Amoebas Anticipate Climate Change

A new experiment demonstrated that amoebas slow their motion in synchronization with periodic hostile changes in their environment. The amoebas even displayed anticipation to the periodically appearing unfavorable conditions. This meant that they even slowed down when the adverse condition was to be expected to appear even it did not occur.A team of scientists from Hokkaido University and the ATR Wave Engineering Laborataries cultured the single-celled slime mold Physarum polycephalum (a member of the amoeba clan) in a bed of oat flakes on an agar media. Every ten minutes the air was made slightly cooler and drier, which had the effect of slowing the movement of the amoebas.Then more favorable air would be restored and the motion continued as before. After several cycles, the amoebas slowed down their motion even when the hostile conditions were not applied. Later still, when the organisms have been tricked into anticipating impending climate change several times, they stop from slowing without an actual change in conditions. One of the researchers, Toshiyuki Nakagaki from Hokkaido , cautions that amoebas do not have a brain and that this is not an example of classic “Pavlovian” conditioned response behavior. Nevertheless, it might represent more evidence for a primitive sensitivity or “intelligence” based on the dynamic behavior of the tubular structures deployed by the amoeba.

Infinity can be big or bigger, countable or not

Infinity is bigger than any number. But saying just how much bigger is not so simple. In fact, infinity comes in infinitely many different sizes—a fact discovered by Georg Cantor in the late 1800s.

Now a mathematician has come up with a new, different proof. Based on a simple game, the proof uses a strategy that might someday shed light on one of the great unsolved questions in mathematics.

The smallest infinity is the one you'd get to if you could count forever. The numbers 1, 2, 3, 4… are called the natural numbers, and they are the most obvious example of this size of infinity. In honor of them, anything that has this size of infinity is called "countable."

Lots of infinite things are countable. For example, suppose you take just the even numbers. They're countable, just like all the natural numbers are. You can prove it by counting them:

This leads to the peculiar result that, in some sense, there are the same number of even numbers as there are of all the natural numbers—even though there are only half as many. Infinity is an odd beast.

Cantor also came up with a clever way to count all the fractions, proving that they're also countable. So there are (in a sense) just as many fractions as whole numbers, too! (To see why, go to http://www.homeschoolmath.net/.)

Not everything infinite is countable, though. Take, for example, all the real numbers—all the counting numbers plus all the fractions plus all the irrational numbers. A real number is any number that can be expressed in decimals, though the expression might continue forever. For example, pi is a real number: It can be written as 3.14159….

What Cantor showed was that no matter what clever counting scheme you come up with, you'll never manage to count every last real number. He did it with a challenge: Just try it. Come up with a counting scheme, any counting scheme, and he'll find a real number you missed.

He reasoned this way. He would write down all your numbers in a list, including only the portion after the decimal point. If the number was rational, he would write it with an infinite number of zeros at the end, or the numbers would start repeating in an infinite loop. The list would look something like this, though it probably wouldn't be these particular numbers:

.48859283404162…
.23190734486346…
.23987932750000…
.34576128733518…
.23758093475639…
etc.

Now Cantor would cook up a new number that wouldn't be anywhere in your list. To find the first digit, he would look at the first digit of the first number, which in this case is a 4. Cantor would make the first digit of his new number something different, say 5.

Now he would look at the second digit of the second number, in this case, 3. He'd make the second digit of his new number something different, say 4. And he'd make the third digit of his new number different from the third digit of the third number in the list (which is 9, so he could make his 0).

By keeping this up forever, he'd get a new real number that was different from every other number in your list. After all, it can't be the same as the first number, because it has a different first digit. And it can't be the same as the second number, because it has a different second digit. For the same reason, it can't be the same as any of the numbers in the list. So he's got you! You didn't count every last real number after all.

Cantor's discovery raised a question that hasn't been fully answered even today: Is there a "medium" size of infinity—bigger than the natural numbers but smaller than the real numbers? The supposition that nothing is in between the two in size is called the "continuum hypothesis," after the continuum of numbers. The question is so puzzling that it led to a genuine crisis in mathematics, and mathematicians still aren't sure of the answer.

When mathematicians get stuck on a problem like this, they usually need a new approach. Using a method entirely different from Cantor's, Matthew H. Baker of the Georgia Institute of Technology in Atlanta recently came up with a new proof that the real numbers aren't countable. Baker started by considering a little mathematical game. Let's say that Alice and Bob decide on some subset of the real numbers between 0 and 1. Alice starts by picking any number she likes between 0 and 1, and Bob follows by choosing a number that is bigger than Alice's but still less than 1. Then they take turns picking new numbers that are always between the last two numbers chosen.

If we call Alice's numbers A₁, A₂, A₃, etc., and Bob's B₁, B₂, B₃, etc., we can draw a picture that would look something like this:

Notice that Alice and Bob's picks get closer and closer to each other over time. An important theorem in calculus says that if they were to keep picking numbers this way forever, Alice's numbers would get closer and closer to just one single number, which will be bigger than all the A_n's and smaller than all the B_n's.

So that brings us to the point of the game. Remember at the beginning that Alice and Bob agreed on some subset of the interval. If the number Alice converges toward is in that interval, Alice wins, and if it's outside, then Bob wins.

Baker found a strategy that Bob can use to win anytime the subset is countable. Bob can make a list of all the numbers in the subset: S₁, S₂, S₃, etc. Bob has to make sure that Alice's numbers can't converge toward any number on that list.

For his first pick, he looks at S₁. If S₁ is smaller than A₁, he doesn't have to worry about Alice's numbers converging toward it, because he knows Alice's numbers have to converge toward something bigger than any of them. So he just picks any number he feels like that is allowed.

If S₁ is bigger than A₁, he can just pick S₁! After all, he also knows Alice's numbers can only converge toward something smaller than all of his numbers. By making each of his choices this way, he can make sure that Alice's numbers can't converge toward any point in the subset.

But then Baker noticed something else. If the subset that Alice and Bob agreed on at the beginning was the entire interval from 0 to 1, Bob obviously couldn't win. But if the subset were countable, Bob could win. So that implies that the whole interval can't be countable.

Baker says his proof doesn't show anything Cantor didn't, but that it's a nice example of how two areas of mathematics that don't seem to have much to do with one another—in this case, game theory and set theory—are in fact tightly linked. Hard problems in mathematics are often solved by bringing together fields of math that seem only distantly related.

Indeed, set theorists are pursuing game theory approaches. "People take some of these games seriously because they can give non-trivial insights into the nature of real numbers," Baker says. "They may be able to shed light on things like the continuum hypothesis."

Fingerprinting diamonds via phosphorescence

The eerie phosphorescence displayed by a rare form of blue diamond can be used as an easy, cheap, and nondestructive way to identify individual gemstones and to distinguish natural blue diamonds from synthetic ones, analyses suggest.

Phosphorescence, a "glow-in-the-dark" process in which energy previously absorbed by a substance is released slowly in the form of light, is common in a certain type of blue diamond. After exposure to light, these type IIb diamonds, which have boron- and nitrogen-containing impurities, softly glow in colors ranging from blue through pink to fiery red, says Sally Eaton-Magaña, a chemical engineer at the Gemological Institute of America in Carlsbad, Calif. The orange-red glow from the 45.52-carat Hope Diamond, a type IIb gemstone on display at the Smithsonian Institution in Washington, D.C., is visible for as long as a minute after the lights go out.

Although millions of visitors to the Smithsonian's National Museum of Natural History see the Hope Diamond each year, the gem has received remarkably little scientific attention. While a set of 239 colored diamonds known as the Aurora Heart Collection was on loan to the museum in 2005, Eaton-Magaña and her colleagues studied the set's type IIb diamonds as well as the Hope Diamond and the museum's 30.62-carat Blue Heart Diamond. They also studied the blue diamonds in the Aurora Butterfly Collection in New York City. In all, the researchers studied 67 natural blue diamonds, 3 synthetic ones, and a gray diamond that other researchers had turned blue via treatments at high temperature and high pressure. In some of their tests, the scientists shone a high-intensity ultraviolet light on each gemstone for 20 seconds and then measured its phosphorescence at various wavelengths.

Reddish phosphorescence in diamonds was thought to be rare, says Eaton-Magaña. However, the tests showed that all natural type IIb diamonds glow for several seconds at two visible wavelengths—a 500-nanometer, greenish-blue light and a 660-nm reddish one. The relative strengths of the phosphorescence at the two wavelengths dictate the hue of a stone's overall glow. Differences in the peak intensities of those emissions and the rates at which they wane provide a virtual fingerprint for each stone, the researchers report in the January Geology.

Neither the synthetic stones nor the color-enhanced gray gemstone glowed at the 660-nm wavelength. The new technique's ability to distinguish between artificial diamonds and the true blue gems "solves one of the big problems in diamond markets," says Stephen E. Haggerty, a geologist at Florida International University in Miami.

Tests on the Hope Diamond suggest that variations in phosphorescence from one part of a large gem to another are negligible, says Eaton-Magaña. Scientists would therefore still be able to identify the pieces of a large diamond if it were stolen and cut into smaller stones.

Researchers Create Mathematical Model of Fruit Fly Eyes

Many researchers have tried to create a mathematical model of how cells pack together to form tissue, but most models have many different complicated factors and no model is universal.

Researchers at Northwestern University have now created a functional equation – using only two parameters – to show how cells pack together to create the eyes of Drosophila, better known as the fruit fly. They hope that the pared-down equation can be applied to different kinds of tissues, leading to advances in regenerative medicine.

Sascha Hilgenfeldt, associate professor of engineering sciences and applied mathematics and mechanical engineering, teamed up with Richard W. Carthew, professor of biochemistry, molecular biology, and cell biology in the Weinberg College of Arts and Science, and Sinem Erisken, a McCormick undergraduate studying biomedical engineering, to create the model. Their work was published online Jan. 11 by the Proceedings of the National Academy of Sciences (PNAS).

The interdisciplinary effort among geneticists, engineers and mathematicians began 18 months ago, when Hilgenfeldt, who specializes in foam, soft matter and fluid mechanics, teamed with Carthew, who has studied the biological features of fruit fly eyes.

Hilgenfeldt knew that when it comes to creating a model that shows what determines the shape of functional cells in tissues, the myriad factors – including the bulk of the cell, what’s going on inside of the cell, and how the cell forms – make it very difficult to quantify.

“That’s a nightmare for quantitative scientists,” he said. “It’s extremely complicated.”

But the cells in a fruit fly’s eye act more like foam in that the structure of the cells depends only on the energy of their interfaces, or the surface where the cells touch. That energy is divided into two parts – the energy from the stretching of the cells’ membranes and the energy of the “glue” (the adhesion molecules) that holds the neighboring cell membranes together. Hilgenfeldt took those two factors and created a quantitative model of cell geometries in the fruit fly retina. So instead of needing to know all the different cell factors to create the model, he just needed the two energy components to create the model.

“It’s one of the most quantitative models I’ve seen for a biological system,” Hilgenfeldt said. “For this system, mainly all you need to know is the interfacial energies and everything falls into place.”

Such a model helps researchers understand how the presence of the glue energy changes the shape of the eye and will help them study how those adhesion molecules develop and function during embryo development.

Further down the road, having these kinds of models could help scientists learn how to grow regenerative tissues. Hilgenfeldt also hopes to see how far he can take this model – testing whether it will work in tissues that have much more variation in their cell patterns.

“It is very promising for quantitative science to be able to do something about these complex biological systems,” he said.

Though the undergraduate student who worked on the research has graduated, Hilgenfeldt said another undergraduate student will help continue the research through the Research Training Group (RTG) program in applied mathematics. The program emphasizes interdisciplinary research with teams composed of applied mathematicians, scientists and engineers. It is funded by a $2.1 million National Science Foundation grant.

Ice Clouds put Mars in the Shade

Until now, Mars has generally been regarded as a desert world, where a visiting astronaut would be surprised to see clouds scudding across the orange sky. However, new results show that the arid planet possesses high-level clouds that are sufficiently dense to cast a shadow on the surface.

The results were obtained by the OMEGA Visible and Infrared Mineralogical Mapping Spectrometer instrument on board ESA’s Mars Express.

Mars is not entirely a haven for Sun worshippers. Clouds of water ice particles do occur, for example on the flanks of the giant Martian volcanoes. There have also been hints of much higher, wispy clouds made up of carbon dioxide (CO₂) ice crystals. This is not too surprising, since the thin Martian atmosphere is mostly made of carbon dioxide, and temperatures on the fourth planet from the Sun often plunge well below the ‘freezing point’ of carbon dioxide.

Now, a team of French scientists has shown that such clouds of dry ice do, indeed, exist. Furthermore, they are sometimes so large and dense that they throw quite dark shadows on the dusty surface.

“This is the first time that carbon dioxide ice clouds on Mars have been imaged and identified from above,” said Franck Montmessin of the Service d’Aeronomie, University of Versailles (UVSQ), lead author of the paper in the Journal of Geophysical Research. “This is important because the images tell us not only about their shape, but also their size and density.

“Previously, we had to rely on indirect information – for example, from the SPICAM instrument on board Mars Express - to find out what the clouds are made of. However, it is very difficult to separate the signals coming from the clouds, the atmosphere and the surface.”

Data from the SPICAM Ultraviolet and Infrared Atmospheric Spectrometer indicated that any high altitude clouds are not very thick and made up of much smaller particles, but the CO₂ clouds detected by OMEGA are very different. Not only are they surprisingly high – more than 80 km above the surface – but they can be several hundred kilometres across. They are also much thicker than expected. Instead of looking like the wispy ice clouds seen on Earth, they resemble tall convectional clouds that grow as the result of rising columns of warm air.

Even more surprising is the fact that the CO₂ ice clouds are made of quite large particles - more than a micron (one thousandth of a millimetre) across – and they are sufficiently dense to noticeably dim the Sun. Normally, particles of this size would not be expected to form in the upper atmosphere or to stay aloft for very long before falling back towards the surface.

“The clouds imaged by OMEGA can reduce the Sun’s apparent brightness by up to 40 per cent,” said Montmessin. “This means that they cast quite a dense shadow and this has a noticeable effect on the local ground temperature. Temperatures in the shadow can be up to 10°C cooler than their surroundings, and this in turn modifies the local weather, particularly the winds.”

Since the CO₂ clouds are mostly seen in equatorial regions, the OMEGA team believes that the unexpected shape of the clouds and large size of their ice crystals can be explained by the extreme variations in daily temperature that occur near the equator.

“The cold temperatures at night and relatively high day-time temperatures cause large diurnal waves in the atmosphere,” explained Montmessin. “This means there is a potential for large-scale convection, particularly as the morning Sun warms the ground.”

Bubbles of warm gas rise above the surface and when they reach high levels they become cold enough for CO₂ to condense. This process releases latent heat, which causes the gas and the ice particles to rise even further.

What are the particles around which the CO₂ ice condenses? On Earth, cloud droplets form around tiny nuclei – often particles of dust or salt. On Mars, the answer remains uncertain. One possibility is that Martian dust is carried to high altitudes. Another potential source of condensation nuclei is particles left behind by micrometeorites entering the upper atmosphere. Or the nuclei may simply be tiny crystals of water ice carried aloft on the thermal updraughts.

“This discovery is important when we come to consider the past climate of Mars,” said Montmessin. “The planet seems to have been much warmer billions of years ago, and one theory suggests that Mars was then blanketed with CO₂ clouds. We can use our studies of present-day conditions to understand the role that such high level clouds could have played in the global warming of Mars.”

Portable Device Detects Early Alzheimer

The latest medications can delay the onset of Alzheimer’s disease, but none are able to reverse its devastating effects. This limitation often makes early detection the key to Alzheimer patients maintaining a good quality of life for as long as possible.
Now, a new device developed by the Georgia Institute of Technology and Emory University may allow patients to take a brief, inexpensive test that could be administered as part of a routine yearly checkup at a doctor’s office to detect mild cognitive impairment (MCI) — often the earliest stage of Alzheimer’s. The device is expected to be commercialized later this year.

Current assessment tests capable of detecting early Alzheimer’s typically are taken with a pen and paper or at a computer terminal and last about an hour and a half. They must be given by a trained technician in a quiet environment, because any distractions can influence the patient’s score and reduce the test’s effectiveness. Because of their length and expense, the tests are not used as regular screening tools and typically are given only after there is obvious cognitive impairment such as forgetfulness or unsafe behavior.

“Families usually wait until their mom or dad does something somewhat dangerous, like forgetting to take their medications or getting lost, before bringing them in for testing. At that point, the patient has already lost a significant portion of their cognitive function,” said David Wright, MD, who helped develop the device. Wright is assistant professor of emergency medicine at Emory University School of Medicine and co-director of the Emory Emergency Medicine Research Center. “With this device, we might be able to pick up impairment well before those serious symptoms occur and start patients on medications that could delay those symptoms.”

The Georgia Tech and Emory device, called DETECT, gives individuals a roughly ten-minute test designed to gauge reaction time and memory — functions that, when impaired, are associated with the earliest stages of Alzheimer’s disease. The test is a specially modified, shortened version of the traditional pen and paper test and could be given repeatedly by doctors to evaluate any changes in cognitive functions.

“We really envision this to be part of the normal preventative care a patient receives from a general practitioner,” said Michelle LaPlaca, Ph.D., one of the creators of the device and an associate professor in the Wallace H. Coulter Department of Biomedical Engineering at Georgia Tech and Emory University. “It would be part of a regular preventative medicine exam much like a PSA test or EKG (electrocardiogram), serving as a cognitive impairment vital sign of sorts.”

The portable test runs patients through a battery of visual and auditory stimuli such as pictures and words that assess cognitive abilities relative to age, gauging reaction time and memory capabilities. Its software can track cognitive capabilities — and decline — year to year during annual appointments. And because the device blocks outside sound and light from the patient’s environment, it can be administered in virtually any setting, providing more consistent results.

Preliminary analysis of the first 100 patients of a 400-person clinical study being conducted at Emory’s Wesley Woods Center has shown that the 10-minute DETECT test has similar accuracy to the 90-minute “Gold Standard” pen and paper test.

With millions of baby boomers easing into late adulthood, the number of patients with Alzheimer’s is expected to skyrocket over the next few decades. More than 24 million people worldwide are currently thought to have Alzheimer’s disease and by 2040, an estimated 81 million people worldwide are expected to develop the disease.

To give these millions of potential Alzheimer’s sufferers a chance to slow the disease’s advance before serious symptoms set in, doctors need an inexpensive and easy-to- administer test to detect and track the cognitive decline associated with the early stages of the disease.

The DETECT device is designed to be administered while a patient is still healthy, tracking any abnormal decreases in the patient’s cognitive performance over time. If a patient’s performance declines outside the normal range, the patient would then undergo additional testing and care from a neurologist, neuropsychologist or other specialist.

The DETECT system includes an LCD display in a visor with an onboard dedicated computer, noise reduction headphones and an input device (controller). The display projects the visual aspect of the test, the headphones provide the verbal instructions and the controller records the wearer’s response.

DETECT’s creators have formed a company, called Zenda Technologies, to commercialize the device for MCI, as well as other conditions. Georgia Tech and Emory researchers are exploring other types of cognitive impairment such as Attention Deficit/Hyperactivity Disorder (ADHD) that could be picked up by DETECT. A version of the system designed to detect mild concussions on the sidelines of a football game, during other high-impact sports or on a battlefield is still being tested.