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

Fractions Gain Traction With Real- Life Models

Aug. 27, 2013 — If 3 is greater than 2, then ⅓
must be bigger than ½ -- right? Wrong. As
thousands of students head back to school
next week, many will use exactly that kind of
thinking when faced with fractions for the first
time. New research from Concordia University
shows that for children to understand math,
teachers must constantly make the connection
between abstract numbers and real world
examples.

Helena Osana, associate professor in
Concordia's Department of Education, and PhD
candidate Nicole Pitsolantis put this theory to
the test in a classroom of fifth and sixth
graders. Their findings -- published in the
professional journal Teaching Children
Mathematics, as well as in the British Journal
of Educational Psychology -- show students
understand math much more clearly when
teachers use pictures and concrete models to
demonstrate what fractions actually mean.
Those connections are even stronger when the
model is personally meaningful to the
students. Write out '¾' on the blackboard and
the concept is not so clear. Show kids ¾ of a
shoelace or talk about running ⅓of the way to
school and suddenly they get it.
Although teachers already use models when
talking about fractions -- for instance, to show
a picture of a pie with slices eaten -- they
often put them away too quickly. To prove that
the constant use of models made a bigger
impact, Osana and Pitsolantis tried teaching
with models for only part of the lesson and
then the entire lesson.
They found that students showed much greater
understanding when the models were
continually present. "Our study shows teachers
should not only include pictures and models
while teaching fractions, but also have them
side by side throughout the class while
continually making clear connections between
the concepts and the models," says Osana.

The lessons produced by this research have the
potential to go beyond the classroom. "This is
something not only useful for teachers but
also for parents," says Osana. "Because
children are studying fractions, parents think
they're not able to help. But parents can have
positive effect on learning too. Something as
simple as writing '¾' out on a piece of paper,
then demonstrating what it means to use ¾ of
a cup of sugar, or filling up the gas tank until
it reaches the ⅔ mark, then writing and
pointing to the numbers '⅔ ,' can really go a
long way towards demystifying math," she
says.
Pitsolantis, who also teaches fourth and fifth
grade math at Lower Canada College in
Montreal, says that the depth of
misunderstanding that happens when models
are abandoned surprised her. She and Osana
are now testing out how teachers can
successfully incorporate concrete models into
other grades.

Story Source:

The above story is based on materials provided
by Concordia University .

And ( sciencedaily magazine ).

Formulae----1

Maths photo

Spatial Training Boosts Math Skills

June 25, 2013 — Training young children in
spatial reasoning can improve their math
performance, according to a groundbreaking
study from Michigan State University
education scholars.

The researchers trained 6- to 8-year-olds in
mental rotation, a spatial ability, and found
their scores on addition and subtraction
problems improved significantly. The mental
rotation training involved imagining how two
halves of an object would come together to
make a whole, when the halves have been
turned at an angle.

Past research has found a link between spatial
reasoning and math, but the MSU study is the
first to provide direct evidence of a causal
connection -- that when children are trained in
one ability, improvement is seen in the other.

The findings will be published in a forthcoming
issue of the Journal of Cognition and
Development.
Kelly Mix, professor of educational psychology,
said the findings suggest spatial training
"primes" the brain to better tackle calculation
problems. Mix authored the study with Yi-Ling
Cheng, a doctoral student in MSU's College of
Education.

"What's shocking is that we saw these
improvements in math performance after
giving the students just one 20-minute training
session in spatial ability," Mix said. "Imagine if
the training had been six weeks."
Understanding the connection between spatial
ability and math, she said, is especially
important in the early elementary grades
because many studies indicate early
intervention is critical for closing achievement
gaps in math.

Spatial ability is important for success in many
fields, from architecture to engineering to
meteorology, according to a Johns Hopkins
University paper. An astronomer must visualize
the structure of the solar system and the
motions of the objects in it, for example, while
a radiologist must be able to interpret the
image on an X-ray.
Some education experts have called for
including spatial reasoning in the elementary
math curriculum. But there are many forms of
spatial ability and Mix said it's important to
first figure out how each of them may or may
not relate to the various math disciplines.

To that end, Mix is leading a larger study that
tests elementary students on different forms of
spatial ability and math performance.
Mix's research into spatial ability and math is
funded by two grants totaling $2.8 million
from the Institute of Education Sciences, the
research arm of the U.S. Department of
Education.

Story Source:

The above story is based on materials provided
by Michigan State University .
Note: Materials may be edited for content and
length. For further information, please contact
the source cited above.

Journal Reference:

1. Yi Ling Cheng, Kelly S. Mix. Spatial Training
Improves Children's Mathematics Ability .
Journal of Cognition and Development , 2012; :
120919075341007 DOI:
10.1080/15248372.2012.725186

Stabilizing Aircraft During Takeoff and Landing Using Math

Aug. 20, 2013 — One of the lesser known
concerns about commercial aircraft is their
stability on the ground during taxiing, takeoff,
and landing. During these processes, planes
must maintain stability under various operating
conditions. However, in some situations, the
aircraft landing gear displays unwanted
oscillations, which are referred to as shimmy
oscillations.

In a paper published last month in the SIAM
Journal on Applied Dynamical Systems, authors
Chris Howcroft, Bernd Krauskopf, Mark
Lowenberg, and Simon Neild study the
dynamics of aircraft landing gear using
nonlinear models. The dynamics of landing
gear shimmy and the wheel-ground interaction
are fundamentally nonlinear.

"Shimmy oscillations of aircraft landing gear
have long been a problem, and their
prediction and prevention remains an ongoing
challenge in landing gear design," explains
author Chris Howcroft. "The issue is that a
landing gear may display the desired behavior
during ground take-off/landing manoeuvres
over several hundred or so flights, but then
suddenly oscillate given just the right -- or
rather, the wrong -- conditions."

Fortunately, mathematical models provide
cost-effective ways to study the dynamics of
the main landing gear (MLG) and determine the
types of oscillations that may occur under
different conditions. "The work we conducted
clarifies under which conditions shimmy
oscillations can be encountered in the MLG of
a representative midsize passenger aircraft. We
identified different types of shimmy
oscillations and showed where they occur,"
says Howcroft.

"Having the right mathematical model is really
the key," he adds. "Actual testing is extremely
expensive; however, nonlinear analysis
methods are very well suited to identifying
these hard-to-find dynamics. They may also be
employed to determine the shimmy
characteristics before the aircraft has actually
been built."

The model can provide insights not only into
aircraft operation, but also design features,
and can aid in adjusting both for optimum
stability.
Aircraft landing gear supports the weight of
the aircraft during landing and ground
operations. In addition to their wheels, landing
gear also have shock absorbing equipment or
"shock struts" as well as brakes, retraction
mechanisms, controls, and structural entities
that attach the gear to the aircraft.
The model in the paper takes into account tire-
contact dynamics and the orientation of the
side-stay, the part of the aircraft that supports
the shock strut. It characterizes the motion of
the system in terms of dynamics of the MLG,
which are expressed as three degrees of
freedom: rotation about the main strut, and
in-plane and out-of-plane motion with respect
to the plane of main strut and side-stay. After
determining the dynamics for the simplest
geometric case, where the side-stay is
perpendicular to the direction of travel, the
authors use the model to study different side-
stay orientations.

"For the specific case of MLG, we developed a
nonlinear and fully parameterised model that
allowed us to map out how its dynamics
depends on operational parameters, such as
aircraft velocity and loading, and design
parameters describing the geometry of the
landing gear," explains Howcroft. "In contrast
to the more traditional approach of performing
large numbers of simulations, this was
achieved by employing advanced tools from
dynamical systems that track solutions and
stability changes in parameters directly."

Moreover, other parameters could be
incorporated into the model further down the
road, such as runway conditions or tire
pressure, or physical effects such as the
dynamics of the shock absorber.

"Future directions of this research will focus
on the incorporation and assessment of
additional nonlinear effects," says Howcroft.
"For example, mechanical joints loosen over
the lifespan of an aircraft landing gear, and
this may have a dramatic effect on dynamic
performance, service life and maintenance
requirements of the landing gear."

"Nonlinear modeling and analysis are now
being introduced as tools into industrial
practice, via the recent development of a
MATLAB toolbox," says author Simon Neild.

"This is exciting to see, and has allowed our
group to tackle not only the problem of
landing gear shimmy, but of aircraft ground
manoeuvres and airliner loss-of-control in
flight."
Author Bernd Krauskopf adds.

"This project is
part of a larger research effort in collaboration
with Airbus into aircraft ground dynamics via
the bifurcation analysis of nonlinear models.
Related work concerns shimmy in nose landing
gears and its interplay with the dynamics of
the fuselage."
Future work would integrate many different
aspects into a unifying model.

"Ultimately our
current research is moving towards the
integration of landing gear and airframe into
an overall model that allows us to create a full
dynamic picture of aircraft ground dynamics,"
says author Mark Lowenbergm.

Story Source:

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

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

Journal Reference:

1. Chris Howcroft, Bernd Krauskopf, Mark H.
Lowenberg, Simon A. Neild. Influence of
Variable Side-Stay Geometry on the Shimmy
Dynamics of an Aircraft Dual-Wheel Main
Landing Gear . SIAM Journal on Applied
Dynamical Systems , 2013; 12 (3): 1181 DOI:
10.1137/120887643

"Math in Daily Life"

When you buy a car, follow a recipe, or
decorate your home, you're using math
principles. People have been using these same
principles for thousands of years, across
countries and continents. Whether you're
sailing a boat off the coast of Japan or building
a house in Peru, you're using math to get
things done.

How can math be so universal?

First,
human beings didn't invent math
concepts; we discovered them. Also, the
language of math is numbers, not English
or German or Russian. If we are well versed in
this language of numbers, it can help us make
important decisions and perform everyday
tasks. Math can help us to shop wisely, buy the
right insurance, remodel a home within a
budget, understand population growth, or even
bet on the horse with the best chance of
winning the race.

Preschoolers Inability to Estimate Quantity Relates to Later Math Difficulty

Aug. 14, 2013 — Preschool children  who
showed less ability to estimate the number of
objects in a group were 2.4 times more likely
to have a later mathematical learning disability
than other young people, according to a team
of University of Missouri psychologists.

Parents may be able to help their children
develop their skills at approximating group
sizes by emphasizing numerals while interacting
with young children.

"Lacking skill at estimating group size may
impede a child's ability to learn the concept of
how numerals symbolize quantities and how
those quantities relate to each other," said
study co-author David Geary, professor of
psychological sciences at MU. "Not
understanding the values numbers symbolize
then leads to difficulties in math and problems
in school, which our previous studies suggest
may be related to later difficulties with
employment."

Geary said that parents may be able to improve
a child's innate skill at approximating group
size and suggested that caregivers draw
children's attention to quantities in everyday
situations. For example, after a preschool-aged
child completes a series of tasks, a parent can
ask the youth how many tasks they completed.

"Talking to children about how the world can
be represented in numbers may help young
people develop the ability to estimate the size
of a group, which may prepare them for later
mathematics education" said co-author Kristy
vanMarle, assistant professor of psychological
science at MU. "Asking them 'how many'
whenever they encounter a group of objects or
images can help them understand that the
world can be understood in terms of
numbers."

However, the inability to approximate group
size was not the only factor related to later
math problems. The MU team also found that
preschoolers who lagged behind others in their
understanding of the symbolic value of
numerals and other related concepts were 3.6
to 4.5 times more likely to show mathematical
learning difficulties, which corroborates earlier
research by Geary, and extends it to a much
younger age.

Doctoral student Felicia W. Chu was the lead
author of the study, "Quantitative deficits of
preschool children at risk for mathematical
learning disability," which was published in the
journal Frontiers in Psychology.
"One major reason I came to the University of
Missouri was the psychology department's
strong reputation for studying children's
mathematical education," said Chu.
Geary is Curators' Professor and a Thomas
Jefferson Fellow in the Department of
Psychological Sciences in MU's College of Arts
and Science. vanMarle is the director of MU's
Developmental Cognition Lab.

Story Source:

The above story is based on materials provided
by University of Missouri-Columbia .
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. Felicia W. Chu, Kristy vanMarle, David C.
Geary. Quantitative Deficits of Preschool
Children at Risk for Mathematical Learning
Disability . Frontiers in Psychology, 2013; 4
DOI: 10.3389/fpsyg.2013.00195

Questions Answered With the Pupils of Your Eyes

Aug. 5, 2013 — Patients who are otherwise
completely unable to communicate can answer
yes or no questions within seconds with the
help of a simple system -- consisting of just a
laptop and camera -- that measures nothing
but the size of their pupils. The tool, described
and demonstrated in Current Biology , a Cell
Press publication, on August 5 takes advantage
of changes in pupil size that naturally occur
when people do mental arithmetic.

It requires
no specialized equipment or training at all.
The new pupil response system might not only
help those who are severely motor-impaired
communicate, but might also be extended to
assessing the mental state of patients whose
state of consciousness is unclear, the
researchers say.

"It is remarkable that a physiological system as
simple as the pupil has such a rich repertoire
of responses that it can be used for a task as
complex as communication," says Wolfgang
Einhäuser of Philipps-Universität Marburg in
Germany.

The researchers asked healthy people to solve
a math problem only when the correct answer
to a yes or no question was shown to them on
a screen. The mental load associated with
solving that problem caused an automatic
increase in pupil size, which the researchers
showed they could measure and translate into
an accurate answer to questions like "Are you
20 years old?"

They then tested out their pupil response
algorithm on seven "typical" locked-in patients
who had suffered brain damage following a
stroke. In many cases, they were able to
discern an answer based on pupil size alone.

"We find it remarkable that the system worked
almost perfectly in all healthy observers and
then could be transferred directly from them
to the patients, with no need for training or
parameter adjustment," Einhäuser says.
While the system could still use improvement
in terms of speed and accuracy, those are
technical hurdles Einhäuser is confident they
can readily overcome.

Their measures of pupil
response could already make an important
difference for those who need it most.
"For patients with altered state of
consciousness -- those who are in a coma or
other unresponsive state -- any communication
is a big step forward," he says.

Story Source:

The above story is based on materials provided
by Cell Press, via EurekAlert!, a service of
AAAS.
Note: Materials may be edited for content and
length. For further information, please contact
the source cited above.
And ( science daily magzine ).
Journal Reference:

1. Josef Stoll, Camille Chatelle, Olivia Carter,
Christof Koch, Steven Laureys, Wolfgang
Einhäuser. Pupil responses allow
communication in locked-in syndrome
patients. Current Biology, 2013; 23 (15): R647
DOI: 10.1016/j.cub.2013.06.011

Computer Scientists Develop 'Mathematical Jigsaw Puzzles' to Encrypt Software

July 29, 2013 — UCLA computer science
professor Amit Sahai and a team of researchers
have designed a system to encrypt software so
that it only allows someone to use a program
as intended while preventing any deciphering
of the code behind it. This is known in
computer science as "software obfuscation,"
and it is the first time it has been
accomplished.
Sahai, who specializes in cryptography at
UCLA's Henry Samueli School of Engineering
and Applied Science, collaborated with Sanjam
Garg, who recently earned his doctorate at
UCLA and is now at IBM Research; Craig
Gentry, Shai Halevi and Mariana Raykova of
IBM Research; and Brent Waters, an assistant
professor of computer science at the
University of Texas at Austin. Garg worked with
Sahai as a student when the research was
done.

Their peer-reviewed paper will be formally
presented in October at the 54th annual IEEE
Symposium on Foundations of Computer
Science, one of the two most prominent
conferences in the field of theoretical
computer science. Sahai has also presented
this research in recent invited talks at Stanford
University and the Massachusetts Institute of
Technology.
"The real challenge and the great mystery in
the field was: Can you actually take a piece of
software and encrypt it but still have it be
runnable, executable and fully functional,"
Sahai said. "It's a question that a lot of
companies have been interested in for a long
time."
According to Sahai, previously developed
techniques for obfuscation presented only a
"speed bump," forcing an attacker to spend
some effort, perhaps a few days, trying to
reverse-engineer the software. The new
system, he said, puts up an "iron wall," making
it impossible for an adversary to reverse-
engineer the software without solving
mathematical problems that take hundreds of
years to work out on today's computers -- a
game-change in the field of cryptography.

The researchers said their mathematical
obfuscation mechanism can be used to protect
intellectual property by preventing the theft of
new algorithms and by hiding the vulnerability
a software patch is designed to repair when
the patch is distributed.
"You write your software in a nice, reasonable,
human-understandable way and then feed that
software to our system," Sahai said. "It will
output this mathematically transformed piece
of software that would be equivalent in
functionality, but when you look at it, you
would have no idea what it's doing."
The key to this successful obfuscation
mechanism is a new type of "multilinear jigsaw
puzzle." Through this mechanism, attempts to
find out why and how the software works will
be thwarted with only a nonsensical jumble of
numbers.
"The real innovation that we have here is a way
of transforming software into a kind of
mathematical jigsaw puzzle," Sahai said. "What
we're giving you is just math, just numbers, or
a sequence of numbers. But it lives in this
mathematical structure so that these individual
pieces, these sequences of numbers, can only
be combined with other numbers in very
specified ways.
"You can inspect everything, you can turn it
upside-down, you can look at it from different
angles and you still won't have any idea what
it's doing," he added. "The only thing you can
do with it is put it together the way that it was
meant to interlock. If you tried to do anything
else -- like if you tried to bash this piece and
put it in some other way -- you'd just end up
with garbage."

Functional encryption

The new technique for software obfuscation
paved the way for another breakthrough called
functional encryption. With functional
encryption, instead of sending an encrypted
message, an encrypted function is sent in its
place. This offers a much more secure way to
protect information, Sahai said. Previous work
on functional encryption was limited to
supporting very few functions; the new work
can handle any computable function.

For example, a single message could be sent to
a group of people in such a way that each
receiver would obtain different information,
depending on characteristics of that particular
receiver. In another example, a hospital could
share the outcomes of treatment with
researchers without revealing details such as
identifying patient information.
"Through functional encryption, you only get
the specific answer, you don't learn anything
else," Sahai said.
The UCLA-based researchers were funded in
part by the National Science Foundation, a
Xerox Faculty Research Award, a Google
Faculty Research Award, an equipment grant
from Intel and an Okawa Foundation Research
Grant.

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The above story is based on materials provided
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And ( science daily )

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