Saturday, March 29, 2008

About Isaac Newton

December 164220 March 1727])[1] was an English physicist, mathematician, astronomer, natural philosopher, alchemist and theologian. His PhilosophiƦ Naturalis Principia Mathematica, published in 1687, is said to be the greatest single work in the history of science. In this work, Newton described universal gravitation and the three laws of motion, laying the groundwork for classical mechanics, which dominated the scientific view of the physical universe for the next three centuries and is the basis for modern engineering. Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws by demonstrating the consistency between Kepler's laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the scientific revolution.

In mechanics, Newton enunciated the principles of conservation of momentum and angular momentum. In optics, he invented the reflecting telescope and developed a theory of colour based on the observation that a prism decomposes white light into a visible spectrum. He also formulated an empirical law of cooling and studied the speed of sound.

In mathematics, Newton shares the credit with Gottfried Leibniz for the development of calculus. He also demonstrated the generalized binomial theorem, developed the so-called "Newton's method" for approximating the zeroes of a function, and contributed to the study of power series.

In a 2005 poll of the Royal Society of who had the greatest effect on the history of science, Newton was deemed much more influential than Albert Einstein.[5]

Friday, March 28, 2008

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The Theory of Evolution

Why Is Evolution Important?
The discovery and understanding of the processes of evolution represent one of the most
powerful achievements in the history of science. Evolution successfully explains the diversity of
life on Earth and has been confirmed repeatedly through observation and experiment in a broad
spectrum of scientific disciplines.
Evolutionary science provides the foundation for modern biology. It has opened the door to
entirely new types of medical, agricultural, and environmental research, and has led to the development
of technologies that can help prevent and combat disease. Regrettably, effective science
education in our schools is being undermined by efforts to introduce non-scientific concepts
about evolution into science classrooms.
How Science Works
The study of evolution provides an excellent example of how scientists go about their work. They
observe nature and ask testable questions about the natural world, test those questions through
experiment and new observations, and construct explanations of evolution based on evidence.
As scientists gather new results and findings, they continue to refine their ideas. Explanations are
altered or sometimes rejected when compelling contradictory evidence comes to light.
Some scientific explanations are so well established that no
new evidence is likely to alter them. The explanation becomes
a scientific theory. In everyday language a theory means a
hunch or speculation. Not so in science. In science, the word
theory refers to a comprehensive explanation of an important
feature of nature that is supported by many facts gathered over
time. Theories also allow scientists to make predictions about
as yet unobserved phenomena.
A good example is the theory of gravity. After hundreds of
years of observation and experiment, the basic facts of gravity
are understood. The theory of gravity is an explanation of those
basic facts. Scientists then use the theory to make predictions
about how gravity will function in different circumstances. Such
predictions have been verified in countless experiments, further
confirming the theory. Evolution stands on an equally solid foundation
of observation, experiment, and confirming evidence
The Theory of Evolution
Has Been Repeatedly Tested and Confirmed
We all know from our experience that biological traits pass from parents to offspring. This is the
basis of evolution.
Sometimes traits change between generations. If a new trait results in an offspring doing better
in its natural surroundings and producing more offspring that also inherit the trait, that trait
will become more widespread over time. If the new trait makes the offspring less able to survive
and thus leave fewer offspring, the trait will tend to fade from existence. Natural selection is the
process by which some traits succeed and others fail in the environment where the organism
lives. For every type of life we see today, there were many other types that were unsuccessful
and became extinct.
Scientists no longer question the basic facts of evolution as a process. The concept has withstood
extensive testing by tens of thousands of specialists in biology, medicine, anthropology,
geology, chemistry, and other fields. Discoveries in different fields have reinforced one another,
and evidence for evolution has continued to accumulate for 150 years.
The Fossil Record The concept of evolution
is supported by fossil findings in rock layers from different
ages of Earth’s history. In general, fossils that
more closely resemble today’s life forms are found in
younger rock layers, while many fossils that only distantly
resemble life today occur in older layers. Based
on such findings, naturalists proposed that species
change, or evolve, over time. Natural selection has been
identified as a driving force behind these changes. Since
then, scientists have found an overwhelming number
of fossils in rock layers of different ages that repeatedly
confirm the changes in life forms that are predicted by
the theory of evolution.
DNA Research Molecular biology and genetics have revealed how evolution works at the
level of molecules. Unknown when evolution and natural selection were first proposed in 1859,
genetics has shown that traits are passed from parent to offspring through DNA, a molecule in all
living things that directs how cells grow and reproduce. DNA studies support findings from other
branches of science. For example, species that appear to be more distantly related from their positions
in the fossil record are found to have correspondingly greater differences in their DNA than species that
appear more closely related in the fossil record.
A near complete skeleton of a transitional bird-like
fossil that was discovered in China and reported in
2006.
GTGCCCATCCAAAAAGTCCAAGATGACACCAAAACCCTCATCAAGACAATTGTCACCAGG
GTGCCCATCCAAAAAGTCCAGGATGACACCAAAACCCTCATCAAGACAATTGTCACCAGG
human
gorilla
chimp
A
ATCAATGACATTTCACACACGCAGTCAGTCTCCTCCAAACAGAAAGTCACCGGTTTGGAC
ATCAATGACATTTCACACACGCAGTCAGTCTCCTCCAAACAGAAGGTCACCGGTTTGGAC
human
gorilla
chimp
G
TTCATTCCTGGGCTCCACCCCATCCTGACCTTATCCAAGATGGACCAGACACTGGCAGTC
TTCATTCCTGGGCTCCACCCTATCCTGACCTTATCCAAGATGGACCAGACACTGGCAGTC
human
gorilla
chimp
C
TACCAACAGATCCTCACCAGTATGCCTTCCAGAAACGTGATCCAAATATCCAACGACCTG
TACCAACAGATCCTCACCAGTATGCCTTCCAGAAACATGATCCAAATATCCAACGACCTG
human
gorilla
chimp
A
GAGAACCTCCGGGATCTTCTTCAGGTGCTGGCCTTCTCTAAGAGCTGCCACTTGCCCTGG
GAGAACCTCCGGGACCTTCTTCAGGTGCTGGCCTTCTCTAAGAGCTGCCACTTGCCCTGG
human
gorilla
chimp
C
Comparison of the human and chimp DNA sequences for the gene that encodes the hormone leptin (which is
involved in the metabolism of fats) reveals only five differences in 250 nucleotides. Where the human and chimpanzee
sequences differ, the corresponding nucleotide in the gorilla (shaded bars) can be used to derive the nucleotide
that likely existed in the common ancestor of humans, chimpanzees, and gorillas. In two cases, the gorilla and
human nucleotides match, while in the other three cases, the gorilla and chimpanzee sequences are the same. The
common ancestor of the gorilla, chimpanzee, and human is most likely to have had the nucleotide that is the same
in two of the three modern-day organisms because this would require just one DNA change rather than two
Common Ancestry There are common
structures and behaviors among many species. A person
writes, a cow walks, a whale swims, and a bat
flies with structures built of bones that are different
in detail but also remarkably similar to each other.
When fossils are compared to one another in structure
and in age, it becomes clear that an ancestral
species gave rise to an array of successor species
with the same basic arrangement of limb bones. As
new findings have repeatedly demonstrated, for any
two species living today, their evolutionary lines can
be traced back in time until the two lines intersect in
a common ancestor.
The fossil record, DNA research, the evidence that
species have common ancestors, and other findings
add up to overwhelming evidence that evolution
by natural selection is how life on Earth arose and
became diverse.
Creationism Does Not Belong
in the Science Classroom
Some people argue that the diversity of life did not evolve through natural processes. They advocate
that creation be added to the school science curriculum alongside biological evolution.
But creationism is not science. Creationist arguments are based on beliefs about an entity
outside the natural world. But science can only investigate naturally occurring phenomena. In
fact, the many questions about evolution raised by creationists are readily answered by available
and accumulating scientific evidence. For example --
• Creationists argue that the theory of evolution is faulty because of gaps in the fossil record
(creationists identify as gaps those situations where intermediate fossil forms between two related
species are as yet undiscovered). But an increasing number of intermediate forms have been and
continue to be found. Even without actual fossils in hand, scientists can use modern techniques
Nature imposes a direction to evolutionary development. Though dolphins (left) are more closely related to humans
than they are to sharks, they have evolved bodies adapted to an aquatic environment.
Humerus
Radius
Ulna
Carpals
Metacarpals
Phalanges
Whale Bird
Dog Human The bones in the
forelimbs of terrestrial
and some
aquatic vertebrates
are remarkably
similar because
they have all
evolved from the
forelimbs of a
common ancestor.
in molecular biology and genetics along with the principles
of evolution to infer what forms of life existed and predict
where and what kinds of fossils will likely be found.
• Some creationists claim that certain features of living
beings are too complex to have evolved through natural processes.
They claim that structures such as a bacterium’s flagellum
(the hair-like part that gives the bacterium motion) ,
the human eye, or the immune system are “irreducibly complex”
and must have been created intact by an “intelligent
designer.” But biologists have discovered that components of
the flagellum have their own individual functions and also
have found intermediate forms of flagella. Both of those findings
support the idea of the flagellum evolving from existing
structures over time. Also, the creationist argument that such
features “must” have been designed is based on their preconceived
idea of a Creator, while the scientific position is based
on observable facts and falsifiable explanations.
• Some creationists argue based on scripture that the Earth cannot be old enough for the
diversity of life to have emerged through evolution. Yet measurements from geology, astronomy,
and other fields have repeatedly confirmed the ancient age of the Earth (approximately
4.5 billion years).
Because science has no way to accept or refute creationists’ assertions, creationist beliefs
should not be presented in science classrooms alongside teaching about evolution. Teaching
non-scientific concepts in science class will only confuse students about the processes,
nature, and limits of science.
Science and Religion Offer Different Ways of
Understanding the World
Science and religion address separate aspects of human experience.
Many scientists have written eloquently about how their scientific studies of biological
evolution have enhanced rather than lessened their religious faith. And many religious
people and denominations accept the scientific evidence for evolution.
Our education system and our society as a whole are best served when we teach science,
not religious faith, in science classrooms.
Electron micrograph of a bacterial
flagellum.
EvoluTioN iN ACTioN
Medicine’s Challenge in Countering Resistant Strains
of Harmful Bacteria
In late 2002, several hundred people in China came down with a severe form of pneumonia
caused by an unknown infectious agent. Dubbed “severe acute respiratory syndrome,”
or SARS, the disease soon spread to Vietnam, Hong Kong, and Canada and led to hundreds
of deaths. In March 2003, a team of researchers at the University of California, San
Francisco, received samples of a virus isolated from the tissues of a SARS patient. Using a
new technology known as a DNA microarray, the researchers compared the genetic material
of the unknown virus with that of known viruses. Within 24 hours, they assigned the
virus to a particular family based on its evolutionary relationship to other viruses -- a result
confirmed by other researchers using different techniques. Immediately, work began on
a blood test to identify people with the disease (so they could be quarantined), on treatments
for the disease, and on vaccines to prevent infection with the virus.
Understanding the evolutionary origins of human pathogens will become increasingly
important as new threats to human health arise. For example, many people have suffered
from severe medical problems as bacteria have evolved resistance to antibiotics. When a
bacterium undergoes a genetic change that increases its ability to resist the effects of an
antibiotic, that bacterium can survive and produce more copies of itself while non-resistant
bacteria are being killed. Bacteria that cause tuberculosis, meningitis, staph infections
(sepsis), sexually transmitted diseases, and other illnesses have evolved resistance to an
increasing number of antibiotics and have become serious problems throughout the world.
Knowledge of how evolution leads to increased resistance will be critical in controlling
the spread of infectious diseases.
TikTaalik
A Case Study in Scientific Prediction
Using the principles of evolution, scientists have been able to predict what new fossils might be discovered.
For example, scientists had found fossils of ancient fish that lived in shallow waters in earlier
times and fossils of four-limbed land dwellers that appeared later in time. What happened in between?
Evolutionary theory predicts that there would be one or more creatures with characteristics of both
the ancient fish and the later land-dwellers. A team of scientists decided to look in sedimentary rock
in northern Canada that was deposited about 375 million years ago, about the time these intermediate
species were thought to have lived, based on other evidence from the fossil record.
In 2004, the team found what they had predicted: the fossil of a creature with features of fish
(scales and fins) and features of land-dwellers (simple lungs, flexible neck, and fins modified to support
its weight). The bones in the limbs of this fossil, named Tiktaalik, resemble the bones in the
limbs of land-dwelling animals today.
By understanding evolution, scientists were able to predict what type of creature existed and in
what geologic layer it would be found. The discovery of Tiktaalik fills another gap in the fossil record.
Tiktaalik and other fossil intermediates between fish and tetrapods. These fossils
represent an assortment of species that lived between 385 and 359 million years
ago, spanning the evolution of fish to amphibians.
Paleontologists searched this remote valley in north central
Canada for a species intermediate between fish and limbed
animals capable of living on land because they knew the
sedimentary rocks there were deposited during the period
when such a transition had taken place.
Tiktaalik’s left and right fins had
a single upper bone (the large
bone at the bottom of each of
these drawings) followed by two
intermediate bones, giving the
creature an elbow and a wrist,
as in more recent organisms.
site of fossils
The content of this informational brochure was adapted from the full-length, 88-page
version of Science, Evolution, and Creationism (2008), produced by a committee of
the National Academy of Sciences and the Institute of Medicine. This brochure and the
full-length report on which it is based are available for downloading in pdf format at
http://www.nap.edu/catalog.php?record_id=11876.
AUTHORING COMMITTEE
FRANCISCO J. AYALA, Chair, University of California, Irvine*
BRUCE ALBERTS, University of California, San Francisco*
MAY R. BERENBAUM, University of Illinois, Urbana-Champaign*‡
BETTY CARVELLAS, Essex High School (Vermont)
MICHAEL T. CLEGG, University of California, Irvine*‡
G. BRENT DALRYMPLE, Oregon State University*
ROBERT M. HAZEN, Carnegie Institution of Washington
TOBY M. HORN, Carnegie Institution of Washington
NANCY A. MORAN, University of Arizona*
GILBERT S. OMENN, University of Michigan†
ROBERT T. PENNOCK, Michigan State University
PETER H. RAVEN, Missouri Botanical Garden*
BARBARA A. SCHAAL, Washington University in St. Louis*‡
NEIL deGRASSE TYSON, American Museum of Natural History
HOLLY WICHMAN, University of Idaho
* Member, National Academy of Sciences
† Member, Institute of Medicine
‡ Member, Council of the National Academy of Sciences
The National Academy of Sciences is a private, nonprofit, self-perpetuating society to which
distinguished scholars are elected for their achievements in research, and is dedicated to the
furtherance of science and technology and to their use for the general welfare. Upon the
authority of the charter granted to it by the Congress in 1863, the Academy has a mandate to
advise the federal government on scientific and technical matters.
The Institute of Medicine was established in 1970 by the National Academy of Sciences as
both an honorific and a policy research organization, to which members are elected on the
basis of their professional achievement and commitment to service in the examination of
policy matters pertaining to the health of the public.

Theoretical Computer Science Cheat Sheet

Theoretical Computer Science Cheat Sheet
De nitions Series
f(n) = O(g(n)) i9 positive c; n0 such that
0  f(n)  cg(n) 8n  n0.
n
Xi=1
i = n(n + 1)
2 ;
n
Xi=1
i2 = n(n + 1)(2n + 1)
6 ;
n
Xi=1
i3 = n2(n + 1)2
4 :
In general:
n
Xi=1
im =
1
m + 1(n + 1)m+1 − 1 −
n
Xi=1

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