[math-fun] Bird 'backpacks' help scientists discover the longest oversea migration
FYI -- This article is relevant to the recent discussion about ocean navigation by birds, etc. http://www.theguardian.com/science/2015/apr/01/bird-backpacks-help-scientist... Bird 'backpacks' help scientists discover the longest oversea migration By fitting it with tiny geolocators, scientists have proven that the blackpoll warbler completes the longest known oversea journey for any land bird Hannah Devlin, science correspondent Wednesday 1 April 2015 00.00 BST Last modified on Wednesday 1 April 2015 00.03 BST A tiny North American songbird migrates 1,500 miles non-stop over the Atlantic, scientists have discovered, in the longest known oversea journey for any land bird. The blackpoll warbler weighs only as much as a £2 coin and normally lives in forest environments, but once a year it embarks on a perilous three-day journey, scientists have found. By fitting the birds with tiny geolocator backpacks, they were able to track their route from North America and Canada to Puerto Rico and Cuba and then onwards to South America. Chris Rimmer, an ornithologist at the Vermont Center for Ecostudies and a co-author of the study, said: ÂThere is no longer any doubt that the blackpoll undertakes one of the most audacious migrations of any bird on earth. Although other migratory birds such as the albatross and arctic tern are known for travelling thousands of miles across oceans, the blackpoll warbler has the added challenge of making the journey without stopping, as a water landing would be fatal. ÂItÂs a fly-or-die journey, said Ryan Norris, the Canadian team leader at the University of Guelph, said. Other North American songbirds that travel south in winter take a less risky, continental route south through Mexico and Central America. However, ornithologists suspected the blackpoll warbler was taking a water route, based on observations of birds landing on boats during stormy Atlantic weather. It had also been noted that the birds put on significant amounts of weight in the autumn  sometimes almost doubling in size  hinting that they were preparing for a long journey ahead. ÂThey get basically so fat that they donÂt move, said Norris. Until now, there was no conclusive proof that they were migrating across open ocean, however. ÂSome people said thereÂs no way they could do this, Norris added. ÂThey donÂt seem particularly athletic birds. In the latest study, published in Biology Letters, scientists equipped 20 birds in Vermont and 20 more in Nova Scotia with tiny backpacks fitted with a clock and a sensor to measure ambient light levels. The number of hours of daylight gives the birdÂs latitude and the time of sunrise gives longitude. But the packs, weighing just 0.5g, were too small to include transmitters, meaning that the researchers had to search for the birds back at their nesting ground in the North American forest the following year. ÂThese birds come back every spring very close to the same place they used in the previous breeding season, so with any luck you can catch them again, said Norris. ÂOf course there is high mortality among migrating songbirds on such a long journey; we believe only about half return. The team worried that the extra 0.5g  added to the birdÂs roughly 12g body weight  could make an already challenging journey insurmountable. In the end, they were able to recapture three birds from the Vermont group and two from the Nova Scotia group for analyses. ÂIt was pretty thrilling to get the return birds back, because their migratory feat in itself is on the brink of impossibility, said Bill DeLuca, of the University of Massachusetts Amherst and the paperÂs first author. The locators showed that the blackpolls took a route directly over the Atlantic, with distances ranging from 1,410 to 1,721 miles (2,270 to 2,770 km). Grahame Madge, of the RSPB, said the findings help explain why the songbirds have occasionally been seen in Britain: records show 45 sightings, mostly in the Scilly Isles, since the 1960s. ÂItÂs quite easy to imagine how a storm system could sweep them up, he said. ÂThey set out thinking theyÂre heading for the Caribbean and end up in Europe. http://i.guim.co.uk/static/w-300/h--/q-95/sys-images/Guardian/Pix/pictures/2...
Is the blackpoll warbler by any chance a distant relative of the great orc? WFL On 4/1/15, Henry Baker <hbaker1@pipeline.com> wrote:
FYI -- This article is relevant to the recent discussion about ocean navigation by birds, etc.
http://www.theguardian.com/science/2015/apr/01/bird-backpacks-help-scientist...
Bird 'backpacks' help scientists discover the longest oversea migration
By fitting it with tiny geolocators, scientists have proven that the blackpoll warbler completes the longest known oversea journey for any land bird
Hannah Devlin, science correspondent
Wednesday 1 April 2015 00.00 BST Last modified on Wednesday 1 April 2015 00.03 BST
A tiny North American songbird migrates 1,500 miles non-stop over the Atlantic, scientists have discovered, in the longest known oversea journey for any land bird.
The blackpoll warbler weighs only as much as a £2 coin and normally lives in forest environments, but once a year it embarks on a perilous three-day journey, scientists have found.
By fitting the birds with tiny geolocator backpacks, they were able to track their route from North America and Canada to Puerto Rico and Cuba and then onwards to South America.
Chris Rimmer, an ornithologist at the Vermont Center for Ecostudies and a co-author of the study, said: “There is no longer any doubt that the blackpoll undertakes one of the most audacious migrations of any bird on earth.”
Although other migratory birds such as the albatross and arctic tern are known for travelling thousands of miles across oceans, the blackpoll warbler has the added challenge of making the journey without stopping, as a water landing would be fatal.
“It’s a fly-or-die journey,” said Ryan Norris, the Canadian team leader at the University of Guelph, said.
Other North American songbirds that travel south in winter take a less risky, continental route south through Mexico and Central America. However, ornithologists suspected the blackpoll warbler was taking a water route, based on observations of birds landing on boats during stormy Atlantic weather. It had also been noted that the birds put on significant amounts of weight in the autumn sometimes almost doubling in size hinting that they were preparing for a long journey ahead. “They get basically so fat that they don’t move,” said Norris.
Until now, there was no conclusive proof that they were migrating across open ocean, however.
“Some people said there’s no way they could do this,” Norris added. “They don’t seem particularly athletic birds.”
In the latest study, published in Biology Letters, scientists equipped 20 birds in Vermont and 20 more in Nova Scotia with tiny backpacks fitted with a clock and a sensor to measure ambient light levels. The number of hours of daylight gives the bird’s latitude and the time of sunrise gives longitude. But the packs, weighing just 0.5g, were too small to include transmitters, meaning that the researchers had to search for the birds back at their nesting ground in the North American forest the following year.
“These birds come back every spring very close to the same place they used in the previous breeding season, so with any luck you can catch them again,” said Norris. “Of course there is high mortality among migrating songbirds on such a long journey; we believe only about half return.”
The team worried that the extra 0.5g added to the bird’s roughly 12g body weight could make an already challenging journey insurmountable.
In the end, they were able to recapture three birds from the Vermont group and two from the Nova Scotia group for analyses. “It was pretty thrilling to get the return birds back, because their migratory feat in itself is on the brink of impossibility,” said Bill DeLuca, of the University of Massachusetts Amherst and the paper’s first author.
The locators showed that the blackpolls took a route directly over the Atlantic, with distances ranging from 1,410 to 1,721 miles (2,270 to 2,770 km).
Grahame Madge, of the RSPB, said the findings help explain why the songbirds have occasionally been seen in Britain: records show 45 sightings, mostly in the Scilly Isles, since the 1960s. “It’s quite easy to imagine how a storm system could sweep them up,” he said. “They set out thinking they’re heading for the Caribbean and end up in Europe.”
http://i.guim.co.uk/static/w-300/h--/q-95/sys-images/Guardian/Pix/pictures/2...
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MIT had a particularly good showing in the most recent Putnam exam: Its team came in #1, and among the 6 Putnam fellows this year, 5 of them were from MIT: < http://kskedlaya.org/putnam-archive/putnam2014results.html >. --Dan
I notice that those of us from the last half of the alphabet did very well! :-) Rich ------ Quoting Dan Asimov <asimov@msri.org>:
MIT had a particularly good showing in the most recent Putnam exam:
Its team came in #1, and among the 6 Putnam fellows this year, 5 of them were from MIT:
< http://kskedlaya.org/putnam-archive/putnam2014results.html >.
--Dan
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Clearly that cannot be a mere coincidence. --Dan
On Apr 1, 2015, at 1:18 PM, rcs@xmission.com wrote:
I notice that those of us from the last half of the alphabet did very well! :-)
------ Quoting Dan Asimov <asimov@msri.org>:
MIT had a particularly good showing in the most recent Putnam exam:
Its team came in #1, and among the 6 Putnam fellows this year, 5 of them were from MIT:
< http://kskedlaya.org/putnam-archive/putnam2014results.html >.
The game called "Set", in case you don't know, is a deck of 81 cards, each one having a visual image on it. The image displays 4 characteristics, each of which is a choice of one of 3 possible versions. The characteristics happen to be: Color, Number, Shape, and Shading. Color = {Red, Green, Purple}; Number = {One, Two, Three}; Shape = {Oval, Diamond, Squiggle}; Shading = {Light, Medium, Heavy}. All of which details are irrelevant to the math behind it. We may as well assume the 81 cards is the vector space V = (F_3)^4 of dimension 4 over the field of 3 elements. The goal of the game is to find affine lines in V, namely subsets of the form L + v where L is any 1-dimensional subspace of V and v is any element of v. These are all, of course, subsets of size 3. DIFFICULT PROBLEM: What is the largest size of a subset of V that contains no affine line? The answer is 20. Every known proof of this is a tedious case-by-case analysis or else by computer search. GENERALIZED DIFFICULT PROBLEM: Let V_n denote the vector space (F_3)^n. What is the largest size of a subset of V_n containing no affine line? Let M(n) denote this number: the maximum size of any subset of V_n containing no affine line. Apparently even the n=5 case borders on being too large for computers to handle in any reasonable time, but that has been solved. In fact, here is what is known: n 1 2 3 4 5 6 7+ M(n) 2 4 9 20 45 112-114 ? ---------------------------------------------------------- QUESTION: Is there a nice asymptotic expression for M(n) ? --Dan
I think the best paper about this is the one by Diane Maclagan and Ben Davis, which I edited for the Intelligencer (MI 25#3, 2003). http://homepages.warwick.ac.uk/staff/D.Maclagan/papers/set.pdf The asymptotic size of the largest line-free subset of (F_3)^n is definitely q^n for some q, but the bounds on q are pretty poor. In particular, the paper says it is an open question whether q=3, and as far as I know, that is still the case. --Michael On Thu, Apr 2, 2015 at 4:13 PM, Dan Asimov <asimov@msri.org> wrote:
The game called "Set", in case you don't know, is a deck of 81 cards, each one having a visual image on it.
The image displays 4 characteristics, each of which is a choice of one of 3 possible versions.
The characteristics happen to be: Color, Number, Shape, and Shading.
Color = {Red, Green, Purple}; Number = {One, Two, Three}; Shape = {Oval, Diamond, Squiggle}; Shading = {Light, Medium, Heavy}.
All of which details are irrelevant to the math behind it.
We may as well assume the 81 cards is the vector space
V = (F_3)^4
of dimension 4 over the field of 3 elements.
The goal of the game is to find affine lines in V, namely subsets of the form
L + v
where L is any 1-dimensional subspace of V and v is any element of v. These are all, of course, subsets of size 3.
DIFFICULT PROBLEM: What is the largest size of a subset of V that contains no affine line?
The answer is 20. Every known proof of this is a tedious case-by-case analysis or else by computer search.
GENERALIZED DIFFICULT PROBLEM: Let V_n denote the vector space (F_3)^n. What is the largest size of a subset of V_n containing no affine line?
Let M(n) denote this number: the maximum size of any subset of V_n containing no affine line.
Apparently even the n=5 case borders on being too large for computers to handle in any reasonable time, but that has been solved. In fact, here is what is known:
n 1 2 3 4 5 6 7+
M(n) 2 4 9 20 45 112-114 ?
----------------------------------------------------------
QUESTION: Is there a nice asymptotic expression for M(n) ?
--Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.
See http://oeis.org/A090245 Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Thu, Apr 2, 2015 at 4:31 PM, Michael Kleber <michael.kleber@gmail.com> wrote:
I think the best paper about this is the one by Diane Maclagan and Ben Davis, which I edited for the Intelligencer (MI 25#3, 2003).
http://homepages.warwick.ac.uk/staff/D.Maclagan/papers/set.pdf
The asymptotic size of the largest line-free subset of (F_3)^n is definitely q^n for some q, but the bounds on q are pretty poor. In particular, the paper says it is an open question whether q=3, and as far as I know, that is still the case.
--Michael
On Thu, Apr 2, 2015 at 4:13 PM, Dan Asimov <asimov@msri.org> wrote:
The game called "Set", in case you don't know, is a deck of 81 cards, each one having a visual image on it.
The image displays 4 characteristics, each of which is a choice of one of 3 possible versions.
The characteristics happen to be: Color, Number, Shape, and Shading.
Color = {Red, Green, Purple}; Number = {One, Two, Three}; Shape = {Oval, Diamond, Squiggle}; Shading = {Light, Medium, Heavy}.
All of which details are irrelevant to the math behind it.
We may as well assume the 81 cards is the vector space
V = (F_3)^4
of dimension 4 over the field of 3 elements.
The goal of the game is to find affine lines in V, namely subsets of the form
L + v
where L is any 1-dimensional subspace of V and v is any element of v. These are all, of course, subsets of size 3.
DIFFICULT PROBLEM: What is the largest size of a subset of V that contains no affine line?
The answer is 20. Every known proof of this is a tedious case-by-case analysis or else by computer search.
GENERALIZED DIFFICULT PROBLEM: Let V_n denote the vector space (F_3)^n. What is the largest size of a subset of V_n containing no affine line?
Let M(n) denote this number: the maximum size of any subset of V_n containing no affine line.
Apparently even the n=5 case borders on being too large for computers to handle in any reasonable time, but that has been solved. In fact, here is what is known:
n 1 2 3 4 5 6 7+
M(n) 2 4 9 20 45 112-114 ?
----------------------------------------------------------
QUESTION: Is there a nice asymptotic expression for M(n) ?
--Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Nice to see that entry, thanks. I didn't understand the comment about the sequence for the game of Set possibly turning out to be different from . . . some related question. Help? Thanks, Dan
On Apr 2, 2015, at 4:48 PM, Neil Sloane <njasloane@gmail.com> wrote:
Best regards Neil
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