Sunday, August 31, 2008

World record ($100,000) prime number found?

Researchers may have turned up the 45th example of a Mersenne prime—a type of prime number rare enough that months or years of computerized searching are required to pick one out among the throngs of mere primes.Details are still sketchy but the Great Internet Mersenne Prime Search (GIMPS) has announced on its Web site that a computer turned up a candidate Mersenne (pronounced mehr-SENN) prime on August 23. Checking began this week and should be completed by September 16.If it checks out, the finding of the 45th Mersenne prime (MP) might qualify for a $100,000 prize offered by the Electronic Frontier Foundation for anyone who a prime number having at least 10 million digits. The 44th MP, discovered in September 2006 by two researchers at Central Missouri State University, clocked in at 9.808358 million digits.Mersennse primes, named for 17th-century French smarty-pants monk Marin Mersenne (left), follow the formula 2^p – 1, where the power p is itself a prime number. (Commenters, don't hesitate to pounce on errors in my arithmetic.)
Take p=3:2^3 – 1= 8 – 1= 7, which is prime(QED)But not all p's yield the Mersenne variety.Consider p=11:2^11 – 1= 2048 – 1= 2047= 23 * 89(T4P = thanks for playing)The 44th MP had p of 32,582,657.People aren't hunting for Mersenne primes in order to prove anything about them, according to Mike Breen of the American Mathematical Society. "They're doing it because it's there, and it's an interesting challenge," he says. Math nerds also go ga-ga for really big numbers, as we all do I'm sure.Here's a side note courtesy of Breen (to whom no errors of mine should be attributed): Mersenne primes are all associated with "perfect numbers," those such as 6 or 28 whose factors add up to themselves (or to double themselves if you include the number itself as a factor). E.g., the factors of 28 are 1, 2, 4, 7 and 14, which add up to 28.There's a simple formula relating the two:
Perfect Number = MP * 2^(p-1)
Take p=3 again:
(2^3 – 1) * (2^[3-1])= 7 * 2^2= 7 * 4= 28
I leave the proof of the relationship to the reader.

Think when the Night is brighter than Day!

We know in a time-span of 24 hours there are altered sessions of day and night. Certain part of the world illuminates when it faces the bright Sun and the rest of the part sleeps in dark during the moment. Though the darker side is also not completely dark all the times in a month as it manages to get some lumen from the moon. Think for a possibility that if there is a star in the Universe which is probably brighter than the sun and can throw its rays to darker part of the earth and lighten the earth? Now you will say that the star would be billion light years far so it may take billions of years for this event to happen. It may be partly true but we can't reject the fact that the said star may on its way to complete its cycle might be nearing earth so the light may reach the earth in lesser billion years as assumed before. Well,this is one school of thought.
Now think if there is a star which is not a emitter of light but bigger in size than the star in the picture and it is right now blocking the path of the light emitting star. So, whenever this bigger star while moving unblocks the view of the illuminated star from the earth then the chances are there that the darker side of the earth which is not illuminated by the sun rays may get illumination from that particular star. And probably the lumen reaching the earth may be more than the lumen received from the sun so it can be concluded that the night can be brighter than the Day!


Saturday, August 30, 2008

Minding Mistakes: How the Brain Monitors Errors and Learns from Goofs

Key Concepts
The brain contains neural machinery for recognizing errors, correcting them, and optimizing behavior.
The neurotransmitter dopamine plays a major role in our ability to learn from our mistakes. Genetic variants that affect dopamine signaling may partly explain differences between people in the extent to which they learn from errors or negative consequences.
Certain patterns of cerebral activity often foreshadow errors, opening up the possibility of preventing blunders with portable devices that can detect error-prone brain states.
April 26, 1986: During routine testing, reactor number 4 of the Chernobyl nuclear power plant explodes, triggering the worst catastrophe in the history of the civilian use of nuclear energy.
September 22, 2006: On a trial run, experimental maglev train Transrapid 08 plows into a maintenance vehicle at 125 mph near Lathen, Germany, spewing wreckage over hundreds of yards, killing 23 passengers and severely injuring 10 others.
Human error was behind both accidents. Of course, people make mistakes, both large and small, every day, and monitoring and fixing slipups is a regular part of life. Although people understandably would like to avoid serious errors, most goofs have a good side: they give the brain information about how to improve or fine-tune behavior. In fact, learning from mistakes is likely essential to the survival of our species.
In recent years researchers have identified a region of the brain called the medial frontal cortex that plays a central role in detecting mistakes and responding to them. These frontal neurons become active whenever people or monkeys change their behavior after the kind of negative feedback or diminished reward that results from errors.
Much of our ability to learn from flubs, the latest studies show, stems from the actions of the neurotransmitter dopamine. In fact, genetic variations that affect dopamine signaling may help explain differences between people in the extent to which they learn from past goofs. Meanwhile certain patterns of cerebral activity often foreshadow miscues, opening up the possibility of preventing blunders with portable devices that can detect error-prone brain states.
Error DetectorHints of the brain’s error-detection apparatus emerged serendipitously in the early 1990s. Psychologist Michael Falkenstein of the University of Dortmund in Germany and his colleagues were monitoring subjects’ brains using electroencephalography (EEG) during a psychology experiment and noticed that whenever a subject pressed the wrong button, the electrical potential in the frontal lobe suddenly dropped by about 10 microvolts. Psychologist William J. Gehring of the University of Illinois and his colleagues confirmed this effect, which researchers refer to as error-related negativity, or ERN.

An ERN may appear after various types of errors, unfavorable outcomes or conflict situations. Action errors occur when a person’s behavior produces an unintended result. Time pressure, for example, often leads to misspellings while typing or incorrect addresses on e-mails. An ERN quickly follows such action errors, peaking within 100 milliseconds after the incorrect muscle activity ends.
A slightly more delayed ERN, one that crests 250 to 300 milliseconds after an outcome, occurs in response to unfavorable feedback or monetary losses. This so-called feedback ERN also may appear in situations in which a person faces a difficult choice—known as decision uncertainty—and remains conflicted even after making a choice. For instance, a feedback ERN may occur after a person has picked a checkout line in a supermarket and then realizes that the line is moving slower than the adjacent queue.
Where in the brain does the ERN originate? Using functional magnetic resonance imaging, among other imaging methods, researchers have repeatedly found that error recognition takes place in the medial frontal cortex, a region on the surface of the brain in the middle of the frontal lobe, including the anterior cingulate. Such studies implicate this brain region as a monitor of negative feedback, action errors and decision uncertainty—and thus as an overall supervisor of human performance.
In a 2005 paper, along with psychologist Stefan Debener of the Institute of Hearing Research in Southampton, England, and our colleagues, I showed that the medial frontal cortex is the probable source of the ERN. In this study, subjects performed a so-called flanker task, in which they specified the direction of a central target arrow in the midst of surrounding decoy arrows while we monitored their brain activity using EEG and fMRI simultaneously. We found that as soon as an ERN occurs, activity in the medial frontal cortex increases and that the bigger the ERN the stronger the fMRI signal, suggesting that this brain region does indeed generate the classic error signal.

Learning from LapsesIn addition to recognizing errors, the brain must have a way of adaptively responding to them. In the 1970s psychologist Patrick Rabbitt of the University of Manchester in England, one of the first to systematically study such reactions, observed that typing misstrikes are made with slightly less keyboard pressure than are correct strokes, as if the typist were attempting to hold back at the last moment.
More generally, people often react to errors by slowing down after a mistake, presumably to more carefully analyze a problem and to switch to a different strategy for tackling a task. Such behavioral changes represent ways in which we learn from our mistakes in hopes of avoiding similar slipups in the future.
The medial frontal cortex seems to govern this process as well. Imaging studies show that neural activity in this region increases, for example, before a person slows down after an action error. Moreover, researchers have found responses from individual neurons in the medial frontal cortex in monkeys that implicate these cells in an animal’s behavioral response to negative feedback, akin to that which results from an error.
In 1998 neuroscientists Keisetsu Shima and Jun Tanji of the Tohoku University School of Medicine in Sendai, Japan, trained three monkeys to either push or turn a handle in response to a visual signal. A monkey chose its response based on the reward it expected: it would, say, push the handle if that action had been consistently followed by a reward. But when the researchers successively reduced the reward for pushing—a type of negative feedback or error signal—the animals would within a few trials switch to turning the handle instead. Meanwhile researchers were recording the electrical activity of single neurons in part of the monkeys’ cingulate.
Shima and Tanji found that four types of neurons altered their activity after a reduced reward but only if the monkey used that reduction as a cue to push instead of turn, or vice versa. These neurons did not flinch if the monkey did not decide to switch actions or if it did so in response to a tone rather than to a lesser reward. And when the researchers temporarily deactivated neurons in this region, the monkey no longer switched movements after a dip in its incentive. Thus, these neurons relay information about the degree of reward for the purpose of altering behavior and can use negative feedback as a guide to improvement.
In 2004 neurosurgeon Ziv M. Williams and his colleagues at Massachusetts General Hospital reported finding a set of neurons in the human anterior cingulate with similar properties. The researchers recorded from these neurons in five patients who were scheduled for surgical removal of that brain region. While these neurons were tapped, the patients did a task in which they had to choose one of two directions to move a joystick based on a visual cue that also specified a monetary reward: either nine or 15 cents. On the nine-cent trials, participants were supposed to change the direction in which they moved the joystick.
Similar to the responses of monkey neurons, activity among the anterior cingulate neurons rose to the highest levels when the cue indicated a reduced reward along with a change in the direction of movement. In addition, the level of neuronal activity predicted whether a person would act as instructed or make an error. After surgical removal of those cells, the patients made more errors when they were cued to change their behavior in the face of a reduced payment. These neurons, therefore, seem to link information about rewards to behavior. After detecting discrepancies between actual and desired outcomes, the cells determine the corrective action needed to optimize reward.
But unless instructed to do so, animals do not generally alter their behavior after just one mishap. Rather they change strategies only after a pattern of failed attempts. The anterior cingulate also seems to work in this more practical fashion in arbitrating the response to errors. In a 2006 study experimental psychologists Stephen Kennerley and Matthew Rushworth and their colleagues at the University of Oxford taught rhesus monkeys to pull a lever to get food. After 25 trials, the researchers changed the rules, dispensing treats when the monkeys turned the lever instead of pulling it. The monkeys adapted and switched to turning the lever. After a while, the researchers changed the rules once more, and the monkeys again altered their behavior.

Each time the monkeys did not immediately switch actions, but did so only after a few false starts, using the previous four or five trials as a guide. After damage to the anterior cingulate, however, the animals lost this longer-term view and instead used only their most recent success or failure as a guide. Thus, the anterior cingulate seems to control an animal’s ability to evaluate a short history of hits and misses as a guide to future decisions.
Chemical IncentiveSuch evaluations may depend on dopamine, which conveys success signals in the brain. Neurophysiologist Wolfram Schultz, now at the University of Cambridge, and his colleagues have shown over the past 15 years that dopamine-producing nerve cells alter their activity when a reward is either greater or less than anticipated. When a monkey is rewarded unexpectedly, say, for a correct response, the cells become excited, releasing dopamine, whereas their activity drops when the monkey fails to get a treat after an error. And if dopamine quantity stably altered the connections between nerve cells, its differential release could thereby promote learning from successes and failures.
Indeed, changes in dopamine levels may help to explain how we learn from positive as well as negative reinforcement. Dopamine excites the brain’s so-called Go pathway, which promotes a response while also inhibiting the action-suppressing “NoGo” pathway. Thus, bursts of dopamine resulting from positive reinforcement promote learning by both activating the Go channel and blocking NoGo. In contrast, dips in dopamine after negative outcomes should promote avoidance behavior by inactivating the Go pathway while releasing inhibition of NoGo.
In 2004 psychologist Michael J. Frank, then at the University of Colorado at Boulder, and his colleagues reported evidence for dopamine’s influence on learning in a study of patients with Parkinson’s disease, who produce too little of the neurotransmitter. Frank theorized that Parkinson’s patients may have trouble generating the dopamine needed to learn from positive feedback but that their low dopamine levels may facilitate training based on negative feedback.
In the study the researchers displayed pairs of symbols on a computer screen and asked 19 healthy people and 30 Parkinson’s patients to choose one symbol from each pair. The word “correct” appeared whenever a subject had chosen an arbitrarily correct symbol, whereas the word “incorrect” flashed after every “wrong” selection. (No symbol was invariably correct or incorrect.) One of them was deemed right 80 percent of the time, and another 20 percent. For other pairs, the probabilities were 70:30 and 60:40. The subjects were expected to learn from this feedback and thereby increase the number of correct choices in later test runs.
As expected, the healthy people learned to prefer the correct symbols and avoid the incorrect ones with about equal proficiency. Parkinson’s patients, on the other hand, showed a stronger tendency to reject negative symbols than to select the positive ones—that is, they learned more from their errors than from their hits, showing that the lack of dopamine did bias their learning in the expected way. In addition, the patients’ ability to learn from positive feedback outpaced that from negative feedback after they took medication that boosted brain levels of dopamine, underscoring the importance of dopamine in positive reinforcement.
Dopamine-based discrepancies in learning ability also appear within the healthy popu­lation. Last December, along with psychology graduate student Tilmann A. Klein and our colleagues, I showed that such variations are partly based on individual differences in a gene for the D2 dopamine receptor. A variant of this gene, called A1, results in up to a 30 percent reduction in the density of those receptors on nerve cell membranes.

We asked 12 males with the A1 variant and 14 males who had the more common form of this gene to perform a symbol-based learning test like the one Frank used. We found that A1 carriers were less able to remember, and avoid, the negative symbols than were the participants who did not have this form of the gene. The A1 carriers also avoided the negative symbols less often than they picked the positive ones. Noncarriers learned about equally well from the good and bad symbols.
Thus, fewer D2 receptors may impair a person’s ability to learn from mistakes or negative outcomes. (This molecular quirk is just one of many factors that influence such learning.) Accordingly, our fMRI results show that the medial frontal cortex of A1 carriers generates a weaker response to errors than it does in other people, suggesting that this brain area is one site at which dopamine exerts its effect on learning from negative feedback.
But if fewer D2 receptors leads to impaired avoidance learning, why do drugs that boost dopamine signaling also lead to such impairments in Parkinson’s patients? In both scenarios, do­pa­mine signaling may, in fact, be increased through other dopamine receptors; research indicates that A1 carriers produce an unusually large amount of do­pa­­mine, perhaps as a way to compensate for their lack of D2 receptors. Whatever the reason, insensitivity to unpleasant consequences may contribute to the slightly higher rates of obesity, compulsive gambling and addiction among A1 carriers than in the general population.
Foreshadowing FaultsAlthough learning from mistakes may help us avoid future missteps, inexperience or inattention can still lead to errors. Many such goofs turn out to be predictable, however, foreshadowed by telltale changes in brain metabolism, according to research my team published in April in the Proceedings of the National Academy of Sci­ences USA.
Along with cognitive neuroscientist Tom Eichele of the University of Bergen in Norway and several colleagues, I asked 13 young adults to perform a flanker task while we monitored their brain activity using fMRI. Starting about 30 seconds before our subjects made an error, we found distinct but gradual changes in the activation of two brain networks.
One of the networks, called the default mode region, is usually more active when a person is at rest and quiets down when a person is engaged in a task. But before an error, the posterior part of this network—which includes the retrosplenial cortex, located near the center of the brain at the surface—became more active, indicating that the mind was relaxing. Meanwhile activity declined in areas of the frontal lobe that spring to life whenever a person is working hard at something, suggesting that the person was also becoming less engaged in the task at hand.
Our results show that errors are the product of gradual changes in the brain rather than unpredictable blips in brain activity. Such adjustments could be used to foretell errors, particularly those that occur during monotonous tasks. In the future, people might wear portable devices that monitor these brain states as a first step toward preventing mistakes where they are most likely to occur—and when they matter most.
Editor's Note: This story was originally published with the title "Minding Mistakes"

Markus Ullsperger is a physician and head of the cognitive neurology research group at the Max Planck Institute for Neurological Research in Cologne, Germany.


A Natural Log: Our Innate Sense of Numbers is Logarithmic, Not Linear

We humans seem to be born with a number line in our head. But a May 30 study in Science suggests it may look less like an evenly segmented ruler and more like a logarithmic slide rule on which the distance between two numbers represents their ratio (when ­di­vided) rather than their difference (when subtracted).
The mathematical idea of a number line—a line of numbers placed in order at equal intervals—is a simple yet surprisingly powerful tool, useful for everything from taking measure­ments to geometry and calculus.
Previous studies of Westerners showed that people tend to map numbers on a linear scale, with the numerals evenly spaced along the line. But if the numbers are presented as hard-to-count groups of dots, people will logarithmically group the larger numbers closer together on one end of the scale in what researchers call a “compression effect.” Preschoolers also group numbers this way before they begin their formal education in math.

To investigate which number-line concept is innate, neuroscientist Stanislas Dehaene of the College of France in Paris worked with the Mundurukú, an Amazonian culture with little exposure to modern math or measuring devices. The Mundurukú were immediately able to place numbers on a line when asked, but they grouped them logarithmically.
Dehaene says the research suggests that a logarithmic number line might be an intuitive mathematical concept, whereas the idea of a linear number line might have to be learned.
Editor's Note: This story was originally printed with the title "A Natural Log"


A Murder in Broad Daylight!

(pics taken on 29th august 08 near teen haath naka,thane)

The Government of India though spends numerous of crores on the advertisement to save power but what about its own discipline and committment to really save the power?

Power is the backbone for any country. It should be strong and should be preserved and used with great care. Wastage of power not only degrades our Industrial Growth but also supports the devil of Global Warming.

The following pics really pains me that the government authorities are least careful and It will not be a hyper if I say that they are muderers who do murder in the "Broad Daylight".


Live Earth Destop Wallpaper-Pics taken from satellite

I have come across a very useful and interesting weblink:-
You can watch Live:-
1. Global Temperature
2. Position of Moon
3. Recent Hurricanes
4. recent Earthquakes
5. Weather Forecast
6. Ship Location
7. Global Warming Temperature
8. Live Volcano activities
9. Satellite Locations

and much more.......

just try out and defacto it is worth not missing!

Friday, August 8, 2008


"Fighting with physical pain shows the strength of your patience though fighting with mental pain shows your attitude"


Sunday, August 3, 2008

Doomsday 2012?

Apparently, the world is going to end on December 21st, 2012. Yes, you read correctly, in some way, shape or form, the Earth (or at least a large portion of humans on the planet) will cease to exist. Stop planning your careers, don't bother buying a house, and be sure to spend the last years of your life doing something you always wanted to do but never had the time. Now you have the time, four years of time, to enjoy yourselves before… the end.
So what is all this crazy talk? We've all heard these doomsday predictions before, we're still here, and the planet is still here, why is 2012 so important? Well, the Mayan calendar stops at the end of the year 2012, churning up all sorts of religious, scientific, astrological and historic reasons why this calendar foretells the end of life as we know it. The Mayan Prophecy is gaining strength and appears to be worrying people in all areas of society. Forget Nostradamus, forget the Y2K bug, forget the credit crunch, this event is predicted to be huge and many wholeheartedly believe this is going to happen for real. Planet X could even be making a comeback.
For all those 2012 Mayan Prophecy believers out there, I have bad news. There is going to be no doomsday event in 2012, and here's why…
The Mayan CalendarSo what is the Mayan Calendar? The calendar was constructed by an advanced civilization called the Mayans around 250-900 AD. Evidence for the Maya empire stretches around most parts of the southern states of Mexico and reaches down to the current geological locations of Guatemala, Belize, El Salvador and some of Honduras. The people living in Mayan society exhibited very advanced written skills and had an amazing ability when constructing cities and urban planning. The Mayans are probably most famous for their pyramids and other intricate and grand buildings. The people of Maya had a huge impact on Central American culture, not just within their civilization, but with other indigenous populations in the region. Significant numbers of Mayans still live today, continuing their age-old traditions.
The Mayans used many different calendars and viewed time as a meshing of spiritual cycles. While the calendars had practical uses, such as social, agricultural, commercial and administrative tasks, there was a very heavy religious element. Each day had a patron spirit, signifying that each day had specific use. This contrasts greatly with our modern Gregorian calendar which primarily sets the administrative, social and economic dates.

Most of the Mayan calendars were short. The Tzolk'in calendar lasted for 260 days and the Haab' approximated the solar year of 365 days. The Mayans then combined both the Tzolk'in and the Haab' to form the "Calendar Round", a cycle lasting 52 Haab's (around 52 years, or the approximate length of a generation). Within the Calendar Round were the trecena (13 day cycle) and the veintena (20 day cycle). Obviously, this system would only be of use when considering the 18,980 unique days over the course of 52 years. In addition to these systems, the Mayans also had the "Venus Cycle". Being keen and highly accurate astronomers they formed a calendar based on the location of Venus in the night sky. It's also possible they did the same with the other planets in the Solar System.
Using the Calendar Round is great if you simply wanted to remember the date of your birthday or significant religious periods, but what about recording history? There was no way to record a date older than 52 years.
The end of the Long Count = the end of the Earth?The Mayans had a solution. Using an innovative method, they were able to expand on the 52 year Calendar Round. Up to this point, the Mayan Calendar may have sounded a little archaic - after all, it was possibly based on religious belief, the menstrual cycle, mathematical calculations using the numbers 13 and 20 as the base units and a heavy mix of astrological myth. The only principal correlation with the modern calendar is the Haab' that recognised there were 365 days in one solar year (it's not clear whether the Mayans accounted for leap years). The answer to a longer calendar could be found in the "Long Count", a calendar lasting 5126 years.
I'm personally very impressed with this dating system. For starters, it is numerically predictable and it can accurately pinpoint historical dates. However, it depends on a base unit of 20 (where modern calendars use a base unit of 10). So how does this work?

The base year for the Mayan Long Count starts at "". Each zero goes from 0-19 and each represent a tally of Mayan days. So, for example, the first day in the Long Count is denoted as On the 19th day we'll have, on the 20th day it goes up one level and we'll have This count continues until (about one year), (about 20 years) and (about 400 years). Therefore, if I pick an arbitrary date of, this represents the Mayan date of approximately 1012 years, 7 months and 1 day.
This is all very interesting, but what has this got to do with the end of the world? The Mayan Prophecy is wholly based on the assumption that something bad is going to happen when the Mayan Long Count calendar runs out. Experts are divided as to when the Long Count ends, but as the Maya used the numbers of 13 and 20 at the root of their numerical systems, the last day could occur on When does this happen? Well, represents 5126 years and the Long Count started on, which corresponds to the modern date of August 11th 3114 BC. Have you seen the problem yet? The Mayan Long Count ends 5126 years later on December 21st, 2012.
DoomsdayWhen something ends (even something as innocent as an ancient calendar), people seem to think up the most extreme possibilities for the end of civilization as we know it. A brief scan of the internet will pull up the most popular to some very weird ways that we will, with little logical thought, be wiped off the face of the planet. Archaeologists and mythologists on the other hand believe that the Mayans predicted an age of enlightenment when comes around; there isn't actually much evidence to suggest doomsday will strike. If anything, the Mayans predict a religious miracle, not anything sinister.
Myths are abound and seem to be fuelling movie storylines. It looks like the new Indiana Jones and the Kingdom of the Crystal Skull is even based around the Mayan myth that 13 crystal skulls can save humanity from certain doom. This myth says that if the 13 ancient skulls are not brought together at the right time, the Earth will be knocked off its axis. This might be a great plotline for blockbuster movies, but it also highlights the hype that can be stirred, lighting up religious, scientific and not-so-scientific ideas that the world is doomed.

Some of the most popular space-based threats to the Earth and mankind focus on Planet X wiping most life off the planet, meteorite impacts, black holes, killer solar flares, Gamma Ray Bursts from star systems, a rapid ice age and a polar (magnetic) shift. There is so much evidence against these things happening in 2012, it's shocking just how much of a following they have generated. Each of the above "threats" needs their own devoted article as to why there is no hard evidence to support the hype.
But the fact remains, the Mayan Doomsday Prophecy is purely based on a calendar which we believe hasn't been designed to calculate dates beyond 2012. Mayan archaeo-astronomers are even in debate as to whether the Long Count is designed to be reset to after, or whether the calendar simply continues to (approximately 8000 AD) and then reset. As Karl Kruszelnicki brilliantly writes:
"…when a calendar comes to the end of a cycle, it just rolls over into the next cycle. In our Western society, every year 31 December is followed, not by the End of the World, but by 1 January. So in the Mayan calendar will be followed by - or good-ol' 22 December 2012, with only a few shopping days left to Christmas." - Excerpt from Dr Karl's "Great Moments in Science".


Friday, August 1, 2008


" Faith is the only widely used though cheapest tool available in the world"