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I just can't resist: there are infinitely many pairs of primes at most 59470640 apart May 30, 2013Posted by Scott Morrison in Number theory, polymath.
Tags: admissible-set, polymath8, primes, zhang
Everyone by now has heard about Zhang's landmark result showing that there are infinitely many pairs of primes at most 70000000 apart.
His core result is that if a set of 3.5 * 10^6 (corrected, thanks to comment #2) numbers is admissible (see below), then there are infinitely many so that contains at least two primes. He then easily constructs an admissible set wherein the largest difference is 7 * 10^7, obtaining the stated result.
A set is admissible if there is no prime so occupies every residue class. For a given this is clearly a checkable condition; there's no need to look at primes larger than .
(While Zhang went for a nice round number, Mark Lewko found his argument in fact gives 63374611, if you're being overly specific about these things, which we are right now. :-)
In a short note on the arXiv yesterday, Tim Trudgian (whose office is not far from mine) pointed out another way to build an admissible set, giving a smaller largest difference, obtaining the result that there are infinitely many pairs of primes at most 59874594 apart. He considers sets of the form (where is Zhang's constant 3.5 * 10^7). These aren't necessarily admissible, but they are for some values of , and both Zhang and Tim noticed certain values for which this is easy to prove. Zhang used with , while Tim's observation is that also works. (Comment #2 below points out this isn't right, and Zhang also intended , and the slack in his estimate is coming from just looking at the largest element of , rather than the largest difference.) Thus the bound in his result is .
It turns out that checking admissibility for a given isn't that hard; it takes about an hour to check a single value for (but if you find a prime witnessing not being admissible, it very often gives you a fast proof that is not admissible either, so searching is much faster).
I haven't looked exhaustively, but one can check that gives an admissible , and hence there are infinitely many pairs of primes at most . (Sadly, it's impossible to get below 59 million with this trick; no below 27000 works; all witnessed by or .)
I just couldn't resist momentarily "claiming the crown" for the smallest upper bound on gap size. :-) Of course the actual progress, that's surely coming soon from people who actually understand Zhang's work, is going to be in reducing his 3.5 * 10^6. You can read more about prospects for that in the answers to this MathOverflow question.
- 2. anonymous - May 30, 2013
Trudgian's set is actually the same one Zhang said to construct in the first place. From Zhang's paper: "The bound (1.5) results from the fact that the set H is admissible if it is composed of k_0 distinct primes, each of which is greater than k_0, and the inequality
π(7 * 10^7) − π(3.5 * 10^6) > 3.5 * 10^6." Among the first 3.5 * 10^6 primes above 3.5 * 10^6, the largest is 63374611 as pointed out by Lewko, but the smallest is 3500017, and their difference is 59874594. (The number Zhang uses is 3.5 * 10^6, not 3.5 * 10^7.)
- 4. anonymous - May 30, 2013
It's still not right: the numbers are 3.5*10^6 and 7*10^7, since there are at least 3.5*10^6 primes between 3.5*10^6 and 7*10^7.
- 6. pedant - May 30, 2013
This is a silly comment, but it's been irritating me to see people publicly using an odd number as the bound, so let me point out that Mark Lewko's observation can be trivially improved from 63374611 to 63374610.
- 12. David Roberts - May 31, 2013
Scott, why not write a one-page article and put it on the archive (you could call it "An even poorer man's improvement…") :-P Due credit to Terry of course.
- 13. David Roberts - May 31, 2013
archive -> arXiv :-S
- 18. David Roberts - May 31, 2013
Scott, how long do you think before you now optimize m? Once you do, I suppose then it will take some delving into how is arrived at (and yes, I know this is a whole lot harder).
Terry: Where does Zhang pluck 1/1168 from?
- 32. Vít Tuček - June 2, 2013
It's quite entertaining to watch the ongoing discussion. Do you think it makes sense to create a community wiki thread on mathoverflow.net to concentrate these efforts on one place?
If I understood correctly, the admissible set $H$ doesn't need to consist of primes only. I hacked together a small program to see the behaviour and it turns out that if one allows for nonprimes then the ratio of diameter and length is approximately 10. (So far I've produced admissible set of diameter 64992 and length 5632. Only 1506 of those numbers are primes.) Hence it should be possible to find an admissible set of length 866,805 with diameter around 9,000,000. Possibly breakig the psychological barrier of 10 millions.
If I have time I'll try to optimize memory requirements of my program and see how far I can push it.
- 35. David Roberts - June 2, 2013
Something like "Can the techniques of Morrison-Tao be used to get the prime gap bound below 10 million?" If the answer is yes or no, then either way one could explain how to do so, possibly using Vít Tuček's suggestion. I would like to see at least a push to get below 7M, one factor of ten over Zhang's bound, which feels like a real milestone (or below 1M, but that looks unlikely).
- 36. Vít Tuček - June 2, 2013
It depends on how long can we play this game. If there's not much more to be expected than what is written on this page and Terrence's blog then it doesn't make much sense. I just thought that exposing this fun to a wider audience can be benefactory. Also, possibility of editing one's posts adds a lot to clarity of exposition. I have actually half-written the question but then I decided to ask here first. If there'll be no objections here by tomorrow morning (in GMT+1) I'll post the question and see if it sticks.
As for my admissible set; I just basically start with 1 and work my way towards bigger numbers crossing off those which destroy admissibility.
- 37. David Roberts - June 2, 2013
Ideally people would make their code accessible (at some point), so people would have the benefit of access to that as well as Terry's write-up on improving the theoretical bounds. This might lead to some optimisation on slow searching algorithms.
- 38. Mark Lewko - June 2, 2013
Regarding the possible length of an admissible k-tuple, there's a well-known explicit estimate of Montgomery and Vaughn that gives
Since this is proven via sieve theory it should hold for admissible k-tuples as well (or, for that matter, if you believe the k-tuples conjecture). Thus solving gives around $6.8$ million, which will be a hard lower bound on the distance of a k-tuple with . My guess is that this is probably significantly smaller than one can really achieve. If I recall correctly Richards conjectures that the correct asymptotic is which saves an asymptotic factor of , but then you need explicit bounds on the error terms to be of use here…
The literature on the topic seems surprisingly sparse.
- 39. Scott Morrison - June 2, 2013
@David, thanks for the reminder! My code (mathematica) containing the formulas for and so on, and Terry's updates to them, as well as a very simplistic method for finding the optimal , is available at http://tqft.net/misc/finding%20k_0.nb
(It would be great if someone could check it for typos!)
My current code for optimising for a given is a little hard to disentangle from other stuff, but I'll see what I can do. It's written in Scala.
- 43. Disponible "Bounded gaps between primes" de Yitang Zhang y algunas mejoras a la cota de 70000000 - Gaussianos | Gaussianos - June 3, 2013
[…] en la cota de 70000000 que se da en dicho trabajo: 63374611 (Mark Lewko), 59874594 (Tim Trudgian) o 59470640 (Scott Morrison). En los comentarios de este último enlace y en los de la última fuente que […]
- 44. Vít Tuček - June 3, 2013
- 45. John W. Nicholson - June 3, 2013
If I am not mistaken, Ramanujan primes can bring the value of H down.
- 46. The prime tuples conjecture, sieve theory, and the work of Goldston-Pintz-Yildirim, Motohashi-Pintz, and Zhang | What's new - June 3, 2013
[…] parameter to be optimised over (in practice it is an order of magnitude or two smaller than ); see this blog post for details. The upshot is that one can bound for large by a quantity slightly smaller than (and the large […]
- 48. Vít Tuček - June 3, 2013
The question on mathoverflow has just been closed. I sincerely hope that there actually will be a polymath project.
- 49. Christian Elsholtz - June 3, 2013
Here are three comments on dense prime constellations:
(I had posted this earlier, but probably went into the spam filter, so I try as three individual items)
1) The paper by Gordon and Rodemich "Dense admissible sets"
has some useful information.
This paper and also Hensley and Richards ("Primes in intervals")
both mention an observation of Schinzel on a variant of the sieve of
While one usually sieves the class , for , one now sieves the class , for
and the class for .
It seems that one can increase a dense cluster of primes from about
to , where is larger than in the Hensley-Richards trick using the interval . (For details see the paper by Gordon and Rodemich).
As all this influences only the second order term,
the improvement coming from here is limited.
- 54. NDE - June 3, 2013
"This project is curiously addictive" – T.Tao, May 31
Addictive number theory?
- 55. Polymath proposal: bounded gaps between primes | The polymath blog - June 3, 2013
[…] the explicit upper bound of 70,000,000 given for this gap. Since then there has been a flurry of activity in reducing this bound, with the current record being 4,802,222 (but likely to improve at […]
- 58. Online reading seminar for Zhang's "bounded gaps between primes" | What's new - June 4, 2013
[…] There is an active discussion on trying to improve the constructions of admissible tuples at this blog post; it is conceivable that some combination of computer search and clever combinatorial constructions […]
- 59. Richard - June 4, 2013
"This project is curiously addictive"
As somebody who dropped out of mathematics decades ago (and can barely follow the outlines of arguments and improvements being made here), I can attest that the addictive quality of these sorts of incremental optimizations is exactly that of some types of computer programming.
The primary and sad difference is that I have been paid an obscene amount of money over the years for improving the constant factors hidden inside "Big O" notation while doing no deep thinking at all.
That said, this is all immense fun to follow, and I thank you all for the vicarious pleasure of following along.
Polymath Groupie
- 60. Andrew Sutherland - June 4, 2013
Hi, I hope it's not too late to join the party.
Following suggestion 1 of post 53, I get a bound of 4,801,744 using , with and .
Only a small improvement, but still worth doing.
- 63. Avi Levy - June 4, 2013
I wrote a small program in Python based on Scott's work in Scala that is available at https://github.com/avi-levy/dhl
At the moment, the code has not been optimized and I am trying to improve this.
If anyone has ideas for suggestions/improvements, don't hesitate to contribute!
- 66. David Roberts - June 4, 2013
Scott, why is important, rather than some other small number currently out of reach?
- 68. Andrew Sutherland - June 4, 2013
@Scott, I checked all values of starting from , which corresponds to the symmetric case. The value is optimal for .
But I realized that there is no reason to stick with once you switch to an asymmetric sequence. Allowing both and to vary yields a more substantial improvement.
Using and with I get the bound 4,788,240.
My code is a bit disorganized at the moment, but tomorrow I will try to clean it up and post it.
- 71. Avi Levy - June 4, 2013
I am amazed not only by your mathematical abilities, but also by your ability to find mathematical resources from such obscure corners of the internet…
- 72. Christian Elsholtz - June 5, 2013
Here are three comments on dense prime constellations:
(Part 1 was posted before, see comment at the end).
1) The paper by Gordon and Rodemich "Dense admissible sets"
has some useful information.
This paper and also Hensley and Richards ("Primes in intervals")
both mention an observation of Schinzel on a variant of the sieve of Eratosthenes.
While one usually sieves the class , for , one now sieves the class , for
and the class for .
It seems that one can increase a dense cluster of primes from about to , where is larger than in
the Hensley-Richards trick using the interval .
(For details see the paper by Gordon and Rodemich).
As all this influences only the second order term,
the improvement coming from here is limited.
2) But it still leads to some small improvement, and thus a new record: I was able to implement this type of improvement, with some additional refinement, as follows:
I choose the interval slightly larger,
as I will discard the first part of it later:
Choose (as recommended implicitly by Gordon and Rodemich)
and notice that should be of size larger than
I do this a bit different:
I sieve (so that all remaining classes are even!),
and for .
369,760 integers survived this sieve process.
Then modulo
I tested if the set occupies all classes.
If mod p all classes are occupied I sieve the class 0 mod these primes.
(This was the case for only 1879 of these 3200 primes, the largest being
. As I do not have to do this modulo all primes,
there is some saving, which seems empirically larger than the choice
of the class 1 mod 2.)
357,138 integers survived this second sieving,
so there is some room for shifting the interval:
If one uses the interval one sees that the sequence starts sparse
(powers of 2) powers of 2.
A quite good interval is the last 341,640 of the integers.
a slightly better starts at
{352634, 352642, 352654, 352658,…
5077634, 5077642, 5077648, 5077652, 5077654}
The gap (and therfore the new record) is $\latex 4,725,021$.1
Then modulo larger primes up to
I tested if the set occupies all classes, and no further
example was found where the set occupies all classes.
(This gets increasingly unlikely, but actually,
for a final proof I would need to extend this test! As these numbers
still go down, it did not seem appropriate to put too much effort into
this, at the time being).
Some optimisation seems possible, but probably it's more interesting to see
if a change of search strategy helps more, (see point 3).
3) Apart from a complete search, of all tuples
k tuples in an interval of size about 5,000,000,
which would seem hopeless, it would be interesting,
if the search space of sifted sets with just one arbitrary class
removed modulo each prime, but not necessarily the class 1 or 0,
contains better examples.
Observe that this might heuristically give
surviving integers and so
potentially gains a factor of of the main term.
In other words, one could try different variants of Schinzel's modification.
While I expect that sieving the class 0 for most primes is really good, I do not understand why
it must be the best.
Historical comment:
I had initially written this on June 3rd, when the record was above 13 million,
and I could push it down to 12,870,557.
I posted it, and it was eaten up by the spam filter,
I intended to post it in three shorter bits again,
and the first part appeared above.
The next day the record was down to $k=341,640$,
I rerun my calculations and updated part 2, when I wanted to post
it I saw on Terry's blog a note that Scott had improved the record
to H(341,640) \leq 4,693,068. However, meanwhile on Scott's blog
the record seems to be still weaker and I believe the "4,693,068" may be a typo on Terry's blog (this was in the first long entry), as the second entry links to the polymath record
- 74. Andrew Sutherland - June 5, 2013
A lower would certainly be most welcome!
In the meantime, taking a brute force approach along the lines of Elsholtz's post 72, if I sieve the interval of odd numbers and then for increasing primes for which all residue classes are still occupied, I wind up sieving a total of 4,535 residue classes (including ). The first prime that I don't sieve a residue class for is $p_{3450}=33,113$, and the last prime that I do sieve a residue class for is $p_{5415}=53,087$.
Taking the last unsieved integers that remain, starting with 347,078 and ending with 5,064,638 yields an admissable sequence with diameter 4,717,560, which I believe is a new record.
As noted by Elsholtz, one might expect to do slightly better by not necessarily always sieving , but so far I have not found a situation where this helps. One might sieve intervals that also include negative numbers, but the downside of doing so is that there is a very sparse region around 0 that one must trade off against increased density at the ends of the interval.
- 75. Andrew Sutherland - June 5, 2013
For what it's worth, if I apply the procedure in post 74 using and the interval , taking the last of the unsieved integers yields an admissable sequence beginning with 22,874 and ending with 419,984 that has diameter 397,110.
- 76. Vít Tuček - June 5, 2013
If anyone wants to play with sieving to obtain admissible sets feel free to use my code at https://github.com/vit-tucek/admissible_sets
- 77. Andrew Sutherland - June 5, 2013
I was able to gain additional ground using a "greedy-greedy" approach. For a suitably chosen interval , first sieve and for primes . Then for all primes in the interval , determine the residue class with the fewest unsieved integers in it (in case of ties, minimize ). It may be that there are no unsieved integers in this residue class, in which case move on to the next prime , but otherwise sieve .
Applying this with using and taking the last unsieved integers left in yields an admissable sequence starting with 82,923 and ending with 4.739,222 that has diameter 4,656,298.
A total of only 4,413 residue classes get sieved. The first nonzero residue class is for , the least prime for which no residue class is sieved is , and the largest prime for which a residue class is sieved is .
Playing the same game with the provisional using yields an admissable sequence starting with 9,742 and ending with 399,664 that has diameter 389,922.
- 78. Christian Elsholtz - June 5, 2013
Here is an update on the previous comment that maybe
one should not always sieve 0 mod p (as in Eratosthenes).
I now sieve 1 mod 2 (leaving the even integers) as suggested by Schinzel, and then I sieve the class Floor(p/2) modulo p.
With k=341640, sieving modulo all of the first 3800 primes in the interval [1 to 3 million] and then sieving modulo those primes which occupy all classes, (currently, I do not dynamically update this).
I get 341,640 integers in [164,042; 2,999,700], i.e. an interval size
I am sure Andrew can optimise these parameters quickly.
As this actually dropped by a factor, it seems that the main term of x/log is affected and one could wonder whether this means anything for the theory of sieves.
- 79. Andrew Sutherland - June 5, 2013
@Christian: I'm not sure I follow you. If I sieve [1,3,000,000] of integers congruent to floor(p/2) mod p for the first 3800 primes (which I note includes sieving 1 mod 2), I am left with only 204,446 survivors, even before checking residue classes for any larger primes.
The list of survivors after sieving just the first 3800 primes begins 17,898, 17,900, 17,904, 17,918, 17,934 and ends 2,999,940, 2,999,954, 2,999,960, 2,999,966, 2,999,996.
Am I missing something here?
In general, always sieving floor(p/2) mod p seems to do worse than always sieving 0 mod p (I actually need to use an interval bigger than [1,5080000] just to get 341,640 survivors). Using the greedy-greedy approach described in 77 does work better — even though it greedily chooses to sieve 0 mod p for the first few thousand primes, it sieves nonzero residue classes in most of the remaining cases.
- 80. A (partial) answer to my Goedelian conundrum? | cartesian product - June 5, 2013
[…] I just can't resist: there are infinitely many pairs of primes at most 59470640 apart (sbseminar.wordpress.com) […]
- 81. Wouter Castryck - June 5, 2013
Just a mini-remark on Andrew's greedy-greedy approach. In this case it does seem useful to start from (slightly asymmetric) intervals around 0, at least in case $k_0 = 34429$). E.g. starting from the interval $[-170000,220000]$, sieving $1$ mod $2$, $0$ mod $p$ for $p$ up to $p=443$ and then applying the greedy trick yields a diameter of $388284$. I didn't try this for $k_0=341640$.
- 82. Andrew Sutherland - June 5, 2013
Shifting the sieving interval for the greedy-greedy algorithm given in post 77 gives further improvements. For using the interval [-2289488, 23181174] yields an admissable sequence that starts and ends with the endpoints of the interval, with diameter 4,607,490.
For the provisional using the interval [-189556,198754] similarly gives an admissable sequence with diameter 388,310.
- 84. Andrew Sutherland - June 5, 2013
@Wouter: Hi Wouter! I see our posts crossed. For I clearly made the interval too symmetric (as with the RH sequences, some asymmetry seems to help). But using the interval [-169844,219160] gives an admissable sequence with diameter 388,248 (last sequence entry is 218,404), a further slight improvement.
I'm sure there are still gains to be had by shifting the interval around in the case.
- 85. Andrew Sutherland - June 5, 2013
@Terry: That's fantastic news, thanks! With this small it is should be feasible to do some more sophisticated combinatorial optimizations, rather than sticking to a purely greedy approach.
- 86. Andrew Sutherland - June 5, 2013
After further tweaking of the interval with , using [-185662,202456] with the greedy-greedy algorithm yields an admissable sequence with diameter 388,118 that starts and ends on the end points.
- 88. Vít Tuček - June 5, 2013
aviwlevy: My code produced
H = np.arange(2,399664)
H,primes = greedy_greedy(H,H[-1]-H[0])
diameter: 399660 length: 34749 admissible: True
best diameter of length 34429 is: 389940
But I haven't checked if we have the same bounds in various places. I.e. there could be some off by one errors. Anyway, it's close enough and it seems that Andrew's method works.
- 89. Andrew Sutherland - June 5, 2013
@aviwlevy: I took a quick look at your code, and it appears in your implementation that there are a few places where you are using the index i but should be using the value low+2*i corresponding to the element of the interval indexed by i. Also, the interval [-185662,202456] is closed, but I think you are treating it as half open. In any case, the sequence output by your program is not admissable, it hits every congruence class mod 641, for example.
I have to run now, but tomorrow I can take a closer look.
In the meantime, I have posted the admissable sequence with diameter 388,188 for k0=34429 here:
I will post my own C code once I have a chance to clean it up (it keeps changing!), but at least everyone can see the sequence and easily verify for themselves (e.g. using code posted elsewhere in this thread) that it is indeed admissable and of the size and diameter claimed (verifying the correctness of the results is a lot easier than verifying the correctness of the code in any case).
- 90. More narrow admissible sets | Secret Blogging Seminar - June 5, 2013
[…] It looks like it may be time to roll over the search for narrow admissible sets to a new blog post, as we're approaching 100 comments on the original thread. […]
- 92. ZTOA - June 7, 2013
Is the following true?
Primes are uniformly distributed
Let p, r, n are positive integers with p>1.
U(p, r, n) denotes the number of primes less than n that are equal to r (mod p).
For any prime p and pair of integers r1, r2 between 1 and p-1, we have:
The ratio U(p,r1,n) / U(p,r2,n) has limit 1 as n goes to infinity.
- 93. Bound on prime gaps bound decreasing by leaps and bounds | The Aperiodical - June 8, 2013
[…] As far as I can tell, Tim Trudgian was first to bid, with a bound of 59,874,594, which he called "a poor man's improvement" in a note submitted to the arXiv. Soon after that, Scott Morrison of the Secret Blogging Seminar found a way to reduce it ever so slightly to 59,470,640. […]
- 94. Prime Gaps, Mad Maths, and Castles | Math Munch - June 26, 2013
[…] Two names that you'll see in the list of contributors to the effort are Andrew Sutherland and Scott Morrison. Andrew is a computational number theorist at MIT and Scott has done research in knot theory and is at the Australian National University. They've improved arguments and sharpened figures to lower the prime gap value H. They've contributed by doing things like using a hybrid Schinzel/greedy (or "greedy-greedy") sieve—you know, a sieve—and optimizing Zhang's condition ω > 0. Very complicated stuff that's way over my head. But I love the way that that the mathematicians bounce ideas off each other, like on this thread. […]
- 95. Bounded gaps between primes (Polymath8) – a progress report | What's new - June 30, 2013
[…] reduce a bit and still have admissible; for , it turns out after some computation that this trick lowers the diameter a little bit to ; asymptotically this […]
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Tangy lemon cupcakes hold a sweet raspberry surprise when you bite into them.
Lemon Raspberry Surprise Mini Cupcakes.
Calories: 270
Fat: 10g
Cholesterol: 45mg
Sodium: 220mg
Carbohydrates: 44g
Dietary Fiber: 0g
Protein: 2g
Looks so yummy! Cannot wait to make this.
hAVE MADE SIMILAR CUPCAKES WITH CHOCOLATE CAKE MIX, RASPBERRY JAM AND EITHER CHOCOLATE GANACHE FROSTING, OR CREAM CHEESE FROSTING -- THEY ARE WONDERFUL & SO EASY TO MAKE
Outstanding response from all my guests. Would make it again and again. SUPER
wonderful surprise!!
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Once the temperature drops a few degrees, I'm in full-on fall foods mode. Pumpkin bars, apple crisp, cranberry bread…you name it, I'm making it. However, most of it revolves around sweets. Why doesn't dinner get a fair chance?
Once the temperature drops a few degrees, I'm in full-on fall foods mode. Pumpkin bars, apple crisp, cranberry bread…you name it, I'm making it. However, most of it revolves around sweets. Why doesn't dinner get a fair chance? More ...
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text:
SAN FRANCISCO (MarketWatch) — The dollar fell against the euro Wednesday as stocks recovered and Spanish debt yields fell but pared losses slightly after a Federal Reserve report didn't yield any new clues on a new round of quantitative easing, or QE3.
The ICE dollar index DXY, -0.04% which measures the greenback against a basket of six currencies, traded at 79.791, firming from 79.766 ahead of the release but down versus 79.875 in late North American trading on Tuesday.
German government bonds' new low
European markets are a little calmer with the euro actually rising. But that doesn't prevent a poor German government bond auction. (Photo: Reuters.)
The euro EURUSD, +0.1585% pared gains to $1.3102 from $1.3078 late Tuesday.
The Federal Reserve believes the U.S. economy is continuing to grow at a "modest to moderate pace" over the last month, according to the Beige Book. The phrase is the same one used to describe the economy in two previous reports. Read story on Beige Book.
"The Fed's Beige Book noted modest to moderate expansion for the economy, employment, inflation and residential real estate. With tepid comments like these, this book's name is apt — beige," noted Douglas Borthwick, managing director of Faros Trading, in emailed comments.
Anticipation of further supportive measures from the Fed had been building in the last week as policy makers have pointed to both a sluggish job market and problems in overseas financial markets as a risk to the U.S. economic growth outlook.
The dollar's decline began during the Asian session, shortly after Alcoa Inc. AA, -0.40% reported an unexpected first-quarter profit, supporting Asian stocks.
The safe-haven dollar dipped as "Asian stocks recovered off their lows, prompting a modest bias toward U.S. dollar underperformance," said Sue Trinh, currency strategist at RBC Capital Markets.
A fall in Spanish and Italian yields supported U.S. stocks and the euro on Wednesday, but many analysts see it as a temporary blip as the outlook for Europe's economy remains bleak. See story on Spanish bonds.
"We're pessimistic about Europe," said David Rolley, a global bond portfolio manager at Loomis Sayles & Co. "The negative energy from fiscal contraction will outweigh" any positives of central bank activity.
The euro will have to weaken as part of a shift to make all of Europe – not just Germany – globally competitive and reduce trade and investment imbalances, he said.
"It will require sufficient monetary easing to weaken the euro" to get there, Rolley said.
Fed speeches
Several Fed officials are also speaking this week.


text: [ Long Branch Armed Robbery Suspect Now Charged with Murder By Tom Mongelli November 8, 2013 A Long Branch 18-year-old, already facing armed robbery charges dating back to September 20 in the city, is now accused of mowing a victim down with a gun the next day. Read More|Comment Category: Briefs, New Jersey News Tags: Adrian Anderson, Armed Robbery, Dante Strong, Long Branch, Monmouth County, murder Send to a friend! Share on Facebook Share on Twitter Pin it! Reddit This! Share on Tumblr!


text:
Light use efficiency in a non-nutrient limiting environment.
Klimas, Christie*,1, Potosnak, Mark2, Murthy, Ramesh1, Griffin, Kevin3, 1 Biosphere 2 Center, Oracle, AZ, USA2 N.C.A.R., Boulder, CO, USA3 Columbia University, Palisades, NY, USA
ABSTRACT- This experiment examined leaf level photosynthetic responses of Populus deltoides trees grown in the Intensive Forestry Mesocosm at the Biosphere 2 Center, to light at different canopy positions under two CO2 treatments: ambient (43 Pa) and elevated (120 Pa) CO2 conditions. A fully developed shade (interior) and sun (exterior) leaf was chosen at three canopy levels (high, middle, upper) for 5 trees in each CO2 treatment. PPF (photosynthetic photon flux) sensors were attached to branches adjacent to each leaf. Light curves coupled with maximum photosynthesis (Asat) measurements were done 3 times over a six-week experiment. After photosynthesis measurements, LMA and leaf nitrogen content were determined for the sample leaves. Maximum rates of photosynthesis were significantly higher under elevated CO2 conditions with a concurrent increase in daytime respiration. Photosynthesis was significantly higher in middle and upper canopy and exterior sunlit leaves under both ambient and elevated CO2 conditions. Vertical position also had a significant effect on Rday with leaves in the upper canopy having higher respiration values, and this effect was enhanced under elevated CO2. While elevated CO2 resulted in overall increased quantum efficiency (AQE) the effect of vertical position and shading on AQE showed no significant change between CO2 treatments. Mid-canopy leaves showed a significantly higher AQE than upper and lower canopy leaves in both CO2 treatments and this was mirrored by a lower light compensation point. The leaves at the low canopy position under elevated CO2 showed a significantly lower light compensation point than the ambient low leaves. Nitrogen allocation also differed between the CO2 treatments with the ambient bay having higher percent leaf nitrogen content. These leaf level enhancements translated into greater accumulated biomass in the elevated CO2 treatment. Elevated CO2 resulted in a significant improvement in light utilization irrespective of vertical profile and incident light intensity.
Key words: light, Biosphere 2 Center, nitrogen, photosynthesis


text:
You are here
HIV & AIDS in USA
There are currently around 1.1 million people living with HIV in the United States of America (USA), with 16 percent unaware of their infection. 1 2 Since the beginning of the HIV and AIDS epidemic, 600,000 people have died of AIDS-related illnesses in the United States of America. 3
Although the USA may be the greatest national funder of the global HIV epidemic (largely through the President's Emergency Plan For AIDS Relief, or PEPFAR), it is still facing a major ongoing HIV epidemic itself, with around 50,000 new infections per year. Stigma and discrimination continue to hamper people's access to HIV prevention, testing and treatment services, fuelling the cycle of new infections.
The USA lacked a comprehensive plan on HIV until 2010 when President Obama created a National HIV/AIDS Strategy. It is structured around three core aims: reducing new HIV infections, increasing access to care and improving health outcomes for people living with HIV, and reducing HIV-related disparities and health inequities. 4
Who is affected by HIV in the United States of America?
The HIV epidemic has been more serious among some groups than others. In the 1980s, the most commonly identified ' vulnerable groups' in the USA were men who have sex with men, injecting drug users, haemophiliacs and Haitians. However, the inclusion of Haitians in this group caused a lot of controversy. Find out more on our History of HIV in the United States of America page.
A 2010 study found that wealth also determines vulnerability; HIV prevalence was four times higher among heterosexual people in poor urban neighbourhoods than the national average. 5 Within these high-poverty areas HIV prevalence didn't change depending on race or ethnicity. Rather, higher HIV risk was attributed to high HIV prevalence, limited access to health care and other basic services, and high rates of substance abuse and incarceration. 6
It is not solely individual behaviour, but also a person's sexual network which determines an individual's HIV risk in the USA. For example, African American males are much more likely to be infected because of the high HIV prevalence in this community and a tendency to choose racially similar partners.
The table below compares the percentage of new HIV diagnoses among various ethnic groups to the percentage of the population that each ethnic group represents. There were 42,181 new infections in 2011. 7
|Black/African American
|Multiple races
|American Indian/Alaska Native
|Native Hawaiian/Other Pacific Islander
African Americans
- African Americans accounted for 46 percent of new HIV infections in 2011. 10
As the table above shows, African Americans are disproportionately affected by the HIV epidemic. Both African American men and women are most likely to be infected through unprotected sex with a man, with injecting drug use being the second most likely route of HIV transmission. Factors such as heightened levels of poverty, lack of access to adequate healthcare, and stigma surrounding men who have sex with men characterise the epidemic among African Americans.
A Kaiser Family Foundation survey reported the concern about HIV among the African American community. 40 percent of this community reported feeling 'very concerned' about being infected with HIV, compared to 11 percent among the white community. This figure jumps up to 50 percent among young African Americans - those under 30 years of age. White people are less than half as likely to know a friend or family member living with HIV, or who has died of an AIDS-related illness. 11
- Hispanics/Latinos accounted for 22 percent of new HIV infections in 2011. 12
This is relatively proportionate to their share of 17 percent of the USA population, but they are still more than 3 times as likely to be infected with HIV than whites. 13 14
It is estimated that 1 in every 36 Hispanic/Latino men will be diagnosed with HIV in their lifetime compared to 1 in 106 Hispanic/Latino women. 15 Of all male diagnoses in 2011, 79 percent were transmitted via sex between men, 11 percent via unprotected heterosexual sex, and 8 percent via injecting drug use. Among females, 86 percent of HIV infections were the result of unprotected heterosexual sex, and 14 percent injecting drug use. 16
Language barriers, cultural factors, and migration patterns have been identified as barriers to HIV prevention and treatment within the Hispanic/Latino community. 17
Men who have sex with men
- Men who have sex with men (MSM) accounted for 65 percent of new HIV infections in 2011. 18
MSM are the group most affected by HIV in the USA. The concentrated epidemic among MSM increases the likelihood of HIV exposure for all MSM in the country, partially accounting for the high rate of transmission. Alongside this, only 66 percent of MSM living with HIV in 2011 were aware of their infection. This left 34 percent of MSM remaining unaware of their risk of transmission to others, or that their own health was deteriorating. 19
Higher numbers of sexual partners, greater numbers of sexually transmitted infections (STIs) and having unprotected anal sex are some of the reasons why HIV transmission is more common among MSM. The CDC recommend that MSM test for HIV at least once a year in order to know their HIV status. 20
The availability of antiretroviral treatment may also have lessened the fear surrounding HIV, leading to complacency about using condoms. 21 This complacency is evident in Washington D.C, where a study revealed 40 percent of MSM had not used a condom with their last sexual partner. The study also found that, contrary to popular belief, men older than 30 had more sexual partners and were less likely to use condoms or get tested than their younger counterparts. 22
People who inject drugs
- People who inject drugs (PWID) accounted for 8 percent of new HIV infections in 2010. 23
Among those living with HIV in the USA, around 16 percent are people who inject drugs (PWID). The majority of PWID who are living with HIV are African Americans, both for males and females.
Throughout the epidemic, prevention efforts among PWID have been controversial. At the start of the HIV epidemic, needle exchange services – where users exchange their used needles for new clean ones – were not permitted any federal funding, even though in some areas of the USA these programmes have proved to be successful in reducing the rate of HIV transmission. 24 25 The ban on federal funding for needle exchanges was lifted in 2009. However, in a controversial move Congress failed to allocate funding for needle exchanges for the 2012 fiscal year. 26
Young people
- Young people aged 13-24 accounted for 21 percent of new HIV infections in 2011. 27
This is despite only making up 17 percent of the USA population. Infections among young people follow the same trends as other vulnerable groups. Of all infections among young people in 2010:
- 72 percent were among young MSM
- 57 percent were among young African Americans, 20 percent among Hispanics/Latinos, 20 percent among whites
- 78 percent were among young people aged 20-24 28
It is thought that 60 percent of young people living with HIV are not aware of their infection. 29 This has huge repercussions regarding the onwards transmission to others, via unprotected sex or sharing needles for drug use. Sexually transmitted infections (STIs) are also commonplace amongst this age group, which makes people more vulnerable to HIV infection.
The number of AIDS diagnoses among young people has increased by 29 percent since 2008. 30 A sense of complacency, or an attitude of 'it doesn't affect me' has prevented young people from testing for HIV and subsequently accessing antiretroviral treatment (ART) to prevent the onset of AIDS.
Geographical variations
Geographical differences in HIV and AIDS prevalence are due to concentrations of key populations that are typically at risk of HIV infection in certain areas, and variations in healthcare between different states.
Key populations
The epidemic was once concentrated mainly in the gay populations on the East and West coasts. However, in recent years HIV has also become increasingly prevalent within the African American and Latino communities in many Southern states as well as certain urban areas in the Northeast and West.
The South continues to represent a majority of all HIV and AIDS relation diagnoses, with the Northeast very close behind. However, both areas have seen improvements, or at least stability, in their diagnoses between 2008-2011. This represents the success of targeted HIV prevention, testing and treatment services in specific areas. Despite this, the rates (per 100,000 population) of new HIV diagnoses in the South are still more than double that in the Midwest (20.9 v 9.3 respectively). 31
Healthcare variations
It has become increasingly clear that the quality of HIV prevention and treatment services an individual receives is influenced as much by where they live, as by their socio-economic group.
In 2010, a report criticised the response to the HIV epidemic in the 17 states in "the South", where the risk of HIV transmission and mortality is highest. 32 Factors which contribute towards this include: poverty, poor access to healthcare relative to the rest of the country, a focus on abstinence based sex education, and laws that criminalise HIV transmission and restrict harm reduction programmes for PWID. 33
A study examining data from across the country also found that, for socioeconomic reasons, non-white men and particularly non-white women residing in the South experience the worst clinical outcomes after being diagnosed with HIV. 34 AIDS-related mortality rates vary geographically, far more than within other highly developed countries where national health insurance programmes or health policies are geographically uniform. 35
HIV and AIDS prevention in the United States of America
National prevention strategy
One of the three components of the USA's National HIV/AIDS Strategy is the reduction of new HIV infections. The Strategy recommends that HIV prevention efforts are intensified in the communities where HIV is the most heavily concentrated, and that care should not endorse one prevention method, such as condom use, education or testing, over another. Instead, it insists that 'overlapping, combination' prevention approaches that have been proven to work and are cost-efficient be used to target high-risk populations including MSM, African Americans, Latino Americans and PWID. 36
Treatment as prevention
Taking antiretroviral treatment significantly lowers the risk of HIV transmission to others - this is known as treatment as prevention (TasP). Attention has been placed upon people living with HIV, stating that "prevention for people who are HIV-positive is critical to reducing new HIV infections". 37
Continuing the TasP theme, the USA announced in July 2012 that an antiretroviral drug for use as a pre-exposure prophylaxis had been approved, for HIV-negative persons to take treatment as a form of HIV prevention. The drug with the brand name 'Truvada' can now be prescribed for high-risk groups, such as the partners of HIV-positive people and men who have sex with men. 38
Targeted prevention
American health authorities are placing increased emphasis on the role that 'social determinants of health' such as a person's age, class, race, living environment and poor access to healthcare have on their risk of becoming infected with HIV. 39 For example, there is an increasing number of new HIV infections among people over 50 years old, and some communities have started to provide HIV education for the ageing generation. 40 41 Targeting HIV prevention initiatives at people of high-risk populations has been shown to be effective globally.
Prevention campaigns
The Centers for Disease Control and Prevention (CDC) run multiple campaigns that aim to take the taboo out of HIV. Specifically, their 5-year 'Act Against AIDS' campaign has many strands that target different population groups, for example:
- 'Let's Stop HIV Together' - launched in July 2012 just before the AIDS 2012 Conference in Washington. Uses large-scale advertising and social media to spread its message. The focus is that HIV does not discriminate, we are all at risk, so everyone should be talking about HIV. 42
- 'Start Talking. Stop HIV' - this campaign targets MSM, by encouraging them to talk about HIV with their partners, whatever their relationship status. 43
- 'Testing Makes Us Stronger' & 'Take Charge. Take the Test' - these campaigns target African Americans, specifically men who have sex with men, and women. 44
Funding for prevention
In 2014, just 3 percent of the domestic HIV and AIDS budget was allocated for prevention, making it the smallest category in the budget. 45 Yet, for every HIV infection prevented, $355,000 is saved in the costs of providing lifelong HIV care and treatment. 46 47
A CDC/John Hopkins University study, examined 5 possible 'scenarios' for the future of HIV prevention in the USA. In those scenarios where there was no increase in funding for HIV prevention efforts, there was a possible 38 percent increase in the number of people living with HIV in the USA between 2010 and 2020. 48 As a a result, maintaining current HIV prevention funding levels could cost anywhere between $128 billion to $237 billion in treatment and care costs for the US healthcare system. On the other hand, the study claimed that an investment in HIV prevention of $4.5 billion over ten years would save $104 billion in medical care costs. 49
HIV and sex education in the United States of America
The level and type of HIV and AIDS education received by students in the USA varies depending on state regulations and the type of school or college. In some areas, sex education that incorporates information about HIV is comprehensive and compulsory. In others, children may leave school knowing virtually nothing about HIV and AIDS. 50
Since the Welfare Reform Law earmarked $100 million for abstinence only education in 1996, increased amounts of federal funding became available for this type of education. 51 Abstinence only education encourages people to abstain from sex until after they are married, and does not teach people how to protect themselves during sex from STIs and unwanted pregnancy. A number of studies have shown that abstinence only education is largely ineffective, and as a result it has proved controversial. 52 53 Yet twenty-nine states still mandate that abstinence before marriage be 'stressed' in HIV education lessons at schools. 54
In his 2009 budget, Obama made a radical pledge to replace abstinence only education with funds for programmes that could "prove they delay sexual activity, increase contraceptive use and reduce teen pregnancy." 55 However, funding for abstinence-only education has not been eliminated, but rather supplemented with funding for more comprehensive initiatives. 56
HIV testing in the United States of America
It is thought that 54 percent of American adults have ever had an HIV test. Although more than half of the population, this still leaves a considerable proportion of people unaware of their HIV status. Of those who have not taken the test, 57 percent of them stated it's because they do not think they are at risk. 57
White Americans are least likely to have taken a test, compared to African Americans and Hispanics/Latinos who more regularly access HIV testing services. This is encouraging considering the greater extent to which these ethnicities are affected by the HIV epidemic. Still, people are testing late, and 32 percent of people in 2010 were diagnosed with AIDS just one year after testing positive for HIV. 58
Testing guidelines
In 2006, the CDC published a new set of guidelines on HIV testing which call for automatic, routine HIV testing of all adults and adolescents attending a healthcare setting. 59 The policy allows patients to opt out if they do not wish to take a test, but removes the need for written consent and pre-test prevention counselling, which were viewed as barriers to HIV testing.
In 2010, one of the most hard-hit areas in the United States, Washington D.C, reported a 26 percent rise in the number of people tested in the previous 12 months following the implementation of routine testing, and a marketing campaign among residents to educate them about the new testing measures. 60
HIV test results
It is thought that 93 percent of people who tested for HIV in 2011 received their results, up from 69 percent in 2003. 61 62 Despite this, young people between the ages of 13-19 were the least likely to get their results (85 percent), alongside only 76 percent of women. 63
The government's effort to distribute rapid HIV testing kits has helped increase the number of people receiving their results, as the results can be given in as little as 20 minutes. HIV tests are offered for free on the USA's annual HIV testing day, which takes place on 27th June. 64
In 2013, the FDA approved the first rapid HIV test that detects HIV-1 antigens, and antibodies for HIV-1 and HIV-2. Detecting antigens means that HIV can be diagnosed earlier than having to wait for the body to develop antibodies to the virus. 65 This further increases the likelihood of people obtaining their results, and sooner than before.
Mandatory testing
Whilst mandatory testing of immigrants ended in 2010, following the lifting of the HIV travel ban in January, all military personnel, and prison inmates in certain states, are still required by law to be tested for HIV. 66 67
Mandatory HIV testing among prison inmates is criticised because it can lead to the discrimination and segregation of HIV positive prison inmates. 68 This is evident in the state of South Carolina, and until recently in Alabama, where prisoners living with HIV are not entitled to apply for a prison job or be associated with community group pre-release programs. 69
In a 2012 trial, led by human rights groups, it was asserted that mandatory testing is a prejudiced practice that does not adhere to the Americans with Disabilities Act and should therefore be prohibited. 70 71 Most AIDS organisations advocate a voluntary opt-out policy similar to that offered to pregnant women. 72
HIV and AIDS treatment and care in the United States of America
57 percent of the annual federal HIV/AIDS budget is spent on antiretroviral treatment, reflecting the growing number of people living with HIV as treatment continues to extend life expectancies. 73
Antiretroviral treatment in the USA is available to anyone with good medical insurance. For those who are without insurance or underinsured, Medicaid, Medicare, and funding provided by the Ryan White Comprehensive AIDS Resource Emergency (CARE) Act are available to help with treatment costs. 74
The National HIV/AIDS Strategy admits "large numbers of uninsured and underinsured people with HIV mean that not everyone has sufficient access to HIV therapy". 75 The Strategy places a strong emphasis on the impact of the 2014 health care reform bill or Affordable Care Act, on the future provision of HIV treatment, such as expanded Medicaid eligibility, protection for people with pre-existing conditions that will allow them to access health insurance, and increased access to tax credits. 76
However, a considerable proportion of those who are able to access treatment are not being retained in care. A 2001-2009 study found that only 20 percent of the HIV-positive participants were considered 'highly engaged with specialist outpatient care'. Those who were most likely to be retained in high levels of care included: females as opposed to males, Hispanics and African Americans as opposed to white people, MSM as opposed to heterosexual men and drug users, those diagnosed positive at an older age, and those with lower CD4 cell counts. 77
Federally approved guidelines for the use of antiretroviral therapy in the USA are available here. AVERT.org has more about HIV and AIDS treatment and care in the USA.
Stigma and discrimination
The National HIV/AIDS Strategy admits "addressing stigma and discrimination is perhaps the biggest challenge we face". This is not surprising considering the misconceptions surrounding the transmission of HIV. 78 In a 2011 survey, people were asked if they would be uncomfortable in certain situations regarding people living with HIV. The results of which shows stigma is still very much present in society today:
- 45 percent uncomfortable if their food was prepared by someone HIV-positive
- 36 percent uncomforatble if they had an HIV-positive roommate
- 29 percent uncomfortable if their child had an HIV‐positive teacher
- 18 percent uncomfortable if they had an HIV-positive colleague. 79
Only 4 out of 10 people questioned reported having seen, read or heard about the USA's HIV epidemic that year, compared to 7 in 10 during 2004. Six in 10 people reported that most of what they know about HIV comes from the media, rather than schools, doctors, friends and family and religious settings. 80
Legislation has contributed to the improvement of the lives of those living with HIV and AIDS in the USA. In 1986, the government made clear to employers that they would be prosecuted if they discriminated against HIV-positive people. The 'Americans with Disabilities Act' now makes it illegal to discriminate against someone on the basis of their HIV status. 81
In 2010, President Obama lifted the ban on entry into the country for all HIV-positive people, which had been in place since 1987. This meant that in 2012, the biannual global conference on HIV and AIDS could be held in Washington, as previously people living with HIV would not have been able to attend. 82
Three hundred people have been convicted for exposing others to HIV in the USA. Combining the convictions in the USA and Canada equals more than all other countries in the world put together. Many of these convictions have occurred against people for spitting or biting, despite these not being routes of HIV transmission. 83
Spending on HIV in the United States of America
The federal budget request for fiscal year (FY) 2015 included a total of $30.4 billion for domestic HIV and AIDS, a 2.3 percent increase from the FY 2014 funding, which totalled $29.7 billion. Of this, 57 percent is for care and treatment, 9 percent for research, 10 percent for cash and housing assistance, and 3 percent for prevention. 84
The HIV/AIDS Strategy acknowledges the restricted funding and makes no commitments to increase funding. Instead, it places emphasis on focused resource allocation. Funding must therefore be targeted to the highest prevalence populations and communities, including high-risk populations such as MSM, African Americans and Latino Americans and PWID. 85
The HIV epidemic in the USA is concentrated among certain population groups such as men who have sex with men and African Americans. In order to break to cycle of transmission, greater effort needs to be made to ensure people who fall into these vulnerable groups are testing for HIV regularly, and accessing treatment.
Upscaling the treatment as prevention (TasP) approach has the potential to considerably reduce new infections. If all HIV-positive people were on antiretroviral treatment, specifically those in the most vulnerable groups, then many new transmissions could be averted.
Considering the increase in new infections among young people, a combination approach to HIV prevention education needs to be adopted and heightened, away from the historical abstinence-only approach. Young people are becoming more involved in high-risk behaviours (such as unproteced sex) at a younger age, and need to be educated about how to prevent STIs and HIV infection.
Where next?
- HIV & AIDS Help and Advice in the USA
- HIV & AIDS Among African Americans
- HIV & AIDS Treatment in the USA
- 1. Centers for Disease Control and Prevention (2013, December) ' Today's HIV/AIDS Epidemic'
- 2. Kaiser Family Foundation (2014, May) ' HIV Testing in the United States'
- 3. Centers for Disease Control and Prevention (2013, December) ' Today's HIV/AIDS Epidemic'
- 4. The White House Office of National AIDS Policy (2010, July) ' The National HIV/AIDS Strategy for the United States'
- 5. Centers for Disease Control and Prevention (2010, July 19th) ' New CDC Analysis Reveals Strong Link Between Poverty and HIV Infection'
- 6. CDC (2010, September 23rd) ' 1 in 5 men who have sex with men in 21 U.S. cities has HIV; nearly half unaware'
- 7. Centers for Disease Control and Prevention (2013) 'HIV/AIDS Surveillance Report: Diagnoses of HIV infection and AIDS in the United States and Dependent Areas, 2011' (Vol. 23)
- 8. Centers for Disease Control and Prevention (2013) 'HIV/AIDS Surveillance Report: Diagnoses of HIV infection and AIDS in the United States and Dependent Areas, 2011' (Vol. 23)
- 9. United States Census Bureau ' Quick Facts[accessed June 2014]'
- 10. Centers for Disease Control and Prevention (2013) ' HIV Surveillance by Race/Ethnicity'
- 11. Kaiser Family Foundation (2011, June) ' HIV/AIDS at 30: A Public Opinion Perspective'
- 12. Centers for Disease Control and Prevention (2013) ' HIV Surveillance by Race/Ethnicity'
- 13. Centers for Disease Control and Prevention (2013) ' HIV Surveillance by Race/Ethnicity'
- 14. Centers for Disease Control and Prevention (2013, November) ' HIV among Hispanic/Latinos in the United States and Dependent Areas'
- 15. Centers for Disease Control and Prevention (2013, November) ' HIV among Hispanic/Latinos in the United States and Dependent Areas'
- 16. Centers for Disease Control and Prevention (2013) ' HIV Surveillance by Race/Ethnicity'
- 17. Centers for Disease Control and Prevention (2013, November) ' HIV among Hispanic/Latinos in the United States and Dependent Areas'
- 18. Centers for Disease Control and Prevention (2013) 'HIV/AIDS Surveillance Report: Diagnoses of HIV infection and AIDS in the United States and Dependent Areas, 2011' (Vol. 23)
- 19. Centers for Disease Control and Prevention (2014, May) ' HIV Among Gay and Bisexual Men'
- 20. Centers for Disease Control and Prevention (2014, May) ' HIV Among Gay and Bisexual Men'
- 21. CDC (2007, June) 'HIV/AIDS among men who have sex with men'
- 22. The Washington Post (2010, March 26th) ' Study of gay men in the District finds 14% are HIV positive'
- 23. Centers for Disease Control and Prevention (2013, December) ' Today's HIV/AIDS Epidemic'
- 24. Monterroso, E.R et al (2000, 1st September) 'Prevention of HIV infection in street-recruited injection drug users'. The Collaborative Injection Drug User Study (CIDUS).
- 25. Don, C et al (2005, August) 'HIV incidence among injection drug users in New York City, 1990 to 2002: Use of serologic test algorithm to assess expansion of HIV prevention', American Journal of Public Health, Vol. 9, No. 8.
- 26. Kaiser Health News (2011, 21st December) ' Needle-Exchange Programs Face New Federal Funding Ban'
- 27. Centers for Disease Control and Prevention (2014, March) ' HIV Among Youth'
- 28. Centers for Disease Control and Prevention (2014, March) ' HIV Among Youth'
- 29. Centers for Disease Control and Prevention (2014, March) ' HIV Among Youth'
- 30. Centers for Disease Control and Prevention (2014, March) ' HIV Among Youth'
- 31. Centers for Disease Control and Prevention (2013) 'HIV/AIDS Surveillance Report: Diagnoses of HIV infection and AIDS in the United States and Dependent Areas, 2011' (Vol. 23)
- 32. Human Rights Watch (2010, November) ' Southern Exposure: Human Rights and HIV in the Southern United States'
- 33. D Hanna et al (2012, 2nd January) ' Disparities among US states in HIV-related mortality in persons with HIV infection, 2001–2007', AIDS 26 (1)
- 34. Journal of Infectious Diseases (2011, February) ' Sex, Race, and Geographic Region Influence Clinical Outcomes Following Primary HIV-1 Infection' 203(4):442-51
- 35. D Hanna et al (2012, 2nd January) ' Disparities among US states in HIV-related mortality in persons with HIV infection, 2001–2007', AIDS 26 (1)
- 36. The White House Office of National AIDS Policy (2010, July) ' The National HIV/AIDS Strategy for the United States'
- 37. The White House Office of National AIDS Policy (2010, July) ' The National HIV/AIDS Strategy for the United States'
- 38. FDA (2012, July 16th) ' FDA Approves First Medication to Reduce HIV Risk'
- 39. CDC (2010) ' Establishing a Holistic Framework to reduce inequities in HIV, Viral Hepatitis, STDs and Tuberculosis in the United States'
- 40. CDC (2008, February) 'HIV/AIDS among persons aged 50 and older'
- 41. The Age Company Ltd. (2006) 'Condom Granny's safe sex pitch to Florida's active oldies'
- 42. Centers for Disease Control and Prevention (2012, July) ' New CDC Campaign Fights Stigma and Apathy Fueling HIV Epidemic - Press release'
- 43. Centers for Disease Control and Prevention (2014, May) ' New CDC campaign inspires life-saving conversations about HIV - Press release'
- 44. Centers for Disease Control and Prevention (accessed June 2014) ' HIV Among African Americans - Campaigns'
- 45. The Henry J Kaiser Foundation (2014, January) 'U.S. Federal Funding for HIV/AIDS: The President's FY 2015 Budget Request
- 46. CDC (2010, July) ' CDC's Prevention Progress in the United States'
- 47. Sayles J et al 2009, ' Routine Rapid HIV Screening in Six Community Health Centers Serving Populations at Risk', Journal of General Internal Medicine
- 48. CDC (2010, August) ' Projecting Possible Future Courses of the HIV Epidemic in the United States'
- 49. CDC (2010, August) ' Projecting Possible Future Courses of the HIV Epidemic in the United States'
- 50. Martinez, Gladys, PHD et al, (2010, September) ' Educating Teenagers about Sex in the United States' NCHS Data Brief, No 44
- 51. Advocates for Youth (2007, July) 'The history of federal abstinence-only funding'.
- 52. Stanger-Hall, KF et. al (2011) ' Abstinence-only education and teen pregnancy rates: why we need comprehensive sex education in the U.S.' Plos One 6(10)
- 53. Mathematica Policy Reseach Inc. (2007, April) ' Impacts of four abstinence education programs'.
- 54. Kaiser Family Foundation (2012) ' State Sex and HIV Education Policy'
- 55. US News Health (2009, May 7th) ' Obama Budget Eliminates Funding for Abstinence-only Sex Education'
- 56. The New York Times (2009, May 10th) ' New Spending for a Wider Range of Sex Education'
- 57. Kaiser Family Foundation (2014, May) ' HIV Testing in the United States'
- 58. Kaiser Family Foundation (2014, May) ' HIV Testing in the United States'
- 59. CDC (2006, 22nd September) 'Revised recommendations for HIV testing of adults, adolescents, and pregnant women in health-care settings'. MMWR Weekly Report, Vol. 55
- 60. CDC (2010, June 25th) ' Expanded HIV Testing and Trends in Diagnoses of HIV Infection District of Columbia 2004-2008' MMWR 59(24);737-741
- 61. Centers for Disease Control and Prevention (2013, November) ' HIV Testing at CDC Funded Sites - United States, Puerto Rico and the U.S. Virgin Islands, 2011'
- 62. CDC (2004) 'Quick facts: Rapid testing April 2003 – April 2004'
- 63. Centers for Disease Control and Prevention (2013, November) ' HIV Testing at CDC Funded Sites - United States, Puerto Rico and the U.S. Virgin Islands, 2011'
- 64. CDC ' National HIV Testing Day' accessed Oct 2013
- 65. U.S. Food and Drug Administration (FDA) (2013, August) ' FDA News Release: FDA approves first rapid diagnostic test to detect both HIV-1 antigen and HIV-1/2 antibodies'
- 66. Headquarters Department of the Army USA (2012) ' Identification, Surveillance, and Administration of Personnel Infected with Human Immunodeficiency Virus', Army Regulation 600–110
- 67. Federal Bureau of Prisons, (2011) ' Management of HIV, Clinical Practice Guidelines', U.S. Department of Justice
- 68. Weinstein, C & Greenspan, J (2003) 'Mandatory HIV testing in prisons'. American Journal of Public Health, 2003 October; 93(10): 1617.
- 69. ACLU National Prison Project & Human Rights Watch, (2010) ' Sentenced to Stigma', Human Rights Watch Report
- 70. Gates, V., (2012, 17th September) ' Alabama's segregation for inmates with HIV faces court scrutiny' Reuters
- 71. Reuters (2012, December) ' Judge orders end to HIV prison segregation in Alabama'
- 72. Wohl, D et al, (2010) ' Opt-Out HIV Testing on Prison Entry Increases the Proportion of Individuals Screened for HIV and the Number Testing Seropositive', University of North Carolina and The North Carolina Department of Correction
- 73. The Henry J Kaiser Foundation (2014, June) 'U.S. Federal Funding for HIV/AIDS: The President's FY 2015 Budget Request
- 74. The Henry J. Kaiser Family Foundation (2007, March) 'Fact sheet: Ryan White Program'
- 75. The White House Office of National AIDS Policy (2010, July) ' The National HIV/AIDS Strategy for the United States'
- 76. The White House Office of National AIDS Policy (2010, July) ' The National HIV/AIDS Strategy for the United States'
- 77. aidsmap (2012, May) ' Only 20% of US HIV-positive people have high levels of engagement with specialist HIV care'
- 78. The White House Office of National AIDS Policy (2010, July) ' The National HIV/AIDS Strategy for the United States'
- 79. Kaiser Family Foundation (2011, June) ' HIV/AIDS 30: A Public Opinion Perspective. A Report based on the Kaiser Family Foundation's 2011 Survey of Americans on HIV/AIDS'
- 80. Kaiser Family Foundation (2011, June) ' HIV/AIDS 30: A Public Opinion Perspective. A Report based on the Kaiser Family Foundation's 2011 Survey of Americans on HIV/AIDS'
- 81. The U.S. Equal Employment Opportunity Commission (2005, 17th October) 'Questions and answers about the association provision of the Americans with Disabilities act'.
- 82. Immigration Equality (accessed 2014) ' The HIV Ban'
- 83. Global Network of People Living with HIV (July, 2010) ' Global Criminalisaion Scan Report 2010'
- 84. The Henry J Kaiser Foundation (2014, June) 'U.S. Federal Funding for HIV/AIDS: The President's FY 2015 Budget Request
- 85. The White House Office of National AIDS Policy (2010, July) ' The National HIV/AIDS Strategy for the United States'
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Ever Wonder What Female War Correspondents Go Through?
May 4, 2011 12:03 PM
I've been meaning to post this for a couple weeks now. Just a very interesting read by Emily Wax from the Washington Post about some of the dangers of her job. Emily and others like her risk life and limb to bring us news and opinions from some of the most dangerous places on earth. Back home, many of us look for something entertaining or informative to read with our morning coffee. Sometimes we look for news, sometimes it's the Bears, sometimes it's music, sometimes it's a stupid Youtube video that a friend so generously sent your way… Anyway, a lot of work goes into some of those morning reads and Emily will tell you more about it on the next page.


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Audio Streaming & Archives
Hall of Valor
Hall of Valor Pt 23
-Part 23-Taylor
Hall of Valor Pt 24
-Part 24-Hutchison
Hall of Valor Pt 1
-Part 1
Hall of Valor Pt 2
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Hall of Valor Pt 3
-Part 3
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Opinion Poll
KQV/Trib Total Media Listener Poll Do you agree with Senator John McCain that the hospital bombing by the U.S. is a terrible accident and NOT a war crime? <More Info>
Arizona Sen John McCain, who is the chairman of the Senate Armed Services Committee, says the US bombing of an Afghanistan hospital is a terrible tragedy that would not have occurred if the Taliban had not attacked in Kundoz in the first place. He says it's ludicrous and insulting that people are calling this terrihle accident a war crime. He says to call this a war crime distorts the definition of a war crime.
Yesterday's Poll
KQV/Trib Total Media Listener Poll Do you think the trade agreement reached between the U.S. and other Pacific Rim nations will result in American job losses?


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Trolley, Monument Square, Portland, ca.1900
Click on the image to zoom. Click and drag your mouse over the image to move it left or right. Use the small navigation window to select the area you wish to zoom on.
Purchase a reproduction of this item on VintageMaineImages.com.
Photograph of Monument Square in Portland, looking west on Congress Street with a trolley in view, ca. 1900.


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9th November 2012, in Celebrity, Hot Gossip
At last, we finally get our first look at the newest member of Reese Witherspoon's family – baby Tennessee James Toth. Reese (36) has been out several times since her baby boy's birth six weeks ago, but Tennessee has not been seen in public before. The Sweet Home Alabama star was seen cradling her little boy, before strapping him into his pram during the outing in LA.
Tenessee is the first child for Reese and her talent agent husband Jim Toth. Reese has two other children with ex-husband Ryan Phillippe – Ava (13) and Deacon (9), who are said to be doting on their new brother. "Everyone is bonding with the baby and Jim has had a lighter workload and has been spending a lot of time at home with the baby as well," a source told People magazine.
New mum Reese has cleared her schedule of work commitments for the next few months, but is rumoured to be recording a duet with crooner Michael Buble.


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Also known as: Book Keeper, Payroll Clerk, Account Receivable Clerk, Accounts Receivable Clerk, Accounts Payable Clerk, Accounts Payables Clerk, Accounting Clerk.
A bookkeeper is someone who produces financial records for businesses or organizations. They record financial transactions, update statements, and check financial records for accuracy. Bookkeepers are employed in many industries, including firms that provide accounting, tax preparation, bookkeeping, and payroll services. They are also employed in various levels of government and schools.
Would you make a good bookkeeper? Sokanu's free assessment reveals how compatible you are with a career across 5 dimensions!Take the free career test
A bookkeeper will typically do the following:
The records that a bookkeeper works with include expenditures (money spent), receipts (money that comes in), accounts payable (bills to be paid), accounts receivable (invoices, or what other people owe the organization), and profit and loss (a report that shows the organization's financial health).
Some bookkeepers are full-charge bookkeeping clerks who maintain an entire organization's books. Others are accounting clerks who handle specific tasks. These clerks use basic mathematics (adding, subtracting) throughout the day. As organizations continue to computerize their financial records, many bookkeepers use specialized accounting software, spreadsheets, and databases. Most clerks now enter information from receipts or bills into computers, and the information is then stored electronically. They must be comfortable using computers to record and calculate data. The widespread use of computers also has enabled bookkeepers to take on additional responsibilities, such as payroll, billing, purchasing (buying), and keeping track of overdue bills. Many of these functions require bookkeepers to communicate with clients.
A bookkeeper is often responsible for some or all of an organization's accounts, known as the general ledger. They record all transactions and post debits and credits. They also produce financial statements and other reports for supervisors and managers. Bookkeepers prepare bank deposits by compiling data from cashiers, verifying receipts, and sending cash, checks, or other forms of payment to the bank. In addition, they may handle payroll, make purchases, prepare invoices, and keep track of overdue accounts.
Accounting clerks typically work for larger companies and have more specialized tasks. Their titles, such as accounts payable clerk or accounts receivable clerk, often reflect the type of accounting they do. Often, their responsibilities vary by level of experience. Entry-level accounting clerks may enter (post) details of transactions (including date, type, and amount), add up accounts, and determine interest charges. They also may monitor loans and accounts to ensure that payments are up to date. More advanced accounting clerks may add up and balance billing vouchers, ensure that account data is complete and accurate, and code documents according to an organization's procedures. Auditing clerks check figures, postings, and documents to ensure that they are mathematically accurate and properly coded. They also correct or note errors for accountants or other workers to fix.
A bookkeeper will generally work in an office, but some who are self-employed can work from home.
While the exact duties of bookkeepers vary by employer, many tasks related to recording and balancing financial transactions are common to most bookkeeping positions.
For most bookkeepers, there are several procedures and accounting tasks that are typically performed on a daily base.
Fledgling small-business owners are often told that they should hire a professional to help with the accounting side of their companies. Because both bookkeepers and accountants offer services, understanding which one you need can be puzzling.
Bookkeepers perform general accounting duties. They maintain complete sets of financial records, keep track of accounts, and verify the accuracy of procedures used for recording financial transactions. They are employed by private businesses, governments, and virtually every other type of institution.
Bookkeeping is one of the most versatile career paths--nearly every industry and every business relies on a skilled bookkeeper to update and manage accounting records.


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More than three quarters of the small and disadvantaged businesses questioned in a recent study doubted the value of a Small Business Administration business development plan aimed at helping them garner federal contracts.
According to a study released by Washington, D.C.-based Eddy Communications Corp. in late January, 87 percent of the participants of the SBA's popular 8(a) business development program that aims to help small socially and economically disadvantaged businesses were not sure their participation had brought any advantages, even after completing nine-year terms in the program.
The study's author said it showed that the 8(a) program didn't adequately prepare new contractors for their growth, from a small business into the larger, more competitive environment for federal contracts.
"We knew about the challenges of 8 (a) graduates face when they move into full and open competition—for years, many of our clients have sought us out to help them navigate that growth stage," said Jennifer Eddy, founder and chief strategist of Eddy Communications. "But the results of this study reveal how overwhelming the government market can be to newcomers who don't have anyone in their corner."
The 8(a) set-aside is one of several SBA programs aimed at helping socially and economically disadvantaged small businesses get federal contracts.
The program is divided into two phases -- a four-year developmental stage and a five-year transition stage -- in which small businesses are certified and participate.
Less than half of survey participants said they would confidently recommend the program to a friend in their industry, and nearly 10 percent said they self-terminated their affiliation with the 8(a) program early after determining the burdens of participation outweighed the benefits.
For its part, the SBA said in its fiscal 2014 budget justification that from January 2009 to January 2013, it has supported more than $106 billion in lending to more than 193,000 small businesses. from January 2009 to September 2012, the agency said it helped counsel and train more than three million small business owners and entrepreneurs through its resource partner network and through September 2011 helped small businesses access more than $286.3 billion in federal contracts. That is, SBA said, $32 billion more in small business contracting than the previous three years, even as overall contract spending decreased.
About the Author
Mark Rockwell is a staff writer covering acquisition, procurement and homeland security. Contact him at email@example.com or follow him on Twitter at @MRockwell4.
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Alaskan. Native Companies that are in the 8a program further muddy the water with the ridiculous advantages they have, like spinning off another 8a after they graduate.
Great example - look up CSC's current protégés, and the first one listed is Arctic Slope Management Services, an 8a spinoff off of the parent company ASRC, a BILLION dollar company. If they have a parent organization that is bringing over a billion dollars, why do they need to be in a Mentor Protege with CSC????
I hope this comment gets posted so more people see this.
Unfortunately, the SBA has abandoned small business, and is now more unhelpful than anything.
28 million of the 28.2 million businesses in America, 98%, have 1-19 employees. They need loans of $50-$200,000. In 2007, the average SBA loan was $180,000 and 24% of all SBA loans were under $100,000. Today, the average SBA loan is $485,000 and only 9% are under $100k, and declining. The 98% have been left behind while the SBA supports the 2%. Almost every time the SBA gives out a loan now, it goes to giant businesses who use it to crush the small ones who can't squeeze a dime from the SBA's banks.
How did we get here?
In the last five years under Karen Mills, the SBA aggressively ad proactively expanded the definition of "small" to allow tens of thousands of very large businesses (500+ employees, $30+ million in revenue) to be reclassified as small. As a result, the banks and the SBA can now give a lot fewer loans to much bigger businesses, and still blow their horn that they support small businesses. Nothing could be farther from the truth.
The banks and the venture capitalists (like Startup America) have been lobbying for years to get the SBA to abandon small business in favor of the 2%; the largest businesses in America. It's working. Their next step is to convince the politicians to fold the SBA into the Commerce Department, where it will get lost in the Commerce Department's focus on the top 1/2 of 1% of the largest businesses.
The new SBA leader is a venture capitalist, so this is not likely to get fixed. The SBA world is upside down.
Big surprise. SBA is one of the gatekeepers and road blocks to legitimate small businesses. They make it almost impossible for any real business to qualify, expect you to line the pockets of the ex-staffer-now-consultants to make the list, and then don't do anything. Really too bad given they could be so helpful it they would, well, actually help....
get 8a certificate its waste time and money
for the last two years i don't see no help
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EAST BLACK HILLS. The East Black Hills are a mile east of the Black Hills and twenty miles northeast of the Persimmon Gap Ranger Station in east central Brewster County (centered at 29°49' N, 102°57' W). The hills, at an elevation of 3,365 feet above sea level, rise 525 feet above Dove Mountain Road a half mile to the south. Soils in the hills are generally shallow and stony and support oaks, juniper, and some mesquite.
The following, adapted from the Chicago Manual of Style, 15th edition, is the preferred citation for this article."EAST BLACK HILLS," Handbook of Texas Online (http://www.tshaonline.org/handbook/online/articles/rje04), accessed October 09, 2015. Uploaded on June 12, 2010. Published by the Texas State Historical Association.


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Contact Sue
It is,
so sign up today!
What kind of camera do you need?
Your camera should have manual settings on it for you to get
the most from your lessons.
How do you know if your camera has manual settings?
Look in your owner's manual. Does it list a chapter on f-stops and shutter speed
adjustments? Look at your camera. Does is have M, TV, AV and P or M, S, A, and P on a top knob? Then it has manual settings.
If you aren't sure, contact Susan.
When do classes meet and how long are they?
Classes are designed to be flexible. They are:
Here are some possible locations for classes:
Who teaches the classes?
Susan Lukas, an award-winning photographer, has taught photography to adults since 2003.
She has developed her curriculum by listening to her students and helping them
to achieve their goals. Her enthusiasm will help you become the photographer you want to be. Her classes are all about you and what you need to be a better photographer. TESTIMONIALS
Susan's classes are designed to be flexible for your busy life.The meeting place and time will be determined by mutual agreement before the first class.
Susan will call/e-mail you to schedule your class after your deposit is received.
What to expect in the first class:
Here is an overview:
beginner photo class
We will meet to talk about your camera and how to use your it; handout. Bring your owner's manual and extra battery to each class.
(May combine first and second class for one 2-hour session)
Discuss first
class and talk about depth of field and shutter speeds. Go
out and practice.
Our third class is about lighting and metering. We will review your photos from the second class. Go out and practice; Powerpoint presentation
(May combine third and fourth classes for one two-hour session)
Discuss third class and
talk about composition. What is composition and why should you know about it? Then we go outside for the remainder of class to take photos; Powerpoint presentation
Included in the class is Susan's new book, Naturally, She's Dreaming.
Full-color coffee table book features 32 of Susan's fine-art images with "how to" tips on photography and Photoshop.
As an aspiring photographer, it helps to look at other photo art, try to copy it, and learn from it.
This four-session class is:
Register for 1 photo class (4 one-hour sessions) $250/student
Deposit $100; $150 due at first class OR pay in full
Couples $480
(save $20); Deposit $100; $380 due at first class
Receive signed book, Naturally, She's Dreaming
Register for Beginning and Advanced Photography classes (8 sessions)
Deposit $100; $380 due at first class
OR pay in full and receive another hour of instruction free. (9 hours total)
Register for Classes


text:
- Northern New York Newspapers
- Watertown
- Ogdensburg
- Massena-Potsdam
- Lowville
- Carthage
- Malone
- NNY Business
- NNY Living
- NNY Ads
POTSDAM - The best selling regional author of Adirondack Treasure – The Bonaparte Legacy, Matthew J. Glavin, will be speaking and signing books at noon and again at 7 p.m. Wednesday at the Potsdam Public Library.
One reviewer called Adirondack Treasure – The Bonaparte Legacy the North Countrys own DaVinci Code . . . its a novel you cant put down.
Glavin, will discuss how he blended the history of Joseph Bonaparte, former King of Spain and his time in the North Country, with fiction. The result is a compelling story about a legend that has been rumored in the Adirondack Mountains for more than 180 years.
The fictional Joseph Benton has a 200-year-old bible handed down from his famous ancestor Joseph Bonaparte, the former King of Spain and older brother to Napoleon. Inside the bible is a cipher that family legend says leads to a magnificent treasure stolen from the Spanish Royal Treasury when King Joseph fled Spain.
This exciting treasure hunt blends historical facts with a terrific story and complex characters creating tension pitting environmentalist vs. developer and friend vs. friend. The search involves riddles and ciphers and leads to murder, romance and intrigue that will keep you up at night wondering yourself . . . could the legend be true?
The Bonaparte Legacy is the first installment in the planned Adirondack Treasure trilogy. Adirondack Treasure – Isle Royale is due out in the fall of 2013.
Glavin will be speaking and signing books at the library on Wednesday, May 8th, at 12 Noon in the Tech Room and at 7 PM in the Community Room. The public is welcome. Please call the Library at 265-7230 for reservations.
Readers can follow Adirondack Treasure on Facebook.
Thousands of readers like you have made Northern New York Newspapers the number one ranked website* for local news and sports coverage in the north country.
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text:
DSD-2-PCM -- proof of concept, test sample and source code here
- No over 30 sec clips of copyrighted music. Cite properly and never more than necessary for the discussion.
- No copyrighted software without permission.
- Click here for complete Hydrogenaudio Terms of Service
DSD-2-PCM -- proof of concept, test sample and source code here
Oct 8 2005, 23:55
Post #1
Group: Developer
Posts: 1318
Joined: 20-March 04
From: Göttingen (DE)
Member No.: 12875
The ZIP contains 4 files:
- dsd2pcm.jar (the converter written in Java, outputs raw 24/88 PCM, intel byte order)
- info.txt (contains some infos)
- test2822k.dsd (14 seconds, mono DSD, 5 megs)
- test44k.mp3 (conversion result)
have fun,
Edit-2011: For the latest C/C++ source code see https://code.google.com/p/dsd2pcm/ It is released under the new BSD license. The attatchment to this post is still the first Java release.
This post has been edited by SebastianG: Dec 4 2011, 17:45
Attached File(s)
dsd2pcm.zip ( 3.56MB ) Number of downloads: 3021
Nov 26 2009, 21:14
Post #2
Group: Members (Donating)
Posts: 1985
Joined: 4-January 04
From: Austin, TX
Member No.: 10933
If SACD really did have a similar distortion profile to vinyl, after spending lots and lots of time on the latter subject, I'm here to you that the distortion on SACD would be composed of lots and lots of jitter.
Which nobody really sees, but if we did, it would kinda pop a bubble in the SACD-superiority thing, wouldn't it? (I'm glossing over some details about low order distortion, but really, you have to be splitting some fine hairs to make that distinction here.)
|Lo-Fi Version
|Time is now: 7th October 2015 - 21:39


text:
Abstract. Students with attention and behavior problems oftentimes experience difficulty finishing academic work. On-task behavior is frequently cited as a primary reason for students' failure to complete homework assignments. Researchers have identified self-monitoring and self-management of on-task behavior as effective tools for improving homework completion rates among students who experience difficulty attending to tasks. The purpose of this study was to examine the effectiveness of a 30-min naturalistic, home-based, self-management intervention for students with attention problems and behavioral disorders. Specifically, the current study set out to investigate differences in on-task behavior between baseline and intervention when self-monitoring intervals were set at 3 and 10 min. For all participants, on-task behavior improved significantly over baseline. Furthermore, the improvements in on-task behavior were evident for both the 3- and 10-min intervals, suggesting that shorter intervals did not enhance the intervention's effectiveness. Finally, based on school records, the frequency of completed homework assignments increased.
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