Tag Archives: University of Arkansas

Mathematicians get illustrative

Frank A. Farris, an associate Professor of Mathematics at Santa Clara University (US), writes about the latest in mathematicians and data visualization in an April 4, 2017 essay on The Conversation (Note: Links have been removed),

Today, digital tools like 3-D printing, animation and virtual reality are more affordable than ever, allowing mathematicians to investigate and illustrate their work at the same time. Instead of drawing a complicated surface on a chalkboard, we can now hand students a physical model to feel or invite them to fly over it in virtual reality.

Last year, a workshop called “Illustrating Mathematics” at the Institute for Computational and Experimental Research in Mathematics (ICERM) brought together an eclectic group of mathematicians and digital art practitioners to celebrate what seems to be a golden age of mathematical visualization. Of course, visualization has been central to mathematics since Pythagoras, but this seems to be the first time it had a workshop of its own.

Visualization plays a growing role in mathematical research. According to John Sullivan at the Technical University of Berlin, mathematical thinking styles can be roughly categorized into three groups: “the philosopher,” who thinks purely in abstract concepts; “the analyst,” who thinks in formulas; and “the geometer,” who thinks in pictures.

Mathematical research is stimulated by collaboration between all three types of thinkers. Many practitioners believe teaching should be calibrated to connect with different thinking styles.

Borromean Rings, the logo of the International Mathematical Union. John Sullivan

Sullivan’s own work has benefited from images. He studies geometric knot theory, which involves finding “best” configurations. For example, consider his Borromean rings, which won the logo contest of the International Mathematical Union several years ago. The rings are linked together, but if one of them is cut, the others fall apart, which makes it a nice symbol of unity.

Apparently this new ability to think mathematics visually has influenced mathematicians in some unexpected ways,

Take mathematician Fabienne Serrière, who raised US$124,306 through Kickstarter in 2015 to buy an industrial knitting machine. Her dream was to make custom-knit scarves that demonstrate cellular automata, mathematical models of cells on a grid. To realize her algorithmic design instructions, Serrière hacked the code that controls the machine. She now works full-time on custom textiles from a Seattle studio.

In this sculpture by Edmund Harriss, the drill traces are programmed to go perpendicular to the growth rings of the tree. This makes the finished sculpture a depiction of a concept mathematicians know as ‘paths of steepest descent.’ Edmund Harriss, Author provided

Edmund Harriss of the University of Arkansas hacked an architectural drilling machine, which he now uses to make mathematical sculptures from wood. The control process involves some deep ideas from differential geometry. Since his ideas are basically about controlling a robot arm, they have wide application beyond art. According to his website, Harriss is “driven by a passion to communicate the beauty and utility of mathematical thinking.”

Mathematical algorithms power the products made by Nervous System, a studio in Massachusetts that was founded in 2007 by Jessica Rosenkrantz, a biologist and architect, and Jess Louis-Rosenberg, a mathematician. Many of their designs, for things like custom jewelry and lampshades, look like naturally occurring structures from biology or geology.

Farris’ essay is a fascinating look at mathematics and data visualization.

Predicting how a memristor functions

An April 3, 2017 news item on Nanowerk announces a new memristor development (Note: A link has been removed),

Researchers from the CNRS [Centre national de la recherche scientifique; France] , Thales, and the Universities of Bordeaux, Paris-Sud, and Evry have created an artificial synapse capable of learning autonomously. They were also able to model the device, which is essential for developing more complex circuits. The research was published in Nature Communications (“Learning through ferroelectric domain dynamics in solid-state synapses”)

An April 3, 2017 CNRS press release, which originated the news item, provides a nice introduction to the memristor concept before providing a few more details about this latest work (Note: A link has been removed),

One of the goals of biomimetics is to take inspiration from the functioning of the brain [also known as neuromorphic engineering or neuromorphic computing] in order to design increasingly intelligent machines. This principle is already at work in information technology, in the form of the algorithms used for completing certain tasks, such as image recognition; this, for instance, is what Facebook uses to identify photos. However, the procedure consumes a lot of energy. Vincent Garcia (Unité mixte de physique CNRS/Thales) and his colleagues have just taken a step forward in this area by creating directly on a chip an artificial synapse that is capable of learning. They have also developed a physical model that explains this learning capacity. This discovery opens the way to creating a network of synapses and hence intelligent systems requiring less time and energy.

Our brain’s learning process is linked to our synapses, which serve as connections between our neurons. The more the synapse is stimulated, the more the connection is reinforced and learning improved. Researchers took inspiration from this mechanism to design an artificial synapse, called a memristor. This electronic nanocomponent consists of a thin ferroelectric layer sandwiched between two electrodes, and whose resistance can be tuned using voltage pulses similar to those in neurons. If the resistance is low the synaptic connection will be strong, and if the resistance is high the connection will be weak. This capacity to adapt its resistance enables the synapse to learn.

Although research focusing on these artificial synapses is central to the concerns of many laboratories, the functioning of these devices remained largely unknown. The researchers have succeeded, for the first time, in developing a physical model able to predict how they function. This understanding of the process will make it possible to create more complex systems, such as a series of artificial neurons interconnected by these memristors.

As part of the ULPEC H2020 European project, this discovery will be used for real-time shape recognition using an innovative camera1 : the pixels remain inactive, except when they see a change in the angle of vision. The data processing procedure will require less energy, and will take less time to detect the selected objects. The research involved teams from the CNRS/Thales physics joint research unit, the Laboratoire de l’intégration du matériau au système (CNRS/Université de Bordeaux/Bordeaux INP), the University of Arkansas (US), the Centre de nanosciences et nanotechnologies (CNRS/Université Paris-Sud), the Université d’Evry, and Thales.


Image synapse

© Sören Boyn / CNRS/Thales physics joint research unit.

Artist’s impression of the electronic synapse: the particles represent electrons circulating through oxide, by analogy with neurotransmitters in biological synapses. The flow of electrons depends on the oxide’s ferroelectric domain structure, which is controlled by electric voltage pulses.

Here’s a link to and a citation for the paper,

Learning through ferroelectric domain dynamics in solid-state synapses by Sören Boyn, Julie Grollier, Gwendal Lecerf, Bin Xu, Nicolas Locatelli, Stéphane Fusil, Stéphanie Girod, Cécile Carrétéro, Karin Garcia, Stéphane Xavier, Jean Tomas, Laurent Bellaiche, Manuel Bibes, Agnès Barthélémy, Sylvain Saïghi, & Vincent Garcia. Nature Communications 8, Article number: 14736 (2017) doi:10.1038/ncomms14736 Published online: 03 April 2017

This paper is open access.

Thales or Thales Group is a French company, from its Wikipedia entry (Note: Links have been removed),

Thales Group (French: [talɛs]) is a French multinational company that designs and builds electrical systems and provides services for the aerospace, defence, transportation and security markets. Its headquarters are in La Défense[2] (the business district of Paris), and its stock is listed on the Euronext Paris.

The company changed its name to Thales (from the Greek philosopher Thales,[3] pronounced [talɛs] reflecting its pronunciation in French) from Thomson-CSF in December 2000 shortly after the £1.3 billion acquisition of Racal Electronics plc, a UK defence electronics group. It is partially state-owned by the French government,[4] and has operations in more than 56 countries. It has 64,000 employees and generated €14.9 billion in revenues in 2016. The Group is ranked as the 475th largest company in the world by Fortune 500 Global.[5] It is also the 10th largest defence contractor in the world[6] and 55% of its total sales are military sales.[4]

The ULPEC (Ultra-Low Power Event-Based Camera) H2020 [Horizon 2020 funded) European project can be found here,

The long term goal of ULPEC is to develop advanced vision applications with ultra-low power requirements and ultra-low latency. The output of the ULPEC project is a demonstrator connecting a neuromorphic event-based camera to a high speed ultra-low power consumption asynchronous visual data processing system (Spiking Neural Network with memristive synapses). Although ULPEC device aims to reach TRL 4, it is a highly application-oriented project: prospective use cases will b…

Finally, for anyone curious about Thales, the philosopher (from his Wikipedia entry), Note: Links have been removed,

Thales of Miletus (/ˈθeɪliːz/; Greek: Θαλῆς (ὁ Μῑλήσιος), Thalēs; c. 624 – c. 546 BC) was a pre-Socratic Greek/Phoenician philosopher, mathematician and astronomer from Miletus in Asia Minor (present-day Milet in Turkey). He was one of the Seven Sages of Greece. Many, most notably Aristotle, regard him as the first philosopher in the Greek tradition,[1][2] and he is otherwise historically recognized as the first individual in Western civilization known to have entertained and engaged in scientific philosophy.[3][4]

The geometry of graphene at the University of Arkansas (US)

The University of Arkansas (US) has announced the development of a new mathematical framework useful for studying graphene according to a May 5, 2014 news item on Nanowerk,

Scientists studying graphene’s properties are using a new mathematical framework to make extremely accurate characterizations of the two-dimensional material’s shape.

“The properties of two-dimensional materials depend on shape,” said Salvador Barraza-Lopez, an assistant professor of physics at the University of Arkansas. “And this mathematical framework allows you to make extremely accurate characterizations of shape. This framework is a novel tool to understand shape in materials that behave as atom-thin membranes.”

A May 5, 2014 University of Arkansas news release, which originated the news item, provides more details,

The mathematical framework being used is known as discrete differential geometry, which is the geometry of two-dimensional interlaced structures called meshes. When the nodes of the structure, or mesh points, correspond with atomic positions, discrete differential geometry provides direct information on the potential chemistry and on the electronic properties of two-dimensional materials, Barraza-Lopez said.

The application of discrete differential geometry to understand two-dimensional materials is an original interdisciplinary development, he said.

“Since two-dimensional materials can be easily visualized as meshes, we asked ourselves how these theories would look if you express them directly in terms of the positions of the atoms, bypassing entirely the common continuum approximation,” Barraza-Lopez said. …

Two papers have been produced about this work,

Quantitative Chemistry and the Discrete Geometry of Conformal Atom-Thin Crystals by Alejandro A. Pacheco Sanjuan, Mehrshad Mehboudi, Edmund O. Harriss, Humberto Terrones, and Salvador Barraza-Lopez. ACS Nano, 2014, 8 (2), pp 1136–1146 DOI: 10.1021/nn406532z Publication Date (Web): January 8, 2014

Copyright © 2014 American Chemical Society

Graphene’s morphology and electronic properties from discrete differential geometry by Alejandro A. Pacheco Sanjuan, Zhengfei Wang, Hamed Pour Imani, Mihajlo Vanević, and Salvador Barraza-Lopez. Phys. Rev. B 89, 121403(R) – Published 6 March 2014 DOI: http://dx.doi.org/10.1103/PhysRevB.89.121403

©2014 American Physical Society

Both papers are behind paywalls.

Be still my heart: e-bras and e-vests

Have they thought about the sweat? Engineers at the University of Arkansas have developed garments (a sports bra for women and a vest for men) than can monitor their physiological responses and track their location. From May 3, 2012 news release on the University of Arkanasa newswire page,

An interdisciplinary team of engineers at the University of Arkansas has developed a wireless health-monitoring system that gathers critical patient information, regardless of the patient’s location, and communicates that information in real time to a physician, hospital or the patient herself.

The system includes a series of nanostructured, textile sensors integrated into a conventional sports bra for women and vest for men. Via a lightweight and wireless module that snaps onto these garments, the sensors communicate with system software that relies on a smart phone to collect information, compress it and send it over a variety of wireless networks.

“Our e-bra enables continuous, real-time monitoring to identify any pathophysiological changes,” said Vijay Varadan, Distinguished Professor of electrical engineering. “It is a platform on which various sensors for cardiac-health monitoring are integrated into the fabric. The garment collects and transmits vital health signals to any desired location in the world.”

The system monitors blood pressure, body temperature, respiratory rate, oxygen consumption, some neural activity and all the readings provided by a conventional electrocardiograph (ECG), including the ability to display inverted T waves, which indicate the onset of cardiac arrest. The system does not require a cuff or any extra accessories to measure blood pressure and could therefore replace conventional blood-pressure monitors. It could also replace the cumbersome combination of ECG sensors and wires attached to patients while they walk on treadmills.

The researchers have provided this image,

The wireless monitoring system includes sensors, integrated into garments, that communicate health information to smart phones.

Here’s a bit more about the technology (from the May 3, 2012 news release),

The sensors, which are smaller than a dime, include gold nanowires, as well as flexible, conducting textile nanosensors. The sensors are made of arrays of gold nano-electrodes fabricated on a flexible substrate. The textile sensors are woven into the bra material. These sensors do not require conventional sticky electrodes or the use of gel.

Electrical signals and other physiological data gathered by the sensors are sent to the snap-on wireless module, the contents of which are housed in a plastic box that is slightly smaller than a ring box. As the critical wireless component, the module is essentially a low-powered laptop computer that includes an amplifier, an antenna, a printed circuit board, a microprocessor, a Bluetooth module, a battery and various sensors. The size of the module depends heavily on power consumption and minimum battery size. Varadan said that anticipated battery and Bluetooth upgrades will allow the researchers to build a smaller – 1.5 inches long, 0.75 inch wide and 0.25 inch deep – lighter and flexible module that will replace the rigid box.

Researchers are considering other applications for this technology (from the May 3, 2012 news release),

Data from the sensors then stream to commercially available cell phones and hand-held devices, which expand the use of the system beyond health care. By carrying a cell phone, athletes can monitor all signs mentioned above and other metrics, such as number of calories burned during a workout. To render clean data, the software includes filtering algorithms to mitigate problems due to motion of the hand-held device during exercise.

In light of the suggestion that this could be used by athletes I’m repeating my rhetorical question, have they thought about the sweat?

Thanks to Nanowerk where I first found out about this research at the University of Arkansas in their May 4, 2022 news item.