Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Physicists eye neural fly data, find formula for Zipf's law

06.08.2014

Physicists have identified a mechanism that may help explain Zipf’s law – a unique pattern of behavior found in disparate systems, including complex biological ones. The journal Physical Review Letters is publishing their mathematical models, which demonstrate how Zipf’s law naturally arises when a sufficient number of units react to a hidden variable in a system.

“We’ve discovered a method that produces Zipf’s law without fine-tuning and with very few assumptions,” says Ilya Nemenman, a biophysicist at Emory University and one of the authors of the research.


The Zipf's law mechanism was verified with neural data of blowflies reacting to changes in visual signals.


Neurons turn visual stimuli into units of information.

The paper’s co-authors include biophysicists David Schwab of Princeton and Pankaj Mehta of Boston University. “I don’t think any one of us would have made this insight alone,” Nemenman says. “We were trying to solve an unrelated problem when we hit upon it. It was serendipity and the combination of all our varied experience and knowledge.”

Their findings, verified with neural data of blowflies reacting to changes in visual signals, may have universal applications. “It’s a simple mechanism,” Nemenman says. “If a system has some hidden variable, and many units, such as 40 or 50 neurons, are adapted and responding to the variable, then Zipf’s law will kick in.”

... more about:
»Health »activity »flies »fly »mathematical »mechanism »neural »neurons »signals

That insight could aid in the understanding of how biological systems process stimuli. For instance, in order to pinpoint a malfunction in neural activity, it would be useful to know what data recorded from a normally functioning brain would be expected to look like. “If you observed a deviation from the Zipf’s law mechanism that we’ve identified, that would likely be a good place to investigate,” Nemenman says.

Zipf’s law is a mysterious mathematical principle that was noticed as far back as the 19th century, but was named for 20th-century linguist George Zipf. He found that if you rank words in a language in order of their popularity, a strange pattern emerges: The most popular word is used twice as often as the second most popular, and three times as much as the third-ranked word, and so on. This same rank vs. frequency rule was also found to apply to many other social systems, including income distribution among individuals and the size of cities, with a few exceptions.

More recently, laboratory experiments suggest that Zipf’s power-law structure also applies to a range of natural systems, from the protein sequences of immune receptors in cells to the intensity of solar flares from the sun.

“It’s interesting when you see the same phenomenon in systems that are so diverse. It makes you wonder,” Nemenman says.

Scientists have pondered the mystery of Zipf’s law for decades. Some studies have managed to reveal how a feature of a particular system makes it Zipfian, while others have come up with broad mechanisms that generate similar power laws but need some fine-tuning to generate the exact Zipf’s law.

“Our method is the only one that I know of that covers both of these areas,” Nemenman says. “It’s broad enough to cover many different systems and you don’t have to fine tune it: It doesn’t require you to set some parameters at exactly the right value.”

The blowfly data came from experiments led by biophysicist Rob de Ruyter that Nemenman worked on as a graduate student. Flies were turned on a rotor as they watched the world go by, hundreds of times. The moving scenes that the flies repeatedly experienced simulated their natural flight patterns. The researchers recorded when neurons associated with vision spiked, or fired. All sets of the data largely matched within a few hundred microseconds, showing that the flies’ neurons were not randomly spiking, but instead operating like precise coding machines.

If you think of a neuron firing as a “1” and a neuron not firing as a “0,” then the neural activity can be thought of as words, made up of 1s and 0s. When these “words,” or units, are strung together over time, they become “sentences.”

The neurons are turning visual stimuli into units of information, Nemenman explains. “The data is a way for us to read the sentences the fly’s vision neurons are conveying to the rest of the brain.”

Nemenman and his co-authors took a fresh look at this fly data for the new paper in Physical Review Letters. “We were trying to understand if there is a relationship between ideas of universality, or criticality, in physical systems and neural examples of how animals learn,” he says.

In order to navigate in flight, the flies’ visual neurons adapt to changes in the visual signal, such as velocity. When the world moves faster in front of a fly, these sensitive neurons adapt and rescale. These adaptions enable the flies to adjust to new environments, just as our own eyes adapt and rescale when we move from a darkened theater to a brightly lit room.

“We showed mathematically that the system becomes Zipfian when you’re recording the activity of many units, such as neurons, and all of the units are responding to the same variable,” Nemenman says. “The fact that Zipf’s law will occur in a system with just 40 or 50 such units shows that biological units are in some sense special – they must be adapted to the outside world.”

The researchers provide mathematical simulations to back up their theory. “Not only can we predict that Zipf’s law is going to emerge in any system which consists of many units responding to variable outside signals,” Nemenman says, “we can also tell you how many units you need to develop Zipf’s law, given how variable the response is of a single unit.”

They are now researching whether they can bring their work full circle, by showing that the mechanism they identified applies to Zipf’s law in language.

“Letters and words in language are sequences that encode a description of something that is changing over time, like the plot line in a story,” Nemenman says. “I expect to find a pattern similar to how vision neurons fire as a fly moves through the world and the scenery changes.”

Carol Clark | Eurek Alert!
Further information:
http://esciencecommons.blogspot.de/2014/08/physicists-eye-neural-fly-data-find.html

Further reports about: Health activity flies fly mathematical mechanism neural neurons signals

More articles from Physics and Astronomy:

nachricht Knots in chaotic waves
29.07.2016 | University of Bristol

nachricht International team of scientists unveils fundamental properties of spin Seebeck effect
29.07.2016 | Johannes Gutenberg-Universität Mainz

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Self-assembling nano inks form conductive and transparent grids during imprint

Transparent electronics devices are present in today’s thin film displays, solar cells, and touchscreens. The future will bring flexible versions of such devices. Their production requires printable materials that are transparent and remain highly conductive even when deformed. Researchers at INM – Leibniz Institute for New Materials have combined a new self-assembling nano ink with an imprint process to create flexible conductive grids with a resolution below one micrometer.

To print the grids, an ink of gold nanowires is applied to a substrate. A structured stamp is pressed on the substrate and forces the ink into a pattern. “The...

Im Focus: The Glowing Brain

A new Fraunhofer MEVIS method conveys medical interrelationships quickly and intuitively with innovative visualization technology

On the monitor, a brain spins slowly and can be examined from every angle. Suddenly, some sections start glowing, first on the side and then the entire back of...

Im Focus: Newly discovered material property may lead to high temp superconductivity

Researchers at the U.S. Department of Energy's (DOE) Ames Laboratory have discovered an unusual property of purple bronze that may point to new ways to achieve high temperature superconductivity.

While studying purple bronze, a molybdenum oxide, researchers discovered an unconventional charge density wave on its surface.

Im Focus: Mapping electromagnetic waveforms

Munich Physicists have developed a novel electron microscope that can visualize electromagnetic fields oscillating at frequencies of billions of cycles per second.

Temporally varying electromagnetic fields are the driving force behind the whole of electronics. Their polarities can change at mind-bogglingly fast rates, and...

Im Focus: Continental tug-of-war - until the rope snaps

Breakup of continents with two speed: Continents initially stretch very slowly along the future splitting zone, but then move apart very quickly before the onset of rupture. The final speed can be up to 20 times faster than in the first, slow extension phase.phases

Present-day continents were shaped hundreds of millions of years ago as the supercontinent Pangaea broke apart. Derived from Pangaea’s main fragments Gondwana...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Clash of Realities 2016: 7th Conference on the Art, Technology and Theory of Digital Games

29.07.2016 | Event News

GROWING IN CITIES - Interdisciplinary Perspectives on Urban Gardening

15.07.2016 | Event News

SIGGRAPH2016 Computer Graphics Interactive Techniques, 24-28 July, Anaheim, California

15.07.2016 | Event News

 
Latest News

Vortex laser offers hope for Moore's Law

29.07.2016 | Power and Electrical Engineering

Novel 'repair system' discovered in algae may yield new tools for biotechnology

29.07.2016 | Life Sciences

Clash of Realities 2016: 7th Conference on the Art, Technology and Theory of Digital Games

29.07.2016 | Event News

VideoLinks
B2B-VideoLinks
More VideoLinks >>>