Fighting violent gang crime with math
LOS ANGELES — UCLA mathematicians working with the Los Angeles Police Department to analyze crime patterns have designed a mathematical algorithm to identify street gangs involved in unsolved violent crimes. Their research is based on patterns of known criminal activity between gangs, and represents the first scholarly study of gang violence of its kind. The research appears on the website of the peer-reviewed mathematical journal Inverse Problems and will be published in a future print edition. In developing their algorithm, the mathematicians analyzed more than 1,000 gang crimes and suspected gang crimes, about half of them unsolved, that occurred over a 10-year period in an East Los Angeles police district known as Hollenbeck, a small area in which there are some 30 gangs and nearly 70 gang rivalries.
To test the algorithm, the researchers created a set of simulated data that closely mimicked the crime patterns of the Hollenbeck gang network. They then dropped some of the key information out — at times the victim, the perpetrator or both — and tested how well the algorithm could calculate the missing information. "If police believe a crime might have been committed by one of seven or eight rival gangs, our method would look at recent historical events in the area and compute probabilities as to which of these gangs are most likely to have committed crime," said the study's senior author, Andrea Bertozzi, a professor of mathematics and director of applied mathematics at UCLA.
About 80 percent of the time, the mathematicians could narrow it down to three gang rivalries that were most likely involved in a crime. The mathematicians also found that the correct gang was ranked No. 1 — rather than just among the top three — 50 percent of the time, compared with just 17 percent by chance.
"The algorithm we devised could apply to a much broader class of problems that involve activity on social networks," Bertozzi said. "You have events — they could be crimes or something else — that occur in a time series and a known network. There is activity between nodes, in this case a gang attacking another gang. With some of these activities, you know exactly who was involved and with others, you do not. The challenge is how to make the best educated judgment as to who was involved in the unknown activities.
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Mathematics' Nearly Century-Old Partitions Enigma Spawns Fractals Solution
For someone who died at the age of 32 the largely self-taught Indian mathematician Srinivasa Ramanujan left behind an impressive legacy of insights into the theory of numbers – including many claims that he did not support with proof One of his more enigmatic statements, made nearly a century ago, about counting the number of ways in which a number can be expressed as
a sum, has now helped researchers find unexpected fractal structures in the landscape of counting.
Ramanujan's statement concerned the deceptively simple concept of partitions—the different ways in which a whole number can be subdivided into smaller numbers. Ken Ono of Emory University and his collaborators have now figured out new ways of counting all possible partitions, and found that the results form fractals—namely, structures in which patterns or shapes repeat identically at multiple different scales. "The fractal theory we've discovered completely answers Ramanujan's enigmatic statement," Ono says. The problems his team cracked were seen as holy grails of number theory, and its solutions may have repercussions throughout mathematics.
One way to think of partitions is to consider how a set of any (indistinguishable) objects can be divided into subsets. For example, if you need to store five boxes in your basement, you can pile them all into a single stack; lay them individually on the floor as five subsets containing one box apiece; put them in one pile, or subset, of three plus one pile of two; and so on—you have a total of 7 options:
5 = 1+1+1+l+l, 1+1+1+2, 1+1+3, 1+4, 1+2+2 or 2 + 3.
Mathematicians express this by saying p(5) = 7, where p is short for partition. For the number 6 there are 11 options: p(6) = 11. As the number n increases, p(n) soon starts to grow very fast, so that for example p{ 100) - 190,569,292 and p( 1,000) is a 32-figure number.
The concept is so basic and fundamental that it is central to number theory and pops up in most other fields of math as well. Mathematicians have long known that the sequence of numbers made by the p(n)'s for all values of n is far from being random. Ramanujan and others after him found formulas to predict the value of any p(n) with good approximation. And general "recursive" formulas have long existed to calculate p(n), but they don't speed up calculations very much because to find p(n) you first need to know p(n - 1), p(n - 2) and so on. "That's impractical even with the help of a computer today," Ono says.
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Can Next-Generation Reactors Power a Safe Nuclear Future?
By Clay Dillow
As nations around the world rush to reconsider their nuclear plans, nuclear experts look toward a future of smaller, safer reactors designed to greatly reduce the likelihood of a Fukushima-sized catastrophe.
At this time last week, the Nuclear Renaissance was in full swing. Plans were moving forward to use the $36 billion in loan guarantees for new reactors in President Obama's 2012 budget. China was approving reactor stations at a steady pace, and nations across Europe were considering new nuclear sites of their own. Seven days later, the push toward more and better nuclear power has come to a full stop, as the crisis at Japan’s crippled Fukushima Daiichi power station threatens to unravel into the worst nuclear disaster in history.
But amid a strong, worldwide nuclear backlash, it's important to remember that the next generation of nuclear reactors are designed to prevent exactly what went wrong at the 40-year-old Fukushima Daiichi plant. Which is good, because according to the experts, a future weaned from fossil fuels will include nuclear power whether we like it or not. Here's what that future may look like.
In the days since the 9.0-magnitude quake and resulting tsunami heaped human tragedy and potential atomic disaster on Japan, things have gone from bad to worse at Fukushima Daiichi, sparking a flood of conjecture about the future of nuclear energy worldwide. Switzerland quickly suspended the approval process for three new plants, Germany's Chancellor announced that country would undertake a "measured" exit from nuclear power, and even China - the vanguard of the global nuclear energy charge - showed apprehension, freezing all new approvals for new nuclear power plants.
It’s too early to begin tallying the lessons learned in Japan, but technically speaking most of what’s gone wrong with Fukushima Daiichi's 1970s-era reactors has already been learned and accounted for in the latest nuclear power plant technology.
Keeping a nuclear plant safe means keeping it cool in any circumstances, including those in which man-made or natural disaster knocks out the usual cooling methods. This highlights the importance of safety features built into so-called Generation III-plus nuclear plant models, the latest feasible plant designs. These redundant and passive safety systems work without the help of an operator, or even electricity, during times of duress, be it man-made or natural.
Тема 3.Техническое описание
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