensions to the Abaqus computed load, Collier said.

The HyperSizer software surveyed millions of dimensions and laminates for a composite design. It works in a feedback loop with the FEA program to identify the optimum design and composite variables, he said.

The software helped the NASA engineers reduce structural weight, and to find the best dimensions and composite materials for the shroud, Collier added.

NEW MATH

A congruent number, to a mathematician, is a positive integer that is equal to the area of a right triangle with three rational number sides. For instance, 6 is the area of the famous right triangle with sides three, four, and five; so 6 is a congruent number.

Finding all possible congruent numbers is a problem that mathematicians have tackled for centuries. “Old problems like this may seem obscure, but they generate a lot of interesting and useful research as people develop new ways to attack them,” said Brian Conrey, director of the American Institute of Mathematics, in Palo Alto, Calif.

That’s why mathematicians from around the globe recently worked together, relying heavily on computer code and hard-drive space, to find congruent numbers up to one trillion.

The first few congruent numbers are 5, 6, 7, 13, 14, 15, 20, and 21. Many congruent numbers were known prior to the new calculation. But the recent calculation found 3,148,379,694 congruent numbers, Conrey said.

The numbers involved were so enormous that if their digits were written out by hand they would stretch to the moon and back, Conrey said. Those numbers couldn’t fit into the main memory of the computers the mathematicians had to work with, so they made extensive use of the computers’ hard drives.

“The difficult part was developing a fast general library of computer code for doing these kinds of calculations,” said team member Bill Hart, a mathematician at Warwick University of Coventry, England. “Once we had that, it didn’t take long to write the specialized program needed for this particular computation.”

The software used for the calculation is freely available, and anyone with a large computer can use it to break the team’s record or do other similar calculations, Hart added.

Results such as these are sometimes viewed with skepticism because of the complexity of carrying out such a large calculation and the potential for bugs in either the computer or the programming, he said. But according to Hart, researchers verified their results, doing the calculation twice, on different computers, using different algorithms, written by two independent groups.

NETWORKED BRAIN

When two researchers at Northwestern University wanted to get a look at how neurons within the brain actually work, they turned to evolution run on a computer.

The pair has been relying for more than a decade on a balance of experimentation and computer modeling, said Bill Kath, professor of engineering sciences and applied mathematics in the McCormick School of Engineering and Applied Science at Northwestern University in Evanston, Ill.

Kath works with Nelson Spruston, professor of neurobiology and physiology in the university’s Weinberg College of Arts and Sciences. Recently, Spruston has been studying the way ion channels of neurons change their shape when activated. This shape shifting enables sodium to enter from outside the neuron; that changes the neuron’s voltage and causes the neuron to fire off a chain of neural activity within the brain.

“If you want to understand how this neural circuit is processing information and memory, you have to understand how these neurons behave in different situations,” Kath said. “If you leave out key details, you might miss something important.”

But the difficulty in modeling such behavior lies in the time scale over which this happens—anywhere from fractions of a millisecond to several seconds, Kath said.

To find a model that can work over this wide time scale, the researchers took a cue from nature and designed an evolutionary algorithm to study the problem.

Evolutionary algorithms work like this: rather than making one model, researchers create 100 models with many different parameters. They then run those models—using high-speed computers—and compare the results to the experimental data to see how well they match, Kath said. Researchers then keep the best traits of different models and mix and match—a process that mirrors breeding—to make 100 more models. These new models are then run and the process starts again.

Thousands of generations later they get a model that matches the characteristics of the real thing, Kath said.

Researchers have used this technique in modeling before, but this time the researchers introduced a new twist: they allowed the structure of the model—not just its parameters—to be mutated during the breeding.

“In the end, the computer found a quite simple state-dependent model for the sodium channels that provides a very accurate behavior on short time scales and out to several seconds, as well,” Kath said.

FEELING AFRAID

Researchers at the University of Missouri are also building computational models of the brain. But that team seeks to understand how the brain reacts long-term to fear.

Their findings could help victims of post-traumatic stress disorder, said Guoshi Li, an electrical and computer engineering doctoral student at the school in Columbia, Mo.

The modeling method has helped Li and his colleagues discover new evidence on how the brain reacts to fear.

“Computational models make it much easier to study the brain because they can integrate different types of information related to a problem into a computational framework and analyze possible neural mechanisms from a systems perspective,” Li said. “We can simulate activity and test a variety of what-if scenarios in a rapid and inexpensive way.”

They’ve been able to do this without using human subjects.

Previous experiments have demonstrated that that fear gradually diminishes over time as someone begins to disassociate a fear response from a particular stimulus. But—via computer models that capture neuron response in rats—Li and his team found that the fear response is never completely lost.

In other words, triggers around an event—even a memory of the event—that originally inspired the fear can bring it on anew. Over time, the trigger won’t lead to as strong a fear response, but the fear response will always be there.

The finding that fear is never completely lost can perhaps lead to new therapies for post-traumatic stress victims, Li said. One day, researchers may find a way to completely erase a victim’s fear of a particular event or situation.

AILMENTS FOR ALL

To help reduce the number of workplace and general injuries in the United States, researchers need to know the most common types of injuries. That way, research could first focus on preventing those injuries, said Mark Lehto, an associate industrial engineering professor at Purdue University in West Lafayette, Ind.

Lehto is working to develop computer models to comb through thousands of injury reports in large administrative medical or insurance-claims databases to automatically classify them based on specific words or phrases.

“One goal is to identify the most important causes of injuries so that efforts could be directed toward reducing the burden of injuries in society,” Lehto said.

The reports are usually filled out by employers, health-care professionals or claimants themselves. After that, the reports are manually coded by employees of the National Center for Health Statistics, by hospital staff, or by insurance industry handlers. These people review thousands of injury narratives included in reports, Lehto said.

“This is obviously very labor-intensive,” Lehto said.

Teaming up with researchers at the Liberty Mutual Research Institute for Safety in Hopkinton, Mass., Lehto and his colleagues assigned codes to injury reports from workers’ compensation claims using two different computer models.

“The predictions were quite good,” Lehto said. “The results were comparable to the human coders. The accuracy is surprising considering all of the misspellings and abbreviations seen in these workers’ compensation claim narratives.”

Lehto detailed the findings in a paper published in the August edition of the journal Injury Prevention. Quick and accurate coding will lead to an updated and accurate database detailing the most-common injuries.

CHEAPER STORAGE

Server-type data storage never seems to be fast enough or cheap enough. But researchers at Carnegie Mellon University in Pittsburgh and Intel Labs Pittsburgh have combined low-power, embedded processors of the type typically used in netbooks and flash memory to create a server architecture that is not only fast, but is more energy efficient for data-intensive applications than the systems now used for most Internet services.

An experimental computing cluster based on this so-called Fast Array of Wimpy Nodes architecture was able to handle 10 to 100 times as many queries for the same amount of energy as a conventional, disk-based cluster.

The FAWN cluster had 21 nodes, each with a low-cost, low-power, off-the-shelf processor and a four-gigabyte compact flash card. Even at peak use, the cluster operates on less energy than a 100-watt light bulb, said David Anderson, Carnegie Mellon assistant professor of computer science.

Anderson and Michael Kaminsky, senior research scientist at Intel Labs Pittsburgh, led the research.
“FAWN will probably never be a good option for challenging real-time applications such as high-end gaming,” Kaminsky said. “But we’ve shown it is a cost-effective, energy efficient approach to designing storage systems, and we are now working to extend the approach to applications such as large-scale data analysis.”

BRIEFLY NOTED

CPFD Software LLC of Albuquerque, N.M., which makes the Barracuda simulation package for particle-fluid systems, has upgraded Barracuda to version 14. /// Delcam of Birmingham, England, has released the 2010 version of its FeatureCAM feature-based machining software. /// Mastercam of Tolland, Conn., has released X4 Wire for part modeling and EDM programming. /// Quickparts of Atlanta, a provider of custom designed parts, has made its instant quotes capability available via email. /// Soft Gold Ltd. of Tula, Russia, has released ABViewer 7.2, a combined CAD viewer, converter, and editor. /// Simpoe SAS, of Torcy, France, a software developer specializing in plastic injection molding simulation solutions, has signed a partner agreement with Siemens PLM Software of Plano, Texas, to develop integration between Siemens PLM Software’s Solid Edge CAD software and Simpoe plastic injection simulation solutions. The Solid Edge plug-in will be named SimpoEdge. /// Sigma Technology of Moscow has released IOSO 2.0, design optimization software. /// PTC of Needham, Mass., is now shipping the CAD program CoCreate 16.5. /// SolidProfessor of San Diego has listed its 2010 series of on-demand SolidWorks content beginning with Update Training 2010. This course is designed to help users get the most out of their SolidWorks upgrade by providing an in-depth review of each SolidWorks enhancement and how to best use it. /// CogniTens of London, a provider of 3-D measurement systems, is shipping CongniTens version 4.1.