Arresting Model Stops Cars

Sep. 5, 2013 — Researchers in China have
developed a mathematical model that could
help engineers design a flexible vehicle-arrest
system for stopping cars involved in criminal
activity or terrorism, such as suspect car
bombers attempting break through a check
point, without wrecking the car or killing the
occupants.

Writing in a forthcoming issue of the
International Journal of Vehicle Design, Pak Kin
Wong and colleagues in the Department of
Electromechanical Engineering at the
University of Macau, in Taipa, Macao, explain
how common vehicle-arrest systems used by
law enforcement, the military and in anti-
terrorism activities, usually cause serious
damage to the vehicle and maim or kill the
occupants. A more positive system for bringing
a car chase to a halt or stopping a car-bomber
in their tracks is needed if perpetrators,
witnesses and evidence are to be protected.

A flexible system would increase the stopping
distance of a vehicle involved in criminal or
terrorist activity and allow its kinetic energy to
be dissipated without the complete destruction
of the vehicle as otherwise occurs with solid,
immovable barriers and equipment currently
used. The team's mathematical model of
vehicle arrest with different flexible materials
and designs bears up to theoretical and
experimental scrutiny and offers engineers a
new set of variables to embed in their design
program in the development of new, effect
vehicle arrest systems. Moreover, the system
could allow the design of an "intelligent"
vehicle-arrest system for roadblocks and
checkpoints that could respond differently
depending on vehicle speed and type and allow
for greater control in bringing a vehicle to a
stop

Story Source:

The above story is based on materials provided
by Inderscience Publishers , via EurekAlert!, a
service of AAAS.
And ( science daily magazine ) .

Note: Materials may be edited for content and
length. For further information, please contact
the source cited above.

Journal Reference:

1. Pak Kin Wong et al. Modelling and testing of
arresting process in flexible vehicle
arresting systems. Int. J. Vehicle Design ,
2013, 64, 1-25

Generosity Leads to Evolutionary Success, Biologists Show

Sep. 2, 2013 — With new insights into the
classical game theory match-up known as the
"Prisoner's Dilemma," University of
Pennsylvania biologists offer a mathematically
based explanation for why cooperation and
generosity have evolved in nature.
Their work builds upon the seminal findings of
economist John Nash, who advanced the field
of game theory in the 1950s, as well as those
of computational biologist William Press and
physicist-mathematician Freeman Dyson, who
last year identified a new class of strategies for
succeeding in the Prisoner's Dilemma.
Postdoctoral researcher Alexander J. Stewart
and associate professor Joshua B. Plotkin, both
of Penn's Department of Biology in the School
of Arts and Sciences, examined the outcome of
the Prisoner's Dilemma as played repeatedly by
a large, evolving population of players. While
other researchers have previously suggested
that cooperative strategies can be successful in
such a scenario, Stewart and Plotkin offer
mathematical proof that the only strategies
that succeed in the long term are generous
ones. They report their findings in the
Proceedings of the National Academy of
Sciences the week of Sept. 2.
"Ever since Darwin," Plotkin said, "biologists
have been puzzled about why there is so much
apparent cooperation, and even flat-out
generosity and altruism, in nature. The
literature on game theory has worked to
explain why generosity arises. Our paper
provides such an explanation for why we see
so much generosity in front of us."
The Prisoner's Dilemma is a way of studying
how individuals choose whether or not to
cooperate. In the game, if both players
cooperate, they both receive a payoff. If one
cooperates and the other does not, the
cooperating player receives the smallest
possible payoff, and the defecting player the
largest. If both players do not cooperate, they
receive a payoff, but it is less than what they
would gain if both had cooperated. In other
words, it pays to cooperate, but it can pay
even more to be selfish.
In the Iterated Prisoner's Dilemma, two players
repeatedly face off against one another and can
employ different strategies to beat their
opponent. In 2012, Press and Dyson "shocked
the world of game theory," Plotkin said, by
identifying a group of strategies for playing
this version of the game. They called this class
of approaches "zero determinant" strategies
because the score of one player is related
linearly to the other. What's more, they
focused on a subset of zero determinant
approaches they deemed to be extortion
strategies. If a player employed an extortion
strategy against an unwitting opponent, that
player could force the opponent into receiving
a lower score or payoff.
Stewart and Plotkin became intrigued with this
finding, and last year wrote a commentary in
PNAS about the Press and Dyson work. They
began to explore a different approach to the
Prisoner's Dilemma. Instead of a head-to-head
competition, they envisioned a population of
players matching up against one another, as
might occur in a human or animal society in
nature. The most successful players would get
to "reproduce" more, passing on their
strategies to the next generation of players.
It quickly became clear to the Penn biologists
that extortion strategies wouldn't do well if
played within a large, evolving population
because an extortion strategy doesn't succeed
if played against itself.
"The fact that there are extortion strategies
immediately suggests that, at the other end of
the scale, there might also be generous
strategies," Stewart said. "You might think
being generous would be a stupid thing to do,
and it is if there are only two players in the
game, but, if there are many players and they
all play generously, they all benefit from each
other's generosity."

In generous strategies, which are essentially
the opposite of extortion strategies, players
tend to cooperate with their opponents, but, if
they don't, they suffer more than their
opponents do over the long term.
"Forgiveness" is also a feature of these
strategies. A player who encounters a defector
may punish the defector a bit but after a time
may cooperate with the defector again.
Stewart noticed the first of these generous
approaches among the zero determinant
strategies that Press and Dyson had defined.

After simulating how some generous strategies
would fare in an evolving population, he and
Plotkin crafted a mathematical proof showing
that, not only can generous strategies succeed
in the evolutionary version of the Prisoner's
Dilemma, in fact these are the only approaches
that resist defectors over the long term.
"Our paper shows that no selfish strategies will
succeed in evolution," Plotkin said. "The only
strategies that are evolutionarily robust are
generous ones."
The discovery, while abstract, helps explain the
presence of generosity in nature, an inclination
that can sometimes seem counter to the
Darwinian notion of survival of the fittest.

"When people act generously they feel it is
almost instinctual, and indeed a large
literature in evolutionary psychology shows
that people derive happiness from being
generous," Plotkin said. "It's not just in
humans. Of course social insects behave this
way, but even bacteria and viruses share gene
products and behave in ways that can't be
described as anything but generous."
"We find that in evolution, a population that
encourages cooperation does well," Stewart
said. "To maintain cooperation over the long
term, it is best to be generous."

Story Source:

The above story is based on materials provided
by University of Pennsylvania , via
EurekAlert!, a service of AAAS.

How Vegetation Competes for Rainfall in Dry Regions

Aug. 30, 2013 — The greater the plant density
in a given area, the greater the amount of
rainwater that seeps into the ground. This is
due to a higher presence of dense roots and
organic matter in the soil. Since water is a
limited resource in many dry ecosystems, such
as semi-arid environments and semi-deserts,
there is a benefit to vegetation to adapt by
forming closer networks with little space
between plants.

Hence, vegetation in semi-arid environments
(or regions with low rainfall) self-organizes into
patterns or "bands." The pattern formation
occurs where stripes of vegetation run parallel
to the contours of a hill, and are interlaid with
stripes of bare ground. Banded vegetation is
common where there is low rainfall. In a paper
published last month in the SIAM Journal on
Applied Mathematics, author Jonathan A.
Sherratt uses a mathematical model to
determine the levels of precipitation within
which such pattern formation occurs.

"Vegetation patterns are a common feature in
semi-arid environments, occurring in Africa,
Australia and North America," explains
Sherratt. "Field studies of these ecosystems are
extremely difficult because of their remoteness
and physical harshness; moreover there are no
laboratory replicates. Therefore mathematical
modeling has the potential to be an extremely
valuable tool, enabling prediction of how
pattern vegetation will respond to changes in
external conditions."
Several mathematical models have attempted
to address banded vegetation in semi-arid
environments, of which the oldest and most
established is a system of partial differential
equations, called the Klausmeier model.
The Klausmeier model is based on a water
redistribution hypothesis, which assumes that
rain falling on bare ground infiltrates only
slightly; most of it runs downhill in the
direction of the next vegetation band. It is
here that rain water seeps into the soil and
promotes growth of new foliage. This implies
that moisture levels are higher on the uphill
edge of the bands. Hence, as plants compete
for water, bands move uphill with each
generation. This uphill migration of bands
occurs as new vegetation grows upslope of the
bands and old vegetation dies on the
downslope edge.

In this paper, the author uses the Klausmeier
model, which is a system of reaction-diffusion-
advection equations, to determine the critical
rainfall level needed for pattern formation
based on a variety of ecological parameters,
such as rainfall, evaporation, plant uptake,
downhill flow, and plant loss. He also
investigates the uphill migration speeds of the
bands. "My research focuses on the way in
which patterns change as annual rainfall varies.
In particular, I predict an abrupt shift in
pattern formation as rainfall is decreased,
which dramatically affects ecosystems," says
Sherratt. "The mathematical analysis enables
me to derive a formula for the minimum level
of annual rainfall for which banded vegetation
is viable; below this, there is a transition to
complete desert."

The model has value in making resource
decisions and addressing environmental
concerns. "Since many semi-arid regions with
banded vegetation are used for grazing and/or
timber, this prediction has significant
implications for land management," Sherratt
says. "Another issue for which mathematical
modeling can be of value is the resilience of
patterned vegetation to environmental change.

This type of conclusion raises the possibility of
using mathematical models as an early warning
system that catastrophic changes in the
ecosystem are imminent, enabling appropriate
action (such as reduced grazing)."
The simplicity of the model allows the author
to make detailed predictions, but more
realistic models are required to further this
work. "All mathematical models are a
compromise between the complexity needed to
adequately reflect real-world phenomena, and
the simplicity that enables the application of
mathematical methods.

My paper concerns a
relatively simple model for vegetation
patterning, and I have been able to exploit this
simplicity to obtain detailed mathematical
predictions," explains Sherratt. "A number of
other researchers have proposed more realistic
(and more complex) models, and
corresponding study of these models is an
important area for future work. The
mathematical challenges are considerable, but
the rewards would be great, with the potential
to predict things such as critical levels of
annual rainfall with a high degree of
quantitative accuracy."

Story Source:

The above story is based on materials provided
by Society for Industrial and Applied
Mathematics.
And ( sciencedaily magzine  ).

Journal Reference:

1. Jonathan A. Sherratt. Pattern Solutions of the
Klausmeier Model for Banded Vegetation in
Semiarid Environments V: The Transition
from Patterns to Desert. SIAM Journal on
Applied Mathematics, 2013; 73 (4): 1347 DOI:
10.1137/120899510

Maths cartoons

See maths cartoons photos.

Do Girls Really Experience More Math Anxiety?

Aug. 27, 2013 — Girls report more math
anxiety on general survey measures but are
not actually more anxious during math classes
and exams, according to new research
forthcoming in Psychological Science , a journal
of the Association for Psychological Science.

Existing research suggests that females are
more anxious when it comes to mathematics
than their male peers, despite similar levels of
achievement. But education researchers
Thomas Götz and Madeleine Bieg of the
University of Konstanz and the Thurgau
University of Teacher Education and colleagues
identified a critical limitation of previous
studies examining math anxiety: They asked
students to describe more generalized
perceptions of mathematics anxiety, rather
than assessing anxiety during actual math
classes and exams.

To address this limitation, the researchers
conducted two studies in which they collected
data from approximately 700 students from
grades 5 to 11. In the first study, they
compared students' responses on two different
measures: A questionnaire measuring anxiety
about math tests, and their real-time self-
reports of anxiety directly before and during a
math exam. In the second study, they
compared questionnaire measures of math
anxiety with repeated real-time assessments
obtained during math classes via mobile
devices.

Findings from the two studies replicated prior
research and existing gender stereotypes,
showing that girls reported more math anxiety
than boys on generalized assessments, despite
similar math achievement.
However, the data obtained during math exams
and classes revealed that girls did not
experience more anxiety than boys in real-life
settings.
The data further suggest that lower self-
reported competence in mathematics may
underlie the discrepancy between the levels of
anxiety reported by girls in the two settings.

The researchers note that general
questionnaires may allow inaccurate beliefs
about math ability to negatively bias girls'
assessments of their math abilities and
exacerbate their math anxiety.
According to Götz, Bieg, and colleagues, these
results suggest that stereotyped beliefs
regarding math ability, rather than actual
ability or anxiety differences, may be largely
responsible for women not choosing to pursue
careers in math-intensive domains.
Co-authors include Oliver Ludtke of Humboldt
University Berlin (Germany), Reinhard Pekrun
of the University of Munich (Germany), and
Nathan C. Hall of McGill University (Canada).
This research was supported by grants from
the German Research Foundation to the fourth
author (Project for the Analysis of Learning
and Achievement in Mathematics Grants PE
320/11-1, PE 320/11-2, PE 320/11-3, and PE
320/11-4).

Story Source:

The above story is based on materials provided
by Association for Psychological Science .
And ( sciencedaily magazine ).

Matroid Theory: Mathematician Solves 40-Year-Old Problem

Aug. 28, 2013 — A team of mathematicians
has solved a problem first posed more than 40
years ago that has confounded modern
mathematicians, until now.
Professor Jim Geelen of the University of
Waterloo and his colleagues, Professor Bert
Gerards of Centrum Wiskunde & Informatica
and the University of Maastricht in the
Netherlands, and Professor Geoff Whittle of
Victoria University of Wellington in New
Zealand have proved the famous Rota's
Conjecture.

The three men worked for almost 15 years to
solve this problem posed by the famous
mathematician and philosopher Gian-Carlo
Rota in 1970. Earlier this year, in Waterloo,
the trio completed the final step in their epic
project.
Rota's Conjecture relates to a specialized area
of mathematics known as matroid theory, a
modern form of geometry, which was
pioneered by the mathematician Bill Tutte.
The theory investigates the embedding of
abstract geometric structures, or matroids,
into concrete geometric frameworks - namely,
projective geometries over a given finite field.

The conjecture is that, for each finite field,
there is a finite set of obstructions preventing
such a realization. The conjecture was posed by
Rota at the International Congress of
Mathematics in 1970, serendipitously, one
week before Geelen was born.
"For me the most rewarding part of the
research project has been the collaboration
with Bert and Geoff. We work together about
three times a year typically for periods of
three weeks either here in Waterloo or in New
Zealand or the Netherlands," said Professor
Geelen. "Those visits are intense; we sit in a
room together, all day every day, in front of a
whiteboard. The discussion can be very lively
at times, while at other times, when we are
stuck, we might sit there for two hours without
saying a word; each just thinking about ways
to overcome the particular obstacle."
In 1999, Geelen, Gerards and Whittle joined
forces to work on Rota's Conjecture as well as
generalizing the famous Graph Minor Theory
developed by Robertson and Seymour to
matroids.

Last year they completed their Matroid Minor
Theory which gives deep insights into the
structure of matroids. The proof of Rota's
Conjecture relies on the full power of that
theory and, in addition, required
groundbreaking new results on matroid
connectivity.

According to the trio, the real hard work only
just began when early this year they started
writing up the results of their work. The Graph
Minors Theory itself filled more than 600
journal pages and the Matroid Minors Theory
is set to be at least as long. The team expects
that it will take them at least three years to
complete the writing.
Jim Geelen is a Professor in the Department of
Combinatorics and Optimization at the
University of Waterloo and holds a Canada
Research Chair.

Story Source:

The above story is based on materials provided
by University of Waterloo .

And ( science daily magazine ).

New Energy Model Offers Transparency to Let Others Replicate Findings

Aug. 27, 2013 — Computer models are used to
inform policy decisions about energy, but
existing models are generally "black boxes"
that don't show how they work, making it
impossible for anyone to replicate their
findings. Researchers from North Carolina
State University have developed a new open-
source model and are sharing the data they
put into it, to allow anyone to check their
work -- an important advance given the
environmental and economic impact of energy
policy decisions.

"Most models show you the math behind how
they work, but don't share the source code
that is supposed to implement that math -- so
you can't tell how faithful the model is to the
mathematics," says Dr. Joseph DeCarolis, an
assistant professor of civil, construction and
environmental engineering at NC State and co-
author of a paper on the new model. "And the
people utilizing existing models often don't
share the data they use. So, in effect, you can't
check their work.

"That's a problem, because the results of those
models are informing policy decisions with
billions of dollars on the line."
The new open-source model, called Temoa, is
an energy economy optimization (EEO) model.
EEO models are computer models that inform
policy and industry decisions by offering
insights into how energy costs and production
are likely to change over time.

For example,

EEO models could be used to identify strategies
that would drive down energy costs and
reduce greenhouse gas emissions over the next
10, 20 or 30 years.
DeCarolis's team designed Temoa to be flexible,
allowing users to look at any timeframe and on
any scale, from a global model to a model of a
single city. They also designed Temoa to be
more rigorous than existing models when it
comes to addressing uncertainty. Specifically,
they plan to combine multiple forms of
analysis to give policymakers more information
on the potential impact of specific policy
alternatives.

Story Source:

The above story is based on materials provided
by North Carolina State University.
And ( sciencedaily magzine )

Journal Reference:

1. Kevin Hunter, Sarat Sreepathi, Joseph F.
DeCarolis. Modeling for insight using Tools
for Energy Model Optimization and Analysis
(Temoa) . Energy Economics, 2013; 40: 339
DOI: 10.1016/j.eneco.2013.07.014