Applying a mathematical model to the social dynamics of people presents difficulties not involved with more physical – and perhaps more rational – applications. The many factors that influence an individual's fate to meet an acquaintance and decide to become a friend are impossible to capture, but physicists have used techniques from physical systems to model social networks with near precision.

By modeling people's interactions based on how particles bounce off each other in an enclosed area, physicists Marta Gonzalez, Pedro Lind and Hans Herrmann found that the characteristics of social networks emerge "in a very natural way." In a study recently published in Physical Review Letters, the scientists compared their model to empirical data taken from a survey of more than 90,000 U.S. students regarding friendships, and found similarities indicating that this model may serve as a novel approach for understanding social networks.

"The idea behind our model, though simple, is different from the usual paradigmatic approaches," Gonzalez told PhysOrg.com. "We consider a system of mobile agents (students), which at the beginning have no acquaintances; by moving in a continuous space they collide with each other, forming their friendships."

After a collision, a particle moves in a different direction with an updated velocity, just as how an individual's chance of meeting a new person depends on their most recent acquaintances.

At a critical point, the system reaches a quasi-stationary state, for the first time allowing the scientists to reproduce several features of social networks in a single model and in a natural way. Specifically, this technique accurately describes social clustering, the way friendships evolve over time, the shortest path length in a large group, and some features related to group structure.

"With this new framework, we show that specific velocity and collision rules are able to reproduce the statistical and structural features of empirical social networks," said Gonzalez. "Therefore, this model seems to have the novelty of bringing together all the previous developments for collision theory with the empirical results of socio-dynamics."

The scientists were also able to apply this model to describe specific types of contacts to produce a distribution that again closely resembles real-life acquaintances. For example, to separate sexual contacts from all social contacts, the scientists assigned to the sexual contacts an intrinsic property that could then be used to model these distinct networks. In this case, the model reproduced the real sexual contact network found in a tracing study of HIV tests.

Although this particle motion does not literally model human motion, it represents connections among people – and it's these links that contain the most significance for social networking theories. For example, links can represent the flow of information traveling through a community. By knowing the shortest path, communicators can optimize the information flow and improve productivity in a business. With the ability to determine hot hubs or holes in a community, business managers can identify leaders or points that require an organizational change.

As Gonzalez sees it, statistical physics and human behavioral studies have a history of inspiring each other, which makes physicists' desire to understand social networks a natural interest.

"As Philip Ball [Nature Editor] remarks," said Gonzalez, "'by seeking to uncover the rules of collective human activities, today's statistical physicists are aiming to return to their roots: Social statistics also guided Maxwell and Boltzmann towards the utilization of probability distributions in the development of the kinetic theory of gases – the foundation of statistical mechanics' (Physica A 314 (2002) 1-4)."

Citation: Gonzalez, Marta C., Lind, Pedro G. and Herrmann, Hans J. System of Mobile Agents to Model Social Networks. Physical Review Letters. 96, 088701 (2006).

Copyright 2006 PhysOrg.com

Rarely has medieval Christian history had such a field day in court, but then Mr Justice Smith, who is hearing the Chancery Division case alleging infringement of copyright, is equal to the task.

Having done his homework, he knows that the Second Crusade lasted from 1147 to 1149.

In his third day in the witness box Michael Baigent, co-author of The Holy Blood and The Holy Grail, was being cross-examined on his claim that Mr Brown had lifted his book wholesale. John Baldwin, QC, for the defendant, Random House, which published The Da Vinci Code, suggested that Mr Brown had got his information from an entirely different book, a history of the Knights Templar.

The judge turned to Mr Baigent: "Well, he certainly didn't get it from you, because you wouldn't have made the date error that he has." Mr Baigent has been having a tough time at the hands of his inquisitor, and has been forced to concede that numerous details of his case are wrong. But there are moments when he fights back gamely, and is even conciliatory towards Mr Brown, who sits silently absorbing every word and awaiting his turn in the witness box next week.

"I don't hold it against Mr Brown, as he is not writing a work of history," Mr Baigent said of the thriller writer's getting the wrong Crusade. "But I don't feel it's up to me to correct his creative use of history."

Mr Baigent was beaten into retreat on his assertion - a vital plank of his case - that all the historical conjectures in The Da Vinci Code were lifted from The Holy Blood and The Holy Grail. "I concede that 'all' is far too strong, and that we should have said 'most'; I confess we over-egged that one," he said after Mr Baldwin had pointed out that Jesus having children, Lazarus being his brother-in-law and Mary Magdalene and Mary Bethany being the same person, all postulated in The Holy Blood and The Holy Grail, did not figure in The Da Vinci Code.

"Does it not trouble you that you claim Mr Brown reached all the same historical conjectures when he plainly didn't?" Mr Baldwin asked. Mr Baigent refused to take that entirely lying down. "Mr Brown is writing a novel; he doesn't need to go through all the arguments. We agree that Mr Brown uses the marriage of Jesus in DVC; that is a development of our researches."

Another major theme of The Holy Blood and The Holy Grail is that the Holy Grail is not a chalice but the bloodline of Christ and his descendants. "None of the situations you develop in HBHG in connection with the Grail romances is in DVC, is it?" Mr Baldwin challenged.

"But our conclusion [about Jesus's bloodlines being continued through the early Merovingian kings of France] forms an integral part of DVC. The novel is using the fruits of our conjecture," Mr Baigent said.

The judge, who adjourned the hearing for six days so that he could absorb both books, is sitting without a jury. He told the claimants yesterday that the part of their case that relied on similarities of language between the books was "extremely peripheral", and that "casting a Nelsonian eye" over selected passages was unlikely to get them very far.

Sales of The Holy Blood and The Holy Grail, first published in 1982, have increased sevenfold since the hearing began last week - 3,000 copies - and a few days ago British sales of The Da Vinci Code passed 4 million to add to worldwide sales of 40 million.

The hearing continues.

If you don't believe you'll have a good memory when you get older, then you might as well forget about this article.

But if you can just believe, then it might come true.

So says Margie Lachman, professor of psychology at Brandeis University. Lachman and her colleagues asked 335 adults, ages 21 to 83, to recall a list of 30 words that could be categorized as types of fruit, flowers and so on. Among the middle-aged and older people, those who had more confidence in their ability to control their cognitive functioning did better on the test.

Belief in your ability to retain a good memory helps make it happen, Lachman concludes.

"Our study shows that the more you believe there are things you can do to remember information, the more likely you will be to use effort and adaptive strategies and to allocate resources effectively, and the less you will worry about forgetting," she said.

Memory problems in youth get blamed on distraction or some other factor. But older people tend to blame their mental lapses on age. Many see memory decline as an "inevitable, irreversible, and uncontrollable part of the aging process," Lachman said today. "These beliefs are detrimental because they are associated with distress, anxiety, and giving up without expending the effort or strategies needed to support memory."

Lachman and her colleagues, writing in the Journals of Gerontology: Psychological Sciences, say preventing memory decline should involve interventions that target conceptions of control over memory.

And if nothing else, remember these tips: Mental exercises can cut your risk for dementia almost in half, another study showed, and just two weeks of memory training and improved diet and exercise can boost your recall abilities.

Whether Arizonans saw flares and airplanes, a top-secret government project or something otherworldly, Kitei said interest about that night has not faded after nearly a decade.

In fact, the curious can relive it all at an exclusive showing on Sunday of an updated documentary.

Kitei, a physician and health educator from Paradise Valley, wrote a book about the subject in 2004, chronicling what she and others saw.

She also co-produced an award-winning documentary with cinematographer Steve Lantz that debuted last March in Scottsdale. She will host Sunday's showing at the same theater, Harkins Shea 14, 7354 E. Shea Blvd.

The revamped documentary includes new footage Kitei shot last summer of large amber-colored orbs in the night sky, plus additional witness interviews, including several with children.

"It's just been amazing how this has really opened up people. I didn't believe when the book came out how much positive response I got," she said.

"People have really thanked me for coming forward and know they can share. That's the most gratifying thing for me."

It has become her life's mission to get the word out about the lights. Kitei has traveled extensively, talking about the Phoenix Lights. She will be a keynote speaker at a conference in Riccione, Italy, on March 25.

"It has been such a joy. People have really embraced this. I guess they're ready for it, the idea that we are not alone," she said.

"It's time we move forward and acknowledge it, and accept it and study it."

Kitei said people should keep an open mind about the subject.

"This is available for anybody who chooses to read it or see it. The data speaks for itself," she said.

"I did get a feeling there was something strange about the thing," she said.

Entranced, Michelle signalled to her colleague Peter Gardiner, 53, to take a look.

He said: "At first I thought it was a big piece of rubbish or a clear tarpaulin sheet.

"But then it glistened and it was shiny. It had a strange pattern of movement. It was a significant size, possibly the size of a roof or even a house."

The pair watched it for a couple of minutes, rotating in the distance and heading towards Wandsworth Town. Then, as soon as it had appeared it vanished.

Michelle said if it was a piece of rubbish it would have caused severe damage when it came down, because of its size and density.

"I can't explain it and therefore I'm calling it a UFO. It took my breath away. It did feel weird.

"The more I looked at it I realised there was something not quite right. It wasn't moving like anything I've ever seen before," she said.

A spokesman for the Ministry of Defence (MoD) said it had not been notified of any sighting of the pyramid.

"The MoD does not have any expertise or role in respect of UFO/flying saucer' matters or to the question of the existence or otherwise of extraterrestrial lifeforms, about which it remains totally open-minded."

He said it examined the reports of UFO sightings it received solely to establish whether what was seen might have some defence significance, namely whether there was any evidence the UK's airspace might have been compromised by hostile or unauthorised air activity.

Michelle and Peter said there has been a lot of activity in the skies over Putney recently.

Michelle said they had seen several Chinook helicopters over the past week and believes something must be happening.

Chinooks are used to transport troops, artillery, supplies and equipment, but also used for operations such as medical evacuation, disaster relief and search and rescue.

When travelling to Putney, our reporter saw what looked to be three Apache helicopters travelling east.

A spokesman for the MoD said the helicopters were probably part of general aviation traffic over London and there was no specific activity or event they were involved in. He added such movements were "not unusual".

Did you see the flying silver pyramid? Call the newsdesk on 020 8254 5409.

ctaylor@london.newsquest.co.uk

The study, conducted by Terry Hunt of the University of Hawaii, Manoa and Carl Lipo of California State University, Long Beach, is detailed today in the online version of the journal Science.

The conventional story

According to one widely held view, a small band of Polynesian settlers, perhaps no more than a few dozen people, arrived on the Easter Island sometime between 400 and 1000 AD.

The settlers lived in harmony with the environment for hundreds of years and the population slowly grew. Some scientists estimate that at its height, Easter Island's population may have been as much as 20,000 people.

Around 1200 AD, the story goes, the inhabitants began cutting down the island's subtropical trees and giant palms in large numbers to build canoes and to transport the giant stone statues, which started going up around this time.

The large-scale deforestation led to soil erosion and over a span of several centuries, the island's ability to support wildlife and farming was compromised. People began to starve. In a last ditch effort at survival, they became cannibals.

The collapse of both the island's ecology and civilization was so complete that by the time the Dutch arrived in the 1700s, Easter Island was a sandy grassland void of nearly all its native wildlife; its human inhabitants were reduced to a starving population of 3,000 or less.

This is the story pieced together by researchers over the past several decades, but Hunt and Lipo think it is wrong.

No Garden of Eden

Crucial to the conventional account of events on Easter Island is the time when settlers first arrived. If colonization didn't begin until 1200 AD, then the island's population wouldn't have had time to swell to tens of thousands of people.

"You don't have this Garden of Eden period for 400 to 800 years," Hunt said in an accompanying Science article. "Instead, [humans] have an immediate impact."

Also, the few thousand people Europeans encountered when they first arrived on Easter Island might not have been the remnants of a once great and populous civilization as widely believed. The researchers think a few thousand people might have been all the island was ever able to support.

"There may not have actually been any collapse," Lipo told LiveScience. "With only 500 years, there's no reason to believe there had to have been a huge [population] growth."

Europeans and rats to blame

The researchers also dispute the claim that Easter Island's human inhabitants were responsible for their own demise. Instead, they think the culprits may have been Europeans, who brought disease and took islanders away as slaves, and rats, which quickly multiplied after arriving with the first Polynesian settlers.

"The collapse was really a function of European disease being introduced," Lipo said. "The story that's been told about these populations going crazy and creating their own demise may just be simply an artifact of [Christian] missionaries telling stories."

At a scientific meeting last year, Hunt presented evidence that the island's rat population spiked to 20 million from the years 1200 to 1300. Rats had no predators on the island other than humans and they would have made quick work of the island's palm seeds. After the trees were gone, the island's rat population dropped off to a mere one million.

Lipo thinks the story of Easter Island's civilization being responsible for its own demise might better reflect the psychological baggage of our own society than the archeological evidence.

"It fits our 20th century view of us as ecological monsters," Lipo said. "There's no doubt that we do terrible things ecologically, but we're passing that on to the past, which may not have actually been the case. To stick our plight onto them is unfair."

Whatever it is, the anomaly of interest rests at 15,300 feet (4,663 meters) on the northwest corner of Mt. Ararat, and is nearly submerged in glacial ice. It would be easy to call it merely a strange rock formation.

But at least one man wonders if it could be the remains of Noah's Ark-a vessel said to have been built to save people and selected animals from the Great Flood, the 40 days and 40 nights of deluge as detailed in the Book of Genesis.

The Genesis blueprint of the Ark detailed the structure as 6:1 length to width ratio (300 cubits by 50 cubits). The anomaly, as viewed by satellite, is close to that 6:1 proportion.

Newfound optimism

Identifying the Ararat anomaly has been a 13-year-long quest of Porcher Taylor, an associate professor in paralegal studies at the University of Richmond's School of Continuing Studies in Virginia.

Taylor has been a national security analyst for more than 30 years, also serving as a senior associate for five years at the Center for Strategic and International Studies (CSIS) in Washington, D.C.

"I've got new found optimism ... as far as my continuing push to have the intelligence community declassify some of the more definitive-type imagery," Taylor told SPACE.com/LiveScience. He points to a "new and significant development," a high-resolution image taken by DigitalGlobe's impressive QuickBird satellite and shown here publicly for the first time [alternate version with no annotation].

"I'm calling this my satellite archeology project," Taylor said. It's an effort that has now included use of QuickBird, GeoEye's Ikonos spacecraft, Canada's Radarsat 1, as well as declassified aerial and satellite images taken by the various U.S. intelligence agencies.

Making the mountain transparent

Taylor said his goal is straightforward: Combining this imagery to make the Ararat anomaly transparent to the public, as well as to the discerning, dispassionate eyes of scientists, imagery analysts, and other experts.

"I had no preconceived notions or agendas when I began this in 1993 as to what I was looking for," Taylor said.

As for the saga of Noah's Ark, he is quick to note that there are those who say it is fable while some take it as truth.

Nevertheless, the anomaly may not be a ridge line of ice, snow and possibly rock, but an artificial ridge line, Taylor said. "I maintain that if it is the remains of something manmade and potentially nautical, then it's potentially something of biblical proportions."

While chiding the intelligence communities to release more of their closely guarded satellite imagery, Taylor said that soon-to-fly commercial remote sensing spacecraft are sure to help his archeological undertaking.

"We've got three new birds that are going up. I'm using all my clout, rapport and lobbying to, hopefully, have them at least fly calibration runs over Mt. Ararat," Taylor said. Those images would make the mountain even more transparent, he said.

Will it float?

Meanwhile, Taylor has an ever-expanding network of experts to help tease out the truth about the anomaly.

For example, satellite imagery analyst Rod Franz of SunTek Media Group/RiteImage, Inc., located in Henderson, Nevada, has taken a look at imagery provided by Taylor of the Ararat anomaly and carried out additional analysis of the area. As director of training for the firm, Franz sharpened his skills by serving nearly 25 years as a military intelligence imagery analyst.

For the anomaly assessment, the same software tools used for studying government and commercial remote sensing data were employed, Franz told SPACE.com/LiveScience. Ground distances and scales of the anomaly were determined. That software also has the ability to adjust brightness, haze, sharpness, contrast and other factors of the area of interest, he said.

"Along with many other image manipulation functions ... I also used the pseudo-color function trying to determine if I could detect anything under the ice and snow," Franz said.

The face of the anomaly measured 1,015 feet (309 meters) across, Franz said. "I also found the shape of the anomaly appears to fit on a circle. I am not sure what this means, if anything, but I find it curious."

Given that length, Taylor pointed out, the anomaly dwarfs the Titanic and Bismarck in size, and equals the size of the largest modern aircraft carrier. That analysis would seem to call into question whether the anomaly is a wooden ship and raises a key question: If a boat were truly that huge, would it float?

There are also experts in remote sensing who offer a skeptical view.

"Image interpretation is an art," said Farouk El-Baz, Director of the Boston University Center for Remote Sensing.

"One has to be familiar with Sun lighting effects on the shape of observed features," El-Baz said. "Very slight changes in slope modify shadow shapes that affect the interpretations. Up to this time, all the images I have seen can be interpreted as natural landforms. The feature that has been interpreted as the 'Ararat Anomaly' is to me a ledge of rock in partial shadow, with varied thickness of snow and ice cover.

Visual truth serum

Thanks to more satellite imagery in the offing, as well as other studies underway, Taylor said his remote archeological research is on the upswing.

There is an ultimate end-game. That is, on-the-spot ground truth ... and Taylor hopes his research findings will catalyze a top-notch expedition to the area. "It is whatever it is," he said.

But for now, satellite remote sensing to carry out archeological "digs" from space will fill in for an in-the-field expedition.

Just a few weeks ago, for example, NASA scientists utilizing space- and aircraft-based remote sensing hardware and techniques uncovered Maya ruins hidden in the rainforests of Central America for more than 1,000 years.

"For explorers, imagery from GeoEye's Ikonos satellite married with Global Positioning System (GPS) satellite data has become as indispensable as water and freeze dried food for any expedition. One does not want to leave home without it," said Mark Brender, GeoEye Vice President for communications and marketing, headquartered in Dulles, Virginia.

For researchers, imagery from space like those provided by GeoEye provides "the ultimate high shot" and a contextual view you could never get from observations on the ground or even from a plane, Brender told SPACE.com/LiveScience. "It's visual truth serum."

This radical suggestion would get round some fundamental problems posed by the existence of black holes. One such problem arises from the idea that once matter crosses a black hole's event horizon – the point beyond which not even light can escape – it will be destroyed by the spacetime "singularity" at the centre of the black hole. Because information about the matter is lost forever, this conflicts with the laws of quantum mechanics, which state that information can never disappear from the universe.

Another problem is that light from an object falling into a black hole is stretched so dramatically by the immense gravity there that observers outside will see time freeze: the object will appear to sit at the event horizon for ever. This freezing of time also violates quantum mechanics. "People have been vaguely uncomfortable about these problems for a while, but they figured they'd get solved someday," says Chapline. "But that hasn't happened and I'm sure when historians look back, they'll wonder why people didn't question these contradictions."

While looking for ways to avoid these physical paradoxes, Chapline and Laughlin found some answers in an unrelated phenomenon: the bizarre behaviour of superconducting crystals as they go through something called "quantum critical phase transition" (New Scientist, 28 January, p 40). During this transition, the spin of the electrons in the crystals is predicted to fluctuate wildly, but this prediction is not borne out by observation. Instead, the fluctuations appear to slow down, and even become still, as if time itself has slowed down.

"That was when we had our epiphany," Chapline says. He and Laughlin realised that if a quantum critical phase transition happened on the surface of a star, it would slow down time and the surface would behave just like a black hole's event horizon. Quantum mechanics would not be violated because in this scenario time would never freeze entirely. "We start with effects actually seen in the lab, which I think gives it more credibility than black holes," says Chapline.

With this idea in mind, they – along with Emil Mottola at the Los Alamos National Laboratory in New Mexico, Pawel Mazur of the University of South Carolina in Columbia and colleagues – analysed the collapse of massive stars in a way that did not allow any violation of quantum mechanics. Sure enough, in place of black holes their analysis predicts a phase transition that creates a thin quantum critical shell. The size of this shell is determined by the star's mass and, crucially, does not contain a space-time singularity. Instead, the shell contains a vacuum, just like the energy-containing vacuum of free space. As the star's mass collapses through the shell, it is converted to energy that contributes to the energy of the vacuum.

The team's calculations show that the vacuum energy inside the shell has a powerful anti-gravity effect, just like the dark energy that appears to be causing the expansion of the universe to accelerate. Chapline has dubbed the objects produced this way "dark energy stars".

Though this anti-gravity effect might be expected to blow the star's shell apart, calculations by Francisco Lobo of the University of Lisbon in Portugal have shown that stable dark energy stars can exist for a number of different models of vacuum energy. What's more, these stable stars would have shells that lie near the region where a black hole's event horizon would form (Classical Quantum Gravity, vol 23, p 1525).

"Dark energy stars and black holes would have identical external geometries, so it will be very difficult to tell them apart," Lobo says. "All observations used as evidence for black holes – their gravitational pull on objects and the formation of accretion discs of matter around them – could also work as evidence for dark energy stars."

That does not mean they are completely indistinguishable. While black holes supposedly swallow anything that gets past the event horizon, quantum critical shells are a two-way street, Chapline says. Matter crossing the shell decays, and the anti-gravity should spit some of the remnants back out again. Also, quark particles crossing the shell should decay by releasing positrons and gamma rays, which would pop out of the surface. This could explain the excess positrons that are seen at the centre of our galaxy, around the region that was hitherto thought to harbour a massive black hole. Conventional models cannot adequately explain these positrons, Chapline says.

He and his colleagues have also calculated the energy spectrum of the released gamma rays. "It is very similar to the spectrum observed in gamma-ray bursts," says Chapline. The team also predicts that matter falling into a dark energy star will heat up the star, causing it to emit infrared radiation. "As telescopes improve over the next decade, we'll be able to search for this light," says Chapline. "This is a theory that should be proved one way or the other in five to ten years."

Black hole expert Marek Abramowicz at Gothenburg University in Sweden agrees that the idea of dark energy stars is worth pursuing. "We really don't have proof that black holes exist," he says. "This is a very interesting alternative."

The most intriguing fallout from this idea has to do with the strength of the vacuum energy inside the dark energy star. This energy is related to the star's size, and for a star as big as our universe the calculated vacuum energy inside its shell matches the value of dark energy seen in the universe today. "It's like we are living inside a giant dark energy star," Chapline says. There is, of course, no explanation yet for how a universe-sized star could come into being.

At the other end of the size scale, small versions of these stars could explain dark matter. "The big bang would have created zillions of tiny dark energy stars out of the vacuum," says Chapline, who worked on this idea with Mazur. "Our universe is pervaded by dark energy, with tiny dark energy stars peppered across it." These small dark energy stars would behave just like dark matter particles: their gravity would tug on the matter around them, but they would otherwise be invisible.

Abramowicz says we know too little about dark energy and dark matter to judge Chapline and Laughlin's idea, but he is not dismissing it out of hand. "At the very least we can say the idea isn't impossible."

Avis said it is too early to say for certain that the apparent toxic shock syndrome was caused by infection at the site of the piercing. An anatomical autopsy was performed, but other microscopic tests need to be conducted before the source of the staphylococcus infection can be pinpointed, he said.

"We're still in the process of investigating," he said. "We can't be absolutely sure that body piercing had anything to do with the infection."

Still, Avis conceded that of the many possible origins of the toxic shock syndrome, "I think it would be fair to say that we're suspicious that that (body piercing) was the source of the infection, yes."

Toxic shock syndrome is characterized by sudden fever, chills, vomiting, diarrhea, muscle aches and rash, says the U.S. Centers for Disease Control and Prevention. The cause is usually toxins produced by strains of Staphylococcus aureus, a bacterium commonly found on the skin and on mucous membranes, such as the mouth.

Toxic shock can occur as a complication of skin abscesses or surgery. In females, it has been linked to the use of tampons and intravaginal contraceptive devices.

Avis said his office is now investigating the circumstances surrounding the teen's nipple piercing.

"This girl came to hospital almost moribund," he said. "All we know is she had a piercing recently. We are now trying to investigate when that was done."

Part of that investigation will involve talking to the grieving family of the teen, who was a senior at Booth Memorial High School in St. John's.

Avis said her death might be "an extreme example" of what can occur when people have lips, tongues, eyebrows, genitals and other body parts punctured in the name of fashion.

"This is health dollars that are essentially wasted treating infections that shouldn't have occurred because of some desire to have a piece of metal sticking out of your body. It doesn't make much sense to me."