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While great theorems are arguably the end goal of mathematics, it is often a great conjecture that does the most to advance understanding and create new theories. For no field has this been truer than computational complexity, the study of which computational problems are within reach of a standard computer. The famous P versus NP conjecture, still unsolved after 40 years, has done more than perhaps any other single mathematical assertion in modern times to set the ground rules and the very language of its field.
Formulated in 1971, the conjecture focused the attention of computer scientists on the contrast between two classes of problems: P, the class of problems a computer can solve efficiently, and NP, the class of problems for which a computer can check efficiently whether a proposed solution is correct, even if it doesn’t have the capability to come up with that solution in the first place. Natural computation problems tend to fall into one of these two categories. The conjecture states—and most computer scientists believe—that these two classes are distinct, meaning that there are some problems in NP whose solutions are beyond the reach of any efficient computer algorithm.
Now, the field of computational complexity has been electrified by a new conjecture, which, while not as monumental as the P versus NP conjecture, in some sense picks up where that conjecture leaves off. If the ʻUnique Games Conjectureʼ is correct, then for many of the problems people would most like to solve, it’s hard not only to find an exact solution—finding even a good approximation of the solution is beyond the reach of a computer.
Over the four decades since the original P versus NP conjecture was formulated, it has stubbornly resisted proof. But at the same time, computer scientists have amassed a wealth of evidence suggesting that it is correct. They have shown that thousands of practical problems—for example, figuring out the best design for a chip, the best airplane schedule, or the lowest-energy configuration of a protein—are NP-hard, meaning that an efficient algorithm for any one of them would automatically produce an efficient solution to all the problems in NP (which would mean that P = NP). So far, no one has managed to produce an efficient algorithm for any one of these thousands of problems, and not for want of trying. If the conjecture is correct, no one ever will.
But suppose that instead of, say, a perfect chip design, you would be content with one that is simply pretty good. Over the past few decades, computer scientists have come up with good approximation algorithms for some such problems, and for other problems they have proved that good approximation algorithms do not exist. However, for many of the problems people are most interested in solving, computer scientists are in the dark about whether, and how well, they can be approximated.
Now, the Unique Games Conjecture (UGC) has given researchers a new hook on which to try to catch some of these slippery problems. Formulated in 2002 by Subhash Khot, currently at New York University, the UGC simply proposes that one particular problem about assigning colors to the nodes of a network is NP-hard to solve even approximately.
This conjecture may seem, on the face of it, like a pretty parochial statement (though possibly hard to prove, or even false). Over the past decade, however, computer scientists have found to their surprise that if the conjecture is true, then a host of problems—some of them seeming to bear little resemblance to the original Unique Games problem—are also hard to approximate. The findings have left researchers scratching their heads about just what is so special about this particular network-coloring problem.
Like many great conjectures, the UGC has led to findings in a wide range of fields seemingly far removed from computational complexity, including the structure of foams, the geometry of different ways to measure distance, and even the merits of different voting systems.
And also like many great conjectures, the UGC has the potential to advance the field of computational complexity regardless of whether it is eventually proved or disproved. If it is proved, it will give exact hardness results for a wide range of approximation problems, and in the case of a wide class of problems known as constraint satisfaction problems, it will show that the ‘obvious suspect’ method for solving these problems truly is the best one, bringing a satisfying closure to that research area. Disproving the UGC might be even more exciting, since it would require the creation of a powerful new approximation algorithm that would presumably be very different from the approximation algorithms known today.
To get a sense of the types of approximation problems on which the UGC has the potential to shed light, let’s turn our microscope on a classic problem known as Minimum Vertex Cover, which has applications in communications, civil and electrical engineering, and bioinformatics. Given a network—a collection of nodes (also called vertices) and edges connecting some of the vertices—a vertex cover is a subset of the vertices (called the cover) such that every edge in the network touches at least one vertex in the cover. The Minimum Vertex Cover problem asks for a vertex cover with the smallest possible number of vertices.
Vertex Cover: In the four networks above, the red vertices form a vertex cover, since every edge touches at least one red vertex.
One way to find the smallest possible vertex cover is simply to look at all subsets of the vertices, weed out the ones that aren’t vertex covers, and then see which of the remaining subsets are the smallest. However, for a network with n vertices, there are 2n subsets to check. Exponential functions such as 2n grow so quickly that even for fairly small values of n, this algorithm would take longer than the age of the universe for even the fastest computer to run.
The consensus among computer scientists is that for a computer algorithm to be efficient, its running time must be at most a polynomial function of the size of the input, n—that is, something like 2n2+1 or 4n3+n (this is, in fact, what it means for an algorithm to belong to the class P). In 1972, Richard Karp of the University of California, Berkeley famously showed that a polynomial-time algorithm for Minimum Vertex Cover does not exist unless P = NP: in other words, this problem is NP-hard.
Thus, short of a proof that P = NP, the best that researchers can hope for is an efficient approximation algorithm: one that is guaranteed to produce vertex covers that are pretty small, but maybe not the smallest.
Luckily, one very simple such algorithm exists: Start by choosing any one edge of your network, and put both its endpoints in your subset. Delete from the network those two vertices and all edges that touch either one of them, and then repeat the process by choosing any one edge from the new, smaller network and putting its two endpoints in your subset. Keep repeating this process until all the edges have been deleted. This will take at mostn⁄2 steps, so it is very efficient, unlike the previous algorithm. The resulting subset is a vertex cover, and although it may not be the smallest, it has at most twice as many vertices as it needs, since every vertex cover must have at least one of the two vertices chosen in each round. Computer scientists say this algorithm achieves a factor-of-2 approximation.
Since this algorithm is so simple, it might seem likely that a more ingenious algorithm could do better, coming closer to the smallest number of vertices needed. Indeed, in the first couple of decades after the P versus NP conjecture was formulated, many computer scientists believed that getting good approximations must be easier than finding the exact answer to an NP-hard question, says Sanjeev Arora, of Princeton University. “The intuition was that there are so many different things you could throw at a problem to get approximate solutions,” he says.
But no one has ever come up with an algorithm that approximates Minimum Vertex Cover to within any constant factor better than 2. Experiences such as this one made computer scientists start to wonder whether there are some problems for which finding a good approximation is every bit as hard as finding an exact solution—that is, NP-hard.
In 1992, computer scientists achieved a breakthrough: the famous PCP theorem, a powerful but very technical result that allowed researchers to prove that some problems are NP-hard even to approximate beyond some factor. Using the PCP theorem, for example, Irit Dinur, currently at the Weizmann Institute of Science in Rehovot, Israel, and Samuel Safra of Tel Aviv University showed in 2002 that assuming P is not equal to NP, there is no efficient algorithm for Minimum Vertex Cover with an approximation factor better than 10 √ 5 – 21, or about 1.36—that is, an algorithm guaranteed always to produce a vertex cover at most 36% larger than the minimum size.
Results like this one—in which there is a gap between the approximation factor of the best known algorithm and the approximation factor of the hardness result—create a tantalizing question for researchers. In the case of Minimum Vertex Cover, is the factor-of-2 approximation achieved by the simple algorithm we described indeed the best possible, and the PCP theorem is simply not powerful enough to prove that? Or is there a better algorithm out there, one perhaps that achieves a factor of 1.36?
Such questions are of interest not just to theoretical computer scientists. Improving a chip design algorithm from a factor-of-3 approximation to a factor-of-2 approximation might mean millions of dollars saved in improved efficiency, but it would be useful to know ahead of time if there is no point in searching for such an improvement because none exists.
In the late 1990s, in a landmark paper, Johan Håstad, of the Royal Institute of Technology in Stockholm, figured out how to get exact hardness results for a few specific problems. Some researchers managed to adapt his arguments to handle more problems, but for many problems, there were seemingly insurmountable technical obstacles to applying this paradigm.
“There were a lot of important problems we just couldn’t do,” says Wigderson.
And that’s where matters stood in 2001, when a young Princeton graduate student knocked on his advisor’s door to share a new approximation-hardness idea he had been playing around with.
The student, Subhash Khot, had noticed that a lot of the hard parts about an approximation problem he was working on seemed to be encapsulated in a conjecture about the hardness of assigning colors to the vertices of a network. A few days later, he told his advisor, Sanjeev Arora, that the conjecture was helpful in another problem as well. Arora thought the conjecture was worth writing up, but probably not important enough to submit to the best computer science conferences.
“We had no idea it would become so central,” Arora recalls.
Khot’s Unique Games Conjecture has its roots in the Network Coloring problem: Given a network and a set of colors, is it possible to color the vertices of the network in such a way that two vertices that share an edge always have different colors?
Vertex Coloring: Given a network, is there a way to color the vertices red, green and blue such that vertices that share an edge are always different colors? Figuring out which networks have this property is an NP-hard problem.
In the case of only two colors (say, red and green), it’s easy to answer this question efficiently for any given network: Simply start with a random vertex and color it (say) red. Now all the vertices connected to that one have to be colored green. Color those, and continue to color every vertex connected to an already colored vertex, until you’ve either reached a contradiction or successfully colored the whole network.
If you are working with more than two colors, choosing the color of one vertex does not force the color of any of the vertices connected to it, so it’s impossible to carry out an algorithm as simple as the one described above. In fact, for more than two colors, deciding which networks can be colored is an NP-hard problem.
Khot decided to bridge the gulf between the two-color algorithm and the situation with more than two colors by considering networks that come equipped with a set of coloring rules, or constraints, such that if two vertices are connected by an edge, then whenever one edge gets colored, the constraint specifies what the color of the other edge must be. For such networks, an algorithm similar to the one for two colors determines, easily enough, whether the network can be colored in a way that satisfies the constraints.
For theoretical computer scientists, the natural next question is the optimization version of this problem: For a network that can’t be colored in a way that satisfies all the constraints, which coloring satisfies the most constraints possible? We will call this the Unique Games problem (the name has its origin in a different form of the problem, which is more complicated to state).
Khot conjectured that this innocent-looking question is in some sense the ultimate in hard-to-approximate problems.
More precisely, Khot’s Unique Games Conjecture makes the following rather technical statement: For every value of ε > 0, no matter how small, there is a number of colors k (possibly very large) for which, looking at constraint networks with k colors, it is NP-hard to tell the difference between networks for which at least (100 – ε)% of the constraints can be satisfied and networks for which at most ε% of the constraints can be satisfied.
So for example, choosing ε = 1, there is some number of colors k for which it is NP-hard (that is, effectively impossible) to distinguish between networks in which it is possible to satisfy at least 99% of the constraints and networks in which it is possible to satisfy at most 1% of the constraints.
On the face of it, this seems like an improbable assertion. Intuition suggests that constraint networks in which almost all the coloring constraints can be satisfied should look fundamentally different from constraint networks in which almost none of the constraints can be satisfied, and it should be easy to spot the differences between them. Yet when the colors and size of the networks start to number in the billions or trillions, this intuition suddenly starts feeling a lot less obvious.
It follows from the conjecture that the Unique Games coloring problem cannot be approximated efficiently up to anyconstant factor (in contrast with, for example, Minimum Vertex Cover, which you may recall can easily be approximated to within a factor of 2). To see why this is so, we’ll show that the Unique Games problem can’t be approximated up to a factor of ½. A similar argument (with different numbers) works for any other factor you choose.
So suppose, for a moment, that we could approximate Unique Games up to a factor of ½—that is, we could produce an efficient algorithm that, for any number of colors k and any constraint network, would produce a coloring of that network that satisfied at least half as many constraints as the best possible coloring.
This algorithm would immediately give us an efficient way to distinguish between (for example) networks in which one can satisfy at least 99% of the constraints and networks in which one can satisfy at most 1%: For the former networks, the algorithm would produce a coloring that satisfied at least 99/2 or 44.5% of the constraints, whereas for the latter networks, by their very nature the algorithm could produce no coloring that satisfied more than 1%. Thus, the existence of such an algorithm would violate the UGC. In other words, assuming the UGC is true, approximating the Unique Games problem up to a factor of ½—or indeed any constant factor—is NP-hard.
This reasoning is called a reduction argument: we reduced one problem (distinguishing between the 99% and 1% cases) to another problem (approximating the Unique Games problem up to a factor of ½), and then we used the hardness of the former problem to argue about the hardness of the latter problem. Reductions are the standard approach to proving hardness results in computational complexity.
Perhaps because of the relative simplicity of the coloring problem Khot studied, in the years following his statement of the UGC, computer scientists started noticing that the problem seemed to lend itself to reduction arguments—much more so than the complicated PCP theorem. Thus, it gave researchers a way to make hardness arguments for problems that had previously been beyond their reach.
“The UGC seems to encapsulate and simplify some very hard technical stuff,” O’Donnell says.
The first glimmer of the importance of the UGC came in 2003, when Khot and Oded Regev, of Tel Aviv University and the École Normale Supérieure in Paris, proved that if UGC is true, then computer scientists’ intuition about the Minimum Vertex Cover problem is correct: the problem is NP-hard to approximate up to any constant better than 2.
Max Cut: Given a network, which division of the vertices into two clumps produces the most edges that go from one clump to the other? The above division “cuts” through the six red edges.
Two years later, the UGC generated a truly startling finding, one that made computer scientists sit up and take note. It concerned a problem called Max Cut, which asks, given a network, how to divide up the vertices into two subsets in such a way that this division cuts through as many edges as possible (that is, separates the two endpoints of the edge into opposite subsets).
In 1994, Michel Goemans of MIT and David Williamson of Cornell University used a geometric argument involving trigonometric identities to come up with an efficient approximation algorithm for Max Cut that comes within about 87% of the best possible cut. Most computer scientists, says Luca Trevisan of Stanford University, believed that this particular number was an artifact of the geometric arguments involved and that there was probably a better approximation algorithm out there, since Max Cut is not inherently a deeply geometric problem. Håstad had used the PCP theorem to show in 1999 that it is NP-hard to approximate Max Cut better than about 94%, but that left plenty of room to improve on the 87% algorithm.
In 2005, however, Khot, O’Donnell, Guy Kindler of the Hebrew University of Jerusalem and Elchanan Mossel of the Weizmann Institute showed that if UGC is true, then the 87% algorithm is the best possible efficient approximation to Max Cut.
Since that time, researchers have proved numerous results of the form ‘If the UGC is true, then problem X is NP-hard to approximate better than a factor of Y.’ And in 2008, while at the University of Washington, Prasad Raghavendra—now of the Georgia Institute of Technology—astonished computer scientists by proving that UGC gives exact hardness results for all constraint satisfaction problems—problems such as the Unique Games problem in which the goal is to fulfill as many of a given set of constraints as possible. “Almost all problems in all disciplines have versions that look like that,” Wigderson says.
What’s more, Raghavendra showed that the UGC implies that the best approximation for any such problem is achieved by a very simple algorithm that uses a paradigm known as semidefinite programming.
In a certain sense, the results we’ve just described are like a house of cards: If someone disproves the UGC, they will all collapse (although some weaker versions might survive). As computer scientists started making this observation to Khot, he became determined, O’Donnell says, to show that it is possible to use the ideas in the UGC to prove some unconditional theorems: statements whose conclusions do not depend on the UGC ultimately getting proved.
Taxicab Geometry: The effective distance between two buildings is different for a bird than for a taxicab confined to city streets. The distortion between different ways of measuring distance turns out to be intimately connected to the Unique Games Conjecture.
Khot zeroed in on something called the Goemans-Linial Conjecture, an assertion about the geometry of metric spaces: spaces that come equipped with a metric, that is, a definition of the distance between any two points. While we’re all familiar with everyday, ʻas the crow fliesʼ distance (which mathematicians call the L2 metric), many other metrics exist. For example, there’s the taxicab metric, also known as the L1 metric: it specifies that the distance between two points is the length of the shortest route that follows a combination of North-South and East-West streets. And for some subsets of an L2 space, the square of the L2 metric is another metric, called the L22metric.
A fundamental geometric question is how much distortion occurs if you take objects in a metric space and view them through the lens of a different metric. For example, if you take two buildings in Manhattan, how much distance would you save if you could fly instead of drive between them?
The Goemans-Linial Conjecture asserts, roughly, that the L22metric is a not-too-distorted version of the L1 metric. Specifically, it says that there is some universal distortion constant K such that if you take any finite collection of points in an L22metric space, there’s a way to embed them (or in unscientific terms, to plunk them down) in an L1space so that the distance between any pair of points has been distorted by at most a factor of K.
Computer scientists have known for years that this conjecture is related to the problem of finding a good approximation algorithm for a problem called Sparsest Cut. This problem asks how to divide the vertices of a network into two clusters of roughly equal size, in such a way that as few edges as possible go from one cluster to the other. Algorithms that divide networks into natural clusters are useful for problems in fields such as computer vision and data analysis, since they give a way to find collections of related objects in large data sets.
The Sparsest Cut problem is NP-hard to solve exactly, so the best computer scientists can hope for is a good approximation. One approach to creating such an algorithm is to try to embed the vertices of the network in an L1space in such a way that the vertices are far apart on average, but those vertices connected by an edge are fairly close together. Doing so would give a geometric way to ‘see’ the natural clusters in the network, and computer scientists have shown that this process would lead to a good approximation algorithm for Sparsest Cut. Unfortunately, no one has found an efficient way to create such an embedding.
What computer scientists can do quite well, however, is embed the vertices in an L22space. If the Goemans-Linial conjecture could be proven, then computer scientists would know that this embedding was just a distorted version of a similar embedding in an L1 space. Using this knowledge, they could prove that there was an algorithm that approximated Sparsest Cut up to a constant factor.
In the early years of the new millennium, computer scientists had proved various results that seemed to be leading towards a potential proof of the Goemans-Linial conjecture, and by 2005, excitement was running high. However, working with Nisheeth Vishnoi, currently at Microsoft Research India in Bangalore, Khot found that if UGC is true then Sparsest Cut cannot be approximated up to any constant factor. This would imply that the Goemans-Linial conjecture is in fact false.
Since the Goemans-Linial conjecture is a purely geometric statement, Khot and Vishnoi felt that it should be possible to disprove it without depending on the UGC, a statement that is, after all, about computational complexity. In 2005, they managed to do just that, using ideas from the UGC but not relying on the statement of the UGC itself.
This finding is not the only unconditional result to emerge from studying the UGC. The conjecture has led researchers to prove fundamental results about voting systems and the structure of foams (see, respectively, the sidebars Stable Elections and Spherical Cubes).
While the unconditional results that have emerged from the UGC have already proved its value to the mathematics and computer science community, it would nevertheless be nice (to put it mildly) to know whether it is in fact true.
What has emerged is a jumble of intriguing, halfway-there results. One finding, for example, says roughly that if the UGC is indeed true, it takes a very, very large number of colors to make a Unique Games network coloring hard to approximate, much more so than in corresponding problems involving the PCP theorem. Researchers have also shown that, unlike with many problems, randomly chosen networks are not hard to approximate and so will not be an avenue to proving the UGC.
And last year, Arora, together with Boaz Barak and David Steurer of Microsoft Research New England, proved that there is a sub-exponential algorithm for Unique Games—that is, one that is faster than an exponential algorithm, but still not as fast as a polynomial algorithm. That means that Unique Games joins a small and exclusive clique of problems for which the best known algorithm falls between exponential and polynomial time. “That was a surprise,” Arora says.
The assortment of findings about the UGC are reminiscent of the allegory in which a collection of blind people touch different parts of an elephant and each get a different impression of the elephant’s nature, says Dana Moshkovitz of MIT.
If someone does unveil the UGC’s inner elephant and comes up with a proof some day, it will be a cause for celebration, since that would mean (among many other things) that constraint-satisfaction problems have been thoroughly understood. “It would very much complete the theory,” O’Donnell says.
At the same time, if someone can disprove the UGC, it might give researchers even more to think about. “People suspect that to show the UGC is wrong, someone would have to come up with an amazing algorithm involving a lot of new ideas,” Arora says.
Unlike some other famous conjectures such as the Riemann Hypothesis and the P versus NP problem, for which most mathematicians agree about the expected answer, the UGC’s believers and disbelievers form two pretty even camps, O’Donnell says. “This may be an open problem for a very long time,” he says.
As anyone who has gone on a cross-country road trip will know, trying to fit a large assortment of objects into the trunk of a car may require many attempts, a very long time, and a bit of divine inspiration. By contrast, if someone else is kind enough to pack your trunk for you, checking whether he has accidentally left any items on the curb takes a matter of seconds.
The P versus NP conjecture concerns the difference between problems that can be solved efficiently and problems, such as trunk packing, that may be hard to solve, but for which it’s easy to check efficiently whether a proposed solution is correct.
Efficiency is an intuitively clear concept, but what precisely does it mean for a computational problem to have an efficient solution? One thing it does not mean is that every instance of the problem can be solved in a reasonable amount of time. For most computational problems, the length of time it takes to get an answer increases as the size of the ‘input’ — the lengths of some numbers we are trying to add, or the number of objects we are trying to fit in a suitcase—grows. For even a simple problem like adding two numbers, there are numbers long enough that adding them together would take longer than a year, or a million years, or any length of time we’d care to specify.
In practice, though, we never need to add numbers that large. To be practical, an algorithm does not have to solve every instance of a problem quickly—just those instances with reasonable input sizes (something that will vary from problem to problem). As long as the running time of the algorithm doesn’t grow too fast as the size of the input grows, the algorithm should be able to handle the practical examples we would actually want to throw at it. But how fast is too fast?
In the 1960s, computer scientists decided that the most reasonable definition of not-too-fast growth is what is called polynomial time. An algorithm is said to run in polynomial time if, for some constants C and k, the algorithm takes at most Cnk steps to solve any instance of the problem with inputs of size n.
It’s not hard to show that this concept is independent of which computational model we use: if a problem has a polynomial-time algorithm on one type of computer, that algorithm can be translated into a polynomial-time algorithm on any other type of computer. Computer scientists have named the class of problems that can be solved by polynomial-time algorithms class P.
Polynomial functions grow comparatively slowly—much, much more slowly than exponential functions such as 2n, which typically appear, for example, as the running time of brute-force search algorithms. Algorithms whose running times grow like exponential functions are so slow that they are impractical for all but the very smallest inputs. And while an algorithm whose running time is bounded by a large polynomial such as n100 may not be very practical to run either, such algorithms don’t seem to happen a whole lot, for some reason: for most of the problems known to be in P, computer scientists have found algorithms whose running time is bounded by a polynomial with a small exponent, such as n3 or n4. Thus, most computer scientists take the view that for a problem to belong to class P is equivalent to it being feasible to solve.
The problem of adding two numbers belongs to P, since the standard algorithm schoolchildren learn is efficient (though it may not seem so when being carried out by a seven-year-old): Its running time is proportional to the length of the two numbers. By contrast, computer scientists have not so far been able to find a polynomial-time algorithm to solve the trunk packing problem. Thus, this problem may not belong to class P; however, as we have seen, it does belong to another class, which computer scientists call NP: the class of problems for which there is a polynomial-time algorithm to verify whether a proposed solution is indeed correct.
Any problem in P is automatically in NP, but what about the reverse? In the early 1970s, Stephen Cook, currently at the University of Toronto, and Leonid Levin, currently at Boston University, independently formulated the famous P versus NP conjecture: that these two classes are not the same. In other words, there are problems in NP that can never be solved in polynomial time by any computer algorithm, no matter how clever.
In a sense, the conjecture asserts that creativity cannot be automated—that there is a fundamental gulf between the ability to solve a problem and the ability merely to appreciate someone else’s solution. If the conjecture is false, a proof of that fact would have profound implications for a wide range of disciplines.
For example, in mathematics, it is a simple matter to create an efficient algorithm that checks the correctness of any proposed mathematical proof. A proof that P = NP would allow mathematicians to transform this algorithm into an efficient algorithm to come up with a proof of any true mathematical statement. If this could be done, the field of mathematics would be transformed from its current form into something completely unrecognizable.
To many mathematicians, it seems unfathomable that mathematical insight could be automated in this way, and indeed the majority of mathematicians and theoretical computer scientists believe that P does not equal NP. Yet the conjecture has held out against all attempts to prove or disprove it over the last 40 years.
Sometimes, even a failed attempt to prove the UGC can bear fruit. When O’Donnell, Kindler and Uriel Feige of the Weizmann Institute tried to get at the UGC using a technique called parallel repetition, they found that the statement they wanted to prove reduced to a simple, elegant question about the structure of foams.
Spherical Cube: While studying the UGC, Kindler, O’Donnell, Rao and Wigderson discovered this three-dimensional shape, which tiles all of space when copies of the shape are placed along a cubical lattice. Of all known shapes with this property, the shape above has the lowest surface area..
The most basic question about foams, which has been studied for more than 200 years, asks, for each dimension d, for the shape with the smallest surface area that divides up d-dimensional space into bubbles of volume 1. This problem was solved for dimension 2 in 1999 by Thomas Hales of the University of Pittsburgh—the best shape is simply the regular hexagon, although proving that fact was no easy matter. In dimension 3, a candidate shape has been identified, but a proof has eluded researchers. In higher dimensions, even less is known.
The researchers’ attempt to prove the UGC boiled down to a question closely related to the basic foam problem, which we’ll call the integer lattice foam problem: If the allowable bubble shapes are limited to those that can tile space by shifting copies of the bubble whole numbers of steps along the coordinate axes, which shape has the lowest possible surface area?
So for example, in dimension 2, a square would be a viable candidate, since it tiles the plane by shifts to the left and right, up and down. The regular hexagon, however, would not be a candidate, since to fill space with regular hexagons involves some diagonal shifts of the hexagon, and some horizontal shifts that are not by whole numbers. It turns out, though, that the best integer lattice tiling is in fact a hexagon, though not a regular one: In 1989, Jaigyoung Choe of the Korea Institute of Advanced Study in Seoul proved that the best shape is an irregular hexagon whose perimeter is about 3.86, slightly edging out the square, whose perimeter is 4.
A d-dimensional cube has 2d sides, so the cube of volume 1 has surface area equal to 2d. Thus, the shape that solves the integer lattice foam problem in dimension d must have surface area at most 2d (since otherwise the cube would beat it out). And since the shape of volume 1 with the lowest surface area overall is the sphere, the solution to the problem must have surface area at least that of the sphere, which in large dimensions is roughly proportional to the square root of d.
The researchers expected—and needed for their attempted proof of the UGC—for the solution to the integer lattice problem to have surface area roughly proportional to that of a cube (that is, 2d) when d is a large number. To their surprise, however, O’Donnell and Kindler—together with Wigderson and Anup Rao, currently at the University of Washington in Seattle—found that for large dimensions d, there exist shapes that tile space by whole-number steps, and whose surface area is roughly proportional to the square root of d—in other words, their surface area behaves more like that of a sphere than that of a cube.
“There are shapes that are almost spherical but still tile space in a cubical pattern, which is rather counterintuitive,” O’Donnell says. The fact that the UGC led researchers to such an intrinsically interesting, natural question about foams “adds to its mystique,” he says.
In a typical election, there’s a reasonable chance that some votes will be misrecorded. How likely are misrecorded votes to alter the outcome, and how does that likelihood depend on which voting system is being used? This question is not just theoretical: In the 2000 Presidential Election, after all, the outcome hinged on whether a handful of votes in Florida had been counted correctly. Had plurality voting been the law of the land, instead of the Electoral College system, the outcome would not have been in dispute: Everyone agrees that in the national vote, Al Gore won by more than half a million votes.
The voting methods that are the most stable with respect to misrecorded votes—that is, the least likely to flip outcomes if a few votes are misrecorded—are rather unsavory ones. A system that always chooses the candidate selected by Voter A, or that always awards the win to Candidate 1, will seldom or never be affected by a misrecorded vote. Since no one presumably would choose such a system for a democratic election, it makes sense to ask which voting system is stablest among those systems that give all voters roughly equal weight and are not biased toward or against any particular candidate.
When there are two candidates, this problem is, in fact, related to the Sparsest Cut problem. Imagine a network in which each vertex stands for one possible combination of candidate choices by all the voters (so if there are n voters, this network will have 2n vertices). If your election is happening in a setting in which, say, about 1% of the votes are typically misrecorded, then connect two vertices by an edge if they are identical except for about 1% of the voters.
A voting system is simply a rule that assigns a winner to each vertex in the network. Thus, it divides the network into two subsets: the vertices that result in a win for Candidate 1, and the vertices that result in a win for Candidate 2. These two sets will be roughly equal in size, assuming we’ve left out the unfairly slanted voting systems discussed above.
For the voting system to be stable with regard to misrecorded votes, it should assign the same outcome to both the endpoints of each edge—in other words, it should not put vertices that are connected by an edge into opposite subsets. Thus, looking for the most stable voting system corresponds to looking for the sparsest cut of the network.
The researchers found that when they plugged Max Cut into the framework of the UGC, the statement about 87% being the best approximation for Max Cut boiled down to proving a simple statement about voting systems: namely, that if the two types of extremely unbalanced voting systems are excluded from consideration, then majority voting is the stablest system. The following year, O’Donnell, Mossel and Krzysztof Oleszkiewicz of Warsaw University were able to prove this “Majority is Stablest” theorem, vindicating the intuition from the 2000 Presidential Election.
“Other people had thought about voting stability before, but the UGC really narrowed us in on the exact statement and gave us a strong motivation for proving it,” O’Donnell says.
S. Arora, B. Barak and D. Steurer. Subexponential algorithms for unique games and related problems. InProc. 51st IEEE Symposium on Foundations of Computer Science, 2010.
U. Feige, G. Kindler, and R. O’Donnell. Understanding parallel repetition requires understanding foams. InProceedings of the Annual IEEE Conference on Computational Complexity, pages 179-192, 2007.
J. Håstad. Some optimal inapproximability results. Journal of the ACM, 48: 798-859, 2001.
S. Khot. On the power of unique 2-prover 1-round games. In Proc. 34th ACM Symposium on Theory of Computing, 2002.
S. Khot. On the Unique Games Conjecture. In Proc. 25th IEEE Conference on Computational Complexity, 99-121, 2010.
S. Khot, G. Kindler, E. Mossel, and R. O’Donnell. Optimal inapproximability results for MAX-CUT and other two-variable CSPs? In Proc. 45th IEEE Symposium on Foundations of Computer Science, 146-154, 2004.
S. Khot and O. Regev. Vertex cover might be hard to approximate to within 2-ɛ. In Proc.18th IEEE Conference on Computational Complexity, 2003.
S. Khot and N. Vishnoi. The unique games conjecture, integrability gap for cut problems and embeddability of negative type metrics into l1. In Proc. 46th IEEE Symposium on Foundational of Computer Science, 2005.
G. Kindler, R. O’Donnell, A. Rao, and A. Wigderson. Spherical cubes and rounding in high dimensions. InProc. Annual IEEE Symposium on Foundations of Computer Science, 189-198, 2008.
E. Mossel, R. O’Donnell, and K. Oleszkiewicz. Noise stability of functions with low influences: invariance and optimality. Annals of Mathematics 171 no.1, 295-341, 2010.
P. Raghavendra. Optimal algorithms and approximability results for every CSP? In Proc. ACM Symposium on the Theory of Computing, 245-254, 2008.
L. Trevisan. On Khot’s Unique Games Conjecture. AMS Current Events Bulletin, 1-21, 2011.

industry_corpus2: Programming


text:
Best way to beat 100F weather? Spend the day making a dress in the basement! A few years ago, I had made a Wiksten tank dress with some fabric I picked up at Fancy Tiger Crafts (visiting family). I’m super inspired by both these women run businesses and this dress was the first article of clothing I had made with a pattern. I love the step-by-step instructions the Wiksten pattern provides and how quickly it comes together.
For my second dress, I knew I wanted to make a couple of adjustments. I raised the neckline by 1.5″, lowered the armholes by 1.5″, and increased the length of the front & back pieces (3″ & 5″ respectively). Lowering the armholes was a little tricky because I wasn’t sure how the front & back should line up. I followed the advice here of just lowering and redrawing the curve. It worked out pretty well, as the dress isn’t tight, giving me more wiggle room to adjust the armholes incorrectly.
I’m looking forward to working a couple more up, maybe one in black linen a la Jai_Jai_Ma’s instagram, and another in an army green for the fall/winter. There are so many other patterns I want to try out too. I’m definitely taking recommendations. What’s been your favorite pattern or piece you’ve made recently?

industry_corpus2: Others


text: Buy your SJF74PS-SL Fridge / Freezer spares at 4Sharp. If your Fridge / Freezer needs a spare part then you will find it here at 4Sharp. We have Fridge / Freezer spares available for next day delivery in the UK, provided they are in stock. Our range of SJF74PS-SL Fridge / Freezer spares can be bought online or by calling 0844 55 72 510.

industry_corpus2: Manufacturing


text: The serotine bat, Eptesicus serotinus is the most frequently rabies-infected (European bat lyssavirus 1-type, EBLV-1) bat species in Europe. To confirm Lyssavirus infection of this bat in Poland, we tested for the presence of rabies virus RNA from oropharyngeal swabs using RT-PCR. There was a 0.9% (two out of 212 individuals) level of infection within the overall population of serotine bats studied. However, an appreciation of the potential for pathogen transmission and disease risk requires an understanding of the dispersal of the primary host, and any large-scale geographic barriers that may impede gene flow. Thus, we also studied the patterns of bat dispersal via population genetics using nuclear (seven microsatellite loci) and mitochondrial (mtDNA control region) markers, examined in 12 subpopulations distributed across the country. Molecular analyses of microsatellite loci indicated high genetic diversity at all sites (heterozygosity observed, Ho = 0.53–0.78), and extremely weak genetic structure in the Polish population of the species. The overall FST was 0.012 (95% confidence interval: 0.006–0.020), and pairwise values ranged from 0.00 to 0.05. Only 22% of individuals were assigned to the subpopulation from which they were sampled. The Bayesian approach implemented in STRUCTURE also confirmed that all examined subpopulations should be treated as a single group, indicating a high level of gene flow. There was some evidence for female philopatry (genetic differentiation was greater in maternally-inherited mtDNA than nuclear DNA) and male-biased dispersal, e.g., Ho and the variance of mean assignment were significantly higher in males than in females. Twelve individuals (seven females and five males) were identified as potential first generation migrants. Their migration routes ranged from 60–283 km in females ( ± SE = 177.9 ± 29.37) to 27–385 km in males (206.4 ± 58.95); surprisingly, no sexual differences were observed and this finding suggests that female-mediated gene flow may occur. MtDNA also produced a strong genetic signal for the demographic expansion (Fu's FS statistics, FS = -26.30, P < 0.01 and a star-shaped haplotype network), which took place roughly 33,000 years BP, i.e., before the Last Glacial Maximum. The genetic uniformity of the Polish population implies that there is no migration barrier to EBLV-1, at least within the country, and the potential threat of rabies virus spreading via migration of infected animals may be higher than previously thought.

industry_corpus2: Health & Medicine


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It is a well known fact that your memory and smells are tied closely together (this is called the Proust phenomenon). More than pictures or sounds, a scent can really bring back memories and invoke emotions. Companies know this all too well and make use of scents and sounds to jolt your brain into liking or enjoying something. The true secret of successfully marketing a product is to pair a store or a product with a specific scent. If you feel at home in a store, you are more likely to buy.
Buyers of Apple computers, iPhones and other products know it all too well, the smell of a new device. This very specific smell is rumored to come from inside the devices, but some have suggested that the packaging is responsible. The plastic iPhone has the same smell as the aluminum MacBook, so the scent is probably not added to the plastic. Apple has never owned up to these tactics, but an Apple Mac scent has been produced by the Air Aroma company, combining the smells of cardboard, ink and other ingredients. If you can’t afford a Mac, you can at least make your old PC smell like one.
MacDonald’s use aggressive tactics to sell you their fries and other products. Focusing on ‘hot’ times in the day (lunch time for example) the company throws adverts out that are specifically aimed at those driving a car. Examples of one of these ads: one advert for fries features a sound that you could describe as something in between a deep fat fryer and a car heating system. The voice over even announces that the smell of fries being cooked will be transferred to your car, after which you are prompted to go and buy some. This type of advertising can hardly be called subliminal. Apparently the company thinks that subtlety should not be wasted on its customers. That’s why their restaurants feature so much red. Pay, eat fast and go away quickly. Before you can even ask for the wireless password and stay.
Nike stores use a mixed flower scent to direct you towards the more expensive shoe designs inside, but after an incident in which their shoes started smelling of cat urine after wearing them once, maybe they should have added it to the insoles of their designs instead. Apparently you want to spend up to $10 more on their shoes if they are diffusing flowery scents. The shops are light and often have white walls with black decorations or images in neutral colors. This makes you relaxed enough to pay up for their shoes.
The famous M&M World Store in London has a surprisingly strong chocolate scent when you walk in. You would expect that wouldn’t you? You want to feel like you are entering Willy Wonka’s chocolate lab when you go there. But then you look around and realize that all their wares are prepackaged. And you realize that the strong smell of chocolate is being sprayed at you with a vengeance. And your happy chocolate bubble bursts.
Scents mess with our rational thoughts and connect with our emotions. And what can be more irrational than blowing your monthly pay check on a slot machine or casino game? The scent masters at Aromasys have been involved in choosing the right scents for the right resort. The Mirage hotel and casino uses a scent that is based on Polynesian tones and the well known Bellagio may subtly remind you of Italy. The venetian uses a strong Aromasys scent called Seduction, with strong notes of musk. The scents are aimed at the type of surroundings, the theme of the venue and the type of clientele visiting the venue. Musk is often referred to as the strong manly scent of success. Unfortunately this slightly primitive notion is not supported by the Moschus deer, who would like to hold on to their musk gland sac, if you please.
If you think that you are overweight because you ingest more calories that you burn off, or because your digestion is slow, think again! You’re just not sniffing up the right scent. Apparently tests have shown that surrounding yourself with the right weight loss promoting scent can help you shed those pounds in a heartbeat. There is a huge marketing machine behind this notion and companies like Slimscents, Aromapatch and Prends-Moi really want you to drop your money on that new scent that makes you lose weight. Just make sure to stop driving around in your car to avoid hearing MacDonald’s adverts. Here’s a tip, surround yourself with the smells of peeling fresh fruit and cooking vegetables around dinner time.
Net Cost is pretty big on using scents to make you put some more stuff in your shopping trolley. The scents of chocolate and of fresh bread are used in the shops air system. The Net Cost grocery store in Brooklyn New York was one of the first supermarkets to use this to influence their customers senses, and apparently it really works to make people slow down and check out the products displayed in the shop areas where the goods can be found.
Most morgue and funeral home workers know the smell of a slowly decomposing body all too well. The favorite scent to use in a funeral home is a type of industrial strength cinnamon spray. This spray is a great deal as cinnamon creates a trusting and homely warm feel for visitors to the home, and does a great job in disguising the smells of human decay. If a body is not embalmed before a funeral service or cremation, you can be sure to notice a slight hint of cinnamon during your relative’s service. The icing on the commercial cake is the fact that this scent will make you want to come back and book your own service there too.
Imagine a long haul flight whilst breathing in perfumed air. It seems weird to imagine that even airlines use scented air on their jets. Singapore Airlines has used its scent called Stefan Florida Waters, on its hot towels and on its flight attendants. This way the plane smells fresh when you board, and the scent is spread every time an attendant walks past. According to the airline this enhances the travelers experience of a relaxed flight. After your holiday you will want to book with them again.

industry_corpus2: Hospitality & Catering


text: Bathroom Best Whirlpool Tub Shower Combo Porcelain Jacuzzi Bathtub Bathroom Tubs And Sinks Some Basic Types of Bathroom Tubs Faucet. Soaking. Bathtub.

industry_corpus2: Real Estate & Construction


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The Pistol Annies performs on The Tonight Show Starring Jimmy Fallon on Nov. 1, 2018.
The Pistol Annies — the country supergroup made up of Miranda Lambert, Ashley Monroe and Angaleena Presley — charmed The Tonight Show with the velvety “Best Years of My Life” off their new album Interstate Gospel on Thursday night (Nov. 2).
Lambert took the third, regretful chorus, “I was looking forward to/ Staying here forever/ ‘Cause you asked me to/ Didn't think that I could do better/ So I settled down/ In this ten-cent town/ It's about to break me.” The trio made news earlier this week when they dropped the provocative video for "Got My Name Changed Back," in which they take take a visit to the courthouse to get their divorce papers finalized.
Watch the Pistol Annies’ contemplative Tonight Show performance below.

industry_corpus2: Film & Entertainment


text:
The premise certainly sounds interesting. Sorry to hear that the book didn’t quite deliver though especially in regards to the multiple narrators. Great review!
Thank you. I’m glad you enjoyed reading my review.
Thank you. So far, I do and can’t wait to write about it too.
Well, I usually don’t mind multiple POV’s. But it honestly depends on the story, if it adds to it or anything. If it doesn’t I’m not as into it usually. Like this book I thought was okay. I just felt like some character’s perspectives just weren’t needed.

industry_corpus2: Literature & Emotions


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I continue my love in making accordian books.
I added some plants and tea bag paper and a few doodles with pen and ink.
And I sent it to my daughter.
My daughter is presently attending her first year of university about 4000 miles away from home.
She is exploring possibilities, as was I in the creation of this little book.
After an inital cold snap in early September, we have had unseasonably warm temperatures.
So warm that I could sit outside for the whole afternoon and draw. It was a beautiful day!
I drew some butterflies in pencil, and then got brave and drew some in pen. Just after that I visited Stephanie's blog, and saw her lovely little book (with no pages) and felt the urge to make one.
And the next day, I had the urge to make another. This one decorated with a little original collage.
With leaves and bits of paper on the outiside.
Here they are wrapped up with a piece of fabric that is attached to the covers.
this accordian book I made, and then changed on my computer.
This photograph happened the same way from the same little book.
and the back cover of this book I just finished binding.
When you open the book it has a flower image transfered to a tea bag wrapped around the blank pages.
I had no plan on making a book, and then this one happened.
Or a drawing of a bird I did.
and went with the bird.
Some pieces are such a struggle, while others come together so easily.
Today was a perfect day for a fall photo shoot.
These flowers are no longer blooming as the frost took them away last week, and the snow came far down the mountainside.
are showing off with their finest colours.
from the beauty of a fall day, and cover it with the beauty of winter.
Perhaps it is because the snow is quickly moving down the mountainsides, and will soon be covering all of the rocks. Perhaps it is because the plants are finishing their season of growth and will soon be resting under that layer of snow. Perhaps this is why I have been so busy collecting rocks and botanical bits - knowing it will be many months before I see them again. Perhaps this is why I have so many bowls of rocks around the house right now, and numerous trays of pressed botanical bits.
and layers of paste wax buffed to a smooth finish.
Seeing and feeling them increases my happiness and helps me relax.
I also collected some small pieces of drift wood from my favourite stretch of lake beach, to decorate in this way.
And I find the back of it as beautiful as the front.


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Gujarat is the western most state of India that has the longest coastline. This vibrant state is famous for its ancient temples, natural beauty, architectural assets, wild life sanctuaries, fascinating handicrafts, colourful festivals and delicious cuisines.
Gujarat will amaze you with its wonderfully connected and perfectly maintained road network. Taxi service in Ahmedabad is available for tourists who would like to get on a road trip and explore this diverse land that has an eventful history.The best time to visit the state is between October and February to enjoy the optimal weather.
Start from Sabarmati, the Ashram of Mahatma Gandhi to learn about the Father of the Nation. Book cabs in Rajkot to go around the city and visit the Buddhist caves of Khambadila and Wankenar Palace, the Watson Museum, that narrate tales of ‘Rangilu Rajkot’s rich cultural past.
Archaeology lovers can dig into the past by visiting the world heritage sites of Lothal and Dholavira dating back to the Harappa and MohenjoDaro civilization.
The ancient fortifications of Surat Castle and Bhujia Fort of Bhuj have witnessed major historical battles. TheBhadra Fort of Ahmadabad and Lakhota Fort of Jamnagar will enthrall all tourists with their architecture. The major monuments of Patan including Rani Ki Vav step wells and Sahashtralinga Tank are top attractions are representations of the prosperous past of Gujarat.
Devotees flock to pray at the most significant temples of Gujarat.
The legendary Somnath Temple is a beautiful seven-story structure that reflects the Chalukya style of architecture.
The Dwarkadhish Temple of Dwarka is a magnificent sandstone structure which is highly referred as a part of Chardham Yatra in Hinduism.
While in Dwarka, do not miss the Rukmini Devi Temple to see its splendid carvings.
Swaminarayan Akshardham Temple of Gandhinagar is one of the largest temples which command attention as a centre of research, education and religion. Children would love playing in its picturesque surrounding replete with waterfalls, lakes and herbal gardens.
The Sun Temple of Modhera is set atop a hill where the Suryachakra shines from sunrise to sunset.
Apart from these, the Hutheesing Jain temple, Kirti Stambh, the Palitana Jain temple Complex, the Girnar Jain temple of Pavagadh have a history that is as amazing as the breathtaking beauty of their architecture.
This vivacious state is one of the wealthiest wildlife destinations that is a paradise for nature lovers and a Mecca for ornithologists, Gujarat is the perfect wildlife getaway with an abundance of flora and fauna. Khijadiya Bird Sanctuary is one of the best sanctuary of India.
Meet the King of the Jungle at the Gir National Reserve forest and the last home of the true Asiatic Lions. Take on the adventure trip in a jeep safari on this distinctive landscape and start looking for the Black Bucks and hyenas.
There are facilities for tourists to do camping at the cottages of Jambughoda Wildlife Sanctuary located in Central Gujarat. If you want to catch a glimpse of the Sloth Bear,then you must Jessore Sanctuary is the place to be. The Kedarnath Mahadev Temple is also located within this reserve forest.
If you want to spread awareness about wildlife conservation among your children, then take them to Hingolgadh Sanctuary in Rajkot.
Meet these elusive Flamingos birds while riding the Camel Safari on this vast stretch of the white desert of Rann of Kutch that lay between the Thar and the Arabian Sea.
Relax in this beautiful Saputara hill station by indulging in some leisurely activities like boating, visiting the tribal museum, artisan village to rejuvenate your senses.
A multitude of festivals are celebrated in Gujarat demonstrates the mix of different religions, cultures, language and ethnic groups of people living here. Dance to the rhythmic beats of Garba during Navratri or fly colourful kites during Makar Sankranti at the International Kite Festival.Watch classical dance festivals at the annual Modhera Dance festival highlighting talents of dancers.The sights and sounds of the Kutch Mahotsava appeal to all visitors who come here to see the display of native arts and crafts of the artisans of Gujarat. The Kankaria carnival, Tarnetar Fair or the BhavnathMahadev Fair of Junagadh are also worth visiting.
Taste the rich flavours of Gujarati cuisine by ordering a thali meal or try the snack items like Khammam Dhokla, Gathiya, Khichdi Kadhi, Thepla, Khandvi and Bhakri Shak. Dessert items like Shrikhand and Handvoare a must-try and will certainly melt in your mouth.
The specialties of Gujarat are the Patola sarees, traditional GhagraCholi, applique quilts, tie and dye Bandhni works of Kutch. Do shop for the zari work of Surat and the shawls of Jamnagar. Ahmedabad’s Law Garden Market, Sindhi Market, Laal Darwaza are the best places to visit. Diamond lovers must visit Surat’s diamond industry. Bhuj is known for its enamel work bangles, lacquered wood and seashell items.The narrow lanes of Bangadi Bazaar of old Rajkot are similarly popular among tourists. Handcrafted handicraft and furniture items are best available at Vadodara.
Pick some exquisite gold and silver articles of Chaandi Bazaar in Jamnagar as souvenirs from Gujarat for folks back home.

industry_corpus2: Travel & Geography


text:
I tried stati but it doens't look right.
'Statuses' is the common lazy slap an 'es' on the end method that has made it into American dictionaries.
If you want to be a purist, you should treat this Latin word as intended and go with the fourth declination of it, resulting in the plural of 'status' remaining as 'status'.
Consider it this way: the Latin plural for 'Alumnus' is 'Alumni'. You wouldn't try to refer to the plural as 'Alumnuses' would you? Well, not without pedants everywhere lighting their torches, sharpening their favourite pitchforks and marching over to your house.
There is absolutely nothing wrong with saying "statuses" if you happen to need to use a plural form of "status" on occasion.
If the British National Corpus is anything to go by, the use of "statuses" is not limited to North America.
In your whole life, have you ever heard a native speaker say 'stati'?
So you would say sheeps then?
Your leap in logic is puzzling.
English words take plurals in different ways.
Why would you think that because we use a widely accepted form of a plural word using one method that we would apply it to every other word?
When English words are borrowed from other languages, they may take the plural in the form they took their plural in their original language, or they may become Anglicized. Or they may start as the former and evolve to the latter. Or they may even take one plural form in one vernacular and another form in another vernacular.
Miriam Webster lists "statuses" as the plural form.
You apparently do not know how lexicographers (the professionals who compile dictionaries) work. They don't invent language, words, or word forms, but document how people use words in actual practice. This has been their modus operandi since Samuel Johnson's first English dictionary.
That's why radius has its 1st plural as radii, and a 2nd plural as radiuses, but for alumnus, the only plural is alumni. The dictionary documents how our dynamic language changes.
woops! Definitely spoke too soon. Touche', redacted.
I Need Help (To Check Spelling ) Urgently?

industry_corpus2: Subject Education


text:
Children are very vulnerable to fires and burns because of their curiosity and ignorance of the danger of fire. Hundreds of children in the United States die and countless others are disfigured every year as a result of burn injuries. Children ages five or younger are especially vulnerable to burns and have one of the highest fire death rates.
Hot liquids—not fire—are the most common cause of burns to young children. Hot liquids burn like fire and can cause serious and painful burns. However, fires caused by playing with matches and lighters are the number one cause of fire-related deaths among young children.
Planning ahead and practicing fire prevention skills can reduce the chances of a fire occurring, protect children and adults, and reduce property damage.
Provide safety education. Help the children learn about hazards that can cause fires and burns. They should be taught that some objects are off-limits for play.
Check for environmental hazards and limit access to burn-producing objects.
Safety devices such as smoke alarms and fire extinguishers should be present and in working condition.
Plan the escape routes in advance. Children should also have regular practice drills for fire evacuation and should know how to crawl low under smoke, and how to stop, drop to the ground and roll if their clothes catch fire.
Model preventive behaviors that will reinforce fire and burn accident prevention.
Communicate your prevention activities to parents so they can support your efforts and prevent burns and fires at home.
Invite a community service representative from the local fire department to your program for a safety workshop.

industry_corpus2: Safety Management


text: Introduced in the 1830s by German immigrants in Pennsylvania, the Christmas Tree has gone through many generations. While some families still make use of a needle and timber tree, many have opted for the evergreener option of the plastic tree. Ornaments and lighting have likewise changed over the years, migrating towards more power efficient and less flammable options such as LEDs.


text:
For today’s demographic note we present the chipper consensus viewpoint of the UK government and the mainstream media, followed by a realistic perspective from Mark Steyn.
Karen Dunnell, the National Statistician, will bring together a wide range of evidence on the growing number of older people, and examine the changes this will bring to society and the economy.
It is the first time the National Statistician has focused on the issue in her “annual article”, which offers an in-depth examination of a particular aspect of Britain’s population figures.
At the same time, the Office for National Statistics (ONS) will publish figures showing that the UK’s birth rate surged last year to a 30-year high, driven by a baby boom among immigrant families. Among all babies born in the UK, 23 per cent had mothers who were born abroad. Whereas British-born women have only 1.7 children each on average, the figure is 3.9 for Bangladeshi-born women in Britain, and almost five for Pakistani-born women.
The conventional solution of homo economicus to the lack of homegrown young people is to import them. The remorseless aging of Britain suggests that no society in serious demographic decline can have an immigration rate high enough to compensate for it.
… By the way, that British-born 1.7 is only kept that high by the significantly higher birth rates of British-born women of Pakistani and Bangladeshi descent who now account for the main demographic energy in most English cities. Britain’s future will be more Muslim. The only question is how much more. But, at some point, those fertility rates put a question mark over the social compact. In 20 or 30 years’ time, will a young, demographically healthy Muslim working population with vast extended families be willing to pay confiscatory tax rates for the shuffleboard years of an aged, childless, fast shriveling Anglo-Celtic population? All welfare societies presuppose a commonality of interest that in the Britain of 2025 will no longer be there.
The burden of the ‘oldest old’ on the health care system (pp 21-22 in the report)raises the question if medical research should be shifted from prolonging human lifespan by curing illnesses/postponing death onto drugs which improve old peoples ability of fending for themselves even if it reduces lifespan.
Given that the people in schools today WILL be among the survivors who live to retire in 60 years or so, the demographics are a LOT more certain than climate change ever will be.
Just like us Social Security is bankrupt/ unsustainable.
Whether changing from Anglo-Celt to more Pakistani Muslim is a problem worth using gov’t force to try to fix or not is one issue; what the gov’t should do is a further issue (more gov’t tax reductions on those with kids — so that having two kids allows more consumption than having none?).
Japan’s demographics should be followed closely since they’re aging even faster, but without immigrant substitution.
If current trends in UK continue , those young working Pakistani Muslims in 2050 will be indistinguishable from the Phoenician Celtic Viking Mongol Saxon Dutch Jamacian Ugandan Polish Kosovan elderly they will be supporting.
Fabius Maximus replies: Do you have data on intermarriage rates to support this? From what I have seen in the general media (no studies), their intermarriage rates were quite low. Palistani in the UK typically either marry within their community or to spouses from Pakistan.
Pakistani women’s high birth rate will indeed produce the result Steyn predicts (along with a substantial mixed comunity with little Pakistani imput).
Those who have big families are subsidised by mainly white taxpayers at the moment through welfare benefits, you don’t think they will be grateful when they are in the majority?
Fabius Maximus replies: Thank you for the link to this interesting conference!
British Pakistani men will send home for first cousin wives, many wives. On the dole, with children, and an attitude. Not an attitude of gratitude toward taxpayers, no. Decapitate all those who offend Islam, is more the style.
Only one British marriage in fifty is of mixed race? 2%? Bloody hell, that’s nothing. Cohabitation is probably more common among mixed race couples.
Illegitimacy is quite high in mixed race relationships of cohabitation. Pregnancy is unlikely to lead to marriage, so the mixed race child often grows up without a father, or with a succession of “fathers.” Instead of leading to a happy population of mixed race peoples, a growing criminal and delinquent underclass is likely. Youth gangs of varying self-identification competing to make names for themselves as most to be feared.
I’m not a social scientist in any way .
But I dont think ethnicity or religion are as important as the way a society evolves and takes everyone with it , like different streams joining a river .
Maybe we will all work till we drop , live in extended families , refuse or be refused expensive grey healthcare , as society evolves in a different direction .
Are not state pensions , a giant Ponzi scheme ?
“birth rates of British-born women of Pakistani and Bangladeshi” are statistically insignificant, because of their small percentage and because their fertility rates is nearer to the national average than the foreign-born average. The 1.70 might be 1.68 if we take all second-generation immigrants out, thus both round to 1.7.
The problem is not one of immigrants–be they Muslim or not–overwhelming a “fast shriveling Anglo-Celtic population” that is only a distraction of the real problem in UK society, one that you have presented in a very nice graph sometime ago, namely the unequal distribution of wealth!!
The 1.7 does not represent five children on average for every three randomly selected women, because children are also unequally distributed in the UK society. A minority of wealthy housewives–husbands working in finance for example–have 3 to 4 children each; on the other side poor single-mothers on welfare have 3 to 4 children each. This leaves those in the middle with 0 to 1 child each. I think that is a much more relevant issue than the fertility of foreign-born women.
Looking back at the last 500 years Europeans have demographically overwhelmed large parts of the world: First ethnically cleansing Muslims out of what is now considered “Christian” Europe, then they immigrated to the Americas, Southern Africa, Australia, et cetera. They even tried to settle in Muslim lands like Algeria and Libya, even today Polish settlers in Palestine are well entrenched. Russians maybe now declining, but one has to remember that they went out of Muscovy and overwhelmed Muslims for centuries.
The solution for demographic decline is VERY easy: bar women with less than two children from higher education and employment and encourage early marriage!! This of course will have to be accompanied by a set of social-regulation unacceptable to the most conservative, e.g. anti-adulatory laws, family-friendly public domain, gender-separated schools, et cetera. You can’t have Victorian demographics without Victorian morals!
Fabius Maximus replies: Do you have any links to support your data? Esp the following?
You might be right. These seem incorrect to me, but this is not a field in which I have any expert knowledge. More important — as you can see even on this brief thread — this subject seems to attract folks making confident but unsupport assertions.
“The next largest group were the 8.7 per cent who were recorded as Asian – of whom Pakistanis formed the biggest section with 3.7 per cent…Bangladeshi 8,241 (1.3 per cent)”.
“The Muslim population in the United Kingdom may now number as many as 2 million, the home secretary, Jacqui Smith, disclosed yesterday during an official visit to Pakistan…/… The 400,000 increase in the size of the Muslim community in less than seven years demonstrates its position as the fastest growing faith community in Britain, and also reflects the age structure of the community, with more than one-third under the age of 16 at the time of the 2001 census. Outside London, Pakistani Muslims make up more than 43% of the community, with Bangladeshis accounting for 17%, and those from India at 9%. In London, the Muslim community is more evenly split between Pakistani and Bangladeshi Muslims”.
What if the British welfare system doesnt survive ? Its good , but its not that good now . If you own your home , have savings , OR are self employed , OR are illiterate and inarticulate ( complex forms to fill in ) you are likely to be left out in the welfare cold .
There are proably other ideas / models to be explored .
The extended family model is one that stands the test of time and geography . You pay in through help and care , rather than money , while you can ; and hope that the family in which you were born , or into which you slid yourself , will care for you in turn .
If your extended family are true Muslims or Christians , your chances are even better .

industry_corpus2: Politics & Administration


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Welcome to Victoria Hopkins Interiors! We offer a range of interior design services as well as a collection of vibrant and unique soft furnishings. Get in touch now to discuss your project.
We offer a wide range of services, from online design packages to bespoke interior design and project management. We have a range of bright and vibrant soft furnishings available to buy online and can also create bespoke designs for your home.
Our interior design and project management service is perfect for those looking for a personalised design service.
Getting your home ready for sale is crucial to maximise offers. My home styling packages can help you get achieve your asking price.
We offer a range of products in my online shop, they are all designed and handmade in our Edinburgh studio.
The journal is where you will find our latest articles and news updates! Expect pieces on the latest trends and industry events, as well as business tips, advice and stories. To be sure you stay up to date why not sign up to our monthly newsletter?
Early morning challenge: So am I a morning person after just one week?
Early morning challenge: Can I become a morning person in one week?
Giving up the day job: How I started my interior design business!


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Throughout December, SQLServerCentral and Simple-Talk hosted the second annual Tribal Awards. With these awards, the SQL community choose members who they felt deserved recognition by opening up both nominations and voting to the public. We’re very pleased to be able to announce the winners for each category in the video below. The winners were decided by sheer number of votes, some won by a landslide and others by the smallest of margins. We’d like to thank the 839 (more than last year!) voters who got involved to make the Tribal Awards something special, and congratulations to our victors!
To make the announcement something special, we had various members of the SQL community record themselves announcing a winner for each category, you can watch the video below. It’s the community that makes these awards special, so it made sense to try and get the community involved in the presentations.
Thank you to everyone who helped out by making an announcement video: Jason Strate, Steve Jones, Grant Fritchey, Mickey Steuwe, Tim Ford, Donald Wert, Jonathan Allen, Tony Davis, Andrew Clarke, Brent Ozar, and Simon Galbraith. We'll post the winners and runners up in the discussion section for those who want to see the winners but skip the video.
Congratulations to all the winners, finalists, and nominees, and thank you to anyone who voted, or nominated someone for an award.
Voting is now open for the Tribal Awards. Vote for one of the 5 finalists in each category to win a fabulous* prize.
Nominations open until December 10. The Tribal Awards are back and looking to recognize some of the great contributors to the SQL community. Nominations are now open for 11 different categories, but closing soon so make sure your user group, favorite twitter account, or person who’s helped you the most this year is nominated.
Voting is open for the Tribal Awards finalists. Choose which community warriors you think went above and beyond the call of duty with their blog, presentation, advice, user group, and more.
SQLServerCentral and Simple-Talk are co-hosting the Tribal Awards. Nominations open today for each of the 11 categories which recognize technical excellence, willingness to help the wider community, and exceptional SQL Karaoke skills.
If you will be in London on June 17th, this is an event you do not want to miss.

industry_corpus2: Computing & Telecommunications


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Looking to get away from the city for a little while ? Now and then the city can get a little overwhelming, but not to worry – we have some great getaway tours that are perfect for couples, small groups of friends, and more!
Hua Hin beach is one of the top escapes for people living in Bangkok, and is one of the most beautiful seaside resorts in Thailand. Hua Hin is an extremely family-friendly town that lacks the vibrant party atmosphere or some of the seedier aspects of other cities in Thailand. It is a small, peaceful town that is perfect for anyone looking for a break from the craziness of the city. There is plenty to do besides relaxing by the beach. Take a stroll through the Cicada weekend night market or visit the San Phan Nam floating market. There are also some stunning nature areas to visit, including Kaeng Krachan National Park and the nearby Pran Buri Forest park. For anyone looking for a little more excitement, there are plenty of water-based activities that the whole family can participate in, including boat tours, fishing, or spending the day at the Vana Nava water park. Hua Hin is an amazing place you have to visit during your stay in Thailand and choosing party bus Bangkok is the best way to discover it !
Take advantage of the one and only Bangkok to Hua Hin tour with Party Bus Bangkok and discover the delights of this little corner of paradise through party bus Bangkok.
Our driver will take you to all the attractions you want to visit in the comfort of our state-of-the-art bus in Hua Hin, so you won’t have to worry about transport on your own. While you’re out and about, all your belongings will be safe on the party bus. You can also add any of our additional services to make your tour even more special and unique. We guarantee your group will love the serenity of a Hua Hin trip after the hustle and bustle of the city in Bangkok.


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I got this recipe from Samantha Miller and I have made it quite often! I love it because it is so simple and fast to make. The cole slaw mix is already prepared so it's easy to toss everything together with just a few ingredients. BAM... your done! No cooking required! I also love that slightly sweetened apple flavor you get from the apple cider vinegar and Stevia. I swear it reminds me of eating apples! Maybe I have been on Medifast too long or maybe I am just wishing I was eating apples, but nonetheless, this is some mighty tasty cole slaw! Love, love, love! I hope you enjoy this as much as I have!
Combine all ingredients in a medium size bowl. Enjoy!


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Dr. Ghazanfar Ahmed, MD, practices Family Medicine in East Liverpool, OH at Columbiana Action Agency. Dr. Ahmed received his medical degree from American University of the Caribbean School of Medicine.
DrScore strives to maintain current information on US doctors. Please let us know about any inaccuracies with our profile of Dr. Ghazanfar Ahmed. Some information about Dr. Ghazanfar Ahmed provided by Vitals.com.
Are you Dr. Ghazanfar Ahmed? Contact us to start collecting online patient satisfaction today!


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$3.50 Rails and Select Beer.
Ryan's Pub (formerly 3 Monkeys), was bought by an Irishman named Andrew who's got a good knowledge of whiskey) is a new addition to the Loring Park/Eat Street bar strip at the base of Nicollet Ave. Granite counter tops, brick fireplace, and well positioned flat screens make it a perfect neighborhood hangout. More of a sports bar during game days, hangout bar during off days; Ryan's sees a range of all types of guests and demographics.
Mandi Schroeder: Their food is seriously AMAZING. get the deluxe nachos... to die for!!


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With their victory over No. 2 Syracuse, the 11th seed in the South Dayton (25-10) now advances to the regional semifinals against fellow upsetter, 10th-seeded Stanford. Syracuse was in position to pull this one out, but Tyler Ennis missed a foul-line jumper with eight seconds left and a game-winning shot at the top of the key with two seconds.
After an ugly first half that saw both teams commit 16 turnovers and shoot 32 percent from the field, No. 10 seed Stanford settled down and pulled away from No. 2 seed Kansas to earn a 60-57 upset win in a Round of 32 game in the South Regional.
Dwight Powell had 15 points and seven rebounds despite playing with four fouls much of the second half and Randle added 13 points, six steals and four assists for the Cardinal (23-12), who were making their first NCAA appearance since 2008.
Andrew Wiggins, a likely NBA lottery pick if he decides to leave school, was saddled with four turnovers for Kansas (25-10). Wiggins had averaged 28 points the previous four games but the Jayhawks were missing 7-foot freshman Joel Embiid who was sidelined by a stress fracture in his back.
Stanford is now tasked with cinderella Dayton in Sweet 16.
The fourteenth-seeded Mercer Bears take down perenial Final Four contender and third-seeded Duke Blue Devils. Senior Jakob Gollon led the way for the Bears with 20 points, 5 rebounds, 2 steals and 2 assists, while fellow senior Daniel Coursey chipped in 17 points, 4 rebounds and 2 assists. Duke's freshman phenom Jabari Parker had 14 points, with four turnovers and shot just 4/14 from the field.
The No. 9 seed Wichita State Shockers dominated the game for the first 30 minutes, but No. 2 seed Ohio State mounted a furious comeback and cut the defecit down to three at 62-59. This Final Four for the Shockers is the first in school history and marks the first time a Missouri Valley program has gone to the last weekend since Larry Bird and the 1979 Indiana State Sycamores.
Even though this was a 12-13 third round matchup, this was still a very big upset. The La Salle Explorers were a team that no one was talking about going into the tournament, they magically found a way to advance to their first sweet 16 in 58 years.
The Florida Gulf Coast University Eagles became the first 15 seed in NCAA tournament history to advance to the sweet 16. It would be an amazing feat by any team, but it's even more impressive that the school's basketball program was granted full division I status in August of 2011.
Cleanthony Early and Ron Baker (pictured) scored 16 points apiece and Wichita State hit a season-high 14 3-pointers, including seven straight late, to knock the No. 1 seeded Bulldogs out of the NCAA tournament 76-70.
In his school's first ever NCAA tournament game, Sherwood Brown (left) led the Florida Gulf Coast Eagles to a stunning 78-68 upset over the Georgetown Hoyas.
Brown led the game with 24 points, but more importantly, his energy propelled the 15th seeded Eagles to their first ever win in the tournament.
Jerrell Wright of the La Salle Explorers dunks on Jordan Henriquez of the Kansas State Wildcats on March 22, 2013.
Wright led all players with 21 points and guided the Explorers to a 63-61 upset victory over the Wildcats of Kansas State.
Siyani Chambers (1) and Laurent Rivard (0) of the Harvard Crimson celebrate as the Crimson defeat the New Mexico Lobos 68-62 during the second round on March 21, 2013 in Salt Lake City, Utah.
Rivard scored 17 points for the Crimson to help lift them over the Lobos.
Phil Pressey, right, of the Missouri Tigers is consoled by Kyle O'Quinn of the Norfolk State Spartans after Pressey missed the potential winning basket at the buzzer in the second round on March 16, 2012 in Omaha, Nebraska.
Norfolk became only the fifth No. 15 seed to win a game in the tournament.
Duke's Andre Dawkins reacts in the second half of his team's loss to the Lehigh Mountain Hawks during the second round on March 16, 2012 in Greensboro, N.C.
C.J. McCollum scored 30 points to lead Lehigh, which was the second No. 15 seed to beat a No. 2.
Walter Offutt of the No. 13 seed Ohio Bobcats celebrates after defeating the Michigan Wolverines during the second round on March 16, 2012 in Nashville, Tenn.
Virginia Commonwealth had to fight its way into the tournament by defeating USC in a play-in game and then had to pull off upsets against 6-seed Georgetown, 3-seed Purdue and 10-seed Florida State (in overtime) just to make it to the Elite 8. After a run like that, no one gave them a chance against Kansas, who was the only remaining No. 1 seed left in the tournament. But VCU overcame the odds again and jumped out to a 14-point halftime lead. Kansas made a run in the second half, but VCU never gave up and walked away with one of the most improbable trips to the Final Four in tournament history.
Favored to win the entire tournament, No. 1 Kansas didn't even make it out of the second round in 2010. The Jayhawks fell behind early against No. 9 Northern Iowa but had pulled within one point with under a minute to go. That's when Ali Farokhmanesh drained a three pointer to give the Panthers a four-point edge. Northern Iowa's first-round win snapped its 20-year NCAA winless drought.
Armon Bassett scored 32 points as the Bobcats -- who were seeded ninth in the MAC tournament yet won the automatic berth -- handed the Hoyas their worst-ever loss in the NCAA tournament. Georgetown entered as 16.5-point favorites. Ohio became just the 16th No. 14 seed to win a tournament game.
The Demon Deacons spent 12 weeks ranked in the Top 10, including one week atop the polls. Led by future first-round NBA draft picks Jeff Teague and James Johnson, they were a No. 4 seed in the 2009 tourney, but were dismantled by the Horizon League tournament champs. It wasn't a fluke, either. Cleveland State had beaten Syracuse earlier in the season.
With the game tied at 77 in the closing seconds, No. 11 VCU could have congratulated itself on a close game and succumbed to the inevitable Duke victory. After all, Duke had made it to the second round every year since 1996. Instead, the Rams drained a pull-up jumper with 1.8 seconds to upset the heavily-favored Blue Devils.
Heading into the 2006 NCAA tournament, George Mason was enjoying one of its best seasons ever, winning a school-record 23 games. They received an 11 seed, but not everyone believed they deserved to be one of the 65 teams competing. George Mason proved them wrong, shocking consensus favorite Connecticut in the Elite Eight. The win came just nine days after George Mason had earned its first-ever victory in the tournament.
No. 2 Wake Forest had more star power and a better record than their second-round opponent, but No. 7 West Virginia had more depth down the stretch. The Mountaineers overcame a 13-point halftime deficit to knock off the Demon Deacons in double overtime, 111-105. The game was West Virginia's sixth in 11 nights, but they got stronger as the game progressed instead of showing fatigue.
Forcing No. 4 Syracuse to commit a season-high 24 turnovers and controlling the game with a deliberate pace, No. 13 Vermont earned the biggest win in school history, 60-57, in the first round of the 2005 tournament. The game was tied 11 times, and there were eight lead changes before Vermont finally prevailed in overtime.
Trailing No. 3 Kansas 63-62 with just seconds remaining, No. 14 Bucknell needed someone to step up. That's what 6-1 center Chris McNaughton did, receiving the ball down low and banking in a hook shot with eight seconds remaining for a one-point lead. In its 110 seasons, it was Bucknell's first NCAA tournament victory and came against a team that began the season ranked No. 1.
No. 15 Hampton upset No. 2 Iowa State in the first round of the 2001 tournament. Hampton, which had a 24-6 record coming into the game, knocked off its 25-5 opponents by one point when Tarvis Williams flipped in a four-foot shot in the lane with 6.9 seconds remaining. After a 19-4 run midway through the second half, Iowa State looked to be in control, but Hampton battled back for the upset win.
In 1997, Coppin State's basketball team didn't have a single starter over 6-7. That was just one of the many reasons no one gave the No. 15 seed much of a chance against No. 2 South Carolina. Instead, with a large majority of the crowd rooting for them, Coppin State pulled off a 78-65 victory. South Carolina took a 52-49 lead with just over eight and a half minutes to play, but Coppin State answered with a 15-4 run to take a lead it would never relinquish.
UCLA, the defending national champions, didn't expect any trouble from No. 13 Princeton when the two teams faced off in the first round of the 1996 tournament. But the Tigers kept the game close by pestering UCLA with a matchup zone that limited the Bruins to just 38.5 percent shooting and forced them to commit 16 turnovers. Princeton finally broke a 41-41 tie with just 3.9 seconds to go. The winning basket was scored on a backdoor pass, the Tigers' trademark play under head coach Pete Carril.
When Boston College shocked the University of North Carolina by a 75-72 score in the second round of the 1994 tournament, it snapped a 13-year stretch in which the Tar Heels had made it at least to the Sweet 16. The game saw UNC's point guard, Derrick Phelps, suffer a concussion early in the second half. The defending champions worked their way back from a 14-point deficit but couldn't pull off the complete comeback, bowing out in a huge upset.
Prior to the 1993 NCAA tournament, one oddsmaker rated No. 2 Arizona as a 7-to-1 choice to win the championship. The Wildcats' first-round opponent, No. 15 Santa Clara, on the other hand, had 800 million-to-1 odds. Neither one would win that year, but Santa Clara would best Arizona. The Broncos outrebounded, outscored and outplayed the Wildcats en route to the upset victory. Santa Clara was just 16-11 heading into the tournament and likely would not have received a tournament spot if it hadn't won its conference title.
In the 1990 tournament, UNLV trounced Duke by 30 points. After another strong year, the Rebels were heavily favored again in the 1991 tournament when the two teams met in the Final Four. Duke's defense shut down UNLV's running game, however, and the Blue Devils were scrappy on offense. It all added up to Duke snapping UNLV's 45-game win streak.
After the field was expanded to 64 teams in 1985, it took seven tournaments for a No. 2 seed to lose in the first round. That changed in 1991 when No. 15 Richmond toppled No. 2 Syracuse, 73-69. The Spiders never trailed. Richmond was no stranger to tournament upsets, having knocked off defending champion Indiana in the first round just three years earlier.
With 11 regular-season losses in 1988 and player issues that had plagued them throughout the year, Kansas was an extreme longshot. But the Jayhawks came on strong when it counted, storming through the tournament and beating No. 5 Duke in the Final Four to advance to a championship showdown against Oklahoma. No. 4 Oklahoma had defeated Kansas twice previously in the season but couldn't sweep. The Jayhawks were on fire in the finals, draining 17 of its first 20 field-goal tries en route to the victory.
In the five weeks prior to the 1989 NCAA tournament, Siena hadn't played a single game in front of a crowd because of an outbreak of measles. That combined with the fact that the Saints were making their first-ever national tournament appearance didn't bode well for their chances against No. 3 Stanford in the first round. Siena stepped up its game, however, taking a 16-point second-half lead and then holding off Stanford's late charge.
Providence, the No. 6 seed, knocked off No. 2 Alabama by 21 points in the Sweet Sixteen to set up a meeting with No. 1 Georgetown. Georgetown had lost one and won two against Providence earlier in the season, including a commanding 84-66 victory in the Big East tournament semifinals. This time, it was Providence that would dominate, upsetting the Hoyas to advance to the Final Four.
Despite starting the season with a perfect 14-0 record, LSU looked to have lost all momentum by the time they entered the 1986 NCAA tournament; the team's bad luck included players suffering from the chicken pox and the loss of their captain and scoring leader. Seeded 11th in the tournament, they reeled off upset victories over Purdue, Memphis State and Georgia Tech before downing No. 3 Kentucky in the Elite Eight to become the lowest seed to reach the Final Four.
Even though No. 8 Villanova had dispatched talented opponents like No. 2 Michigan and No. 7 North Carolina en route to the 1985 championship game, the Wildcats were still big underdogs against No. 1 Georgetown. Putting together a nearly perfect game -- shooting 22-28 from the field and 22-27 from the free-throw line -- Villanova earned the upset. Their shooting success was even more impressive considering Georgetown had held its opponents to just 39 percent that season.
Even if North Carolina State hasn't lost 10 games in the regular season, they still would have been underdogs facing powerhouse Houston in the 1983 NCAA tournament finals. Houston had started the second half with a 17-2 run, but N.C. State didn't let that discourage them, tying the game with two minutes to go. Although Houston boasted an impressive lineup featuring Akeem Abdul Olajuwon, Clyde Drexler and Michael Young, it was N.C. State that escaped with a 54-52 victory after Lorenzo Charles slammed in a dunk with one second remaining.
Sporting an all-back starting five, the first team ever to do so, Texas Western was a huge underdog against Kentucky in the 1966 tournament. Kentucky boasted two legendary guards and one of the best coaching minds of all time, but Texas Western was too strong.

industry_corpus2: Sports


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Owner: Valdosta-Lowndes Parks & Rec.
Project consist of addition of four (4) new baseball fields and one (1) new Miracle League Ballfield with associated equipment and fencing as well as new parking, sidewalks, stairs, ramps, handrails, irrigation system, and installation of asphalt base for the Miracle League Ballfield and boundless playground sport surfacing.
Scope also includes construction of a new concession building, dugouts, pre-engineered metal storage building, and pre-engineered metal structure for a picnic shelter.
MUSCO sports lighting fixtures are also being utilized on this project.


text: 21st Century Technology plc is a specialist provider of tailored solutions to the transport community, solving operational requirements both on and off the vehicle. The Company operates through two segments: Fleet Systems and Passenger Systems. The Fleet Systems segment includes closed-circuit television (CCTV), passenger wireless fidelity (Wi-Fi), telematics and driver behavior, and passenger counting. The Passenger Systems segment includes information estate software and hardware for passenger displays, smart ticketing and way finding. Its fleet solutions include video surveillance for passenger's and driver's safety, vehicle's and driver's performance monitoring and automatic passenger counting. Its services and technologies include integrated solutions, consultative design, maintenance and support, installation, testing and commissioning, and telematics. It provides solutions to fleet operators, train operating companies, local authorities and public transport executives.

industry_corpus2: Transportation