Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Taming chaos: Calculating probability in complex systems

21.03.2018

A new method efficiently transforms trajectories from dynamical systems into a finite set of variables

Daily weather patterns, brain activity on an EEG (electroencephalogram) and heartbeats on an EKG (electrocardiogram) each generate lines of complex data. To analyze this data, perhaps to predict a storm, seizure or heart attack, researchers must first divide up this continuous data into discrete pieces -- a task that is difficult to perform simply and accurately.


The schematic details the steps of the new method for transforming data from a time series into symbols that can be used to calculate probabilities in complex systems.

Credit: Nicolás Rubido

Researchers from the Universidad de la República in Uruguay and the University of Aberdeen in Scotland have devised a new method to transform data from complex systems, reducing the amount of important information lost, while still using less computing power than existing methods. They describe this new method, which enables the estimation of probabilities in dynamical systems, in the current issue of Chaos, from AIP Publishing.

Historically, researchers have divided up data from a dynamical system through Markov partitions -- a function that describes a point in space in relation to time, such as a model that describes the swing of a pendulum. But Markov partitions are often impractical in real scenarios. In the new approach, researchers use movable marginal partitions to search the space of observed variables that make up time series data for an approximate Markov partition.

"Markov partitioning is transforming a continuous trajectory of a dynamical system stored in variables of high resolution into something discrete that can be stored in a finite set of variables with finite resolution, for instance, an alphabet," said Nicolás Rubido of the Universidad de la República.

A commonly used approximate method already exists that slices up the data from a time series into the bins of a histogram, but it uses bins that are all the same size. In this new study, the researcher set the bin boundaries in a way that reduces unpredictability in each bin. The new process transforms bins into easy-to-handle symbolic sequences that contain most of the relevant information from the system. Rubido likens the process to compressing a digital photo to a lower resolution, ensuring you can still make out all the objects in the image.

The new method can be useful in analyzing any kind of time series, such as predicting a power outage by accounting for power plant production, the fluctuating input of renewable energy sources and the changing demands of consumers. Rubido pointed out that this new approach offers no advantage over some of the existing methods for very simple cases, but said it could be especially useful for analyzing high-dimension dynamical systems, which quickly overwhelm existing computing power.

"The higher the complexity, the more applicable and suitable the method will be," Rubido said.

Next, Rubido and his team will work to optimize the method. Currently, researchers use "brute force" to set the boundaries of each bin, but they could try moving the boundaries back and forth in a controlled way to ensure that they're getting the most information possible in each variable. Once their method is optimized, the researchers plan to tackle more complex systems that have eluded analysis.

###

The article, "Entropy-based generating Markov partitions for complex systems," is authored by Nicolás Rubido, Celso Grebogi and Murilo Baptista. The article appeared in Chaos March 20, 2018 (DOI: 10.1063/1.5002097) and can be accessed at http://aip.scitation.org/doi/full/10.1063/1.5002097.

ABOUT THE JOURNAL

Chaos is devoted to increasing the understanding of nonlinear phenomena in all disciplines and describing their manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines. See http://chaos.aip.org.

Media Contact

Julia Majors
media@aip.org
301-209-3090

 @AIPPhysicsNews

http://www.aip.org 

Julia Majors | EurekAlert!

More articles from Physics and Astronomy:

nachricht When fluid flows almost as fast as light -- with quantum rotation
22.06.2018 | The Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences

nachricht Thermal Radiation from Tiny Particles
22.06.2018 | Universität Greifswald

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: Temperature-controlled fiber-optic light source with liquid core

In a recent publication in the renowned journal Optica, scientists of Leibniz-Institute of Photonic Technology (Leibniz IPHT) in Jena showed that they can accurately control the optical properties of liquid-core fiber lasers and therefore their spectral band width by temperature and pressure tuning.

Already last year, the researchers provided experimental proof of a new dynamic of hybrid solitons– temporally and spectrally stationary light waves resulting...

Im Focus: Overdosing on Calcium

Nano crystals impact stem cell fate during bone formation

Scientists from the University of Freiburg and the University of Basel identified a master regulator for bone regeneration. Prasad Shastri, Professor of...

Im Focus: AchemAsia 2019 will take place in Shanghai

Moving into its fourth decade, AchemAsia is setting out for new horizons: The International Expo and Innovation Forum for Sustainable Chemical Production will take place from 21-23 May 2019 in Shanghai, China. With an updated event profile, the eleventh edition focusses on topics that are especially relevant for the Chinese process industry, putting a strong emphasis on sustainability and innovation.

Founded in 1989 as a spin-off of ACHEMA to cater to the needs of China’s then developing industry, AchemAsia has since grown into a platform where the latest...

Im Focus: First real-time test of Li-Fi utilization for the industrial Internet of Things

The BMBF-funded OWICELLS project was successfully completed with a final presentation at the BMW plant in Munich. The presentation demonstrated a Li-Fi communication with a mobile robot, while the robot carried out usual production processes (welding, moving and testing parts) in a 5x5m² production cell. The robust, optical wireless transmission is based on spatial diversity; in other words, data is sent and received simultaneously by several LEDs and several photodiodes. The system can transmit data at more than 100 Mbit/s and five milliseconds latency.

Modern production technologies in the automobile industry must become more flexible in order to fulfil individual customer requirements.

Im Focus: Sharp images with flexible fibers

An international team of scientists has discovered a new way to transfer image information through multimodal fibers with almost no distortion - even if the fiber is bent. The results of the study, to which scientist from the Leibniz-Institute of Photonic Technology Jena (Leibniz IPHT) contributed, were published on 6thJune in the highly-cited journal Physical Review Letters.

Endoscopes allow doctors to see into a patient’s body like through a keyhole. Typically, the images are transmitted via a bundle of several hundreds of optical...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

VideoLinks
Industry & Economy
Event News

Munich conference on asteroid detection, tracking and defense

13.06.2018 | Event News

2nd International Baltic Earth Conference in Denmark: “The Baltic Sea region in Transition”

08.06.2018 | Event News

ISEKI_Food 2018: Conference with Holistic View of Food Production

05.06.2018 | Event News

 
Latest News

Graphene assembled film shows higher thermal conductivity than graphite film

22.06.2018 | Materials Sciences

Fast rising bedrock below West Antarctica reveals an extremely fluid Earth mantle

22.06.2018 | Earth Sciences

Zebrafish's near 360 degree UV-vision knocks stripes off Google Street View

22.06.2018 | Life Sciences

VideoLinks
Science & Research
Overview of more VideoLinks >>>