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This link is an interesting perspective on Little’s Law, L = λW (a fundamental law in queueing theory), which turns 50 this year. (Strictly speaking, it’s the proof of the law that’s turning 50.)
According to the editors of Operations Research:
Little proves that under very general conditions, the average length of a queue, in steady state, will be equal to the arrival rate into the queue times the average wait in the queue. Remarkably, this relationship is not influenced by the arrival process distribution, the service distribution, the service order, or practically anything else. Nor does it depend on the structure of the queueing system: “Little’s Law” holds not just at the individual queue level but also at the system level.
More: John Little’s new paper about his law - “Little’s Law as Viewed on Its 50th Anniversary”
Here’s an interesting article from The Atlantic about STEM education in the US vs. the UK.
Education reform is top on the government’s agenda, and nearly everyone has an opinion on how to solve the learning lag. STEM education has become the poster child for education leaders. And while there is a renewed emphasis on math and science, the same cannot be said of their less popular siblings, engineering and technology. Very rarely are all four concepts taught in one lesson.
Many schools follow the ‘basics-first’ approach where they teach the foundational concepts of a design problem first (like basic math), without actually taking students through the process. How torturous for a curious student to learn about torque, motors and circuits without getting the chance to even unhinge a bolt.
petzoldt:
The “Traveling Sales Man Problem” is a classic in Operations Research. It asked for the shortest round trip through a set of cities given the distances beween them. For 20 cities there are already 2.432.902.008.176.640.000 of such tours. A computer able to calculate a trip length in A computer able to calculate a trip length in one milliseconds would still need 240 billion years checking all of them.
Its fascinating to see how researchers keep pushing the limits when solving ever larger problems using methods from mathematical optimization and Operations Research, such as William Cook who claims to have calculated the best tour visting 1.9 million cities.
The Way You Learned Math Is So Old School
If you’re a parent of a certain age, your kids’ homework can be confounding. Blame it on changes in the way children are taught math nowadays — which can make you feel like you’re not very good with numbers.
Mathematics seems to endow one with something like a new sense.
Bees solve the Traveling Salesman Problem everyday.
The TSP is heavily used in theoretical compute science and in operations research, and is classified as a NP-hard problem.
In its original formulation, the solver is given a list of cities, and their pairwise distances, and is then tasked with finding the shortest possible distance that will allow them to visit each of the cities exactly once.
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“Foraging bees solve traveling salesman problems every day. They visit flowers at multiple locations and, because bees use lots of energy to fly, they find a route which keeps flying to a minimum,” explains Dr Nigel Raine.
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“Despite their tiny brains bees are capable of extraordinary feats of behavior. We need to understand how they can solve the Traveling Salesman Problem without a computer. What short-cuts do they use?” Raine says.
The new investigation could have significant implications for agriculture, because bee pollination patterns are critically important for next year’s crops.
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