UC Davis science, engineering and technology newstips -- March

* Mathematicians unravel knotty problem
* Hummingbirds avoid nectar-robbed flowers
* Cosmologists study wrinkles in early universe

MATHEMATICIANS UNRAVEL KNOTTY PROBLEM

Untangling a knot may seem simple, but the theory of knots has tied up mathematicians for decades. Now, mathematicians Joel Hass, of the University of California, Davis, and Jeffrey Lagarias of AT&T Research have proved an important point. They have shown that when a simple loop of string is tangled up, it is always possible to untangle it in a limited number of steps.

Mathematicians group knots into types, depending on how many times the loops cross each other. The simplest kind of knot is a closed loop. Mathematicians call this a trivial knot, or unknot.

"Imagine a garden hose, with the ends joined together to make a loop. Then if you tangle the hose up, it can be pretty hard to get it back to the loop," said Hass.

What mathematicians did not know was the maximum number of moves it would take to turn a tangled loop of hose back into a plain circular loop. Hass and Lagarias have now found this number, although it is enormously high.

The result should spur other mathematicians to find ways to reduce this number, said Hass.

Knot theory is connected to many other fields, said Hass. For example, every cell in the human body contains over a yard of DNA, which is coiled and tangled up. Knot theory can explain how DNA untangles itself to allow genes to be read, said Hass.

The paper is published in the Journal of the American Mathematical Society.

Media contacts: Joel Hass, Mathematics, (609) 734-8128, [email protected] or [email protected] (Hass is on sabbatical at the Institute of Advanced Study, Princeton University, at present); Jeffrey Lagarias, AT&T Research, (973) 360-8416, [email protected]; Andy Fell, (530) 752-4533, [email protected].

HUMMINGBIRDS AVOID NECTAR-ROBBED FLOWERS

When hummingbirds forage for nectar in the mountains of Colorado, they avoid flowers that have already been raided by nectar-robbing bumblebees. They do this without having to see the nectar, or remember which plants they have visited before, according to postdoctoral researcher Rebecca Irwin at the University of California, Davis.

Broad-tailed and rufous hummingbirds feed on nectar from the long red flowers of scarlet gilia (Ipomopsis aggregata). The birds play an important role in pollinating the plants. But bumblebees also have a taste for nectar. The bees chew holes in the base of the flower to get at the nectar, and do not help pollinate the plants. Nectar-robbed plants are less likely to get pollinated and produce up to 50 percent less seed, said Irwin.

Irwin simulated nectar robbing by artificially removing or adding nectar to flowers, then watched hummingbirds feeding on them. The birds were less likely to visit a plant without nectar, and probed fewer flowers on plants they did visit.

Two possible explanations are that the birds use visual clues that tell them the flower is empty, or that they remember robbed flowers from previous visits, she said.

To block visual clues, she painted over the flower bases to disguise bee holes and nectar content. Despite this, the birds still went for the full flowers.

To test the bird's spatial memory, Irwin set up full and empty flowers in an aviary and let the birds get used to them. Then she moved the flowers around. The birds still went to the full flowers, without wasting energy on empty ones.

Irwin has some more theories to test on why the birds pick the right flowers. One is that their wingbeats make the flowers vibrate, and full flowers have a different frequency to empty ones. She will be testing these ideas in next year's research season at the Rocky Mountains Research Laboratory, Colorado.

EDITOR'S NOTE: Color photographs of hummingbirds, Ipomopsis flowers and bumblebees are available. Contact Andy Fell for details.

Media contacts: Rebecca Irwin, Center for Population Biology, (530) 752-8416, [email protected]; Andy Fell, News Service, (530) 752-4533, [email protected].

COSMOLOGISTS STUDY WRINKLES IN EARLY UNIVERSE

Wrinkles in the early universe will be studied under a NASA grant to cosmologist Lloyd Knox at the University of California, Davis. The grant of $500,000 is part of NASA's Long-Term Space Astrophysics program.

Knox's team will use data from the Microwave Anisotropy Probe (MAP), together with data from other satellites and high-altitude balloons, to study minute temperature variations in the microwave radiation that fills the universe.

The microwave background represents the universe when it was only a few hundred thousand years old, said Knox. Around that time, the hot plasma from the Big Bang cooled and settled into atoms. The universe became transparent, as light could pass through for the first time.

Variations, or anisotropies, in the microwave background of less than 1 part in 100,000 show irregularities in the early universe where the plasma was slightly denser, said Knox. Scientists think that as the universe cooled, gravity attracted more matter to these irregularities, so there was more matter in some places and empty space in between. The denser regions became brighter. Eventually, these irregularities became the source of all the structure we see today, said Knox.

"It's a really interesting probe of the early universe," said Knox. Because the universe was simpler back then, scientists can make predictions of what it should look like and test them, he said.

Studying the early stages in the universe also allows scientists to study physics at very high energies, far higher than can be achieved in a laboratory on Earth, said Knox.

MAP, a joint project of NASA's Goddard Space Flight Center, Princeton University, the University of Chicago and UC Los Angeles, is due to be launched in June this year.

Web site: http://map.gsfc.nasa.gov/.

Media contacts: Lloyd Knox, Physics, (530) 754-7352, [email protected]; Andy Fell, (530) 752-4533, [email protected].