MATH NEWS

“It’s really a race of who can get there first,” says team member Dr. John Bell.
The mathematical model allows researchers to mimic a viral infection, including how the cancer cells put up their defences.
They can then hypothesize how to modify the genetics of the virus to attack cancer cells with enough strength and speed to destroy them.
Photograph by: Ashley Fraser, Ottawa Citizen

An Ottawa research team has developed a mathematical model to test cancer-killing viruses before putting them into action.

The project focuses on the viability and potency of oncolytic viruses: man-made bacteria that target cancer cells but leave the body’s healthy ones alone. The challenge is to make viruses strong enough without having them turn on the wrong tissue.

“Cancer is incredibly complicated, and what we tried to do was just to describe the basic interactions between viruses, normal cells and cancer cells,” says Dr. Mads Kaern, a member of the joint University of Ottawa and Ottawa Hospital Research Institute team. Cancer cells, for example, are distinguished by their rate of growth being faster than normal tissue.

Then there’s the question of how to design the viruses to attack the cancer cells before they can build up defences.

“It’s really a race of who can get there first,” says team member Dr. John Bell.

The mathematical model allows researchers to mimic a viral infection, including how the cancer cells put up their defences. They can then hypothesize how to modify the genetics of the virus to attack cancer cells with enough strength and speed to destroy them.

The simulations only take a few minutes, but the team did “tens of thousands” of attempts while developing the model, says Kaern. When applied in practice, the model’s predictions had 100 per cent accuracy and was successful in eradicating cancer in a mouse.

The team’s findings were published in the research journal Nature Communications Friday. The paper’s bylines represent a rare collaboration between mathematicians specializing in computer modelling and biologists tackling cancer research.

“It was a learning curve for both (groups) to speak each other’s languages,” says Bell. “It was an experiment in and of itself, just the collaboration.”

The partnership came about thanks to one of the paper’s co-authors, Cory Batenchuk, who completed his Master’s degree in Kaern’s lab and is currently completing his PhD in Bell’s. Kaern believes it is the first time applied mathematicians and cancer biologists have directly worked together on a project such as this. It took about a year to develop the model.

So far, the team has only modelled one cancer cell type and one virus. It plans to expand the model’s scope, and partner with a team from New York City that has been working on increasing oncolytic viruses’ potency.

By keeping much of the experimentation to computers, Bell says the model focuses lab work “on things that are more likely to be successful,” reducing the cost and speed of cancer research.

Mathematicians, biologists team up to create cancer-killing viruses

In a paper titled Conditions for Transient Viremia in Deterministic in-Host Models: Viral Blips Need No Exogenous Trigger, published last month in the SIAM Journal on Applied Mathematics, authors Wenjing Zhang, Lindi M. Wahl, and Pei Yu present a model to study persistent infections.

In latent infections (a type of persistent infection), no infectious cells can be observed during the silent or quiescent stages, which involve low-level viral replication. These silent periods are often interrupted by unexplained intermittent episodes of active viral production and release. "Viral blips" associated with human immunodeficiency virus (HIV) infections are a good example of such active periods.

"Mathematical modeling has been critical to our understanding of HIV, particularly during the clinically latent stage of infection," says author Pei Yu. "The extremely rapid turnover of the viral population during this quiescent stage of infection was first demonstrated through modeling (David Ho, Nature, 1995), and came as a surprise to the clinical community. This was seen as one of the major triumphs of mathematical immunology: an extremely important result through the coupling of patient data and an appropriate modeling approach."

Recurrent infections also often occur due to drug treatment. For example, active antiretroviral therapy for HIV can suppress the levels of the virus to below-detection limits for months. Though much research has focused on these viral blips, their causes are not well understood.

Previous mathematical models have analyzed the reasons behind such viral blips, and have proposed various possible explanations. An early model considered the activation of T cells, a type of immune cell, in response to antigens. Later models attributed blips to recurrent activation of latently-infected lymphocytes, which are a broader class of immune cells that include T-cells. Asymmetric division of such latently-infected cells, resulting in activated cells and latently-infected daughter cells were seen to elicit blips in another study.

These previous models have used exogenous triggers such as stochastic or transient stimulation of the immune system in order to generate viral blips.

In this paper, the authors use dynamical systems theory to reinvestigate in-host infection models that exhibit viral blips. They demonstrate that no such exogenous triggers are needed to generate viral blips, and propose that blips are produced as part of the natural behavior of the dynamical system. The key factor for this behavior is an infection rate which increases but saturates with the extent of infection. The authors show that such an increasing, saturating infection rate alone is sufficient to produce long periods of quiescence interrupted by rapid replication, or viral blips.

These findings are consistent with clinical observations where even patients on the best currently-available HIV therapy periodically exhibit transient episodes of viremia (high viral load in the blood). A number of reasons have been proposed for this phenomenon, such as poor adherence to therapy or the activation of a hidden reservoir of HIV-infected cells. "If adherence is the underlying factor, viral blips are triggered when the patient misses a dose or several doses of the prescribed drugs," explains Yu. "If activation is the cause, blips may be triggered by exposure to other pathogens, which activate the immune system. Our work demonstrates that viral blips might simply occur as a natural cycle of the underlying dynamical system, without the need for any special trigger."

The authors propose simple 2- and 3-dimensional models that can produce viral blips. Linear or constant infection rates do not lead to blips in 2-, 3- or 4-dimensional models studied by the authors. However, a 5-dimensional immunological model reveals that a system with a constant infection rate can generate blips as well.

The models proposed in the paper can be used to study a variety of viral diseases that exhibit recurrent infections. "We are currently extending this approach to other infections, and more broadly to other diseases that display recurrence," says Yu. "For example, many autoimmune diseases recur and relapse over a timescale of years, and once again, the 'triggers' for episodes of recurrence are unknown. We would like to understand more fully what factors of the underlying dynamical system might be driving these episodic patterns."

Read another nugget article from the SIAM Journal on Applied Mathematics last month that uses mathematical models to help understand HIV dynamics, and proposes a design for prevention and treatment strategies: http://connect.siam.org/mathematical-models-to-better-combat-hiv/.

Source Article for above nugget:

Conditions for Transient Viremia in Deterministic in-Host Models: Viral Blips Need No Exogenous Trigger
Wenjing Zhang, Lindi M. Wahl, and Pei Yu
SIAM Journal on Applied Matematics, 73(2), 853 (Online publish date: April 20, 2013). The source article is available for free access at the link below until until August 31, 2013.
http://epubs.siam.org/doi/abs/10.1137/120884535

About the authors:

Wenjing Zhang is a graduate student and Lindi M. Wahl and Pei Yu are professors in the Department of Applied Mathematics at the University of Western Ontario in Canada. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC)

About SIAM

The Society for Industrial and Applied Mathematics (SIAM), headquartered in Philadelphia, Pennsylvania, is an international society of over 14,000 individual members, including applied and computational mathematicians and computer scientists, as well as other scientists and engineers. Members from 85 countries are researchers, educators, students, and practitioners in industry, government, laboratories, and academia. The Society, which also includes nearly 500 academic and corporate institutional members, serves and advances the disciplines of applied mathematics and computational science by publishing a variety of books and prestigious peer-reviewed research journals, by conducting conferences, and by hosting activity groups in various areas of mathematics. SIAM provides many opportunities for students including regional sections and student chapters. Further information is available at http://www.siam.org.

Surges in latent infections: Mathematical analysis of viral blips

Spanish and US scientists have successfully identified animal species that can transmit more diseases to humans by using mathematical tools similar to those applied to the study of social networks like Facebook or Twitter. Their research-recently published in the prestigious journal PNAS-describes how parasite-primate interactions transmit diseases like malaria, yellow fever or AIDS to humans. Their findings could make an important contribution to predicting the animal species most likely to cause future pandemics.

Professor Jos- Mar-a G-mez of the University of Granada Department of Ecology is the principal author of this research, in collaboration with Charles L. Nunn (University of Cambridge, Massachusetts, US) and Miguel Verd- (Spanish National Research Council Desertification Research Center, Valencia, Spain). They propose a criterion to identify disease-transmission agents based on complex network metrics similar to those used to study social networks.

As Prof G-mez explains, "most emerging diseases in humans are zoonotic, that is, they are transmitted to humans by animals. To identify animal species that are potential high-risk sources of emerging diseases it's essential we set up mechanisms that control and observe these diseases".

Study of 150 primate species

To conduct their study, the researchers constructed a network in which each node represented one of the approximately 150 non-human primate species about which we have enough data on their parasite fauna. "Each primate species is connected to the other primates as a function of the number of parasites they share. Once the network was constructed, we studied each primate species' position-whether central or peripheral. A primate's centrality is measured by its connection intensity with many other primates that are, in turn, closely connected", says the University of Granada researcher.

The article published in PNAS reports the researchers' discovery that the most central primates could be more capable of transmitting parasites to other species and, therefore, to humans, than the rest. "This is comparable to the idea that, in social networks, web pages that are central and have links to many other pages, spread their contents all through the Web", Jos- Mar-a G-mez affirms.

The researchers have confirmed their hypothesis by relating the centrality value of each primate with the number of emerging pathogens shared with humans. And, in effect, they have found that the most central primates were those that share more emerging pathogens with humans.

In conclusion, the study proposes a simple criterion to detect potential zoonotic agents of emerging disease transmission to humans: the centrality of these agents in their network interaction with their parasites. "The only information needed to construct these networks is the diversity and type of parasite infecting each host-and we already know about many zoonotic organisms. This is why we think that our approach will be useful in developing early warning plans for emerging disease in humans", Prof G-mez concludes.

Source: University of Granada

Scientists use mathematical tools to identify animal species that transmit diseases to humans

Researchers at ETH Zurich have developed a method of assigning classes of complex quantum states to geometric objects known as polytopes.
(Image: Amanda Eisenhut / ETH Zurich)

Andreas Trabesinger

«I think I can safely say that nobody understands quantum mechanics.» Thus spoke the American physicist Richard Feynman — underlining that even leading scientists struggle to develop an intuitive feeling for quantum mechanics. One reason for this is that quantum phenomena often have no counterpart in classical physics. A typical example is the quantum entanglement: Entangled particles seem to directly influence one another, no matter how widely separated they are. It looks as if the particles can «communicate» with one another across arbitrary distances. Albert Einstein, famously, called this seemingly paradoxical behaviour «spooky action at a distance».

When more than two particles are entangled, the mutual influence between them can come in different forms. These different manifestations of the entanglement phenomenon are not fully understood, and so far there exists no general method to systematically group entangled states into categories. Reporting in the journal «Science», a group of mathematicians and physicists around Matthias Christandl, professor at the Institute for Theoretical Physics, provides an important contribution towards putting the «spooky action» to order. The team has developed a method that allows them to assigning a given quantum state to a class of possible entanglement states. Such a method is important because, among other things, it helps to predict how potentially useful the quantum state can be in technological applications.

Putting entangled states in their place

Together with Brent Doran, a professor in the Department for Mathematics at ETH Zurich, and David Gross, a professor at the University of Freiburg in Germany, Christandl and his PhD student Michael Walter, first author of the «Science» publication, introduce a method in which different classes of entangled states are associated with geometric objects known as polytopes. These objects represent the «space» that is available to the states of a particular entanglement class. Whether or not a given state belongs to a specific polytope can be determined by making a number of measurements on the individual particles. Importantly, there is no need to measure several particles simultaneously, as is necessary in other methods. The possibility to characterise entangled states through measurements on individual particles makes the new approach efficient, and means also that it can be extended to systems with several particles.

The ability to gain information about entangled states of several particles is a central aspect of this work, explains Christandl: «For three particles, there are two fundamentally different types of entanglement, one of which is generally considered more useful than the other. For four particles, there is already an infinite number of ways to entangle the particles. And with every additional particle, the complexity of this situation gets even more complex. » This quickly growing degree of complexity explains why, despite a large number of works that have been written on entangled states, only very few systems with more than a handful of particles have been fully characterized. «Our method of entanglement polytopes helps to tame this complexity by classifying the states into finitely many families,» adds Michael Walter.

Quantum technologies on the horizon

Quantum systems with several particles are of interest because they could take an important role in future technologies. In recent years, scientists have proposed, and partly implemented, a wide variety of applications that use quantum-mechanical properties to do things that are outright impossible in the framework of classical physics. These applications range from the tap-proof transmission of messages, to efficient algorithms for solving computational problems, to techniques that improve the resolution of photolithographic methods. In these applications, entangled states are an essential resource, precisely because they embody a fundamental quantum-mechanical phenomenon with no counterpart in classical physics. When suitably used, these complex states can open up avenues to novel applications.

A perfect match

The link between quantum mechanical states and geometric shapes has something to offer not only to physicists, but also to mathematicians. According to Doran, the mathematical methods that have been developed for this project may be exploited in other areas of mathematics and physics, but also in theoretical computer science. «It usually makes pure mathematicians a bit uncomfortable if someone with an applied problem wants to hit it with fancy mathematical machinery, because the fit of theory to problem is rarely good, » says Doran. «Here it is perfect. The potential for long-term mutually beneficial feedback between pure mathematicians and quantum information theory and experiment is quite substantial.»

The method of entanglement polytopes, however, is more than just an elegant mathematical construct. The researchers have shown in their calculations that the technique should work reliably under realistic experimental conditions, signalling that the new method can be used directly in those systems in which the novel quantum technologies are to be implemented. And such practical applications might eventually help to gain a better understand of quantum mechanics.

Reference
Walter M, Doran B, Gross D, Christandl M: Entanglement Polytopes: Multi-Particle Entanglement from single-particle information. Science, 2013

Spooky action put to order

A sympathetic story for you this Saturday.

Andy has a problem. He can’t solve it on his own – he needs your help. This problem vexed Andy so much that he spent four years trying to solve it on his own, to no avail. It really is a very difficult problem. Finally in 1997, out of what must have been sheer desperation, Andy reached out to his fellow man: maybe some kindly type out there could find a solution to his problem, which he would gladly reward with a small consideration.

Can you help a soul in need?

His name is D. Andrew “Andy” Beal, billionaire. He owns a mansion and a yacht1. He’s a businessman from Dallas Texas, he’s worth 8.5 billion dollars, and he has previously spent that money on playing poker, almost launching rockets into space and avoiding prosecution for filing phony tax losses.

The news story is, “Andrew Beal, billionaire and mostly terrible person, will pay money to whoever solves this problem, which he thinks he thought of first but actually didn’t, all despite the complete lack of evidence, or even in spite of the abundance of evidence to the contrary, that mathematicians are motivated or even can be motivated by monetary reward.”

In 1997 an article written by Texas mathematician R. Daniel Mauldin was published in the Notices of the AMS, announcing both the problem and a prize of $5,000 for solving it, offered by Andrew Beal. The problem is this:

Let A, B, C, x, y and z be positive integers, with x,y,z>2.

If A^x+B^y=C^z, then A, B and C have a common prime factor.

If you don’t have a solution but the prospect of a million dollars has bought your attention, first of all what’s wrong with you, and secondly, an overview paper by Noam Elkies on ABC-type problems is a good place to start your investigations.

An unattributed website on the conjecture and prize, bealconjecture.com, is registered to “Beal Aerospace Technologies, Inc.”, a company which was going to do private satellite launches. bealconjecture.com contains a digression complaining about Granville et al’s comments re the attribution of the conjecture, and bealaerospace.com contains two letters whinging about NASA and that hard-working schmoes like Dennis Tito had to pay Russia to have a go on the ISS.

It isn’t unheard of for prizes to be offered to solve a mathematical conjecture – in the late 19th century the King of Sweden offered a prize for a solution to the n-body problem; there are the Clay Millennium prizes, offered by another American businessman and famously turned down by Perelman; and Erdos very often handed out small amounts of money for solutions to problems. What those all have in common is that the bounty offered didn’t increase, and what I object to with Beal is this idea he apparently has that he just needs to find the market price of a solution and it will appear.

Take it away, Pink Floyd!

Scrooge McDuck in Mathmagic land

Contact:
B. Rose Huber rhuber@pitt.edu 412-624-4356

PITTSBURGH—A 350-year-old mathematical mystery could lead toward a better understanding of medical conditions like epilepsy or even the behavior of predator-prey systems in the wild, University of Pittsburgh researchers report.

The mystery dates back to 1665, when Dutch mathematician, astronomer, and physicist Christiaan Huygens, inventor of the pendulum clock, first observed that two pendulum clocks mounted together could swing in opposite directions. The cause was tiny vibrations in the beam caused by both clocks, affecting their motions.

The effect, now referred to by scientists as “indirect coupling,” was not mathematically analyzed until nearly 350 years later, and deriving a formula that explains it remains a challenge to mathematicians still. Now, Pitt professors apply this principle to measure the interaction of “units”—such as neurons, for example—that turn “off” and “on” repeatedly. Their findings are highlighted in the latest issue of Physical Review Letters.

“We have developed a mathematical approach to better understanding the ‘ingredients’ in a system that affect synchrony in a number of medical and ecological conditions,” said Jonathan E. Rubin, coauthor of the study and professor in Pitt’s Department of Mathematics within the Kenneth P. Dietrich School of Arts and Sciences. “Researchers can use our ideas to generate predictions that can be tested through experiments.”

More specifically, the researchers believe the formula could lead toward a better understanding of conditions like epilepsy, in which neurons become overly active and fail to turn off, ultimately leading to seizures. Likewise, it could have applications in other areas of biology, such as understanding how bacteria use external cues to synchronize growth.

Together with G. Bard Ermentrout, University Professor of Computational Biology and professor in Pitt’s Department of Mathematics, and Jonathan J. Rubin, an undergraduate mathematics major, Jonathan E. Rubin examined these forms of indirect communication that are not typically included in most mathematical studies owing to their complicated elements. In addition to studying neurons, the Pitt researchers applied their methods to a model of artificial gene networks in bacteria, which are used by experimentalists to better understand how genes function.

“In the model we studied, the genes turn off and on rhythmically. While on, they lead to production of proteins and a substance called an autoinducer, which promotes the genes turning on,” said Jonathan E. Rubin. “Past research claimed that this rhythm would occur simultaneously in all the cells. But we show that, depending on the speed of communication, the cells will either go together or become completely out of synch with each another.”

To apply their formula to an epilepsy model, the team assumed that neurons oscillate, or turn off and on in a regular fashion. Ermentrout compares this to Southeast Asian fireflies that flash rhythmically, encouraging synchronization.

“For neurons, we have shown that the slow nature of these interactions encouraged ‘asynchrony,’ or firing at different parts of the cycle,” Ermentrout said. “In these seizure-like states, the slow dynamics that couple the neurons together are such that they encourage the neurons to fire all out of phase with each other.”

The Pitt researchers believe this approach may extend beyond medical applications into ecology—for example, a situation in which two independent animal groups in a common environment communicate indirectly. Jonathan E. Rubin illustrates the idea by using a predator-prey system, such as rabbits and foxes.

“With an increase in rabbits will come an increase in foxes, as they’ll have plenty of prey,” said Jonathan E. Rubin. “More rabbits will get eaten, but eventually the foxes won’t have enough to eat and will die off, allowing the rabbit numbers to surge again. Voila, it’s an oscillation. So, if we have a fox-rabbit oscillation and a wolf-sheep oscillation in the same field, the two oscillations could affect each other indirectly because now rabbits and sheep are both competing for the same grass to eat.”

The paper, “Analysis of synchronization in a slowly changing environment: how slow coupling becomes fast weak coupling,” was first published online May 13 in Physical Review Letters. This work was partially supported by a National Science Foundation grant.

Pendulum Swings Back on 350-Year-Old Mathematical Mystery

New, fast and accurate algorithm from the Institute of Physical Chemistry of the Polish Academy of Sciences in Warsaw, based on the mathematical formalism used to model processes accompanying interaction of light with gas planet atmospheres, is a major step towards better understanding of physical and chemical properties of materials’ surfaces studied under laboratory conditions.

The mathematical formalism describing the interaction of light with planetary atmospheres was developed in 1950 by Subramanyan Chandrasekhar, a famous Indian astrophysicist and mathematician. His two hundred pages long derivation involves a complicated function that more recently has been used, i.a., in studies on physical and chemical properties of material surfaces.

Calculation of very accurate values of Chandrasekhar function still presents a challenge. The researchers from the Institute of Physical Chemistry of the Polish Academy of Sciences (IPC PAS) in Warsaw managed to develop a method for calculating the function with the accuracy of up to over a dozen decimal digits. The new algorithm combines different numerical methods and is much faster than the existing approaches.

Light entering a gas planet atmosphere is scattered via different mechanisms (elastically and inelastically). In addition, light waves of certain wavelengths are selectively absorbed by elements and chemical compounds contained in the atmosphere. “Usually, we believe that the star light is simply reflected from a planet as from a mirror. It is not true. The planet’s atmosphere is a place where many phenomena related to radiation transfer take places”, says Prof. Aleksander Jablonski from the IPC PAS.

It turns out that physical models describing interaction of light with the gas giant atmosphere can also be used to describe emission of electrons following irradiation of material samples with x-ray beam. Photoelectrons of specific energy, leaving the surface of the sample, are emitted from a few atomic layers only. The electrons emitted at larger depths loose their energies due to interactions with atoms of a solid. Analysis of photoelectron energies and intensities allows for assessing the properties of tested material.

“Using surface sensitive spectroscopic methods we are able to determine properties of the most external layers of materials, as well as their chemical composition or condition. This knowledge is of crucial importance in materials engineering, microelectronics, various nanotechnologies, and in so important processes as catalysis or ubiquitous corrosion”, explains Prof. Jablonski.

For years Prof. Jablonski has been developing databases for the US National Institute of Standards and Technology (NIST). These databases contain certain parameters required in calculations needed for applications of electron spectroscopies to analyse properties of surfaces.

One of such databases was entirely developed using the mathematical formalism close to that originally proposed by Chandrasekhar for the description of astronomical phenomena.

The calculations needed for processing of results of spectroscopic studies require multiple determinations of Chandrasekhar function values with the highest possible accuracy.

Though the Chandrasekhar function describes a relatively simple physical phenomenon, it is a complicated mathematical expression. There are many methods for determining Chandrasekhar function values with a reasonably good accuracy, close to 1-2%. Some applications related to electron transport in superficial layers of materials require, however, that Chandrasekhar function is determined with a precision of more than 10 decimal digits.

“In recent years, I have been able to develop an algorithm that allows for obtaining such a high accuracy, and is up to a few dozen times faster in operation when compared with the existing algorithms”, says Prof. Jablonski. The increase in speed of algorithm operation is as important as the increase in accuracy. This is due to the fact that in programs for modelling electron transport on surfaces of materials the Chandrasekhar function must be computed thousands, and even tens of thousands times.

The program code with implemented new algorithm for calculating Chandrasekhar function values was published in the “Computer Physics Communications” journal.

It is to be noted that Chandrasekhar function plays an important role not only in astronomy and physical chemistry of surfaces. The function has also found application in the nuclear power industry where it is used, i.a., for analysing electron scattering in nuclear reactor shields.

The Institute of Physical Chemistry of the Polish Academy of Sciences (http://www.ichf.edu.pl/) was established in 1955 as one of the first chemical institutes of the PAS. The Institute's scientific profile is strongly related to the newest global trends in the development of physical chemistry and chemical physics. Scientific research is conducted in nine scientific departments. CHEMIPAN R&D Laboratories, operating as part of the Institute, implement, produce and commercialise specialist chemicals to be used, in particular, in agriculture and pharmaceutical industry. The Institute publishes approximately 200 original research papers annually

titolo

John Elder

Imagine buses turning up every five minutes, and schedules that could deliver passengers to just about anywhere across the city. Impossible? Laughably expensive?

Professor Mark Wallace from the Monash University's Faculty of Information Technology says it's a goer. Mathematics, not massive infrastructure spending, is the key.

"You'd need twice as many buses, not 10 times as most people might imagine," he says.

Some of the initiatives to make it work include adaptive scheduling (where the local schedule is flexible, and responds to direct consumer demand); more bus lanes; and, a system where local bus networks talk to one another and have coordinated changeover stations, so you have more efficient use of the limited bus numbers, which works against traffic congestion.

Some of these strategies are already being trialled in other parts of the world – and adaptive scheduling is already working in some parts of Melbourne.

The bus strategies are the brainchild of Beyond Zero Emissions, a not-for-profit research and education organisation. There are other research organisations around the world working on new ideas to solve ever-worsening traffic conditions.

On Tuesday evening, Professor Wallace will be talking about some of these possibilities at a public lecture "Cheap solutions to the transport problem". He says the term "rush hour" is out-of-date, given that morning traffic congestion in Melbourne lasts from 6.30 until 9.30. The annual cost of congestion to Victoria, he says, is estimated to rise from $3 billion to $6 billion by 2020."

He says an estimated 20,000 trucks move through Melbourne's inner west each day – but most of the freight-carrying is done by vans. He says researchers at Monash and in Tokyo are proposing the introduction of transfer points, where vans from rival companies meet, swap and carry each other's goods across the city.

Professor Wallace says the transfer points would ensure the vans are used more efficiently. "Simulations indicate an immediate 25 per cent reduction in the number of vans on the road," he says. "Of course it requires some trust between carriers."

One of the more exciting and freaky ideas involves automated vehicle control, where convoys of cars travel close together at speed, the vehicles communicating with one another and coordinating breaking and turning. "So the drivers aren't touching the steering wheel," says Professor Wallace. "We have automatic braking and parking systems . . . and an automatic vehicle has gone from Italy to Siberia under its own control."

That was in 2010, and the technology has advanced since then.

"A lot of testing shows automatic systems are safer than manual control," says Professor Wallace. "The one bug risk is you get viruses in the computers. If anybody wants to screw things up, you're in trouble."

Professor Wallace says making better use of existing roads is vastly more cost efficient than building new freeways.

"While the east-west link project – an 18-kilometre inner-urban road connecting the Eastern Freeway and the Western Ring Road – would help reduce traffic, it will cost $13 billion to complete,

with $15 million already spent on writing the business case.”

Mathematical solutions will costs million, not billions he says.

"Cheap solutions to the transport problem" will be held from 5:30-7pm on Tuesday, June 18 in Theatre S3, Building 25, at Monash University's Clayton campus

This year I’ve been co-writing “Mathematics, Live,” an interview series for the Association for in Mathematics newsletter. In my interviews I’m “listening in” on conversations between pairs of female mathematicians. The first interview appeared in the May/June issue of the newsletter (password required). In it, I talked with mathematicians Laura DeMarco of the University of Illinois at Chicago and Amie Wilkinson of the University of Chicago.

Both do research in the field of dynamical systems, the study of how abstract mathematical spaces evolve over time. I got the idea to talk with them when I was at DeMarco’s invited address at the Joint Math Meetings in January. (If you’re interested, Jordan Ellenberg wrote nice post about her talk.) Wilkinson asked a question at the end of the talk, and I realized they would make a great pair for this interview series.

I met with DeMarco and Wilkinson in March, and we talked about how they got interested in math, the importance of female role models for young women in math, and their advice for aspiring mathematicians. This is a slightly abridged version of the interview that appeared in the AWM newsletter. Thank you to DeMarco and Wilkinson for their generosity with their time and advice.

Origins

Evelyn Lamb: Would you like to start by talking about how you got into math?

Amie Wilkinson: I got into math in early infancy. I always liked math.

Laura DeMarco: Early infancy?

AW: I’m exaggerating, but I always liked math.

LD: Did you do stuff outside of school, or was it just in class?

AW: I went to a Montessori kindergarten. I think that’s the first time I actually saw math. What was great about Montessori was that everything was free-form, so you could just spend all your time at one station, all day long. I spent all my time at the math stations, basically. I would just do them all day. Counting base 5 and stuff like that. I think that’s when it was clear that I was passionate about math. You were a physicist, right?

LD: Yes, but not “for real.” In my case, I would say that I definitely always liked math. I always liked class, I always liked learning it and doing it. But my brother, who’s older than me, was always better than me at puzzles and things like that. He was the one who would go into the contests. He was doing MathCounts and whatever the other contests were, and he was really into them. I wasn’t interested in doing the competitions. I sort of found my own path and practiced my flute and did my own thing, but I probably came back to it later than you did.

The first time I thought to myself, “I like math enough to want to do it forever,” was some point in high school, when I thought, “I want to be a math teacher.” The funny thing is, I remember very vividly sitting on the school bus to go home from high school that day and thinking, “I could be a math teacher. I could just do math forever,” thinking that that’s what math means, right, to be a math teacher. I had no idea that there was anything beyond being a teacher.

It was in my second year in college when I learned that professors do research. I had no idea what it meant to do research. I was taking a seminar in social sciences. Each week we went through a different kind of theory with various examples. One day, the professor, who was from the law school, said to us, this group of second-year students, “are you aware that all of your professors are doing research?” And I don’t even know what that means. What does it mean for my math professors to be doing research?

The next day, I went and asked all of my math professors, “What do you do?” I was taking probability at the time, and I went to my probability professor. “I heard you do research. What do you do?” Imagine what it’s like when a student comes and asks you this question. I remember that it was this very awkward conversation. And he said something, and of course I don’t remember what he said, and I’m sure I didn’t understand it anyway. But the moment was very memorable.

At the same time, I was a physics major. I had loved physics classes in high school, and I thought, maybe I’ll just do physics. I knew that scientists do research. That’s obvious, somehow. So learning that mathematicians do research too was eye-opening.

AW: That’s a great story. I have this picture of you walking into the first professor’s office, like: “I’ve heard that you guys do this research thing. That’s not for real, is it?”

EL: Were there any pivotal moments where you knew that you wanted to be a mathematician, beyond learning that math research exists?

AW: My pivotal moment was pretty clear. I went to college, and I was feeling very insecure about my abilities in mathematics, and I hadn’t gotten a lot of encouragement, and I wasn’t really sure this was what I wanted to do, so I didn’t apply to grad school. I came back home to Chicago, and I got a job as an actuary. I enjoyed my work, but I started to feel like there was a hole in my existence. There was something missing. I realized that suddenly my universe had become finite. Anything I had to learn for this job, I could learn eventually. I could easily see the limits of this job, and I realized that with math there were so many things I could imagine that I would never know. That’s why I wanted to go back and do math. I love that feeling of this infinite horizon.

To me, that was a pivotal moment, actually just being away from it. In general, being away from math from time to time has definitely been rejuvenating. Like when I had my kids, and just wasn’t able to do math for a while. Then I would miss it. Then I’d understand why I’m doing it.

LD: You’d get extra excited about it, and really passionate about it.

AW: Yes. And grateful.

LD: I have these moments where I’m kind of overwhelmed by, “Wow, I really like what I’m doing, and isn’t it amazing that I have this job and can live like this!” Of course, I have teaching and other duties, but just the idea that we can be supported, that there is an environment for this. I think that way when it’s going well. When it’s not going well, I think, “What have I gotten myself into?!”

I didn’t know your story, that you had a job the first year after college. I did have some sort of moment that convinced me to go to graduate school. In my last year of undergraduate, my physics professors were very encouraging. There was something about the culture in the physics department that was simply encouraging. Any of their undergraduate students who were doing well were automatically involved in research projects. So I knew most of the faculty members, and it was somehow a natural thing to apply to graduate schools.

The math department didn’t feel like that. But finally in my very last year, we got our first woman professor in the department. She arrived in my very last year, and that semester I had decided to ask her to be my advisor for my undergraduate thesis project. Just having her around made a big difference to me.

Then it was that fall semester of my last year of undergraduate that the TA of one of my classes said, “Oh, where are you applying for graduate school, Laura?” I said, “I’m not applying to graduate school. I actually have an interview tomorrow for a job.” He said, “What? You’re not applying to graduate school?” He was super encouraging. All of a sudden there was this one graduate student who seemed to care and said, “This is crazy! Why aren’t you applying to graduate school?”

AW: It was serendipity.

LD: It was sort of just by chance that one person had thought through the idea of actually asking me.

AW: Or not thought through it.

LD: That’s right, who had simply asked! My physics advisor had certainly talked about this idea. But I just wasn’t passionate about physics by the end.

Calculus

EL: Are there any math topics that are particularly appealing or beautiful for you?

AW: I like calculus a lot, probably because I learned it when I was young, and I learned it well. To me, it’s always comforting to use calculus to do something. The invention of calculus was certainly revolutionary.

LD: A conceptual breakthrough.

AW: It’s funny, because it’s like we just toss it out there to high school students, and I think a lot of them have no idea of the beauty.

LD: What the ideas really were.

AW: Certainly some of the most beautiful mathematics I’ve learned is just calculus.

LD: It’s funny you mention calculus. I don’t think I really appreciated it until I taught it as a graduate student. I was lecturing to these first-year students. I was just wowed by this subject. I had this moment of, holy cow, this is really beautiful! I remember my grandmother asking me what I was thinking about these days. I said, “Well, I’m teaching calculus right now, and you know what, calculus is really beautiful.” She said, “OK, Laura, what is calculus? Can you just tell me in 20 minutes, what is calculus?” And it was just the greatest thing to have this opportunity to just sit down with my grandmother, of all people, and tell her.

AW: The proverbial grandmother.

LD: That’s right. It’s funny because she says that she liked math when she was young, but it wasn’t something in that era that she could have pursued. She certainly never pursued anything beyond some basic courses. But she sat through and listened to my explanation.

AW: Do you think she got it?

LD: I don’t know. I was speaking more about the philosophy. I wasn’t doing any computations. But the idea of differentiation and then integration, and the fundamental theorem of calculus, how it’s connected. I don’t know if she got it or not. But it was a good conversation.

Women in mathematics

EL: Have you faced any challenges as women in math?

LD: Now I would say it’s an advantage. Once we’re at the stage that we’re at, it’s probably more of an advantage than a disadvantage. People want women speakers and women getting involved at different levels, and a certain amount of women at the top levels. Earlier on, it’s a different story.

AW: I would agree. As long as you’re able to say no, it’s an advantage. I think you’re asked to do more. It’s hard to say no to things that involve young people or women. As you get older, you feel a real responsibility to help the younger people. That’s the only disadvantage. I feel like I get asked to do a lot more.

LW: Yes, definitely.

AW: It’s hard for me to say no to a lot of it because it’s worthwhile. But when I was younger, Laura’s story about having the woman math professor really resonates with me because when I was in college there were no women at all at Harvard. No research faculty, zero.

LD: Not even postdocs?

AW: Not even postdocs. And so I think I craved a role model at that point. I think that if one had shown up it would have made a huge difference.

And having kids for me was difficult. It was scary. Partially because I didn’t really have that many people to look up to, to say it’s doable. Even when Beatrice was born, which was only 13 years ago, it wasn’t quite the norm, it wasn’t quite supported. That is another thing that I think is much harder for women. Hugely harder for some women. I was just lucky, for a lot of reasons, that it worked out OK.

In general, the stereotype threat business kind of held true for me. I think there was a little nagging voice that said, well, do you really think you belong here, when I was younger. When your confidence level is low.

LD: Yes, when you’re not so confident. I wasn’t so confident.

AW: No one’s really confident at that point.

LD: That’s right, nobody is. And people react very differently. But I wasn’t the kind of person to react by speaking louder, or by making myself seen. In fact, what I tended to do was try to play down my femininity in many different ways. I dressed like the boys, and I really went out of my way to be less feminine. Now I feel totally comfortable just being who I am. Certainly then I would make an effort not to stand out in some way. I wasn’t so confident, and being the only girl in my classes didn’t help.

AW: I got certainly some inappropriate off-color comments from people. Those kinds of comments, they were a bit alienating, but I don’t think I found any of those kinds of comments particularly discouraging. It was more the general level of apathy that was hard.

LD: Yes, that is something that probably played a role. Personality-wise, I probably needed encouragement. I would have liked to have gotten some explicit encouragement. If I’m doing well, I want to know!

I remember when I finally decided to apply to graduate schools, I had a very close girlfriend who said, “Well, you should certainly apply to Harvard and Princeton, and all the top schools.” I said, “Oh no, I’ll never get in.” So I didn’t even bother applying. But I did apply to Berkeley, and I got into Berkeley, and I went to Berkeley. And of course in the end I ended up transferring to Harvard, and I ended up with a degree from Harvard, so somehow it ended up happening anyways. And this friend, she’s not a mathematician, so I thought she had no idea what she was talking about, but in the end she was right.

AW: It’s so funny that it seemed obvious to her. An ordinary person would think, “Well, of course. You’re a top student. You should apply to the top schools.” In the math world there’s this huge mystique around these top places, and someone who lacks even just a little bit of confidence, it’s like “no, of course I’m not going to apply to a place like that.” I wonder how many women are kept out of the top places by that kind of attitude.

LD: And not realizing that you should actually go for something.

So you want to be a mathematician…

EL: Do you have advice for young people who might be thinking about doing math? LD: If you love it, go for it. It is helpful to have some people to talk to. It helps to have an advisor of some sort or a research project to connect you, to learn how to communicate with people.

AW: I’m glad I did math team in high school.

LD: So you did math team?

AW: I did do math team. In junior high school, I was really good at math. I was clearly kind of a math kid, but a bunch of other kids were doing all these gifted programs and taking all these tests, and I was too scared to do that kind of thing, and I probably wouldn’t have done very well. When I got to high school, I don’t know what pushed me to go check it out, but I did. Doing the math team at my high school was really formative. It gave me a community of other math geeks.

LD: Kids that really enjoyed it. At least now these math circles are starting to pop up around various places.

AW: Yes, the math circles are even cooler because it’s not competition. Although, these math competitions get a bad rap. It wasn’t just sitting in a room and filling out these tests. There were oral contests. I remember I presented something on curves of constant width. You’d be given a topic, and you’d read up ahead of time. They’d ask you questions, and you could prepare an answer. Then you’d stand up at the board and present the answer. Girls, even then, happened to do very well. There was this girl named Nadia in our school, this extremely tall Russian volleyball player. She didn’t do anything else in math team, but she was tops at the oral part of this contest.

Then there was this two-person event, and my high school rival and I were the two-person team. There were all sorts of different things. Different talents could take part, and I’m sure there are things like this now.

That’s a piece of advice, to explore. You don’t have to be the very best to get something out of it. And another piece of advice, for young people, is that there really are second chances, and things can change. As an undergraduate, I kind of had a very mixed academic record. I did lots of things I loved that weren’t necessarily math. I did well in a few math classes, and I did badly in a few math classes. So I was lucky to get into Berkeley. But I found graduate school to be an utterly different experience from college. Suddenly there were no distractions, it was all I was doing.

LD: And you were enjoying it.

AW: I was enjoying it, and I felt at the top of my game. It’s worth a shot. That’s not the time to be scared to give it a try. If it doesn’t work out, it’s a year of your life. Big deal, whatever. I just think more people should try.

Mathematics, Live: A Conversation with Laura DeMarco and Amie Wilkinson

The agency is particularly interesting because it maintains a stable of mathematicians to solve any problems that come up in the course of sleuthing.

In fact, the whole point of the NSA originally was mathematical cryptography following the re-organization of the cryptanalysis divisions of the army and navy after World War Two.

While the exact number of mathematicians the NSA employs is classified, the agency acknowledges that they're the nation's leading employer of mathematicians.

From an NSA job listing explaining the demands of the position:

As an NSA Mathematician, you may find yourself designing and analyzing complex algorithms, or expressing difficult cryptographic problems in mathematical terms, and then applying both your art and science to find a solution ... or demonstrating that a solution cannot be found, given certain computational limitations and reasonable time limits.

The agency is a heavy recruiter from math departments around the country, so we do have some details from applicants and employees about hwo the process goes.

The NSA has maintained a long relationship with the math community, and a 2006 article in Math Horizons by NSA mathematician Michelle Wagner laid out the on-the-record details of the laborious application process:

Applicants should submit their application six to nine months in advance of their potential start date.
They must be U.S. citizens who are able to obtain a security clearance and can pass random drug tests
The first hurdle is a phone screening and a long form background.
Provided you've made it this far, the Mathematics Hiring Authority will interview you at the NSA.
Next, you've got security and mathematics screening. From the article:
In preparation for being put through the paces of security day, I sometimes recommend that applicants watch the movie Meet the Parents. You know, theone where Ben Stiller gets polygraphed by his soon-to-be father-in-law Robert DeNiro. (Enough said.)

Next you've got to take a Mathematics proficiency test
You must pass through a set of crucial interviews with NSA mathematicians
You have an opportunity to give a talk on a topic of your choosing, essentially mandatory for people with Ph. D.s
So, that's what it takes to get a math gig at the NSA.

In fairness, the amenities are legendary — flexible work schedule, casual dress all the time, great government benefits and awesome salaries — provided you can get through the nutty screening.

Some reports of the process include one applicant claiming the NSA said they would "have to stop dating my Czech boyfriend and that I’d need to submit information about all my roommates for the past 10 years, which was uber creepy."

NSA — The Largest Employer Of Mathematicians In The USA