Basic importent topic

18, 2013 — When early elementary math
teachers ask students to explain their problem-
solving strategies and then tailor instruction to
address specific gaps in their understanding,
students learn significantly more than those
taught using a more traditional approach. This
was the conclusion of a yearlong study of
nearly 5,000 kindergarten and first-grade
students conducted by researchers at Florida
State University.
The researchers found that “formative
assessment,” or the use of ongoing evaluation
of student understanding to inform targeted
instruction, increased students’ mastery of
foundational math concepts that are known to
be essential to later achievement in
mathematics and science.
Their results corroborated those of two earlier
pilot projects indicating that implementation of
the Mathematics Formative Assessment System
(MFAS) can markedly improve academic
performance in mathematics. The findings
further suggested that MFAS may help close
the gender gap that often develops by third
grade.
“The results of the most recent study
conducted in schools across Florida are
exciting,” said Laura Lang, principal
investigator who directed development and
testing of MFAS. “The randomized field trial
showed that students in K-3 classes where
teachers used MFAS were well ahead of other
students taught by teachers using more
traditional approaches. As one of the
elementary principals of a participating school
put it, MFAS is a real ‘game changer’ in terms
of student engagement and success in math.”
MFAS was created through the efforts of
researchers at the Florida Center for Research
in Science, Technology, Engineering and
Mathematics (FCR–STEM) who received $2.9
million in competitively awarded grant funds
from the Florida Department of Education’s
Race to the Top program to pursue the
project. MFAS is fully aligned with the Common
Core State Standards adopted in Florida and
many other states.
The randomized field trial was conducted in
partnership with 31 schools and 301 teachers
in three Florida districts across the state —
one urban, one suburban and one rural.
Schools were randomly assigned to either the
MFAS treatment group or to a group that used
a more typical approach to math instruction.
Comparing average annual gains in math on
nationally normed tests to the results, learning
was accelerated when teachers integrated MFAS
in their day-to-day instruction.
“In kindergarten, we can infer that students
learned at a rate equivalent to an extra six
weeks of instruction,” Lang said. “In first
grade, the gains were even greater — two
months of extra instruction. It was as if we
extended the school year without actually
adding any more days to it.”
In constructing MFAS, Lang and her team drew
upon research demonstrating that the learning
of mathematics is facilitated when teachers
gain deeper insights into what their students
already know and are able to do as well as
what students do not know and are unable to
do. Teachers gather these insights through
careful observation and by engaging students
in discussions of their mathematical thinking.
“Formative assessment is a process, not a
test,” Lang said, “and feedback is a key
element.”
The approach enables teachers to address each
child’s instructional needs. Teachers can avoid
holding back those who are ready to advance,
while efficiently helping those who are
struggling. This contrasts sharply with current
practice in many elementary classrooms.
“Based on our classroom observations over the
past four years, teachers typically rely heavily
on a math textbook to guide the planning of
day-to-day instruction and often provide
students feedback only on whether their
answers are correct,” Lang said. “Teachers
integrating formative assessment in instruction
not only ask students to do math tasks but
also to explain their reasoning and to justify
their solutions. As a result, teachers are better
equipped to identify misconceptions,
determine gaps in understanding and adjust
their instruction accordingly.”
Students play a key role in the formative
assessment process. MFAS actively engages
students, encouraging them to monitor and
regulate their own learning. Students also
evaluate each other’s work and provide
productive feedback, working as a team.
MFAS also has potential long-term effects on
closing the gender gap in mathematics, Lang
said. Studies show that even though both boys
and girls enter school with a fundamental
number sense, by the third grade boys tend to
do better in mathematics.
The results of a pilot study conducted in
second- and third-grade classrooms suggest
that, in classrooms where MFAS was used, by
third grade the girls showed no statistically
significant difference in mathematics
achievement from boys, according to Mark
LaVenia, methodologist on the MFAS team.
However, in classrooms with more
conventional instruction, girls continued to lag
behind boys in math achievement.

Story Source:

The above story is based on materials provided
by Florida State University, via Newswise.

Unlocking Biology With Math

Oct. 7, 2013 — Scientists at USC have created
a mathematical model that explains and
predicts the biological process that creates
antibody diversity -- the phenomenon that
keeps us healthy by generating robust immune
systems through hypermutation.
The work is a collaboration between Myron
Goodman, professor of biological sciences and
chemistry at the USC Dornsife College of
Letters, Arts and Sciences; and Chi Mak,
professor of chemistry at USC Dornsife.
"To me, it was the holy grail," Goodman said.
"We can now predict the motion of a key
enzyme that initiates hypermutations in
immunoglobulin (Ig) genes."

Goodman first described the process that
creates antibody diversity two years ago. In
short, an enzyme called "activation-induced
deoxycytidine deaminase" (or AID) moves up
and down single-stranded DNA that encodes
the pattern for antibodies and sporadically
alters the strand by converting one nitrogen
base to another, which is called "deamination."

The change creates DNA with a different
pattern -- a mutation.
These mutations, which AID creates a million-
fold times more often than would otherwise
occur, generate antibodies of all different sorts
-- giving you protection against germs that
your body hasn't even seen yet.
"It's why when I sneeze, you don't die,"
Goodman said.
In studying the seemingly random motion of
AID up and down DNA, Goodman wanted to
understand why it moved how it did, and why
it deaminated in some places much more than
others.

"We looked at the raw data and asked what the
enzyme was doing to create that," Goodman
said. He and his team were able to develop
statistical models whose probabilities roughly
matched the data well, and were even able to
trace individual enzymes visually and watch
them work.

But they were all just
approximations, albeit reasonable ones.
Collaborating with Mak, however, offered
something better: a rigorous mathematical
model that describes the enzyme's motion and
interaction with the DNA and an algorithm for
directly reading out AID's dynamics from the
mutation patterns.
At the time, Mak was working on the
mathematics of quantum mechanics. Using
similar techniques, Mak was able to help
generate the model, which has been shown
through testing to be accurate.

"Mathematics is the universal language behind
physical science, but its central role in
interpreting biology is just beginning to be
recognized," Mak said. Goodman and Mak
collaborated on the research with Phuong
Pham, assistant research professor, and Samir
Afif, a graduate student at USC Dornsife. An
article on their work, which will appear in
print in the Journal of Biological Chemistry on
October 11, was selected by the journal as a
"paper of the week."

Next, the team will generalize the
mathematical model to study the "real life"
action of AID as it initiates mutations during
the transcription of Ig variable and constant
regions, which is the process needed to
generate immunodiversity in human B-cells.

Non-Traditional Mathematics Curriculum Results in Higher Standardized Test Scores

Sept16, 2013 — For many years, studies have
shown that American students score
significantly lower than students worldwide in
mathematics achievement, ranking 25 th among
34 countries. Now, researchers from
theUniversity of Missouri have found high
school students in the United States achieve
higher scores on a standardized mathematics
test if they study from a curriculum known as
integrated mathematics.
James Tarr, a professor in the MU College of
Education, and Doug Grouws, a professor
emeritus from MU, studied more than 3,000
high school students around the country to
determine whether there is a difference in
achievement when students study from an
integrated mathematics program or a more
traditional curriculum. Integrated mathematics
is a curriculum that combines several
mathematic topics, such as algebra, geometry
and statistics, into single courses. Many
countries that currently perform higher than
the U.S. in mathematics achievement use a
more integrated curriculum. Traditional U.S.
mathematics curricula typically organize the
content into year-long courses, so that a 9 th
grade student may take Algebra I, followed by
Geometry, followed by Algebra II before a pre-
Calculus course.
Tarr and Grouws found that students who
studied from an integrated mathematics
program scored significantly higher on
standardized tests administered to all
participating students, after controlling for
many teacher and student attributes. Tarr says
these findings may challenge some long-
standing views on mathematics education in
the U.S.
"Many educators in America have strong views
that a more traditional approach to math
education is the best way to educate high
school students," Tarr said. "Results of our
study simply do not support such impassioned
views, especially when discussing high-
achieving students. We found students with
higher prior achievement scores benefitted
more from the integrated mathematics
program than students who studied from the
traditional curriculum."

Tarr and Grouws' papers, which were recently
published in the Journal for Research in
Mathematics Education, come from a three-
year study measuring educational outcomes
for students studying from different types of
mathematics curricula. Tarr says improving
American mathematics education is vital for
the future of the country
.
"Many countries that the U.S. competes with
economically are outpacing us in many fields,
particularly in mathematics and science," Tarr
said. "It is crucial that we re-evaluate our
school mathematics curricula and how it is
implemented if we hope to remain competitive
on a global stage."
Tarr and Grouws' longitudinal study is funded
by grant of more than $2 million from the
National Science Foundation.

Story Source:

The above story is based on materials provided
by University of Missouri-Columbia.

Journal Reference:

1. James E. Tarr, Douglas A. Grouws, Óscar
Chávez, and Victor M. Soria. The Effects of
Content Organization and Curriculum
Implementation on Students’ Mathematics
Learning in Second-Year High School
Courses .
Journal for Research in Mathematics.

Photo maths

Some maths articles :  only image,  just like topic.

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

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.

Story Source:

The above story is based on materials provided
by University of California - Los Angeles .

And ( science daily )

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

New Light Shed On Cause of Pandemic Influenza

July 24, 2013 — With the use of sophisticated
mathematical modelling techniques, a
mathematician at PolyU and his co-researchers
have completed a study that explains the
phenomenon of multiple waves of influenza
pandemic in the last century.
With the use of sophisticated mathematical
modelling techniques, a mathematician at The
Hong Kong Polytechnic University (PolyU) and
his co-researchers have completed a study that
explains the phenomenon of multiple waves of
influenza pandemic in the last century.

Taking part in this advanced study is Dr Daihai
He, Assistant Professor of PolyU's Department
of Applied Mathematics. He has collaborated
with four researchers in Canada to offer an
explanation to the worst influenza pandemic in
the history of humankind. The research team
found that behavioural response has the
largest impact among three primary factors
causing the waves, thus paving the way for
future enhancement on control strategies to
the spread of influenza virus.

The 1918 flu epidemic was one of the world's
deadliest natural disasters, causing the death of
hundred thousands of people. Influenza
pandemic appears to be characterized by
multiple waves of incidence in one year, but
the mechanism that explains this phenomenon
has so far been elusive.

In explaining the deadly pandemic, Dr Daihai
He and his teammates have incorporated in
their mathematical model three contributing
factors for multiple waves of influenza
pandemic in England and Wales: (i) schools
opening and closing, (ii) temperature changes
during the outbreak, and (iii) changes in
human behaviour in response to the outbreak.

Dr He and the researchers further applied this
model to the reported influenza mortality
during the 1918 pandemic in 334 British
administrative units and estimate the
epidemiological parameters. They have used
information criteria to evaluate how well these
three factors explain the observed patterns of
mortality. The results indicate that all three
factors are important, but behavioural
responses had the largest effect.
The findings have recently been published in
the journal Proceedings of the Royal Society
Biological Sciences (July 2013 Issue).

Dr He's
expertise in advanced mathematics and
statistics has helped improve our
understanding of the spread of influenza virus
at the population level and lead to improved
strategies to control and minimize the spread
of influenza virus.

Story Source:

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

And { science daily magazine }

Journal Reference:

1. D. He, J. Dushoff, T. Day, J. Ma, D. J. D. Earn.
Inferring the causes of the three waves of
the 1918 influenza pandemic in England
and Wales. Proceedings of the Royal Society
B: Biological Sciences , 2013; 280 (1766):
20131345 DOI: 10.1098/rspb.2013.1345

Math Game More Effective Than Paper Exercises

July 8, 2013 — To measure the effectiveness of
Monkey Tales, a study was carried out with 88
second grade pupils divided into three groups.
One group was asked to play the game for a
period of three weeks while the second group
had to solve similar math exercises on paper
and a third group received no assignment. The
math performance of the children was
measured using an electronic arithmetic test
before and after the test period. When results
were compared, the children who had played
the game provided significantly more correct
answers: 6% more than before, compared to
only 4% for the group that made traditional
exercises and 2% for the control group. In
addition, both the group that played the game
and that which did the exercises were able to
solve the test 30% faster while the group
without assignment was only 10% faster.
The quality of experience was also measured
and showed that pupils found Monkey Tales
more enjoyable (which was confirmed by a
parent survey), that the game was described as
being 'fun', 'exciting' and 'fantastic' up to 80%
more often than the paper exercises, and that
60% of the children wished to play more, while
only 39% wished to solve additional exercises.
Broadly speaking, it can be concluded that the
game showed better results both in terms of
motivation and learning efficiency. Further
research should reveal how these additional
learning outcomes are achieved by the game.
Possible reasons are the continuous feedback
players receive during gameplay, that the game
is more motivating, that it adjusts the difficulty
level to the player or -- more generally -- that
it trains additional cognitive skills such as
working memory and attention.

Serious games
Serious or educational games are becoming
increasingly important. Market research
company iDate estimates that the global
turnover was €2.3 billion in 2012 and expects
it to rise to €6.6 billion in 2015. A first
important sector in which serious games are
being used, is defence. The U.S. Army, for
example, uses games to attract recruits and to
teach various skills, from tactical combat
training to ways of communicating with local
people. Serious games are also increasingly
used in companies and organizations to train
staff. The Flemish company U&I Learning, for
example, developed games for Audi in Vorst to
teach personnel the safety instructions, for
Carrefour to teach student employees how to
operate the check-out system and for DHL to
optimise the loading and unloading of air
freight containers.

Games in education

The interest in serious games is also growing in
education. The underlying idea is that children
often have to acquire large amounts of
knowledge and master complex skills to be
able to play "entertainment games." If
educational games could be equally enjoyable
or "intrinsically motivating," children would be
learning for pleasure. Monkey Tales is a game
that was developed according to this
philosophy by the educational publisher die
Keure and game developer Larian Studios. This
three-dimensional adventure game exists in
different versions for children from the second
to the sixth grade and is designed to practice
mental math in a playful way by solving
puzzles and mini-games. Until now, no
independent scientific research had been
conducted into the effectiveness of Monkey
Tales however.

Story Source:

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

And ( science daily )..
     
              ******-*-*

Development of Operation Research In India

In 1949, operation research come into picture when an OR unit was established at the Regional Research laboratory, Hyderabad.
At the same time, Prof. R.S. VERMA ( Delhi university ) setup an OR team in the Defence Science Laboratory to solve the problem of store, purchase and planning.

In 1953,  Prof. P.C. Mahalanobis established an OR team in the Indian Statistical Institute, calcutta, for solving the problem of national planning and survey.

In 1957 , Operation Research Society of india was formed and his society became a member  of  the International  Federation Of Operation Research Societies in 1960.

Presently, India is publishing a number of  Research journals,  namely,  " OPSEARCH " , " INDISTRIAL ENGINEERING AND MANAGEMENT " , " MATERIALS MANAGEMENT  JOURNAL OF INDIA ",  " DEFENCE SCIENCE JOURNAL " ,  "SCIMA" , " JOURNAL OF ENGINEERING PRODUCTION " etc.

As far as the OR education in India concerned University of Delhi was the first to introduce a complete M.Sc. course in OR in 1963. Simultaneously, Institute of Management at calcutta and Ahemdabad started teaching OR in their MBA courses.  Now a days, OR has becomes so popular subject that it has been introduce in almost all institute and University  in various disciplines like,  MATHEMATICS, STATISTICS,  COMMERCE, ECONOMICS, MANAGEMENT SCIENCE, MEDICAL SCIENCE, ENGINEERING, etc. . Also relizing the importance of OR in Accounts and Administration, goverment has introduce this subject for the IAS, CA, ICWA examinations etc.

Some of the industries , namely Hindustan Lever Ltd; Union carbide, TELCO, Hindustan Steel, Imperiel Chemical Industries , Tata Iron & Steel Company, Sarabhi Group, FCI, etc,  have engaged OR teams.
Kirlosker company is using the assignment technique of OR to maximize profit.

Textile firms like, DCM. , Binani's and Calico,  etc., are  using linear programming techniques.

Among other Indian organizations using  OR are the Indian Railways, CSIR, Tata Institute of Fundamental Research, Indian Institute of  Science,  State Trading Corporation, etc ..
       

            ------*******-------

Using Math to Kill Cancer Cells

June 14, 2013 — Here's a good reason to pay
attention in math class. Today Nature
Communications has published a paper from
Ottawa researchers outlining how advanced
mathematical modelling can be used in the
fight against cancer. The technique predicts
how different treatments and genetic
modifications might allow cancer-killing,
oncolytic viruses to overcome the natural
defences that cancer cells use to stave off viral
infection.

"Oncolytic viruses are special in that they
specifically target cancer cells," explains Dr.
Bell, a senior scientist at the Ottawa Hospital
Research Institute and professor at the
University of Ottawa's Faculty of Medicine.
"Unfortunately, cancer is a very complicated
and diverse disease, and some viruses work
well in some circumstances and not well in
others. As a result, there has been a lot of
effort in trying to modify the viruses to make
them safe, so they don't target healthy tissue
and yet are more efficient in eliminating
cancer cells."
Dr. Bell and co-author Dr. Mads Kaern, an
assistant professor in the University of
Ottawa's Faculty of Medicine and Canada
Research Chair at the University's Ottawa
Institute of Systems Biology, led a team that
has used mathematical modelling to devise
strategies for making cancer cells exquisitely
sensitive to virus infection -- killing them
without affecting normal, healthy cells.
"By using these mathematical models to
predict how viral modifications would actually
impact cancer cells and normal cells, we are
able to accelerate the pace of research," says
Dr. Kaern, who is also cross-appointed to the
University's Department of Physics. "It allows
us to quickly identify the most promising
approaches to be tested in the lab, something
that is usually done through expensive and
time-consuming trial and error."
Drs. Bell and Kaern have established a
mathematical model that described an
infection cycle, including the way a virus
replicated, spread and activated cellular
defense mechanisms. From there, they used
knowledge about key physiological differences
between normal cells and cancer cells to
identify how modifying the genome of the
virus might counter the anti-viral defenses of
cancer cells. Model simulations were
remarkably accurate, with the identified viral
modifications efficiently eradicating cancer in
a mouse model of the disease.
"What is remarkable is how well we could
actually predict the experimental outcome
based on computational analysis," says Dr.
Bell. "This work creates a useful framework for
developing similar types of mathematical
models in the fight against cancer."
The research, funded by an innovation grant
from the Canadian Cancer Society, is only the
beginning, explains Dr. Kaern. "We worked
with a specific kind of cancer cell. We will now
expand that to look at other cancer cell types
and see to what degree the predictions we
made in one special case can be generalized to
others, and to identify strategies to target
other types of cancer cells."
The findings may also help researchers better
understand the interaction between these
cancer cells and the virus. While one magic
cure-all will likely never happen due to
cancer's complexity, the researchers have
developed a framework where they can learn
more about the disease in the cases where the
simulations don't match.

"From my perspective, that's the most
interesting part," concluded Dr. Kaern. "The
most fascinating thing is to challenge existing
knowledge represented in a mathematical
model and try to understand why these models
sometimes fail. It's a very exciting opportunity
to be a part of this, and I am glad that our
efforts in training students in computational
cell biology have resulted in such a significant
advancement."

Story Source:
The above story is reprinted from materials
provided by Ottawa Hospital Research
Institute .
Note: Materials may be edited for content and
length. For further information, please contact
the source cited above.

And [ Science daily  ]

Journal Reference:
1. Fabrice Le Bœuf, Cory Batenchuk, Markus
Vähä-Koskela, Sophie Breton, Dominic Roy,
Chantal Lemay, Julie Cox, Hesham Abdelbary,
Theresa Falls, Girija Waghray, Harold Atkins,
David Stojdl, Jean-Simon Diallo, Mads Kærn,
John C. Bell. Model-based rational design of
an oncolytic virus with improved
therapeutic potential . Nature
Communications, 2013; 4 DOI: 10.1038/
ncomms2974

Management Applications Of Operation Research

Some of the areas of manaement decision makinging, where the ' Tools' and 'techniques' of OR ,  are applied, can be outlined as follows :

1) Finance-Budgeting and Investments

(a) cash-flow analysis, long range capital requirements, dividend policies, investment portfolies.

(b) credit policies, credit risks and delinquent account procedures.

(c) claim and complaint procedures.

2). Purchasing, Procurement and Exploration

(a) rules for buying, supplies and stable or varying prices.

(b) determination of quantities and timing of purchases.

(c) bidding policies.

(d) strategies for exploration and exploitation of raw material sources.

(e) replacement policies

3) Production Management
((1)) physical distribution

  (a)  location and size of warehouse, distribution centres and retail outlets

(b) distribution policy

((2)) Facilities Planning
   (a) Number and location of function, warehouse, hospital etc.
 
  (b) Loding and unloading facilities for railroads and trucks determining the transport activity

((3)) Manufacturing
(a) prduction scheduling and sequencing

(b) Stablization of  production and employment traning layoffs and optimum products mix.

((4)) Maintenance and Project Scheduling

(a) Maintence policies and preventive maintenance

(b) Maintenance crew sizes

(c) Project scheduling and allocation of resources

(4) Marketing

(a) product selection,  timing,  competitive actions

(b) Number of salseman,  frequency of calling  on accounts percent of time spent on prospects.

(c) advertising media with respect to cost and time

(5) Personal Management

(a) Selection of suitable personal on minimum salary

(b) mixes of age and skills

(c) Recruitment policies and assitnment of jobs

(6) Research and Development

(a) Determination of the areas of concentration of research and davelopment

(b) Project Selection 

(c) Determination of time cost trade-off and central of development projects

(d) Reliability and alternative design.

From all above area of application, we may conclude that OR can be widely  used in taking management decisions and also  used as a correctiive measure.

             The application of this tool involves certain data and not merly a personality of decision maker and
hence we can say ----------------
           -------"OR A REPLACE A MANAGEMENT BY PERSONALITY."

CONCLUSION ON DEFINITIONS OF OPERATIONS RESEARCH

We read various definitions or opinions about OR,  we arrive at the conclusion that whatever else ' OR ' may be, it is certainly  concerned with optimization problems.    ---- " A decision, which taking  into account all the present circumstances can be considered the best one, is called an optimal decision."

There are three main reasons for why most of the definitions of operation Research are not satisfactory.-------------

1) First of all, Operations research is not a science like any well -defined physical,biological,social phenomena  , while chemists know about atoms and molecules and have theories about their interactions, and biologists know about living organisms and have theories about vital process, operation researchers do not claim to know or have theories about operations.
Operation Research is not a scientific  research into the control of operations. It is essentially a  collection of mathematical techniques and tools which is conjuction with a system approach are applied to solve practical dicision problems of an economic or engineering nature.
Thus it  is very difficult to define operations research precisely.

2) Operation Research is inherently inter-disciplinary in nature with application not only in miitary and business but also in medicine, engineering, physics and so on.  OR make use of experience and expertise of people from different disciplines for developing new methods and procedures.
              Thus inter-disciplinary approach is an important characteristic of OR, which is not included in most of its definitions.
Hence most of definitions are  not satisfactory.

3) Most of the definitions of OR have been offered at different times of  development of OR and hence are bound to emphasise its only one or the other aspect.
For example---- some definitions is only  concerned with war alone.
Many more definitions have been given by various authors must of them fail to consider all basic characteristic of OR ..

However, with further development of operation research perhaps more precise definitions should be forthcoming.

Management Applications of operations research

Some of the areas of management decision making, where the "tools" and " techniques" of OR are applied, can be outlined as follows :

1) Finance-Budgeting and Investments
(1) Cash-flow analysis, long rang capital requirements, dividend policies, investment portfolios.
(2) credit policies, credit risks and delinquent account procedures.
(3) Claim and complaint procedures

2) Purchasing,  Procurement and Exploration
(1) Rules for buying, Supplies and stable or varying prices.
(2) Determination of quantities and timing of purchase
(3) Bidding policies
(4) Strategies for exploration and exploitation of raw material sources
(5) Replacement policies

3. Production Management

(1) Physical Distribution
       (a) Location and size of warehouse, distribution centres and retail  sources.
       (b) Distribution  policy

(2) Facilities planning
       (a) Numbers and location of factories, warehouse, hospitals  etc.
       (b) Loading and unloading facilities for railroads and trucks determine the transport schedule.

(3) Manufacturing
     (a) Production scheduling and sequencing
     (b) Stabilization of production and employment, training, layoffs and optimum product mix.

(4) Maintenance and Project Scheduling
       (a) Maintenance policies and preventive maintance.
       (b) Maintence crew sizes.
       (c) Project scheduling and allocation of resources.

4. Marketing
     (a) Product selection, timing competitive actions.
     (b) Number of salesman, frequency of calling an accounts percent of time spent on prospects
    (c) Advertising  media with respect to cost  and time.

5. Personnel Management
    (a) Selection of suitable personnel on minimum salary
    (b) Mixes of age and skills
    (c) Recruitment policies and assignment of jobs.

6. Research and Development
     (a) Determination of  the areas of concentration of research and development
    (b) Project selection
    (c) Determination of time cost trade-off and control of development  projects
    (d) Reliability and alternative desine.

THE NATURE AND MEANING OF " OPERATION RESEARCH" - "OR"

'OR' has been defined so far in various ways and it is perhaps still too yaung to be defined in some  authoritative way. So it is importent and interesting to give below a few opinions about the definition of OR which has been changed according to development of the subject. -----

1. OR is a scientific method of providing executive with an  analytical and objective basis  for decisions.             ---  P.M.S. Blackett (1948)

2. OR is the art of giving bad answers to problems to which otherwise worse answers are given.     ---- T.L. Saaty (1958)

3. OR is the application of scientific methods , techniques, and tools to problems involving the operations of systems so as to provide these in control of the operations with optimum solutions to the problem. 
                    ---- Churchman,Acorff,Arnoff (1957)

4. OR is a management activity pursued in two complementary ways --- one half by the free and bold exercise of commonsense untrammelled by any routine,  and other half by the application of a repertoire of well established precreated methods and techniques .
                     --- Jagjit Singh (1958)

5. OR is the  attack of modern methods on complex problems arising in the direction and management to large system of men, machines, materials, and money in industry, business and defence. The distinctive approach is to developed a scientific model of the system, incorporating measurements of factors such as chance and risk with which to predict and compare the outcomes of alternative decisions, strategies or controls. The purpose is to help management to determine its policy and actions scientifically.

                            ---  Operations Research Quarterly (1971)

6. OR is a scientific approach to  problem solving fo executive management.
                    --- H.M. Wagner
7. Operation research is the art of wining war without actually fighting it.

Analytic Functions

A complex function is said to be analytic on a region R,  if it is differentiable at every point in R.
The terms " Holomorphic function " are also used for analytic function.

If a complex function is analytic on a region R, it is infinitely differentiable in R. A complex function may fail to be analytic at one or more point through the presence of singularities.

" A complex function that is analytic at all finite points of the complex plane is said to be entire function ."

A single valued function that is analytic in,  all but possibly a discrete subset of its  domain, and at those singularities goes to infinity like a polynomial is called a meromorphic function.

Maths puzzal

See the photo below and give answer :