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Cancer causes: circa 67% are Replication error
"Most textbooks attribute cancercausing mutations to two major sources: inherited and environmental factors. A recent study highlighted the prominent role in cancer of replicative (R) mutations that arise from a third source: unavoidable errors associated with DNA replication." 
Tiny Tweak in Teaching Basic Circuits
I'm sure we have all seen the frequent questions from students who don't understand the difference between potential and voltage in a circuit. They seem to think that zero voltage has physical significance. Even using the phrase "voltage drop" is not sufficient, because they say, "What happens when it drops to zero," leading to the concept that voltage is a consumable... 
Why does formation of snow flakes not violate entropy law?
Snow flakes are highly structured, they form from water vapor which has very little structure. I must be misunderstanding entropy, my interpretation of it is that isolated system must evolve into more chaotic less structured states, which is not what happens with snow flakes. Can someone explain? 
LHCb observes 5 new particles (excited hadrons)
Plain old standard model baryons, but 5 at the same time, and with crystal clear peaks in the decay to ##\Xi_c^+ K^##. Each peak in the figure is a particle never seen before, and the significances of those peaks are about 20 sigma (10 sigma for the 5th one). A broad 6th state might hide around 3200 MeV... 
Math Challenge by Erland #1
A rectangle is divided into a finite number of subrectangles. The sides of the subrectangles are all parallel to sides of the large rectangle. Each subrectangle has at least one side with integer length. Prove that the large rectangle also has at least one side with integer length. 
Fish becoming landdwellers today
And we can watch different related species at different steps in the transition. In this case, the reason is not the availability of food, but the lower number of predators on land. "At low tide, blennies are commonly found swimming in rock pools around the edges of the island. But when high tide moves in, they climb up to dry land and shuffle around the rocks until the tide retreats. The researchers found that this is most likely..." 
Specifications for elephantresistant steel poles
I have camera traps out on the African bush, that are monitoring the responses of leopards to artificial scents. The cameras are in steel boxes to protect them from elephants, the boxes are bolted to brackets 150 mm long and the brackets are bolted to steel poles at a height of either 500 or 700 mm above ground level. The poles are 40 x 40 mm mild steel angle, either 2mm or 3mm thickness... 
Math Challenge by QuantumQuest #1
CHALLENGE:
Prove that if ##P(x), Q(x), R(x)## and ##S(x)## are all polynomials such that ##P(x^{5}) + xQ(x^{5}) + x^{2}R(x^{5}) = (x^{4} + x^{3} + x^{2} + x + 1)S(x)##, ##x  1## is factor of ##P(x)##. 
What is the Quantum of Sound in Gases and Air
It is usually referred to as Phonons for sound waves in solid. But, where it gets confusing, is in gases and air. Some still call it Phonons, others say, Phonons can only be used in solid states. So what is the Quantum of Sound in Gases/Air? 
Math Challenge by Charles Link #1
Beginning with a cube with each side of length 1", drill a 1" diameter hole all the way through in each of the 3 perpendicular directions. Find the remaining volume. 
Why is Hilbert not the last universalist?
It is often said that Poincare was the last universalist, i.e. the last mathematician who understood moreorless all mathematics of his time. But Hilbert's knowledge of math was also quite universal, and he came slightly after Poincare. So why was Hilbert not the last universalist? What branch of math he didn't understood sufficiently well to deserve this title? 
Is the US abandoning its position as a science superpower?
"China is aggressively attempting to displace the US as the world's scientific superpower, and the US is aggressively attempting to abandon it's scientific superpower status, while Europe seems all but recovered from WWII. ....". I was wondering how the rest of you on PF feels on this regard. 
Can modern physics be understood qualitatively?
I'm curious on just how much modern physics can be understood qualitatively, without equations. I know that people can understand F=ma with just words. For example, the acceleration an object experiences is directly proportional to overall force pushing or pulling on the object. The more force the more acceleration and vice versa. Of course, this ignores the fact that its a differential equation... 
Are there really 4 fundamental math operations?
It's strange to me that multiplication and division are considered fundamental operations.
It makes sense for me that addition is a fundamental operation but multiplication is just like a function or algorithm that takes several numbers and apply additions. This is true even for multiplication with real number. 
Do patents inhibit development in the technology?
What do I mean by inhibit, you know taking patent or taking permission to use its license takes some time and money and if we think in large scale, today, almost every company spends lots of time to protect their tech. My point is maybe all these things slows the improvement in technology. I think if everything were free to use things would get faster in terms of tech...
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