Tag Archives: New York University

Mathematicians, political scientists, and cake cutting

If you have a sibling, you’ve likely fought at least once over who got the biggest or ‘best’ piece of cake.  (I do and I did.) In any event, it seems that mathematicians and political scientists have been working on a scheme to avoid disputes over cake.

[downloaded from http://link.springer.com/article/10.1007%2Fs00283-013-9442-0#page-1]

A July 16, 2014 Springer news release (also on EurekAlert) describes the quest for fairly sized cake slices and how that might apply to real life issues such as sharing property,

The next time your children quibble about who gets to eat which part of a cake, call in some experts on the art of sharing. Mathematician Julius Barbanel of Union College, and political scientist Steven Brams of New York University, both in the US, published an algorithm in Springer’s The Mathematical Intelligencer by which they show how to optimally share cake between two people efficiently, in equal pieces and in such a way that no one feels robbed.

The cut-and-choose method to share divisible goods has been regarded as fair and envy-free since Biblical times, when Abraham divided land equally, and Lot could choose the part he wanted. But being free of envy is not the only consideration when sharing something. What happens when more than two cuts can be made, or when people prefer different, specific sections of whatever is to be divided? Barbanel and Brams believe that with a giveback procedure it is possible to make a perfect division between two people that is efficient, equitable and void of jealousy.

An objective referee (such as a Mom or a computer) is essential to the plan. The potential cake eaters first tell the referee which parts of the delicacy they value most. In mathematical terms these are called someone’s probability density functions, or pdfs. The referee then marks out the cake at all points were the pdfs of the disgruntled would-be cake eaters cross, and assigns portions. If at this point the two parties receive the same size of cake, the task is over. If not, the giveback process starts.

The party who received the larger part of the cake during the first round must give a part of it back to the other person, starting with those parts in which the ratio of their pdfs is the smallest. This goes on until the parties value their portions equally, and have the same volume of cake to eat. This method only works with a finite number of cuts if the players’ pdfs are straight-lined, or are so-called piecewise linear sections.

The researchers believe the method can be used to share cake and other divisible goods such as land. In the case of beachfront property being co-owned by two developers, for example, it can help to determine who gets what strips of land to build on based on the pieces of land they value most.

“This allocation is not only equitable but also envy-free and efficient – that is, perfect,” says Barbanel.

“This approach focuses on proving the existence of efficient and envy-free divisions, not on providing algorithms to finding them,” emphasizes Brams.

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

Two-Person Cake Cutting: The Optimal Number of Cuts by Julius B. Barbanel and Steven J. Brams. The Mathematical Intelligencer March 2014 DOI 10.1007/s00283-013-9442.

This paper is behind a paywall although there is a free preview available and a special summer discount (30%) on the purchase price until July 31, 2014.

Dental implants with a surface that affects genetic cellular expression

Intra-Lock International is trumpeting in triumph in the wake  of a study noting their OSSEAN-surfaced dental implants promote better bone-healing than an alternative used for comparison. From the June 10, 2014 news item on Azonano,

As reported in the internationally renowned scientific journal, Bone [in press for Aug. 2014], a research team from New York University [NYU] has confirmed what scientific developers at Intra-Lock® International, Inc. have known for several years: the fractal, nano-rough OSSEAN® surface developed for their dental implants actually changes the cellular genetic expression – or the fate of stem cells – at the nano-level, which in turn induces faster healing of implants.

A June 9, 2014 Intra-Lock news release, which originated the new item, describes what usually occurs when an implant is first situated in the tissue (cellular confusion) and how the OSSEAN surface affects the ‘confusion’,

Typically, when an implant is surgically placed, there is a period of cellular “confusion” and chaos around the implant, and usually a little bone resorbs before being formed again. The implant is then at risk from the moment it is inserted through the time when the bone is healed around it – a time period Giorno [Thierry M. Giorno, DDS, director of research and development, and CEO of Intra-Lock®, International] refers to as “the window of negative opportunity.”

However, the NYU researchers found that bone cells immediately start clustering around the OSSEAN implants and begin accelerated healing, with little confusion whatsoever.

This occurs primarily due to the biomimetic structure of the OSSEAN surface, designed and classified as nanorough and fractalii. Mimicking nature at the nano-level, the OSSEAN surface repeats a similar structural pattern to that of natural bone over and over, essentially “tricking” the body into accepting the implant as a natural substance and igniting the healing process far sooner than would occur with an artificial substance, which is smooth at the nano-level and without natural-seeming pattern repetition.

Typically, with an implant of any sort, whether it’s a dental implant in your jaw or a titanium rod in your leg, several weeks will pass before the bone begins to grow around it. During this time lapse, known as the “catabolic phase,” there can be great risk and instability with the implant.

Naturally, compressing the healing time and accelerating the degree of osseointegration – the merging of implant and bone – are highly desirable outcomes, and implants with an OSSEAN can provide a faster healing process, which thereby reduces patient discomfort and provides a higher potential for successful long-term results with the implant.

“If you’ve ever had dental implants, you can appreciate the outcomes the OSSEAN surface provides,” said Giorno. “The healing process has changed forever, and future patients with an OSSEAN surface implant can look forward to reduced complications, overall.”

Looking further into the future, Giorno said, “I believe the effects of OSSEAN can potentially revolutionize the implant industry beyond dentistry and into all types of orthopedics where patients must wait for their bodies to accept a foreign substance. With OSSEAN, the wait is over.”

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

Nanometer-scale features on micrometer-scale surface texturing: A bone histological, gene expression, and nanomechanical study by Paulo G. Coelho, Tadahiro Takayama, Daniel Yoo, Ryo Jimboemail, Sanjay Karunagaran, Nick Tovar, Malvin N. Janal, and Seiichi Yamano. Bone, Issue 65, Aug. 2014. Bone (2014) DOI: http://dx.doi.org/10.1016/j.bone.2014.05.004 Published Online: May 07, 2014

This article is behind a paywall. You can find out more about Intra-Lock and OSSEAN here.

New York University/Caltech grant is part of the NSF’s Origami Design for Integration of Self-assembling Systems for Engineering Innovation (ODISSEI) program

The US National Science Foundation (NSF) has an origami program,  Origami Design for Integration of Self-assembling Systems for Engineering Innovation (ODISSEI), which recently announced a $2M grant to New York University (NYU) and the California Institute of Technology (Caltech) to create new nanomaterials according to an Aug. 6, 2013 news item on Nanowerk,

The National Science Foundation (NSF) has awarded New York University researchers and their colleagues at the California Institute of Technology (Caltech) a $2 million grant to develop cutting-edge nanomaterials that hold promise for improving the manufacturing of advanced materials, biofuels, and other industrial products.

Under the grant, the scientists will develop biomimetic materials with revolutionary properties—these molecules will self-replicate, evolve, and adopt three-dimensional structures a billionth of a meter in size by combining DNA-guided self-assembly with the centuries-old art of origami folding.

The Aug. 5, 2013 NYU press release, which originated the news item,  provides details about the researchers and the project,

The four-year grant is part of the NSF’s Origami Design for Integration of Self-assembling Systems for Engineering Innovation (ODISSEI) program and includes NYU Chemistry Professors Nadrian Seeman and James Canary and NYU Physics Professor Paul Chaikin. They will team up with Caltech’s William A. Goddard, III and Si-ping Han.

Others involved in the project are molecular biologists John Rossi and Lisa Scherer of City of Hope Medical Center and mathematicians Joanna Ellis-Monaghan and Greta Pangborn of Saint Michael’s College in Vermont.

The work will build upon recent breakthroughs in the field of structural DNA nanotechnology, which Seeman founded more than three decades ago and is now pursued by laboratories across the globe. His creations allow him to arrange pieces and form specific molecules with precision—similar to the way a robotic automobile factory can be told what kind of car to make.

Previously, Seeman has created three-dimensional DNA structures, a scientific advance bridging the molecular world to the world where we live. To do this, he and his colleagues created DNA crystals by making synthetic sequences of DNA that have the ability to self-assemble into a series of 3D triangle-like motifs. The creation of the crystals was dependent on putting “sticky ends”—small cohesive sequences on each end of the motif—that attach to other molecules and place them in a set order and orientation. The make-up of these sticky ends allows the motifs to attach to each other in a programmed fashion.

Recently, the Seeman and Chaikin labs teamed up to develop artificial structures that can self-replicate, a process that has the potential to yield new types of materials. In the natural world, self-replication is ubiquitous in all living entities, but artificial self-replication had previously been elusive. Their work marked the first steps toward a general process for self-replication of a wide variety of arbitrarily designed “seeds”. The seeds are made from DNA tile motifs that serve as letters arranged to spell out a particular word. The replication process preserves the letter sequence and the shape of the seed and hence the information required to produce further generations. Self-replication enables the evolution of molecules to optimize particular properties via selection processes.

Under the NSF grant, the researchers will aim to take these innovations to the next level: the creation of self-replicating 3D arrays. To do so, the collaborators will aim to fold replicating 1D and 2D arrays into 3D shapes in a manner similar to paper origami—a complex and delicate process.

In meeting this challenge, they will adopt tools from graph theory and origami mathematics to develop algorithms to direct self-assembling DNA nanostructures and their origami folds. The mathematical component of the endeavor will be supplemented by the artistic expertise of Portland, Ore.-based sculptor Julian Voss-Andreae, who will advise the team on issues related to design and will use his skills to develop life-size physical models of the nanoscopic structures the scientists are seeking to build. [emphasis mine]

I wasn’t expecting to see a sculptor included in the team and I wonder if there might be plans to use his sculptures not only as models but also in exhibitions and art shows to fulfill any science outreach requirements that the NSF might have for its grantees.

I did a little further digging into the NSF’s ‘origami’ program and found this webpage explaining that ‘origami’ is part of a still larger program,

The Emerging Frontiers in Research and Innovation (EFRI) office awarded 15 grants in FY 2012, including the following 8 on the topic of Origami Design for Integration of Self-assembling Systems for Engineering Innovation (ODISSEI): …

As there wasn’t any information about grants for FY 2013, I gather they haven’t had time to update the page or add any recent news releases to the website.

Looking at glass on the molecular scale

Glass isn’t transparent (at the molecular scale) as it’s cooling and scientists have been curious about this transition from liquid to glass state. According to an Oct. 15, 2012 posting by Carol Clark for Emory University’s eScienceCommons, a team from Emory University (and New York University)  has cracked this mystery. First, here’s more about the mystery (from Clark’s article)

Scientists fully understand the process of water turning to ice. As the temperature cools, the movement of the water molecules slows. At 32 F, the molecules lock into crystal lattices, solidifying into ice. In contrast, the molecules of glasses do not crystallize.The movement of the glass molecules slows as the temperature cools, but they never lock into crystal patterns. Instead, they jumble up and gradually become glassier, or more viscous. No one understands exactly why.

The phenomenon leaves physicists to ponder the molecular question of whether glass is a solid, or merely an extremely slow-moving liquid.

This purely technical physics question has stoked a popular misconception: That the glass in the windowpanes of some centuries-old buildings is thicker at the bottom because the glass flowed downward over time.

“The real reason the bottom is thicker is because they hadn’t yet learned how to make perfectly flat panes of glass,” Weeks says [Emory physicist Eric Weeks]. “For practical purposes, glass is a solid and it will not flow, even over centuries. But there is a kernel of truth in this urban legend: Glasses are different than other solid materials.”

Speaking more technically about the transition,

“Cooling a glass from a liquid into a highly viscous state fundamentally changes the nature of particle diffusion,” says Emory physicist Eric Weeks, whose lab conducted the research. “We have provided the first direct observation of how the particles move and tumble through space during this transition, a key piece to a major puzzle in condensed matter physics.”

Weeks specializes in “soft condensed materials,” substances that cannot be pinned down on the molecular level as a solid or liquid, including everyday substances such as toothpaste, peanut butter, shaving cream, plastic and glass.

The scientists have prepared a video animation of what they believing is occurring as glass cools (no sound),

Here’s what the movie depicts (from the Clark article),

The movie and data from the experiment provide the first clear picture of the particle dynamics for glass formation. As the liquid grows slightly more viscous, both rotational and directional particle motion slows. The amount of rotation and the directional movements of the particles remain correlated.

“Normally, these two types of motion are highly coupled,” Weeks says. “This remains true until the system reaches a viscosity on the verge of being glass. Then the rotation and directional movements become decoupled: The rotation starts slowing down more.”

He uses a gridlocked parking lot as an analogy for how the particles are behaving. “You can’t turn your car around, because it’s not a sphere shape and you would bump into your neighbors. You have to wait until a car in front of you moves, and then you can drive a bit in that direction. This is directional movement, and if you can make a bunch of these, you may eventually be able to turn your car. But turning in a crowded parking lot is still much harder than moving in a straight line.”

There’s more about the work and team in Clark’s article. H/T to the Oct. 16, 2012 news item on Nanowerk for alerting me to this work. You can find the article the researchers have written at the Proceedings of the National Academy of Sciences (PNAS),

Decoupling of rotational and translational diffusion in supercooled colloidal fluids by Kazem V. Edmond, Mark T. Elsesser, Gary L. Hunter, David J. Pine, and Eric R. Weeks. Published online before print October 15, 2012, doi: 10.1073/pnas.1203328109 PNAS October 15, 2012

The article is behind a paywall.