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Central nervous involvement is common in PGM1-CDG.
PGM1, the enzyme responsible for the reversible inter-conversion of glucose-1-P and glucose-6-P, is also involved in glycosylation, leading to a wide range of clinical manifestations, such as congenital malformations, hypoglycemia, hormonal dysregulation, myopathy, hepatopathy, and cardiomyopathy. So far, PGM1 deficiency has not been associated with central nervous system involvement or intellectual disability. Seizures and neurologic involvement in PGM1-CDG were thought to be a consequence of hypoglycemia. We reviewed all reported PGM1 deficient patients for the presence of the central nervous system involvement, their treatment and disease history. We detected 17 patients out of the 41 reported PGM1-CDG cases with significant neurologic involvement. Several of these patients had no severe hypoglycemic episodes, or were adequately treated for hypoglycemia with no recurrent episodes of low blood sugars, while one patient had no reported hypoglycemic episodes. We suggest that neurological symptoms are frequent in PGM1-CDG and could present even in the absence of hypoglycemia. The central nervous system should be assessed early on during the diagnostic process to optimize outcome in patients with PGM1-CDG.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
BOSS Eddie Howe backed Lee Camp to become the cornerstone of Cherries’ defence after snapping up the former loan star on a two-and-a-half year contract.
The expiry of Camp’s short-term deal at parent club West Bromwich Albion coincided with the end of his two-month stint at Dean Court with the 29-year-old becoming a free agent after starring in Wednesday’s 1-1 draw at Brighton.
It is understood negotiations had been ongoing for the past few weeks over the prospect of a permanent switch to Dorset, while Championship rivals Blackburn Rovers are believed to have been tracking the experienced custodian.
But with the vultures circling round the in-form stopper, Cherries acted fast to tie down the Northern Ireland international with the manager citing how quickly Camp settled into his squad as an important factor for both parties.
Howe said: “We were really pleased he (Camp) decided to commit his future to us. He kept goal very well and with the style of play we deploy, the goalkeeper’s distribution is crucial. I think he has helped us in that respect.
“I have said many times what he contributes to the team and the fact that he is now with us for a sustained period of time means we can build for the future in terms of our defence. It’s great knowing you have got a settled back four.
“I got the sense he saw himself as part of our team and I think that was crucial. You could see that in his attitude to the games. He was desperate for us to win and keep clean sheets, all the things you want a good goalkeeper to do.
“His general demeanour, the way he conducts himself, the way he has dedicated himself in his training sessions has been very impressive and it was pretty clear we had to make every effort to sign him.
“Other clubs were aware of how well he was doing, had been to watch him and a good goalkeeper on a free transfer at Lee’s age is going to court attention, so I am delighted he chose us.
“The fact he has signed the contract now means he has committed to us and can hopefully grow with us as well.”
However, as swift as Camp's signing was, it did not beat yesterday's noon registration deadline for today's FA Cup tie with Burton Albion (3pm).
Meanwhile, Howe, who has already acknowledged some of his fringe players could leave on permanent or loan deals during the January transfer window, admitted his quest to strengthen the squad would continue.
On the prospect of more arrivals, he added: “We are looking and I have said before that we will do what we feel we need to do.
“But we are on a good run of form and I think it is important that we acknowledge how good the players are that we have here already.”
Comments
c0ckbeard
6:09am Sat 4 Jan 14
This makes me a very happy man. Less keen on the length of contract but I guess that's why it took a bit longer to tie up. I'd have thought 18 months was more than sufficient. But I'm not surprised Lee held out for longer. Sorry Rocky while I think you will be a brilliant keeper I wonder if promotion came a year too soon.
This makes me a very happy man. Less keen on the length of contract but I guess that's why it took a bit longer to tie up. I'd have thought 18 months was more than sufficient. But I'm not surprised Lee held out for longer. Sorry Rocky while I think you will be a brilliant keeper I wonder if promotion came a year too soon.c0ckbeard
This makes me a very happy man. Less keen on the length of contract but I guess that's why it took a bit longer to tie up. I'd have thought 18 months was more than sufficient. But I'm not surprised Lee held out for longer. Sorry Rocky while I think you will be a brilliant keeper I wonder if promotion came a year too soon.
Score: 7
TedMacsCherryPants
6:15am Sat 4 Jan 14
Great news, welcome back Lee!
Great news, welcome back Lee!TedMacsCherryPants
Great news, welcome back Lee!
Score: 14
Oakdale12
6:25am Sat 4 Jan 14
Rocky for the FA cup and Lee to get us up
Rocky for the FA cup and Lee to get us upOakdale12
Rocky for the FA cup and Lee to get us up
Score: 5
Nat1234
7:12am Sat 4 Jan 14
The best signing since eddies been back , apart from Ritchie . Now all we need is a good striker .
The best signing since eddies been back , apart from Ritchie . Now all we need is a good striker .Nat1234
The best signing since eddies been back , apart from Ritchie . Now all we need is a good striker .
Score: 19
cheeriedriteup
7:23am Sat 4 Jan 14
Good news, it shows that the club really has ambition now, buying instead of selling, I'm sure there will be plenty of movement until EH feels that he has got things 100% to his satisfaction
Good news, it shows that the club really has ambition now, buying instead of selling, I'm sure there will be plenty of movement until EH feels that he has got things 100% to his satisfactioncheeriedriteup
Good news, it shows that the club really has ambition now, buying instead of selling, I'm sure there will be plenty of movement until EH feels that he has got things 100% to his satisfaction
Score: 8
pokesdown1
7:27am Sat 4 Jan 14
General demeanour.
Managers do not use expressions like this.
We are very lucky to have Eddie Howe and lucky to be rid of Mitchell.
General demeanour.
Managers do not use expressions like this.
We are very lucky to have Eddie Howe and lucky to be rid of Mitchell.pokesdown1
General demeanour.
Managers do not use expressions like this.
We are very lucky to have Eddie Howe and lucky to be rid of Mitchell.
Score: -22
STEADY EDDIE 1 for the road
7:36am Sat 4 Jan 14
Fan-bloody-tastic. This signing will give the whole squad a real boost. The Brighton goal aside, i never get that uneasy feeling with Lee in goal. A big welcome to Lee, i have a sneaky feeling this club may just surpass many peoples expectations over the next couple of years, but let's just keep our feet on the ground for now. UTC
Fan-bloody-tastic. This signing will give the whole squad a real boost. The Brighton goal aside, i never get that uneasy feeling with Lee in goal. A big welcome to Lee, i have a sneaky feeling this club may just surpass many peoples expectations over the next couple of years, but let's just keep our feet on the ground for now. UTCSTEADY EDDIE 1 for the road
Fan-bloody-tastic. This signing will give the whole squad a real boost. The Brighton goal aside, i never get that uneasy feeling with Lee in goal. A big welcome to Lee, i have a sneaky feeling this club may just surpass many peoples expectations over the next couple of years, but let's just keep our feet on the ground for now. UTC
Score: 14
Afcbpete
7:41am Sat 4 Jan 14
pokesdown1 wrote…
General demeanour.
Managers do not use expressions like this.
We are very lucky to have Eddie Howe and lucky to be rid of Mitchell.
Completely agree with you!!!
Welcome Lee, delighted to have signed a quality keeper. Nothing against Rocky, his time will come.... UTCIAD
[quote][p][bold]pokesdown1[/bold] wrote:
General demeanour.
Managers do not use expressions like this.
We are very lucky to have Eddie Howe and lucky to be rid of Mitchell.[/p][/quote]Completely agree with you!!!
Welcome Lee, delighted to have signed a quality keeper. Nothing against Rocky, his time will come.... UTCIADAfcbpete
pokesdown1 wrote…
General demeanour.
Managers do not use expressions like this.
We are very lucky to have Eddie Howe and lucky to be rid of Mitchell.
Completely agree with you!!!
Welcome Lee, delighted to have signed a quality keeper. Nothing against Rocky, his time will come.... UTCIAD
Score: -9
eaststandman
7:59am Sat 4 Jan 14
Great news. Real quality.
Its not coincidence that we're doing better since his arrival and Fraser/Ritchie return.
I also think Rocky should be coached by Lee. His quick ball and general 'upping' the tempo is key. There's no doubt that Moss has some very strange views on distribution and timetime wasting. Our goalkeeper coaching has been questionable.
Great news. Real quality.
Its not coincidence that we're doing better since his arrival and Fraser/Ritchie return.
I also think Rocky should be coached by Lee. His quick ball and general 'upping' the tempo is key. There's no doubt that Moss has some very strange views on distribution and timetime wasting. Our goalkeeper coaching has been questionable.eaststandman
Great news. Real quality.
Its not coincidence that we're doing better since his arrival and Fraser/Ritchie return.
I also think Rocky should be coached by Lee. His quick ball and general 'upping' the tempo is key. There's no doubt that Moss has some very strange views on distribution and timetime wasting. Our goalkeeper coaching has been questionable.
Score: 5
bobsworthforever
8:43am Sat 4 Jan 14
HALLELUJAH we wont make a better signig this window didn't think he was coming well done Eddie
HALLELUJAH we wont make a better signig this window didn't think he was coming well done Eddiebobsworthforever
HALLELUJAH we wont make a better signig this window didn't think he was coming well done Eddie
Score: 9
[deleted]
8:49am Sat 4 Jan 14
[deleted]
my co-worker's sister makes 84 dollar hourly on the laptop. She has been without a job for six months but last month her check was 16372 dollar just working on the laptop for a few hours. learn the facts here now... www.Day37.cℴmMariaTHammonds
my co-worker's sister makes 84 dollar hourly on the laptop. She has been without a job for six months but last month her check was 16372 dollar just working on the laptop for a few hours. learn the facts here now... www.Day37.cℴm
Score: -7
the afcb fan
8:59am Sat 4 Jan 14
Nat1234 wrote…
The best signing since eddies been back , apart from Ritchie . Now all we need is a good striker .
Dipstick Grabban is one of the leagues top scorers
[quote][p][bold]Nat1234[/bold] wrote:
The best signing since eddies been back , apart from Ritchie . Now all we need is a good striker .[/p][/quote]Dipstick Grabban is one of the leagues top scorersthe afcb fan
Nat1234 wrote…
The best signing since eddies been back , apart from Ritchie . Now all we need is a good striker .
Dipstick Grabban is one of the leagues top scorers
Score: 6
susi.m
9:09am Sat 4 Jan 14
Great news.
Was at the club the first day he turned up for training. His demeanour and body language immediately made me feel positive.
So pleased we have signed him.
Well done Eddie and Jason.
Great news.
Was at the club the first day he turned up for training. His demeanour and body language immediately made me feel positive.
So pleased we have signed him.
Well done Eddie and Jason.susi.m
Great news.
Was at the club the first day he turned up for training. His demeanour and body language immediately made me feel positive.
So pleased we have signed him.
Well done Eddie and Jason.
Score: 5
chawtoncherry
9:14am Sat 4 Jan 14
MariaTHammonds wrote…
my co-worker's sister makes 84 dollar hourly on the laptop. She has been without a job for six months but last month her check was 16372 dollar just working on the laptop for a few hours. learn the facts here now... www.Day37.cℴm
Will someone get rid of this woman? My co-workers sister makes more than that on her back.
[quote][p][bold]MariaTHammonds[/bold] wrote:
my co-worker's sister makes 84 dollar hourly on the laptop. She has been without a job for six months but last month her check was 16372 dollar just working on the laptop for a few hours. learn the facts here now... www.Day37.cℴm[/p][/quote]Will someone get rid of this woman? My co-workers sister makes more than that on her back.chawtoncherry
MariaTHammonds wrote…
my co-worker's sister makes 84 dollar hourly on the laptop. She has been without a job for six months but last month her check was 16372 dollar just working on the laptop for a few hours. learn the facts here now... www.Day37.cℴm
Will someone get rid of this woman? My co-workers sister makes more than that on her back.
Score: 9
dustbindanny
9:32am Sat 4 Jan 14
Well that was my theory about the situation regarding Lee all wrong! Good news for our Club and good luck with your future career at AFC Bournemouth Lee?
Well that was my theory about the situation regarding Lee all wrong! Good news for our Club and good luck with your future career at AFC Bournemouth Lee?dustbindanny
Well that was my theory about the situation regarding Lee all wrong! Good news for our Club and good luck with your future career at AFC Bournemouth Lee?
Score: 5
nonnogeppetto
9:34am Sat 4 Jan 14
Nothing to add it has all been said above expect that it goes to show EH's power of persuasion . UTHIAD
Nothing to add it has all been said above expect that it goes to show EH's power of persuasion . UTHIADnonnogeppetto
Nothing to add it has all been said above expect that it goes to show EH's power of persuasion . UTHIAD
Nothing to add it has all been said above expect that it goes to show EH's power of persuasion . UTHIAD
And the power of Maxim's wallet..
Nice one Max :-))
[quote][p][bold]nonnogeppetto[/bold] wrote:
Nothing to add it has all been said above expect that it goes to show EH's power of persuasion . UTHIAD[/p][/quote]And the power of Maxim's wallet..
Nice one Max :-))STEADY EDDIE 1 for the road
nonnogeppetto wrote…
Nothing to add it has all been said above expect that it goes to show EH's power of persuasion . UTHIAD
And the power of Maxim's wallet..
Nice one Max :-))
Score: 5
a real supporter
10:03am Sat 4 Jan 14
Wonderful news. A real sign of intent. The length of contract would also fit in with most fans opinion of how well we are performing this year and the confidence that we will be in this division next season.
Wonderful news. A real sign of intent. The length of contract would also fit in with most fans opinion of how well we are performing this year and the confidence that we will be in this division next season.a real supporter
Wonderful news. A real sign of intent. The length of contract would also fit in with most fans opinion of how well we are performing this year and the confidence that we will be in this division next season.
Score: 6
ASM
10:26am Sat 4 Jan 14
brilliant news! and what a relief. We are staying up!
brilliant news! and what a relief. We are staying up!ASM
brilliant news! and what a relief. We are staying up!
Score: 3
swanagecherrie
10:29am Sat 4 Jan 14
Great signing that I didn't think would happen yesterday. Just shows how close Eddie keeps his cards to his chest :). I hope they get the decision for the pitch early so the Burton fans don't have a wasted journey nothing worse as we know only to well.
Great signing that I didn't think would happen yesterday. Just shows how close Eddie keeps his cards to his chest :). I hope they get the decision for the pitch early so the Burton fans don't have a wasted journey nothing worse as we know only to well.swanagecherrie
Great signing that I didn't think would happen yesterday. Just shows how close Eddie keeps his cards to his chest :). I hope they get the decision for the pitch early so the Burton fans don't have a wasted journey nothing worse as we know only to well.
Score: 8
threesidedrectangle
10:30am Sat 4 Jan 14
Unlikely to pass pitch inspection. Heavy burst of rain still to come. Good news is depending on replays and other postponements we may be on TV next week.
Unlikely to pass pitch inspection. Heavy burst of rain still to come. Good news is depending on replays and other postponements we may be on TV next week.threesidedrectangle
Unlikely to pass pitch inspection. Heavy burst of rain still to come. Good news is depending on replays and other postponements we may be on TV next week.
Score: 2
AFCBade
10:54am Sat 4 Jan 14
Great shot stopper but it's the way he organises the defence which stands out combined with this enthusiasm for the team. Great signing for us and on a free!!
Great shot stopper but it's the way he organises the defence which stands out combined with this enthusiasm for the team. Great signing for us and on a free!!AFCBade
Great shot stopper but it's the way he organises the defence which stands out combined with this enthusiasm for the team. Great signing for us and on a free!!
Score: 9
horsted
10:58am Sat 4 Jan 14
Welcome Lee on a full time basis, one of the best signings ever.
Welcome Lee on a full time basis, one of the best signings ever.horsted
Welcome Lee on a full time basis, one of the best signings ever.
Score: 5
Yorkie Cherry
11:18am Sat 4 Jan 14
I would like to echo (pardon the pun!) the above comments. A solid defence is built around a dependable goalkeeper and Eddie has done well to attract someone of Lee's experience to the club. It does speak volumes that the club has beaten others for his signature.
I would like to echo (pardon the pun!) the above comments. A solid defence is built around a dependable goalkeeper and Eddie has done well to attract someone of Lee's experience to the club. It does speak volumes that the club has beaten others for his signature.Yorkie Cherry
I would like to echo (pardon the pun!) the above comments. A solid defence is built around a dependable goalkeeper and Eddie has done well to attract someone of Lee's experience to the club. It does speak volumes that the club has beaten others for his signature.
Score: 7
eaststandman
11:38am Sat 4 Jan 14
pokesdown1 wrote…
General demeanour.
Managers do not use expressions like this.
We are very lucky to have Eddie Howe and lucky to be rid of Mitchell.
Entirely agreed with your post - until you had a stab at EM, who, love him or hate him, did his part to put us where we are.
Have some respect.
[quote][p][bold]pokesdown1[/bold] wrote:
General demeanour.
Managers do not use expressions like this.
We are very lucky to have Eddie Howe and lucky to be rid of Mitchell.[/p][/quote]Entirely agreed with your post - until you had a stab at EM, who, love him or hate him, did his part to put us where we are.
Have some respect.eaststandman
pokesdown1 wrote…
General demeanour.
Managers do not use expressions like this.
We are very lucky to have Eddie Howe and lucky to be rid of Mitchell.
Entirely agreed with your post - until you had a stab at EM, who, love him or hate him, did his part to put us where we are.
Have some respect.
Score: 13
nonnogeppetto
11:48am Sat 4 Jan 14
STEADY EDDIE 1 for the road wrote…
nonnogeppetto wrote…
Nothing to add it has all been said above expect that it goes to show EH's power of persuasion . UTHIAD
And the power of Maxim's wallet..
Nice one Max :-))
I guess that Maxim has to be persuaded to part with it!!!! UEHIAD (Up Eddie Howe In All Department) I missed the E the first time round
[quote][p][bold]STEADY EDDIE 1 for the road[/bold] wrote:
[quote][p][bold]nonnogeppetto[/bold] wrote:
Nothing to add it has all been said above expect that it goes to show EH's power of persuasion . UTHIAD[/p][/quote]And the power of Maxim's wallet..
Nice one Max :-))[/p][/quote]I guess that Maxim has to be persuaded to part with it!!!! UEHIAD (Up Eddie Howe In All Department) I missed the E the first time roundnonnogeppetto
STEADY EDDIE 1 for the road wrote…
nonnogeppetto wrote…
Nothing to add it has all been said above expect that it goes to show EH's power of persuasion . UTHIAD
And the power of Maxim's wallet..
Nice one Max :-))
I guess that Maxim has to be persuaded to part with it!!!! UEHIAD (Up Eddie Howe In All Department) I missed the E the first time round
Score: 1
swanagecherrie
12:01pm Sat 4 Jan 14
eaststandman wrote…
pokesdown1 wrote…
General demeanour.
Managers do not use expressions like this.
We are very lucky to have Eddie Howe and lucky to be rid of Mitchell.
Entirely agreed with your post - until you had a stab at EM, who, love him or hate him, did his part to put us where we are.
Have some respect.
Agree Im not the greatest Mitchell fan but whatever his motives I don't think anyone can fault his enthusiasm and hard work he put into the club to turn it around to what we have today.
[quote][p][bold]eaststandman[/bold] wrote:
[quote][p][bold]pokesdown1[/bold] wrote:
General demeanour.
Managers do not use expressions like this.
We are very lucky to have Eddie Howe and lucky to be rid of Mitchell.[/p][/quote]Entirely agreed with your post - until you had a stab at EM, who, love him or hate him, did his part to put us where we are.
Have some respect.[/p][/quote]Agree Im not the greatest Mitchell fan but whatever his motives I don't think anyone can fault his enthusiasm and hard work he put into the club to turn it around to what we have today.swanagecherrie
eaststandman wrote…
pokesdown1 wrote…
General demeanour.
Managers do not use expressions like this.
We are very lucky to have Eddie Howe and lucky to be rid of Mitchell.
Entirely agreed with your post - until you had a stab at EM, who, love him or hate him, did his part to put us where we are.
Have some respect.
Agree Im not the greatest Mitchell fan but whatever his motives I don't think anyone can fault his enthusiasm and hard work he put into the club to turn it around to what we have today.
Score: 10
alasdair1967
12:12pm Sat 4 Jan 14
Ffs this is a story about us signing lee camp on a permanent basis ,love him hate him Eddie Mitchell has gone ,the club is in a far better position thanks to what he has done for it ,what's in the past is in the past and the club is moving along nicely so can we comment on the present not the past
Ffs this is a story about us signing lee camp on a permanent basis ,love him hate him Eddie Mitchell has gone ,the club is in a far better position thanks to what he has done for it ,what's in the past is in the past and the club is moving along nicely so can we comment on the present not the pastalasdair1967
Ffs this is a story about us signing lee camp on a permanent basis ,love him hate him Eddie Mitchell has gone ,the club is in a far better position thanks to what he has done for it ,what's in the past is in the past and the club is moving along nicely so can we comment on the present not the past
Score: 5
alasdair1967
12:29pm Sat 4 Jan 14
Apparently the match has been deemed playable but is being monitored every 30 mins
Apparently the match has been deemed playable but is being monitored every 30 minsalasdair1967
Apparently the match has been deemed playable but is being monitored every 30 mins
Score: 0
jackafcb
12:58pm Sat 4 Jan 14
Eddie created the squad at Burnley and look where they are now. Now he is shaping out current squad and he will hopefully create the squad he wants. Camp, Ward and Surman have been good additions with experience and now I think all we need is a top striker to finish all the chances. The one area I feel we need is a right back - to either replace or push Francis because he sometimes lacks the pace against top wingers however he is having a good season and is excellent going forward.
Eddie created the squad at Burnley and look where they are now. Now he is shaping out current squad and he will hopefully create the squad he wants. Camp, Ward and Surman have been good additions with experience and now I think all we need is a top striker to finish all the chances. The one area I feel we need is a right back - to either replace or push Francis because he sometimes lacks the pace against top wingers however he is having a good season and is excellent going forward.jackafcb
Eddie created the squad at Burnley and look where they are now. Now he is shaping out current squad and he will hopefully create the squad he wants. Camp, Ward and Surman have been good additions with experience and now I think all we need is a top striker to finish all the chances. The one area I feel we need is a right back - to either replace or push Francis because he sometimes lacks the pace against top wingers however he is having a good season and is excellent going forward.
Score: 3
bmthtillidie
1:09pm Sat 4 Jan 14
Excellent news but feel for Allsop. I was at the Oldham/Bmth game when he saved the penalty and at the end of the game when the players took the applause from the fans who were chanting "Rocky, Rocky" a somewhat embarrassed Allsop was pushed to the front of the group by a laughing EH. If you're a player you must enjoy it wen you can!
Excellent news but feel for Allsop. I was at the Oldham/Bmth game when he saved the penalty and at the end of the game when the players took the applause from the fans who were chanting "Rocky, Rocky" a somewhat embarrassed Allsop was pushed to the front of the group by a laughing EH. If you're a player you must enjoy it wen you can!bmthtillidie
Excellent news but feel for Allsop. I was at the Oldham/Bmth game when he saved the penalty and at the end of the game when the players took the applause from the fans who were chanting "Rocky, Rocky" a somewhat embarrassed Allsop was pushed to the front of the group by a laughing EH. If you're a player you must enjoy it wen you can!
Score: 2
kentcherry
1:25pm Sat 4 Jan 14
It just get's better and better. Under the stewardship of Denim and Howe we have momentum and thanks to Eddie Mitchell's hard work and determination we now have a quality football club both on and off the pitch. I am confident that we will be in the promotion mix next season and will be securing my usual seat at the earliest opportunity.
It just get's better and better. Under the stewardship of Denim and Howe we have momentum and thanks to Eddie Mitchell's hard work and determination we now have a quality football club both on and off the pitch. I am confident that we will be in the promotion mix next season and will be securing my usual seat at the earliest opportunity.kentcherry
It just get's better and better. Under the stewardship of Denim and Howe we have momentum and thanks to Eddie Mitchell's hard work and determination we now have a quality football club both on and off the pitch. I am confident that we will be in the promotion mix next season and will be securing my usual seat at the earliest opportunity.
Score: 5
galadriel
1:48pm Sat 4 Jan 14
DeMiN!!!!!!! Please can you spell his name properly...he's not a fabric for making jeans!!
DeMiN!!!!!!! Please can you spell his name properly...he's not a fabric for making jeans!!galadriel
DeMiN!!!!!!! Please can you spell his name properly...he's not a fabric for making jeans!!
Score: 2
Deejaycee
1:53pm Sat 4 Jan 14
Game off!
Game off!Deejaycee
Game off!
Score: -1
alasdair1967
2:08pm Sat 4 Jan 14
Match off
Match offalasdair1967
Match off
Score: -1
pokboy
2:13pm Sat 4 Jan 14
Come on echo, keep up!!!
Come on echo, keep up!!!pokboy
Come on echo, keep up!!!
Score: 2
alasdair1967
2:24pm Sat 4 Jan 14
At least we will know the reward for victory in this tie
At least we will know the reward for victory in this tiealasdair1967
At least we will know the reward for victory in this tie
Score: 2
abc100
2:27pm Sat 4 Jan 14
If according to Solent it could be next week, with the draw for the 4th round tomorrow knowing we could have a big club for the winners will make it a bit more exciting, on the other hand knowing that we could be away to Grimsby would be another thing!!!!
If according to Solent it could be next week, with the draw for the 4th round tomorrow knowing we could have a big club for the winners will make it a bit more exciting, on the other hand knowing that we could be away to Grimsby would be another thing!!!!abc100
If according to Solent it could be next week, with the draw for the 4th round tomorrow knowing we could have a big club for the winners will make it a bit more exciting, on the other hand knowing that we could be away to Grimsby would be another thing!!!!
Score: 2
devon fan
2:59pm Sat 4 Jan 14
it is rare for a game to be called off at AFCB, back in the 60s the pitch could take any amount of bad weather, its a pity that clubs cannot find suitable covers to protect fom all kinds of weather
it is rare for a game to be called off at AFCB, back in the 60s the pitch could take any amount of bad weather, its a pity that clubs cannot find suitable covers to protect fom all kinds of weatherdevon fan
it is rare for a game to be called off at AFCB, back in the 60s the pitch could take any amount of bad weather, its a pity that clubs cannot find suitable covers to protect fom all kinds of weather
Score: 1
wintonCheryl
3:08pm Sat 4 Jan 14
Does this mean that camp can be available now that today's game has been postponed?? Can't make a midweek fixture as I work nights.gutted
Does this mean that camp can be available now that today's game has been postponed?? Can't make a midweek fixture as I work nights.guttedwintonCheryl
Does this mean that camp can be available now that today's game has been postponed?? Can't make a midweek fixture as I work nights.gutted
Score: 1
smhinto
3:10pm Sat 4 Jan 14
Maybe the postponement is a good thing as it will present the chance to rest the players after the xmas fixtures.
.
Plus the fact if we draw a bigger club it may well change Eddies mind over team selection .i.e. he won't be fielding a weakened line up if we draw Liverpool away for example.
Maybe the postponement is a good thing as it will present the chance to rest the players after the xmas fixtures.
.
Plus the fact if we draw a bigger club it may well change Eddies mind over team selection .i.e. he won't be fielding a weakened line up if we draw Liverpool away for example.smhinto
Maybe the postponement is a good thing as it will present the chance to rest the players after the xmas fixtures.
.
Plus the fact if we draw a bigger club it may well change Eddies mind over team selection .i.e. he won't be fielding a weakened line up if we draw Liverpool away for example.
Score: 0
alasdair1967
3:12pm Sat 4 Jan 14
smhinto wrote…
Maybe the postponement is a good thing as it will present the chance to rest the players after the xmas fixtures.
.
Plus the fact if we draw a bigger club it may well change Eddies mind over team selection .i.e. he won't be fielding a weakened line up if we draw Liverpool away for example.
And if we draw a northern team you might get the chance to actually watch the cherries FOR THE FIRST TIME THIS SEASON !
[quote][p][bold]smhinto[/bold] wrote:
Maybe the postponement is a good thing as it will present the chance to rest the players after the xmas fixtures.
.
Plus the fact if we draw a bigger club it may well change Eddies mind over team selection .i.e. he won't be fielding a weakened line up if we draw Liverpool away for example.[/p][/quote]And if we draw a northern team you might get the chance to actually watch the cherries FOR THE FIRST TIME THIS SEASON !alasdair1967
smhinto wrote…
Maybe the postponement is a good thing as it will present the chance to rest the players after the xmas fixtures.
.
Plus the fact if we draw a bigger club it may well change Eddies mind over team selection .i.e. he won't be fielding a weakened line up if we draw Liverpool away for example.
And if we draw a northern team you might get the chance to actually watch the cherries FOR THE FIRST TIME THIS SEASON !
Score: 7
bmthtillidie
3:39pm Sat 4 Jan 14
smhinto wrote…
Maybe the postponement is a good thing as it will present the chance to rest the players after the xmas fixtures.
.
Plus the fact if we draw a bigger club it may well change Eddies mind over team selection .i.e. he won't be fielding a weakened line up if we draw Liverpool away for example.
Shouldn't you be watching a game?
[quote][p][bold]smhinto[/bold] wrote:
Maybe the postponement is a good thing as it will present the chance to rest the players after the xmas fixtures.
.
Plus the fact if we draw a bigger club it may well change Eddies mind over team selection .i.e. he won't be fielding a weakened line up if we draw Liverpool away for example.[/p][/quote]Shouldn't you be watching a game?bmthtillidie
smhinto wrote…
Maybe the postponement is a good thing as it will present the chance to rest the players after the xmas fixtures.
.
Plus the fact if we draw a bigger club it may well change Eddies mind over team selection .i.e. he won't be fielding a weakened line up if we draw Liverpool away for example.
Shouldn't you be watching a game?
Score: 1
eaststandman
3:47pm Sat 4 Jan 14
smhinto wrote…
Maybe the postponement is a good thing as it will present the chance to rest the players after the xmas fixtures.
.
Plus the fact if we draw a bigger club it may well change Eddies mind over team selection .i.e. he won't be fielding a weakened line up if we draw Liverpool away for example.
The postponement is not a good thing and the players would have been rested for this anyway.
Now the game is nearer the league fixtures.
You really don't understand our club. Lets face it, you weren't gonna go to the game anyway, so why are you on here?
[quote][p][bold]smhinto[/bold] wrote:
Maybe the postponement is a good thing as it will present the chance to rest the players after the xmas fixtures.
.
Plus the fact if we draw a bigger club it may well change Eddies mind over team selection .i.e. he won't be fielding a weakened line up if we draw Liverpool away for example.[/p][/quote]The postponement is not a good thing and the players would have been rested for this anyway.
Now the game is nearer the league fixtures.
You really don't understand our club. Lets face it, you weren't gonna go to the game anyway, so why are you on here?eaststandman
smhinto wrote…
Maybe the postponement is a good thing as it will present the chance to rest the players after the xmas fixtures.
.
Plus the fact if we draw a bigger club it may well change Eddies mind over team selection .i.e. he won't be fielding a weakened line up if we draw Liverpool away for example.
The postponement is not a good thing and the players would have been rested for this anyway.
Now the game is nearer the league fixtures.
You really don't understand our club. Lets face it, you weren't gonna go to the game anyway, so why are you on here?
Score: 6
dekayedcherry
4:56pm Sat 4 Jan 14
Very good news that Lee Camp has signed for us. An experienced Championship goalkeeper that will be the backbone of Eddie's side and complete a trio of goalkeepers with Allsop & Flahavan as reserves. Sadly there will be no place for Jalal who I'm sure will do well for whatever club he joins.
Shame the FA Cup today was postponed due to the weather, however I still think Eddie may still give some of the fringe players some game time against Burton in a re-arranged cup game and young Allsop may get a game to get some of his confidence back. UTC.
Very good news that Lee Camp has signed for us. An experienced Championship goalkeeper that will be the backbone of Eddie's side and complete a trio of goalkeepers with Allsop & Flahavan as reserves. Sadly there will be no place for Jalal who I'm sure will do well for whatever club he joins.
Shame the FA Cup today was postponed due to the weather, however I still think Eddie may still give some of the fringe players some game time against Burton in a re-arranged cup game and young Allsop may get a game to get some of his confidence back. UTC.dekayedcherry
Very good news that Lee Camp has signed for us. An experienced Championship goalkeeper that will be the backbone of Eddie's side and complete a trio of goalkeepers with Allsop & Flahavan as reserves. Sadly there will be no place for Jalal who I'm sure will do well for whatever club he joins.
Shame the FA Cup today was postponed due to the weather, however I still think Eddie may still give some of the fringe players some game time against Burton in a re-arranged cup game and young Allsop may get a game to get some of his confidence back. UTC.
Score: 4
smhinto
7:38pm Sat 4 Jan 14
bmthtillidie wrote…
smhinto wrote…
Maybe the postponement is a good thing as it will present the chance to rest the players after the xmas fixtures.
.
Plus the fact if we draw a bigger club it may well change Eddies mind over team selection .i.e. he won't be fielding a weakened line up if we draw Liverpool away for example.
Shouldn't you be watching a game?
Yes I am. I am at Peterborough. So no too far to travel.
.
Regards
[quote][p][bold]bmthtillidie[/bold] wrote:
[quote][p][bold]smhinto[/bold] wrote:
Maybe the postponement is a good thing as it will present the chance to rest the players after the xmas fixtures.
.
Plus the fact if we draw a bigger club it may well change Eddies mind over team selection .i.e. he won't be fielding a weakened line up if we draw Liverpool away for example.[/p][/quote]Shouldn't you be watching a game?[/p][/quote]Yes I am. I am at Peterborough. So no too far to travel.
.
Regardssmhinto
bmthtillidie wrote…
smhinto wrote…
Maybe the postponement is a good thing as it will present the chance to rest the players after the xmas fixtures.
.
Plus the fact if we draw a bigger club it may well change Eddies mind over team selection .i.e. he won't be fielding a weakened line up if we draw Liverpool away for example.
Shouldn't you be watching a game?
Yes I am. I am at Peterborough. So no too far to travel.
.
Regards
Score: 2
Local fan
10:18am Sun 5 Jan 14
Brilliant news, and great confidence booster for Ryan to be in waiting.
Brilliant news, and great confidence booster for Ryan to be in waiting.Local fan
Brilliant news, and great confidence booster for Ryan to be in waiting.
Ipsoregulated
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1. Field of the Invention
This invention relates generally to folding, collapsible structures, and more particularly relates to an awning assembly for a shelter having a canopy portion with an upper framework, and at least two adjacent legs supporting the canopy portion, the awning assembly adapted to be removably mounted to at least two adjacent legs.
2. General Background and State-of-the-Art
Temporary shelters that can be easily transported and rapidly set up at emergency sites can be particularly useful in providing temporary care and housing. Such shelters can also be useful for non-emergency outdoor gatherings, such as for temporary military posts, field trips, and the like. It would be desirable to provide an improved collapsible shelter with a multipurpose awning that can be moved to different positions to provide shade and to serve as a holder for signage. It would also be desirable to provide a modular multipurpose awning that is adapted to mounted to an existing shelter and that can be moved to different positions to provide shade and to serve as a holder for signage. The present invention fulfills these and other needs.
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At an Oval Office gathering earlier this year, President Donald Trump began touting his administration’s new real estate investment program, which offers massive tax breaks to developers who invest in downtrodden American communities.
He then turned to one of the plan’s strongest supporters.
“Ivanka, would you like to say something?” Trump asked his daughter. “You’ve been pushing this very hard.”
Coverage of Jared Kushner on Globalnews.ca:
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The Opportunity Zone program promoted by Ivanka Trump and her husband Jared Kushner — both senior White House advisers — could also benefit them financially, an Associated Press investigation found.
Government watchdogs say the couple’s financial interests underscore the ethical minefield they created two years ago when they became two of the closest advisers to the president without divesting from their extensive real estate investments.
Trump and Kushner jointly own a big stake in a real estate investment firm, Cadre, that recently announced it is launching a series of Opportunity Zone funds that seek to build major projects under the program from Miami to Los Angeles.
Coverage of Ivanka Trump on Globalnews.ca:
Separately, the couple owns interests in at least 13 properties held by Kushner’s family firm that could qualify for the tax breaks because they are in Opportunity Zones in New Jersey, New York and Maryland — all of which, a study found, were already coming back.
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Six of the Kushner Cos. buildings are in New York City’s Brooklyn Heights area, with views of the Brooklyn Bridge and Manhattan skyline, where a five-bedroom apartment recently listed for $8 million. Two more are in the beach town of Long Branch, N.J., where some oceanfront condos within steps of a white-tablecloth Italian restaurant and a Lululemon yoga shop list for as much as $2.7 million.
There’s no evidence the couple had a hand in selecting any of the nation’s 8,700 Opportunity Zones, and the company has not indicated it plans to seek tax breaks under the new program. But the Kushners could profit even if they don’t do anything — by potentially benefiting from a recent surge in Opportunity Zone property values amid a gold rush of interest from developers and investors.
READ MORE: Jared Kushner likely paid little or no income taxes for 7 years — NYT
Ivanka Trump’s advocacy for the Opportunity Zone program “creates a direct conflict of interest with her spouse’s investment in Cadre,” said Virginia Canter, chief ethics counsel for the nonprofit Citizens for Responsibility and Ethics in Washington. “Jared Kushner’s interests are Ivanka Trump’s interests and vice versa.”
The couple’s financial disclosures show their jointly held financial empire is worth between $200 million and $800 million, with much of it in real estate, including a stake of between $25 million and $50 million in Cadre. Those documents state they must recuse themselves from dealing with policy matters that touch on real estate and “would have a direct and predictable effect on Cadre.” Ivanka Trump also has interests in Trump Organization properties which are not located inside Opportunity Zones.
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“Ms. Trump has divested assets, set up trusts, removed herself from businesses and decisions about her investments,” Abbe Lowell, ethics counsel for the couple, said in a statement.
“In addition, she adheres to the ethics advice she has received from counsel about what issues she can work on and those to which she is recused.” Tweet This
The Kushner Cos. did not respond to requests for comment.
President Trump was scheduled to attend an Opportunity Zone event in Washington on Wednesday that would depict the program as a boon to distressed communities. White House spokesman Hogan Gidley told the AP that individual state governors of both parties nominate communities for Opportunity Zone designation “based on what underserved areas would benefit most. … The White House has nothing to do with those decisions.”
The Investing in Opportunity Act, which became law last December as part of the Republican-sponsored tax overhaul, never gained traction when it was first proposed during the Obama administration, but it quickly found favor in a White House headed and dominated by real estate developers and investors.
Ivanka Trump and Jared Kushner walk to board Marine One on the South Lawn of the White House in Washington, DC, USA, 29 November 2018. President Trump is traveling to the G20 in Argentina where he is scheduled to meet with Russian President Vladimir Putin and Chinese President Xi Jinping. EPA/SHAWN THEW via AP
A significant moment came when the law’s key GOP sponsor, South Carolina U.S. Sen. Tim Scott, met President Trump after the violence-plagued white supremacist rally in Charlottesville, Virginia, in August of 2017.
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Trump promised Scott his support for Opportunity Zones as a way to show his administration’s outreach to minority communities. But Scott had already found a supporter weeks earlier in Trump’s daughter, in conversations that grew out of previous meetings about passing a child care tax credit.
Political sponsors and lobbyists told the AP that Ivanka Trump played an important role in promoting the legislation, while Kushner was also quietly supportive behind the scenes.
“Ivanka was on board with it,” said Sean Smith, Scott’s communications director.
After their first conversation, Smith said Scott and Ivanka Trump talked by phone and in person nearly a dozen times. He added that Scott also spoke to Kushner about the program, but noted, “It was much more Ivanka than Jared.” Tweet This
A team from Economic Innovation Group, or EIG, a Washington think tank that pioneered the Opportunity Zones concept, met with top Kushner aides Reed Cordish and Chris Liddell two weeks before the tax reform bill was passed.
Funded by Napster founder and early Facebook investor Sean Parker, EIG spent more than $1.4 million on lobbying over the past two years, both before and after the Investing in Opportunity Act passed. The group met with White House officials every quarter since the start of the Trump administration, and also met with frequently with officials from Treasury and other White House agencies, records show.
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“Creating the incentive to bring capital into communities that are currently being overlooked is just a tremendous opportunity,” Ivanka Trump said as her father and a crowd of supporters nodded during the White House session February 14.
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1:18 Ivanka Trump shutting down her namesake fashion brand Ivanka Trump shutting down her namesake fashion brand
Last month, at a dinner in Washington put on by the conservative Kemp Foundation, Scott singled out Ivanka Trump as his point person on the initiative. “When we were looking for help to get the tax bill across the finish line,” he said, “I kept looking to the same person for help in the White House.”
There is no indication the couple directly intervened in the shaping of the Opportunity Zone program specifically to advance their financial interests. And public officials say there is no evidence that any actions were taken to influence the selection of Opportunity Zone boundaries.
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But backers of the program acknowledge that Ivanka Trump’s out-front role drummed up interest from public officials and financial stakeholders.
Along with the Kushner-tied Cadre Opportunity Zone funds, more than 50 real estate and private equity interests have made plans in recent weeks to create investment funds under the program, including several with ties to the couple and the Trump administration.
In this Dec. 10, 2018 photo, an apartment building, center, owned by Kushner Companies, is shown in the Brooklyn Heights neighborhood of New York. AP Photo/Mark Lennihan
Last month, former White House Communications Director Anthony Scaramucci launched an opportunity zone fund tied to his Skybridge Capital investment firm, aiming to build projects worth more than $3 billion. Opportunity Zone funds have also been set up recently by New York-based Normandy Real Estate Partners and Heritage Equity Partners, two firms that have worked with Kushner Cos. on real estate ventures.
They are flocking to what financial analysts say are some of the most generous tax benefits they have ever seen. Investors who plow capital gains from previous investments into Opportunity Zone projects can defer taxes on those gains up to 2026. If they decide not to cash out their investment for seven years, they get to exclude up to 15 percent of those gains from taxes. And they can permanently avoid paying taxes on any new gains from investment in the zones if they hold onto the investment for a decade. With capital gains taxes as high as 23.8 percent, the savings can easily add up.
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Government officials have estimated the program would cost $1.5 billion in lost tax revenue over 10 years, but Treasury Secretary Steve Mnuchin has estimated the zones would attract up to $100 billion in renewal efforts.
WATCH: From January 2017 — Trump to name son-in-law senior adviser
0:53 Trump to name son-in-law senior adviser Trump to name son-in-law senior adviser
While the Opportunity Zone program mostly targets census tracts of high poverty and unemployment, it also allows “contiguous” tracts that might not be low-income, but are close enough to deprived communities to be eligible.
Critics say that could allow developers to cash in by targeting zones already teeming with investment and gentrified neighborhoods. Amazon’s recent decision to locate a new headquarters in the bustling New York City neighborhood of Long Island City, for example, drew rebukes following reports it was in an Opportunity Zone.
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A study by the Urban Institute in Washington found that nearly a third of the more than 8,700 Opportunity Zones nationwide — and all 13 of the ones containing Kushner properties — were showing signs of heavy investment and gentrification, based on such factors as rent increases and the percentage of college-educated residents.
The Kushners’ most immediate advantage could come from their investment in Cadre. CEO Ryan Williams announced late last month that Cadre was starting up an Opportunity Zone fund that would aim to build major development projects in designated areas of Los Angeles, San Francisco, Seattle, Portland, Phoenix, Houston, Atlanta, Philadelphia and Miami.
The company said the program “fits with Cadre’s commitment to identifying opportunities in less-advantaged areas that are primed for growth.”
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1. Field of the Invention
The present invention generally relates to an information processing apparatus of an on-vehicle type such as an audio apparatus of the on-vehicle type, and more particularly to an information processing apparatus of an on-vehicle type, which is mounted on a vehicle and which has a fan for cooling and/or removing dust.
2. Description of the Related Art
Conventionally, it is general that an audio apparatus such as a so-called car-radio, a cassette deck, a CD (Compact Disc) player or the like is mounted in a room or cabin of the vehicle, so as to serve music etc., to the users or passengers on the vehicle by the audio apparatus.
Recently, a so-called navigation apparatus is also generalized, which has a display device such as an LCD (Liquid Crystal Display) device or the like in the cabin of the vehicle and helps a movement of the vehicle by displaying a necessary map etc., on the display device.
In such an audio apparatus or a navigation apparatus, a device which generates heat during the operation thereof (e.g., a CPU, an amplifier or the like) and a device which should not be heated up to a certain high temperature during the operation thereof (e.g., an MD (Mini Disc) drive or the like) may be commonly built-in. Thus, a fan for cooling is often built-in so as to restrain the temperature increase by heat from the device generating the heat.
When the supply of the electric power with respect to the audio apparatus or the navigation apparatus is started, the rotation of the fan is started at the same time so as to perform the cooling operation while the rotation speed of the fan (which is defined as a rotation number per unit time, hereinbelow) is constant.
There is recently such a tendency that the silence within the cabin is regarded as an important factor.
However, even if the cabin is designed to attach importance onto the silence, since the audio apparatus or the navigation apparatus is mounted in the cabin of the vehicle, the silence cannot be preserved because of the blowing sound due to the rotation of the fan within the audio apparatus or the navigation apparatus, which is a problem.
On the other hand, if the rotation speed of the fan is reduced since too much importance is attached onto the silence within the cabin, the cooling function of the fan cannot be fulfilled, so that the audio apparatus or the navigation apparatus may be failed due to the heat, which is another problem.
It is therefore an object of the present invention to provide an information processing apparatus of an on-vehicle type, which can operate a fan for cooling or removing dust while preserving the silence in a cabin of the vehicle and at the same time preserving the rotation speed necessary for the fan, which is high enough to appropriately function.
The above object of the present invention can be achieved by a first information processing apparatus of an on-vehicle type provided with: a fan; a detecting device for detecting an operation status of a vehicle; and a controlling device, such as a CPU or the like, for controlling a rotation speed of the fan in accordance with the detected operation status.
According to the first information processing apparatus of the present invention, since the rotation speed of the fan is controlled in accordance with the operation status of the vehicle, it is possible to preserve the silence in the cabin of the vehicle as the unnecessary blowing sound of the fan is restrained by decreasing the rotation speed in case that the priority is given to the silence, for example. It is also possible to preserve the necessary rotation speed of the fan to fulfill the cooling function, the dust sucking function or the like, by increasing the rotation speed in case that the priority is not given to the silence (but to the prevention against a failure of the information processing apparatus, for example).
In this manner, it is possible to preserve both of the silence in the cabin and the necessary rotation speed of the fan, depending upon the operation status of the vehicle.
In one aspect of the first information processing apparatus of the present invention, the detecting device comprises a silence degree detecting device, such as a voice microphone or the like, for detecting a degree of silence within a cabin of the vehicle, and the controlling device sets the rotation speed to a low speed or stops a rotation of the fan if the detected degree of silence is higher than a threshold degree of silence, which may be set in advance or may be changed in operation, and sets the rotation speed to a high speed, which is higher than the low speed, if the detected degree of silence is not higher than the threshold degree of silence.
According to this aspect, since the fan is rotated at the low speed or the rotation of the fan is stopped in case that it is silent in the cabin, and since the fan is rotated at the high speed in case that it is not silent in the cabin, it is possible to preserve both of the silence in the cabin by restraining the blowing sound of the fan and the necessary rotation speed of the fan.
In another aspect of the first information processing apparatus of the present invention, the detecting device comprises a vehicle speed detecting device, such as a travel distance sensor or the like, for detecting a moving speed of the vehicle on the basis of a vehicle speed pulse signal outputted in response to the moving speed, and the controlling device sets the rotation speed to a low speed, which is lower than a reference rotation speed, or stops a rotation of the fan if the detected moving speed is not higher than a threshold moving speed, which may be set in advance or may be changed in operation.
According to this aspect, since the fan is rotated at the low speed or the rotation of the fan is stopped in case that the vehicle is moving slowly, it is possible to preserve the silence in the cabin more surely.
In another aspect of the first information processing apparatus of the present invention, the detecting device comprises a vehicle speed detecting device, such as a travel distance sensor or the like, for detecting a moving speed of the vehicle on the basis of a vehicle speed pulse signal outputted in response to the moving speed, and the controlling device sets the rotation speed to a high speed, which is higher than a reference rotation speed, if the detected moving speed is higher than a threshold moving speed, which may be set in advance or may be changed in operation.
According to this aspect, since the fan is rotated at the high speed in case that the vehicle is moving fast, it is possible to preserve the necessary rotation speed of the fan if it can be assumed that it is not necessary to preserve the silence in the cabin as the vehicle is moving fast.
In another aspect of the first information processing apparatus of the present invention, the detecting device comprises a vibration detecting device, such as an angular velocity sensor or the like, for detecting a vibration of the vehicle, and the controlling device sets the rotation speed to a low speed, which is lower than a reference rotation speed, or stops a rotation of the fan if the detected vibration indicates the operation status that the vehicle is not moving.
According to this aspect, since the fan is rotated at the low speed or the rotation of the fan is stopped in case that the vehicle is not moving, it is possible to preserve the silence in the cabin more surely.
In another aspect of the first information processing apparatus of the present invention, the detecting device comprises a vibration detecting device, such as an angular velocity sensor or the like, for detecting a vibration of the vehicle, and the controlling device sets the rotation speed to a high speed, which is higher than a reference rotation speed, if the detected vibration indicates the operation status that the vehicle is vibrating by a certain magnitude.
According to this aspect, since the fan is rotated at the high speed in case that the vehicle is vibrating, it is possible to preserve the necessary rotation speed of the fan if it can be assumed that it is not necessary to preserve the silence in the cabin as the vehicle is vibrating.
In another aspect of the first information processing apparatus of the present invention, the information processing apparatus further comprises a sound detecting unit, such as a voice microphone or the like, for detecting a sound in a cabin of the vehicle, and the controlling device sets the rotation speed to a high speed, which is higher than a reference rotation speed, if a sound volume of the detected sound is not smaller than a threshold volume, which may be set in advance or may be changed in operation, regardless of a detection result of the detecting device.
According to this aspect, it is possible to preserve the necessary rotation speed of the fan in case that it is not actually silent in the cabin regardless of the operation status of the vehicle.
In another aspect of the first information processing apparatus of the present invention, the information processing apparatus further comprises a sound detecting unit, such as a voice microphone or the like, for detecting a sound in a cabin of the vehicle, and the controlling device sets the rotation speed to a low speed, which is lower than a reference rotation speed, or stops a rotation of the fan if a sound volume of the detected sound is not larger than a threshold volume, which may be set in advance or may be changed in operation, regardless of a detection result of the detecting device.
According to this aspect, it is possible to restrain the generation of the blowing sound of the fan, which disturbs the silence in the cabin, in case that it is actually silent in the cabin regardless of the operation status of the vehicle.
In another aspect of the first information processing apparatus of the present invention, the information processing apparatus further comprises a temperature detecting unit, such as a thermistor or the like, for detecting a temperature within the information processing apparatus, and the controlling device sets the rotation speed to a high speed, which is higher than a reference rotation speed, if the detected temperature is not lower than a threshold temperature, which may be set in advance or may be changed in operation, regardless of a detection result of the detecting device.
According to this aspect, it is possible to cool the information processing apparatus by rotating the fan at the high speed, in case that the temperature in the information processing apparatus is actually high, regardless of the operation status of the vehicle.
In another aspect of the first information processing apparatus of the present invention, the information processing apparatus further comprises a temperature detecting unit, such as a thermistor or the like, for detecting a temperature within the information processing apparatus, and the controlling device sets the rotation speed to a low speed, which is lower than a reference rotation speed, or stops a rotation of the fan if the detected temperature is not higher than a threshold temperature, which may be set in advance or may be changed in operation, regardless of a detection result of the detecting device.
According to this aspect, it is possible to preserve the silence in the cabin, by restraining the unnecessary blowing sound of the fan, in case that the temperature in the information processing apparatus is actually low, regardless of the operation status of the vehicle.
The above object of the present invention can be also achieved by a second information processing apparatus of an on-vehicle type provided with: a fan; a sound volume detecting device, such as a noise microphone or the like, for detecting a sound volume of a sound generated in a cabin of a vehicle; and a controlling device, such as a CPU or the like, for controlling a rotation speed of the fan in accordance with the detected sound volume.
According to the second information processing apparatus of the present invention, since the rotation speed of the fan is controlled in accordance with the sound volume of the sound in the cabin, it is possible to preserve the silence in the cabin of the vehicle as the unnecessary blowing sound of the fan is restrained by decreasing the rotation speed in case that the priority is given to the silence, for example. It is also possible to preserve the necessary rotation speed of the fan to fulfill the cooling function, the dust sucking function or the like, by increasing the rotation speed in case that the priority is not given to the silence (but to the prevention against a failure of the information processing apparatus, for example).
In this manner, it is possible to preserve both of the silence in the cabin and the necessary rotation speed of the fan, depending upon the operation status of the vehicle.
In one aspect of the second information processing apparatus of the present invention, the controlling device sets the rotation speed to a low speed, which is lower than a reference rotation speed, or stops a rotation of the fan if the detected sound volume is not larger than a threshold volume, which may be set in advance or may be changed in operation.
According to this aspect, since the fan is rotated at the low speed or the rotation of the fan is stopped in case that it is silent in the cabin, it is possible to preserve the silence in the cabin by restraining the unnecessary blowing sound of the fan.
In another aspect of the second information processing apparatus of the present invention, the controlling device sets the rotation speed to a high speed, which is higher than a reference rotation speed, if the detected sound volume is larger than a threshold volume, which may be set in advance or may be changed in operation.
According to this aspect, since the fan is rotated at the high speed in case that it is not silent in the cabin, it is possible to preserve the necessary rotation speed of the fan in case that it is not actually silent in the cabin.
In another aspect of the second information processing apparatus of the present invention, the information processing apparatus further comprises a temperature detecting unit, such as a thermistor or the like, for detecting a temperature within the information processing apparatus, and the controlling device sets the rotation speed to a high speed, which is higher than a reference rotation speed, if the detected temperature is not lower than a threshold temperature, which may be set in advance or may be changed in operation, regardless of a detection result of the sound volume detecting device.
According to this aspect, it is possible to cool the information processing apparatus by rotating the fan at the high speed in case that the temperature in the information processing apparatus is actually high, regardless of the sound volume of the sound in the cabin.
In another aspect of the second information processing apparatus of the present invention, the information processing apparatus further comprises a temperature detecting unit, such as a thermistor or the like, for detecting a temperature within the information processing apparatus, and the controlling device sets the rotation speed to a low speed, which is lower than a reference rotation speed, or stops a rotation of the fan if the detected temperature is not higher than a threshold temperature, which may be set in advance or may be changed in operation, regardless of a detection result of the sound volume detecting device.
According to this aspect, it is possible to preserve the silence in the cabin as the unnecessary blowing sound of the fan is restrained by rotating the fan at the low speed in case that the temperature in the information processing apparatus is actually low, regardless of the sound volume of the sound in the cabin.
The above object of the present invention can be also achieved by a third information processing apparatus of an on-vehicle type provided with: a fan; at least two of an operation status detecting device, such as a noise microphone or the like, for detecting an operation status of a vehicle, a sound detecting unit, such as a voice microphone or the like, for detecting a sound in a cabin of the vehicle and a temperature detecting unit, such as a thermistor or the like, for detecting a temperature within the information processing apparatus; and a controlling device, such as a CPU or the like, for setting a rotation speed of the fan to a high speed, which is higher than a reference rotation speed, if a detected value of at least one of the operation status detecting device, the sound detecting unit and the temperature detecting unit is higher than a threshold value, which is set in advance for each of the operation status detecting device, the sound detecting unit and the temperature detecting unit.
According to the third information processing apparatus of the present invention, since the rotation speed of the fan is set to the high speed in case that the detected value of either one of the detecting device is not less than the threshold value thereof, i.e., in case that the generation of the blowing sound of the fan is admitted, it is possible to preserve the necessary rotation speed of the fan, as the occasion demands.
In another aspect of the first information processing apparatus of the present invention, in another aspect of the second information processing apparatus of the present invention or in one aspect of the third information processing apparatus of the present invention, the information processing apparatus reproduces information supplied from a plurality of kinds of sources.
According to this aspect, in case that the information is reproduced in the cabin, it is possible to preserve both of the silence in the cabin and the necessary rotation speed of the fan, by controlling the rotation speed of the fan as the occasion demands.
The nature, utility, and further features of this invention will be more clearly apparent from the following detailed description with respect to preferred embodiments of the invention when read in conjunction with the accompanying drawings briefly described below.
|
{
"pile_set_name": "USPTO Backgrounds"
}
|
/*
* Lexer defines.
*/
#if !defined(DUK_LEXER_H_INCLUDED)
#define DUK_LEXER_H_INCLUDED
typedef void (*duk_re_range_callback)(void *user, duk_codepoint_t r1, duk_codepoint_t r2, duk_bool_t direct);
/*
* A token is interpreted as any possible production of InputElementDiv
* and InputElementRegExp, see E5 Section 7 in its entirety. Note that
* the E5 "Token" production does not cover all actual tokens of the
* language (which is explicitly stated in the specification, Section 7.5).
* Null and boolean literals are defined as part of both ReservedWord
* (E5 Section 7.6.1) and Literal (E5 Section 7.8) productions. Here,
* null and boolean values have literal tokens, and are not reserved
* words.
*
* Decimal literal negative/positive sign is -not- part of DUK_TOK_NUMBER.
* The number tokens always have a non-negative value. The unary minus
* operator in "-1.0" is optimized during compilation to yield a single
* negative constant.
*
* Token numbering is free except that reserved words are required to be
* in a continuous range and in a particular order. See genstrings.py.
*/
#define DUK_LEXER_INITCTX(ctx) duk_lexer_initctx((ctx))
#define DUK_LEXER_SETPOINT(ctx,pt) duk_lexer_setpoint((ctx), (pt))
#define DUK_LEXER_GETPOINT(ctx,pt) duk_lexer_getpoint((ctx), (pt))
/* Currently 6 characters of lookup are actually needed (duk_lexer.c). */
#define DUK_LEXER_WINDOW_SIZE 6
#if defined(DUK_USE_LEXER_SLIDING_WINDOW)
#define DUK_LEXER_BUFFER_SIZE 64
#endif
#define DUK_TOK_MINVAL 0
/* returned after EOF (infinite amount) */
#define DUK_TOK_EOF 0
/* identifier names (E5 Section 7.6) */
#define DUK_TOK_IDENTIFIER 1
/* reserved words: keywords */
#define DUK_TOK_START_RESERVED 2
#define DUK_TOK_BREAK 2
#define DUK_TOK_CASE 3
#define DUK_TOK_CATCH 4
#define DUK_TOK_CONTINUE 5
#define DUK_TOK_DEBUGGER 6
#define DUK_TOK_DEFAULT 7
#define DUK_TOK_DELETE 8
#define DUK_TOK_DO 9
#define DUK_TOK_ELSE 10
#define DUK_TOK_FINALLY 11
#define DUK_TOK_FOR 12
#define DUK_TOK_FUNCTION 13
#define DUK_TOK_IF 14
#define DUK_TOK_IN 15
#define DUK_TOK_INSTANCEOF 16
#define DUK_TOK_NEW 17
#define DUK_TOK_RETURN 18
#define DUK_TOK_SWITCH 19
#define DUK_TOK_THIS 20
#define DUK_TOK_THROW 21
#define DUK_TOK_TRY 22
#define DUK_TOK_TYPEOF 23
#define DUK_TOK_VAR 24
#define DUK_TOK_CONST 25
#define DUK_TOK_VOID 26
#define DUK_TOK_WHILE 27
#define DUK_TOK_WITH 28
/* reserved words: future reserved words */
#define DUK_TOK_CLASS 29
#define DUK_TOK_ENUM 30
#define DUK_TOK_EXPORT 31
#define DUK_TOK_EXTENDS 32
#define DUK_TOK_IMPORT 33
#define DUK_TOK_SUPER 34
/* "null", "true", and "false" are always reserved words.
* Note that "get" and "set" are not!
*/
#define DUK_TOK_NULL 35
#define DUK_TOK_TRUE 36
#define DUK_TOK_FALSE 37
/* reserved words: additional future reserved words in strict mode */
#define DUK_TOK_START_STRICT_RESERVED 38 /* inclusive */
#define DUK_TOK_IMPLEMENTS 38
#define DUK_TOK_INTERFACE 39
#define DUK_TOK_LET 40
#define DUK_TOK_PACKAGE 41
#define DUK_TOK_PRIVATE 42
#define DUK_TOK_PROTECTED 43
#define DUK_TOK_PUBLIC 44
#define DUK_TOK_STATIC 45
#define DUK_TOK_YIELD 46
#define DUK_TOK_END_RESERVED 47 /* exclusive */
/* "get" and "set" are tokens but NOT ReservedWords. They are currently
* parsed and identifiers and these defines are actually now unused.
*/
#define DUK_TOK_GET 47
#define DUK_TOK_SET 48
/* punctuators (unlike the spec, also includes "/" and "/=") */
#define DUK_TOK_LCURLY 49
#define DUK_TOK_RCURLY 50
#define DUK_TOK_LBRACKET 51
#define DUK_TOK_RBRACKET 52
#define DUK_TOK_LPAREN 53
#define DUK_TOK_RPAREN 54
#define DUK_TOK_PERIOD 55
#define DUK_TOK_SEMICOLON 56
#define DUK_TOK_COMMA 57
#define DUK_TOK_LT 58
#define DUK_TOK_GT 59
#define DUK_TOK_LE 60
#define DUK_TOK_GE 61
#define DUK_TOK_EQ 62
#define DUK_TOK_NEQ 63
#define DUK_TOK_SEQ 64
#define DUK_TOK_SNEQ 65
#define DUK_TOK_ADD 66
#define DUK_TOK_SUB 67
#define DUK_TOK_MUL 68
#define DUK_TOK_DIV 69
#define DUK_TOK_MOD 70
#define DUK_TOK_EXP 71
#define DUK_TOK_INCREMENT 72
#define DUK_TOK_DECREMENT 73
#define DUK_TOK_ALSHIFT 74 /* named "arithmetic" because result is signed */
#define DUK_TOK_ARSHIFT 75
#define DUK_TOK_RSHIFT 76
#define DUK_TOK_BAND 77
#define DUK_TOK_BOR 78
#define DUK_TOK_BXOR 79
#define DUK_TOK_LNOT 80
#define DUK_TOK_BNOT 81
#define DUK_TOK_LAND 82
#define DUK_TOK_LOR 83
#define DUK_TOK_QUESTION 84
#define DUK_TOK_COLON 85
#define DUK_TOK_EQUALSIGN 86
#define DUK_TOK_ADD_EQ 87
#define DUK_TOK_SUB_EQ 88
#define DUK_TOK_MUL_EQ 89
#define DUK_TOK_DIV_EQ 90
#define DUK_TOK_MOD_EQ 91
#define DUK_TOK_EXP_EQ 92
#define DUK_TOK_ALSHIFT_EQ 93
#define DUK_TOK_ARSHIFT_EQ 94
#define DUK_TOK_RSHIFT_EQ 95
#define DUK_TOK_BAND_EQ 96
#define DUK_TOK_BOR_EQ 97
#define DUK_TOK_BXOR_EQ 98
/* literals (E5 Section 7.8), except null, true, false, which are treated
* like reserved words (above).
*/
#define DUK_TOK_NUMBER 99
#define DUK_TOK_STRING 100
#define DUK_TOK_REGEXP 101
#define DUK_TOK_MAXVAL 101 /* inclusive */
#define DUK_TOK_INVALID DUK_SMALL_UINT_MAX
/* Convert heap string index to a token (reserved words) */
#define DUK_STRIDX_TO_TOK(x) ((x) - DUK_STRIDX_START_RESERVED + DUK_TOK_START_RESERVED)
/* Sanity check */
#if (DUK_TOK_MAXVAL > 255)
#error DUK_TOK_MAXVAL too large, code assumes it fits into 8 bits
#endif
/* Sanity checks for string and token defines */
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_BREAK) != DUK_TOK_BREAK)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_CASE) != DUK_TOK_CASE)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_CATCH) != DUK_TOK_CATCH)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_CONTINUE) != DUK_TOK_CONTINUE)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_DEBUGGER) != DUK_TOK_DEBUGGER)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_DEFAULT) != DUK_TOK_DEFAULT)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_DELETE) != DUK_TOK_DELETE)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_DO) != DUK_TOK_DO)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_ELSE) != DUK_TOK_ELSE)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_FINALLY) != DUK_TOK_FINALLY)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_FOR) != DUK_TOK_FOR)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_LC_FUNCTION) != DUK_TOK_FUNCTION)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_IF) != DUK_TOK_IF)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_IN) != DUK_TOK_IN)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_INSTANCEOF) != DUK_TOK_INSTANCEOF)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_NEW) != DUK_TOK_NEW)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_RETURN) != DUK_TOK_RETURN)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_SWITCH) != DUK_TOK_SWITCH)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_THIS) != DUK_TOK_THIS)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_THROW) != DUK_TOK_THROW)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_TRY) != DUK_TOK_TRY)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_TYPEOF) != DUK_TOK_TYPEOF)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_VAR) != DUK_TOK_VAR)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_VOID) != DUK_TOK_VOID)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_WHILE) != DUK_TOK_WHILE)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_WITH) != DUK_TOK_WITH)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_CLASS) != DUK_TOK_CLASS)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_CONST) != DUK_TOK_CONST)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_ENUM) != DUK_TOK_ENUM)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_EXPORT) != DUK_TOK_EXPORT)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_EXTENDS) != DUK_TOK_EXTENDS)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_IMPORT) != DUK_TOK_IMPORT)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_SUPER) != DUK_TOK_SUPER)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_LC_NULL) != DUK_TOK_NULL)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_TRUE) != DUK_TOK_TRUE)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_FALSE) != DUK_TOK_FALSE)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_IMPLEMENTS) != DUK_TOK_IMPLEMENTS)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_INTERFACE) != DUK_TOK_INTERFACE)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_LET) != DUK_TOK_LET)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_PACKAGE) != DUK_TOK_PACKAGE)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_PRIVATE) != DUK_TOK_PRIVATE)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_PROTECTED) != DUK_TOK_PROTECTED)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_PUBLIC) != DUK_TOK_PUBLIC)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_STATIC) != DUK_TOK_STATIC)
#error mismatch in token defines
#endif
#if (DUK_STRIDX_TO_TOK(DUK_STRIDX_YIELD) != DUK_TOK_YIELD)
#error mismatch in token defines
#endif
/* Regexp tokens */
#define DUK_RETOK_EOF 0
#define DUK_RETOK_DISJUNCTION 1
#define DUK_RETOK_QUANTIFIER 2
#define DUK_RETOK_ASSERT_START 3
#define DUK_RETOK_ASSERT_END 4
#define DUK_RETOK_ASSERT_WORD_BOUNDARY 5
#define DUK_RETOK_ASSERT_NOT_WORD_BOUNDARY 6
#define DUK_RETOK_ASSERT_START_POS_LOOKAHEAD 7
#define DUK_RETOK_ASSERT_START_NEG_LOOKAHEAD 8
#define DUK_RETOK_ATOM_PERIOD 9
#define DUK_RETOK_ATOM_CHAR 10
#define DUK_RETOK_ATOM_DIGIT 11 /* assumptions in regexp compiler */
#define DUK_RETOK_ATOM_NOT_DIGIT 12 /* -""- */
#define DUK_RETOK_ATOM_WHITE 13 /* -""- */
#define DUK_RETOK_ATOM_NOT_WHITE 14 /* -""- */
#define DUK_RETOK_ATOM_WORD_CHAR 15 /* -""- */
#define DUK_RETOK_ATOM_NOT_WORD_CHAR 16 /* -""- */
#define DUK_RETOK_ATOM_BACKREFERENCE 17
#define DUK_RETOK_ATOM_START_CAPTURE_GROUP 18
#define DUK_RETOK_ATOM_START_NONCAPTURE_GROUP 19
#define DUK_RETOK_ATOM_START_CHARCLASS 20
#define DUK_RETOK_ATOM_START_CHARCLASS_INVERTED 21
#define DUK_RETOK_ATOM_END_GROUP 22
/* Constants for duk_lexer_ctx.buf. */
#define DUK_LEXER_TEMP_BUF_LIMIT 256
/* A token value. Can be memcpy()'d, but note that slot1/slot2 values are on the valstack.
* Some fields (like num, str1, str2) are only valid for specific token types and may have
* stale values otherwise.
*/
struct duk_token {
duk_small_uint_t t; /* token type (with reserved word identification) */
duk_small_uint_t t_nores; /* token type (with reserved words as DUK_TOK_IDENTIFER) */
duk_double_t num; /* numeric value of token */
duk_hstring *str1; /* string 1 of token (borrowed, stored to ctx->slot1_idx) */
duk_hstring *str2; /* string 2 of token (borrowed, stored to ctx->slot2_idx) */
duk_size_t start_offset; /* start byte offset of token in lexer input */
duk_int_t start_line; /* start line of token (first char) */
duk_int_t num_escapes; /* number of escapes and line continuations (for directive prologue) */
duk_bool_t lineterm; /* token was preceded by a lineterm */
duk_bool_t allow_auto_semi; /* token allows automatic semicolon insertion (eof or preceded by newline) */
};
#define DUK_RE_QUANTIFIER_INFINITE ((duk_uint32_t) 0xffffffffUL)
/* A regexp token value. */
struct duk_re_token {
duk_small_uint_t t; /* token type */
duk_small_uint_t greedy;
duk_uint32_t num; /* numeric value (character, count) */
duk_uint32_t qmin;
duk_uint32_t qmax;
};
/* A structure for 'snapshotting' a point for rewinding */
struct duk_lexer_point {
duk_size_t offset;
duk_int_t line;
};
/* Lexer codepoint with additional info like offset/line number */
struct duk_lexer_codepoint {
duk_codepoint_t codepoint;
duk_size_t offset;
duk_int_t line;
};
/* Lexer context. Same context is used for ECMAScript and Regexp parsing. */
struct duk_lexer_ctx {
#if defined(DUK_USE_LEXER_SLIDING_WINDOW)
duk_lexer_codepoint *window; /* unicode code points, window[0] is always next, points to 'buffer' */
duk_lexer_codepoint buffer[DUK_LEXER_BUFFER_SIZE];
#else
duk_lexer_codepoint window[DUK_LEXER_WINDOW_SIZE]; /* unicode code points, window[0] is always next */
#endif
duk_hthread *thr; /* thread; minimizes argument passing */
const duk_uint8_t *input; /* input string (may be a user pointer) */
duk_size_t input_length; /* input byte length */
duk_size_t input_offset; /* input offset for window leading edge (not window[0]) */
duk_int_t input_line; /* input linenumber at input_offset (not window[0]), init to 1 */
duk_idx_t slot1_idx; /* valstack slot for 1st token value */
duk_idx_t slot2_idx; /* valstack slot for 2nd token value */
duk_idx_t buf_idx; /* valstack slot for temp buffer */
duk_hbuffer_dynamic *buf; /* temp accumulation buffer */
duk_bufwriter_ctx bw; /* bufwriter for temp accumulation */
duk_int_t token_count; /* number of tokens parsed */
duk_int_t token_limit; /* maximum token count before error (sanity backstop) */
duk_small_uint_t flags; /* lexer flags, use compiler flag defines for now */
};
/*
* Prototypes
*/
DUK_INTERNAL_DECL void duk_lexer_initctx(duk_lexer_ctx *lex_ctx);
DUK_INTERNAL_DECL void duk_lexer_getpoint(duk_lexer_ctx *lex_ctx, duk_lexer_point *pt);
DUK_INTERNAL_DECL void duk_lexer_setpoint(duk_lexer_ctx *lex_ctx, duk_lexer_point *pt);
DUK_INTERNAL_DECL
void duk_lexer_parse_js_input_element(duk_lexer_ctx *lex_ctx,
duk_token *out_token,
duk_bool_t strict_mode,
duk_bool_t regexp_mode);
#if defined(DUK_USE_REGEXP_SUPPORT)
DUK_INTERNAL_DECL void duk_lexer_parse_re_token(duk_lexer_ctx *lex_ctx, duk_re_token *out_token);
DUK_INTERNAL_DECL void duk_lexer_parse_re_ranges(duk_lexer_ctx *lex_ctx, duk_re_range_callback gen_range, void *userdata);
#endif /* DUK_USE_REGEXP_SUPPORT */
#endif /* DUK_LEXER_H_INCLUDED */
|
{
"pile_set_name": "Github"
}
|
Q:
Task scheduler stops running C# console application periodically
I have a task scheduler which runs a C# console application every minute. It runs the .application file via a .bat file and does so successfully for a period of time before stopping completely.
Un-installing/re-installing my console application doesn't fix the problem and the task scheduler is showing the batch file as succesfully executing. Also, running the program manually works just fine.
My questions are:
How can I get this task to run again via the task scheduler. I have tried deleting and re-creating the task, uninstalling/reinstalling the applcation.
I have a scheduled backup task occuring around the time the application stops working. Volume shadow copy is not enabled. Could this be impacting my application and why?
A:
Despite the help, I did not manage to isolate the cause of this problem.
I have re-developed my scheduler using Quartz.NET and it's now running as a Windows service.
|
{
"pile_set_name": "StackExchange"
}
|
Ultrasound image fusion - clinical implementation and potential benefits for monitoring of renal transplants.
To evaluate the feasibility of US image fusion in the clinical routine and to discuss potential benefits for follow-up after renal transplantation. 15 patients with a renal transplant were prospectively included in the study. For all of them, a previously performed CT- or MRI-scan covering the renal transplant was available. Each patient was investigated using ultrasound image fusion. Time needed for sucessful implementation of image fusion was registered. Subsequently, quality of image fusion was assessed by two experienced radiologists (10 and 5 years of experience) in consensus using a subjective 5 point rank scale (1 = best). Image fusion was successfully performed in all patients. Time needed for setup of image fusion varied from 45-120 sec (85 ± 5 sec). The score for quality of US image fusion was 1.9 ± 0.7. Assessment of renal transplants using US image fusion is feasible and provides several potential benefits for the follow-up of renal transplants.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
Continuous subcutaneous insulin infusion during total parenteral nutrition after gastroscopy complicated by duodenal intramural haematoma in a patient with type 1 diabetes - case repor.
We present the course of the insulin therapy during total parenteral nutrition (TPN) after gastroscopy complicated by duodenal intramural haematoma, in a boy with type 1 diabetes treated with the insulin pump. There is a lack of guidelines regarding the insulin therapy during TPN in children. Additionally, duodenal intramural haematoma is a very rare complication of diagnostic gastroscopy. There are only few cases reported so far.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
Semiconductor devices are used in a variety of electronic applications, such as personal computers, cell phones, digital cameras, and other electronic equipment, as examples. Semiconductor devices are typically fabricated by sequentially depositing insulating or dielectric layers, conductive layers, and semiconductive layers of material over a semiconductor substrate, and patterning the various material layers using lithography to form circuit components and elements thereon.
The semiconductor industry continues to improve the integration density of various electronic components (e.g., transistors, diodes, resistors, capacitors, etc.) by continual reductions in minimum feature size, which allow more components to be integrated into a given area. These smaller electronic components also require smaller packages that utilize less area than packages of the past, in some applications.
One smaller type of packaging for semiconductors is a flip chip chip-scale package (FcCSP), in which a semiconductor die is placed upside-down on a substrate and bonded to the substrate using bumps. The substrate has wiring routed to connect the bumps on the die to contact pads on the substrate that have a larger footprint. An array of solder balls is formed on the opposite side of the substrate and is used to electrically connect the packaged die to an end application.
However, some FcCSP packages tend to exhibit bending, where warping of the substrate occurs during processing, such as during temperature stress. The bending can cause reliability issues, such as bond breakage of the bumps, delamination of an underfill, and delamination of a passivation layer on the die.
|
{
"pile_set_name": "USPTO Backgrounds"
}
|
IN THE COURT OF APPEALS OF IOWA
No. 18-2168
Filed March 4, 2020
IN RE THE DETENTION OF DAVID L. TAFT, JR.,
DAVID L. TAFT, JR.,
Respondent-Appellant.
________________________________________________________________
Appeal from the Iowa District Court for Linn County, Mary E. Chicchelly,
Judge.
David Taft appeals the denial of his petition for discharge from the sexually
violent predator program or placement in a transitional release program.
AFFIRMED.
Philip B. Mears of Mears Law Office, Iowa City, for appellant.
Thomas J. Miller, Attorney General, and Zachary Miller, Assistant Attorney
General, for appellee State.
Considered by Doyle, P.J., and Tabor and Schumacher, JJ.
2
DOYLE, Presiding Judge.
David Taft has been committed to the sexually violent predator (SVP)
program since 2005. Since then, Taft has filed three appeals challenging the
constitutionality of the criteria for determining eligibility for transitional release. See
Taft v. Iowa Dist. Ct. for Linn Cty., 879 N.W.2d 634, 638-39 (Iowa 2016) (holding
that the issue was not ripe for adjudication); Taft v. Iowa Dist. Ct. ex rel. Linn Cty.,
828 N.W.2d 309, 322-23 (Iowa 2013) (holding Taft failed to preserve error); In re
Det. Taft, No. 15-1732, 2017 WL 1088098, at *5 (Mar. 22, 2017) (holding error was
not preserved because the district court never ruled on the issue). Taft now
appeals the 2018 denial of his petition for discharge from the SVP program or
placement in a transitional release program. He alleges the statute and court
violated his due process rights by setting the State’s burden of proof at a
preponderance of the evidence.
After this appeal was ready for submission but before its transfer to this
court, the State filed a new annual report recommending Taft for transitional
release. The parties stipulated to the placement, and the district court ordered Taft
placed in the transitional release program. As a result of his placement in a
transitional release program, the State moves to dismiss Taft’s appeal as moot.
See State v. Hernandez-Lopez, 639 N.W.2d 226, 234 (Iowa 2002) (“[A]n appeal is
deemed moot if the issue becomes nonexistent or academic and, consequently,
no longer involves a justiciable controversy.”). Taft resists dismissal, arguing the
issue is likely to recur. See id. (noting that, although the appellate courts generally
refrain from reviewing moot issues, “an exception exists for issues of broad public
importance likely to recur”). He also notes that if he succeeds in his challenge to
3
the State’s burden of proof, “his entire commitment would be subject to
reconsideration.” We have rejected a claim of mootness in similar circumstances.
See In re Det. of Hutchcroft, No. 15-1489, 2017 WL 108288, at *1 (Iowa Ct. App.
Jan. 11, 2017) (finding appeal of annual review decision placing Hutchcroft in
transitional release program was not rendered moot by later decision to return him
to confinement because “[t]he order from which he appealed addressed the
question of whether he should be discharged from civil commitment, in addition to
the question of transitional release”). Because it also affects his request for
discharge from the SVP program, Taft’s challenge to the State’s burden of proof
at a review hearing is not moot.
But there is another impediment to Taft’s challenge on the State’s burden
of proof. Taft raised this challenge in his last appeal, claiming the court’s
instructions impermissibly allowed the State to prove its case by only a
preponderance of the evidence. Taft, 2017 WL 1088098, at *2-3. Iowa Code
section 229A.8(6)(d)(1) requires the State to prove beyond a reasonable doubt that
the committed person “is likely to engage in predatory acts that constitute sexually
violent offenses.” The jury instructions defined the phrase to mean “that the person
more likely than not will engage in acts constituting sexually violent offenses,”
which mirrors the statutory definition. See Taft, 2017 WL 1088098, at *2 (citing
Iowa Code § 229A.2(5)). In rejecting Taft’s claim that the instructions held the
State to a lesser burden of proof, this court cited In re Detention of Williams, 628
N.W.2d 447, 458-59 (Iowa 2001), which held defining the term “likely” to mean
“more likely than not” or “more probable than not” does not violate due process by
reducing the State’s burden of proof. See Taft, 2017 WL 1088098, at *2-3. The
4
State argues our prior decision is controlling under the law-of-the-case doctrine.
See Wolfe v. Graether, 389 N.W.2d 643, 651 (Iowa 1986) (“[W]here the court of
appeals has determined an issue of law necessary to the decision of a prior appeal,
and its determination is not vacated by this court, the decision of that court is
controlling as to that issue for purposes of further proceedings in both the district
court and subsequent appeals.”). Because Taft essentially raises the same
argument in this appeal, we will not reconsider it. See Bahl v. City of Asbury, 725
N.W.2d 317, 321 (Iowa 2006). But even if the law-of-the-case doctrine did not
apply, our prior decision and that of the supreme court in Williams would lead us
to the same result.
Taft also challenges the statutory criteria for placement in a transitional
release program. See Iowa Code § 229A.8A(2). To the extent that Taft challenges
the evidence supporting the court’s determination that he is not eligible for
transitional release, that issue is now moot. Therefore, we need not consider his
challenges to the criteria set forth in section 229A.8A(2).
Finding no merit to any of the claims we have considered in this appeal, we
affirm.
AFFIRMED.
|
{
"pile_set_name": "FreeLaw"
}
|
I love frittatas. They seem fancy, even though they are easy to whip together, taking just a little longer than regular fried or scrambled eggs. They make a great breakfast, but are more than suitable for lunch or dinner too. They are economical, easily vegetarian or milk free, and, best of all, adaptable to whatever you have on hand.
This salad is a delight. It's so fresh and flavorful and the perfect accompaniment to barbecue, spicy Mexican, or any lighter spring/summer meal. Fresh sweet corn contrasts with salty feta and the zing of the lime bounces around in your mouth with the herby cool of cilantro. The fresh zucchini gets softened by the vinaigrette but keeps a pleasantly firm texture which it otherwise loses when cooked.
We are a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for us to earn fees by linking to Amazon.com and affiliated sites. For more information, view our Disclosure & Privacy Policy.
|
{
"pile_set_name": "Pile-CC"
}
|
Q:
BQ51050B compatibility criteria
I started another project where I need to charge a few devices (preferably simultaneously) wirelessly. They all have BQ51050B and the corresponding coil/battery.
I need to know what I should look at when deciding on what IC to choose to be compatible with the mentioned device.
On the receiver, I am running 3.7V 60mAH batteries and using this coil.
On the charger, I intend to control the chips using the I2C protocol.
A:
Since asking this question I realized that the qi standard really helps you with sorting out which active component (i.e. chip) works with which passive components (i.e. coil, battery). What is more, it can also tell you which device to pair with. For example if you have a transmitter chip, the version of qi helps you determine which receiver chip to use.
Read the datasheets.
|
{
"pile_set_name": "StackExchange"
}
|
{#sp1 .91}
|
{
"pile_set_name": "PubMed Central"
}
|
Q:
SQL Server, find cross value in different columns
I need to help for a sql server query. I have to many rows like this and my table has 3 columns like a, b, c.
a b c
--- --- ---
hello world 10
hey you 80
world hello 20
my day 15
merhaba dunya 40
bugun nasilsin 75
dunya merhaba 20
So I want to find cross values in different columns with add c column values. So after the query I want to see that;
a b c
--- --- ---
hello world 30
hey you 80
my day 15
merhaba dunya 60
bugun nasilsin 75
Sorry for my bad English, thank you for answers...
Edit: answers don't work. I tried them all. Have you any idea for this solution guys?
A:
Here is a way of doing this
create table t(a varchar(10), b varchar(10), c varchar(10))
insert into t values('hello','world',10)
insert into t values('world','hello',20)
select min(a) as a
,max(b) as b
,sum(cast(c as int)) as c
from t as x
group by case when a>b then a
else b
end
|
{
"pile_set_name": "StackExchange"
}
|
Development of the cytodetachment technique to quantify mechanical adhesiveness of the single cell.
Adhesion of cells to biomaterials or to components of the extracellular matrix is fundamental in many tissue engineering and biotechnological processes, as well as in normal development and tissue maintenance. Many cells on adhesive molecules will spread and form an organized actin cytoskeleton and complex transmembrane signaling regions called focal adhesions. Focal adhesions appear to function as both signaling and stabilizing components of normal adherent cell activity. To better understand adhesion formations between cells and their underlying substrata, we have designed, developed, and utilized a novel 'cytodetachment' methodology to quantify the force required to displace attached cells. We allowed bovine articular chondrocytes to attach and spread on a substratum of either fibronectin, bovine serum albumin, or standard microscope glass. The cytodetacher was then employed to displace the cells from the substratum. Our results demonstrate that a significantly greater force is required to detach cells from fibronectin versus the two other substrata, suggesting that a cell's actin cytoskeleton and perhaps focal adhesions contribute significantly to its mechanical adhesiveness. The cytodetacher allows us to directly measure the force required for cell detachment from a substratum and to indirectly determine the ability of different substrata to support cell adhesion.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
This is the second in a **Series** of five papers about maternal and child undernutrition
Introduction
============
This is the second article in the *Lancet* Series on maternal and child undernutrition. The previous article emphasised the magnitude of the problem and its short-term consequences in low-income and middle-income countries.[@bib1] In this paper we address the potential long-term implications of undernutrition.
We start with an assessment of the long-term effects of undernutrition on adult human capital, including height, school achievement, economic productivity, and birthweight of the offspring. We then discuss the relevance to low-income and middle-income countries of the hypothesis on developmental origins of health and disease[@bib2]---namely, that early growth patterns might have long-term effects on risk of development of chronic diseases.[@bib3] Although these issues are still debated,[@bib4; @bib5] published work from high-income countries suggests that intrauterine growth restriction, especially when followed by excessive weight gain in childhood, is associated with increased risk of several chronic diseases. Studies of the developmental origins of adult disease in low-income and middle-income countries are particularly important because adults were born when rates of undernutrition were high and have had to adapt to rapidly changing postnatal diets and environments.
As researchers involved in large cohort studies entailing the long-term follow-up of children born in low-income and middle-income countries, we present a systematic review of published work on the long-term effects of malnutrition, and new analyses of data from cohorts followed up from birth into late adolescence or adult age in Brazil, Guatemala, India, the Philippines, and South Africa.
Key messages•Poor fetal growth or stunting in the first 2 years of life leads to irreversible damage, including shorter adult height, lower attained schooling, reduced adult income, and decreased offspring birthweight•Children who are undernourished in the first 2 years of life and who put on weight rapidly later in childhood and in adolescence are at high risk of chronic diseases related to nutrition•There is no evidence that rapid weight or length gain in the first 2 years of life increases the risk of chronic disease, even in children with poor fetal growth•The prevention of maternal and child undernutrition is a long-term investment that will benefit the present generation and their children
New data analyses
=================
The new analyses presented here are based on the cohorts in [Brazil](http://www.epidemio-ufpel.org.br/_projetos_de_pesquisas/coorte1982/index_english.php),[@bib6] Guatemala,[@bib7; @bib8] India,[@bib9; @bib10] the [Philippines](http://www.cpc.unc.edu/projects/cebu/),[@bib11] and [South Africa](http://www.wits.ac.za/birthto20/)[@bib12] ([table 1](#tbl1){ref-type="table"}). [Panel 1](#box1){ref-type="boxed-text"} shows the exposures that were assessed. Outcomes were measured in late adolescence in South Africa and in adulthood in the other sites ([table 1](#tbl1){ref-type="table"}), and will be referred to as adult outcomes ([panel 1](#box1){ref-type="boxed-text"}).
Potential confounding variables included the participant\'s age when the outcome variables were measured, years of schooling completed by the mother (in India, by the father), and a measure of early childhood socioeconomic status. In India, occupation of the father was classified in an ordinal six-point scale, whereas in the other sites wealth quintiles were calculated through principal component analysis of household assets.
Unless otherwise stated, we present only confounder-adjusted estimates. For glucose concentrations and blood pressure, further analyses incorporated control for adult height and body-mass index, which are potential mediating factors in the association between undernutrition and adult outcomes. Such adjustment is commonly used in published work and might help understand the role of later growth. All analyses were stratified by sex.
In every analysis, we included only participants with full information in the exposure, outcome, confounding, and stratification variables. With the exception of the dichotomous variable for intrauterine growth restriction, all other exposures were initially coded in four categories and tested for linearity with analysis of variance. Because there was no consistent evidence of non-linearity, we used multiple linear regression analyses.
Results from the five studies were combined with a meta-analytic procedure that included examination of heterogeneity with use of the *Q* test;[@bib17] if results were significant, we used a random-effects model.[@bib18]
Findings
========
We have organised our results according to the 14 outcomes studied. For every outcome, we considered maternal size and nutrition, newborn infant size, infant and child size, and growth. For eight outcomes, new information is provided from our cohorts. [Table 2](#tbl2){ref-type="table"} shows descriptive statistics for exposure and outcome variables by study site. Brazil tended to show the lowest prevalence of undernutrition, and Guatemala the highest. Birthweight was lowest and intrauterine growth restriction highest in India. When adult outcomes are compared, it should be noted that South African participants are still in their late teens.
Height
------
Attained height is affected by genetic and environmental factors throughout the growth period. Linear growth failure is largely confined to the intrauterine period and the first few years of life, and is caused by inadequate diets and frequent infections.[@bib19]
Short stature of the mother and poor maternal nutrition stores are associated with increased risk of intrauterine growth retardation.[@bib1; @bib20] Several studies from low-income and middle-income countries report that adult height is positively associated with birthweight[@bib9; @bib21; @bib22; @bib23; @bib24] and length.[@bib9; @bib21; @bib23] A 1 cm increase in birthlength is associated with a 0·7--1 cm increase in adult height.[@bib9; @bib21; @bib22; @bib23; @bib24]
Early growth failure will lead to reduced adult stature unless there is compensatory growth (so-called catch-up growth) in childhood, which is partly dependent on the extent of maturational delay that lengthens the period of growth. Because maturational delays in low-income and middle-income countries are usually shorter than 2 years,[@bib25] only a small part of the growth failure is compensated for. In Guatemala,[@bib26] there was little evidence of catch-up growth after 3 years of age but in Senegal, where maturational delays were substantial, adults heights were only about 2 cm shorter than the reference despite severe stunting in childhood.[@bib27] In both countries, differences in height between stunted and non-stunted children younger than 5 years remained largely unchanged into adulthood. People who remain in the setting in which they developed childhood undernutrition tend to become short adults.[@bib9; @bib24; @bib25] Improvements in living conditions such as those brought on through adoption can trigger catch-up growth but do so more effectively in very young children.[@bib25; @bib28]
Data from Guatemala suggest that the contributions of the intrauterine and early postnatal period to reduced adult stature are about equal.[@bib29] Because nutrition interventions during pregnancy and early life reduce stunting,[@bib26; @bib30] these interventions might be expected to lead to increased adult stature.[@bib31]
Analyses of height data from our five cohorts are shown in [webtables 1a and b](#sec1){ref-type="sec"} and [webfigures 1a--f](#sec1){ref-type="sec"}, and are summarised in [table 3](#tbl3){ref-type="table"}.
Crude and adjusted results were much the same ([webtables 1a and b](#sec1){ref-type="sec"}). Every 1 cm of maternal height was associated with an increase of about 0·5 cm in adult offspring; the only outliers were male adolescents from South Africa, who had not yet attained adult height, which possibly attenuated the association (coefficient 0·16 cm). Highly consistent cross-site effects were noted for birthweight (3·3 cm per kg), intrauterine growth restriction (2·2 cm shorter), weight-for-age at 2 years (2·7 cm per *Z* score), and height-for-age at 2 years (3·2 cm per *Z* score). When effect sizes are compared, it is noteworthy that the standard deviation for birthweight is roughly 500 g ([table 2](#tbl2){ref-type="table"}), so that a difference of 1 kg is quite large. The association with body-mass-index-for-age at 2 years was much weaker (0·2 cm per *Z* score) and---for reasons that are unclear---varied substantially among countries, with Guatemala showing a negative coefficient.
Pooled results for all exposures are shown in the webfigures, and those for height-for-age in [figure 1](#fig1){ref-type="fig"}. [Figure 2](#fig2){ref-type="fig"} shows the corresponding categorical analyses. There is remarkable similarity across studies, and between males and females. 1 *Z* score of length-for-age or height-for-age at 2 years equals 3·1 cm for boys and 3·2 cm for girls. Because the adult height difference associated with a difference of 1 *Z* score at 2 years is also 3·2 cm, our results suggest that differences observed in the first 2 years will on average remain until adulthood. This finding is consistent with studies on the secular trend in increasing height recorded in all societies as child undernutrition is reduced.[@bib32]
Achieved schooling and educational performance
----------------------------------------------
Undernutrition can affect cognitive development by causing direct structural damage to the brain and by impairing infant motor development[@bib33] and exploratory behaviour.[@bib34] Long-term effects can arise through structural and functional adaptation; the persistence of early deficits, partly because of the absence of opportunities for remediation in deprived environments; and by altering the way in which individuals deal with learning.[@bib35]
Birthweight is positively associated with cognitive skills in children, but the effect of environmental factors weakens this association over time.[@bib36] A review of studies from high-income countries---nine investigating adolescent outcomes and six adult outcomes---showed that intrauterine growth restriction had little or no measurable effect on cognitive performance.[@bib37]
Studies from Guatemala[@bib38; @bib39] and Zimbabwe[@bib40] report long-term associations between early child growth and education. In Guatemala, height and head circumference at 2 years (but not birthsize) were inversely associated with educational achievement in adult women.[@bib29] In Cebu, stunting at 2 years was associated with delayed school entry, greater grade repetition and dropout rates, decreased graduation rates from primary and secondary school, and lower school performance.[@bib41] In Guatemala, food supplementation during early childhood improved schooling in women by 1·2 years, and tests scores in men and women.[@bib42] In Zimbabwe, a difference of 3·4 cm in height-for-age at 3 years was associated with almost an additional grade of achieved schooling.[@bib40]
Although there are few follow-up studies from childhood to adult age, substantial evidence suggests an association between stunting and present or later cognitive ability or school performance in children from low-income and middle-income countries. Of 18 cross-sectional studies reviewed, only three did not report significant associations with height-for-age. Excluding studies of children admitted for severe malnutrition, four of five longitudinal studies report that height-for-age predicts school or cognitive test performance in later life. A re-analysis of longitudinal data from the Philippines, Jamaica, Peru, and Indonesia, together with new data from Brazil and South Africa, showed that stunting between 12 and 36 months of age predicted poorer cognitive performance and/or lower school grades attained in middle childhood.[@bib43]
Analyses of attained schooling are shown in [webtables 2a and b](#sec1){ref-type="sec"} and [webfigures 2a--f](#sec1){ref-type="sec"}, and summarised in [table 3](#tbl3){ref-type="table"}. Data from South Africa were not included in the pooled estimates because most 15-year-old children were still at school. Almost all undernutrition indicators were associated with lower educational achievement.
In several analyses ([webtables 2a and b](#sec1){ref-type="sec"}), adjustment for confounding reduced the magnitude of the crude effects. After adjustment, the strongest positive predictors of schooling were height-for-age (about 0·50 years of schooling per *Z* score; [figure 3](#fig3){ref-type="fig"}) and weight-for-age (0·52 years per *Z* score). For birthweight, every 1 kg (roughly 2 *Z* scores) was associated with an additional 0·30 years of schooling. Intrauterine growth restriction showed an inverse association, whereas associations with child body-mass-index-for-age and maternal height were much weaker. These results are consistent with recent analyses.[@bib43; @bib44]
Income and assets
-----------------
Poverty is both a cause and an outcome of poor human development, and investments in child nutrition are being promoted as a strategy for economic development.[@bib40; @bib45; @bib46; @bib47] Better child nutrition improves cognition and schooling, as discussed. It can also affect adult earnings through reduced lean body mass (including shorter height) and decreased productivity in jobs requiring manual labour. In the Guatemala trial, the nutrition intervention led to increased body size and improved work capacity.[@bib31; @bib48]
These indicators of physical and intellectual human capital, in turn, have been associated with increased earnings. Adult height is positively associated with income, even in urban settings and even after adjustment for education.[@bib49] The economic returns to schooling are substantial; for central America, 1 additional year of schooling is associated with 12--14% increased lifetime earnings,[@bib50] and much the same effects were estimated in Brazil.[@bib51] Exposure to famine in early life in China was associated with shorter stature and lower incomes.[@bib52] Exposure to improved nutrition before, but not after, 3 years of age was associated with higher hourly wages in Guatemalan men. For exposure from 0 to 2 years, the increase was US\$0·67 per h (95% CI 0·16--1·17), which equates to a 46% increase in average wages.[@bib53]
The only study showing a direct association between growth in infancy and adult income was undertaken in a high-income country, Finland.[@bib54] Data for adult income levels are available for Brazil and Guatemala, and for household assets from India ([webtable 3](#sec1){ref-type="sec"}). We made no attempt to do pooled analyses. Individuals from Brazil and Guatemala who had no independent income were excluded, but similar results were obtained when they were included.
Income levels were much the same in Guatemala and Brazil, although the cohort in Brazil was just entering the labour market ([table 2](#tbl2){ref-type="table"}). Confounder adjustment led in most cases to reduced effect estimates ([webtables 3a and b](#sec1){ref-type="sec"}). Most indicators of undernutrition were associated with lower income in Brazil and fewer assets in India, but in Guatemala few associations were significant. The most consistent results for men were for height-for-age: 1 *Z* score was associated with an 8% increase in income in Brazil (p\<0·0001) and Guatemala (p=0·07), as well as with an increase of 0·27 household assets in India (p\<0·0001). Associations with weight were less consistent.
Salaries were substantially lower for women than for men ([table 2](#tbl2){ref-type="table"}). The only significant associations for women were between height-for-age and income in both Brazil and Guatemala (8% and 25%, respectively), and with number of assets in India. In Brazil and India, there were also positive associations with weight-for-age. Body-mass index was not associated with income or assets in any of the three countries.
Birthweight in the next generation
----------------------------------
Maternal bodysize is strongly associated with size of newborn children.[@bib55] As shown above, undernourished girls tend to become short adults, and thus are more likely to have small children. However, evidence from low-income and middle-income countries for the intergenerational effects of undernutrition is scarce.
Ramakrishnan and colleagues[@bib56] have shown that for every 100 g increase in maternal birthweight, her child\'s birthweight increased by 10--20 g, but studies were primarily undertaken in high-income countries. In Guatemala, birthweight rose by 29 g per 100 g increase in maternal birthweight, and birthlength rose by 0·2 cm for every 1 cm increase in mother\'s birthlength.[@bib56] In India, maternal birthweight is a strong predictor of offspring birthweight, even after adjustment for maternal adult size.[@bib20]
In Guatemala, weight and height were assessed in children younger than 3 years whose mothers participated in the nutrition supplementation trial as children.[@bib57] Children born to women who had received a protein-energy supplement were on average 0·8 cm taller (95% CI 0·16--1·44) than were those whose mothers received a low-energy supplement.
Data for birthweight of firstborn offspring were available for all sites except South Africa ([webtable 4](#sec1){ref-type="sec"}, [figure 4](#fig4){ref-type="fig"}, and [table 3](#tbl3){ref-type="table"}). Undernutrition was associated with lower birthweight in the next generation. Adjustment for confounding led to reductions of about 10--20% in the crude effect sizes. Every 1 kg of birthweight was associated with a 208 g increase in offspring birthweight, roughly to 100 g per *Z* score of maternal birthweight. Maternal intrauterine growth restriction was associated with a pooled reduction of 127 g, and both weight-for-age and height-for-age---but not body-mass-index-for-age---were associated with increases of about 70--80 g per *Z* score ([figure 5](#fig5){ref-type="fig"}). There was a small association between maternal height and birthweight of their grandchildren.
Body-mass index, body composition, and obesity
----------------------------------------------
Maternal nutritional status during pregnancy can affect offspring bodysize and composition by production of long-term deficits in fetal lean body mass,[@bib58] altering sensitivity of the hypothalamic-pituitary-adrenal axis[@bib59] which affects appetite and physical activity,[@bib60; @bib61] or through the action of specific components of the maternal diet on gene expression.[@bib62; @bib63]
Four studies from low-income and middle-income countries showed that impaired fetal nutrition results primarily in long-term deficits in lean rather than in fat mass.[@bib64] In New Delhi (India)[@bib9] and Guatemala,[@bib29] birthweight was positively related to adult lean mass in both men and women, but with fat mass or sum of skinfolds[@bib9] only in women. Birthlength was positively related to adult lean mass and sum of skinfolds (Indian men and women), fat mass (Guatemalan men and women), fat-free mass (Guatemalan men), and percentage of body fat (Guatemalan women). In Brazil, birthweight was associated with lean mass in 18-year-old men.[@bib65] In Shanghai adults, waist circumference was higher in those who weighed less than 2·5 kg or more than 3·5 kg than it was in those in the middle of the distribution.[@bib66] This bimodal distribution is consistent with two different pathways---undernutrition and maternal obesity or gestational diabetes affecting the risk of bigger babies,[@bib67; @bib68] which is not part of this review.
There are few data for associations between birthweight and fat distribution. A review of evidence mainly from European studies reports that with adjustment for adult body-mass index, lower birthweight relates to central adiposity represented by the subscapular to triceps skinfold ratio and in some cases, waist to hip ratio.[@bib64] In men and women from New Delhi[@bib9] and in men from Cebu,[@bib21] birthweight and birthlength were inversely related to skinfold ratio. In adults from New Delhi, birthweight was not associated with the waist to hip ratio, but by contrast, birthweight was positively associated with adult waist to hip ratio in women from Guatemala.[@bib9; @bib29]
Recent reviews of how infant size and growth relate to later risk of obesity[@bib69; @bib70; @bib71] focused on heavy rather than undernourished children, and included very few studies of adults or people from low-income and middle-income countries. In nearly all studies, larger size and growth rates were directly associated with increased risk of obesity in later life. By contrast, linear growth retardation in the first 2 years of life is associated with lower lean body mass in adulthood. In Guatemala, a difference of 1 standard deviation in length at 2 years of age was associated with an effect size of nearly 0·5 standard deviations for adult fat-free mass.[@bib29] In Delhi, body-mass index gain in infancy was more strongly associated with adult lean than fat mass.[@bib9] However, in Brazil weight gain in the first 2 years of life was associated with lean mass in 18-year-old men, whereas later weight gain was more strongly associated with fat mass.[@bib65]
Early childhood stunting was associated with lower adult body-mass index but greater central adiposity in Guatemalan adults after adjustment for overall fatness and confounders.[@bib72] However, previous stunting was not associated with total or central adiposity in adults from New Delhi[@bib9] or in Jamaican 17--18-year-olds.[@bib73]
[Webtables 5a and b](#sec1){ref-type="sec"}, [figure 5](#fig5){ref-type="fig"}, and [webfigures 3a--f](#sec1){ref-type="sec"} show analyses of body-mass index, and [table 3](#tbl3){ref-type="table"} provides a summary. Crude and adjusted results were much the same. There was an inverse association with intrauterine growth restriction and no association with maternal height. Adult body-mass index was strongly and positively associated with birthweight, weight-for-age, and body-mass index at 2 years of age, and less strongly associated with height-for-age ([figure 5](#fig5){ref-type="fig"}). Guatemalan men showed a different pattern for most exposures.
Blood lipids
------------
Intrauterine malnutrition and early life growth patterns can result in metabolic and physiological programming, with lifelong effects on the risk of cardiovascular disease. Unhealthy lipid profiles can be a potential mechanism underlying these associations,[@bib74] and animal studies have supported this notion.[@bib75] Changes in liver microstructure can mediate this effect.[@bib76]
Three systematic reviews on newborn size and lipid concentrations are available from high-income countries.[@bib77; @bib78; @bib79] The most recent study[@bib79] reported a pooled estimate of −1·39 mg/L total cholesterol (95% CI −1·81 to −0·97 mg) per kg of birthweight. Stronger associations were noted in small studies and in infancy. Several studies reported fractions and triglycerides, but most of these associations were null and, as for total cholesterol, inverse associations were most common in small studies.[@bib79] Abdominal circumference, showing liver size, could be a better predictor of adult lipid concentrations than could birthweight,[@bib74] but data for this association are scarce.
Five studies from low-income and middle-income countries are available. In South Africa, intrauterine growth restriction was not associated with lipid concentrations at 20 years of age.[@bib80] In people aged 45 years from Beijing, low birthweight was related to raised triglycerides and reduced HDL cholesterol, after adjustment for sex and adult body-mass index.[@bib81] In Guatemala, birthweight was not associated with serum lipids at 24 years of age; in men, there were inverse trends with total cholesterol and LDL cholesterol, with borderline significance.[@bib82] A Gambian study[@bib83] assessed lipid concentrations in men (mean age 36 years) born in the season of nutritional deprivation (known as the hungry season) and in the harvest seasons, and reported no differences in total, HDL, or LDL cholesterol, or triglycerides. In Brazil, birthweight was not associated with total cholesterol, its fractions, or triglycerides, in 18-year-old men (Horta BL, Universidade Federal de Pelotas, personal communication).
The reviews have shown that adjustment for adult nutritional status increased the negative association of birthweight and lipids, suggesting that postnatal growth plays an important part.[@bib84] The Brazilian study noted no association with birthweight, but rapid weight gain between 2 and 4 years was associated with increased concentrations of VLDL cholesterol and triglycerides at age 18 years (Horta BL, personal communication). However, the only randomised trial---from Guatemala---did not accord with this finding; children supplemented in utero or up to 36 months of age had lower triglycerides and higher HDL cholesterol (men only) in adulthood. Improved nutrition at any age before 7 years was not associated with total or LDL cholesterol.[@bib85] Specific components of the young child\'s diet, such as breastmilk, might have a role.[@bib86]
Insulin resistance and type 2 diabetes
--------------------------------------
Type 2 diabetes results from a combination of insulin resistance and insulin secretory failure. The so-called thrifty phenotype hypothesis[@bib87] proposed that undernourished fetuses and infants make changes (reduced lean-tissue growth and insulin sensitivity, up-regulation of the cortisol axis, and impaired pancreatic development) that cause diabetes in later life. There is strong evidence from animals that maternal dietary deprivation leads to diabetes and insulin resistance in offspring.[@bib60; @bib88; @bib89]
Published work shows inconsistent evidence for the effect of maternal size and nutrition on insulin resistance and type 2 diabetes. Poorer glucose tolerance was associated with higher maternal weight in India[@bib90] but lower maternal body-mass index in China.[@bib81] Fasting glucose was unrelated to maternal size or nutritional supplementation in the Guatemala trial,[@bib39; @bib82; @bib85] or to season of birth in The Gambia.[@bib83]
All studies from high-income countries show associations of lower birthweight with later type 2 diabetes and insulin resistance.[@bib22; @bib91] The risk is greatest for people who became obese, and adjustment for adult body-mass index consistently strengthens the association with low birthweight, suggesting an important effect of weight gain in later life. There is an increased risk of diabetes associated with very high birthweight,[@bib22; @bib92] which has been linked to maternal diabetes in pregnancy. Three studies from low-income and middle-income countries (all adjusting for adult weight) showed higher glucose concentrations in people with lower birthweight,[@bib10; @bib80; @bib81] whereas the two studies that did not adjust showed no associations.[@bib82; @bib93] In four studies of diabetes and impaired glucose tolerance, one (Mysore, India) showed a positive association with ponderal index at birth,[@bib90] one (Delhi, India) showed no association with birth size,[@bib10] one (China) showed an association with low birthweight,[@bib66] and one (South Africa, adjusted for adult size) showed a higher prevalence in small for gestational age births.[@bib80] Three studies[@bib81; @bib90; @bib91] (all adjusting for adult size) showed inverse associations between birthweight and insulin resistance, whereas two without adjustment showed no relation.[@bib80; @bib93] Three studies recorded no associations between birth size and insulin secretion.[@bib80; @bib90; @bib94]
Two studies in high-income countries showed an increased risk of diabetes in people who had low weight in infancy.[@bib95] In studies in low-income and middle-income countries, fasting insulin was positively related to 18-month weight in The Gambia, but there was no association between 18-month weight and fasting glucose.[@bib83] In Delhi, India, diabetes and impaired glucose tolerance were associated with low weight at 1 and 2 years of age (adjusted for adult body-mass index).[@bib10] This study showed a strong association of accelerated body-mass index gain in childhood, after infancy, with diabetes and impaired glucose tolerance. In the Guatemala trial, supplementation during infancy was associated with a small reduction in adult fasting glucose concentration.[@bib85]
Concentrations of fasting blood glucose were available in Guatemala and the Philippines; in Brazil, we obtained a random glucose measurement, and measured fasting and 120-min concentrations from a glucose tolerance test in Delhi. Because the random measurements in Brazil were close to fasting levels in the other sites ([table 2](#tbl2){ref-type="table"}), the pooled analyses included the four sites.
Results are expressed in natural log scale ([webtables 6a and b](#sec1){ref-type="sec"}, [figure 6](#fig6){ref-type="fig"}, and [table 3](#tbl3){ref-type="table"}). Adjustment for socioeconomic confounders, age, and skin colour (in Brazil and South Africa only) did not produce consistent changes in effect sizes. None of the pooled adjusted estimates was significant but after additional adjustment for adult body-mass index and height, birthweight, weight-for-age, and body-mass- index-for-age at 2 years showed significant inverse associations with blood glucose concentrations ([table 3](#tbl3){ref-type="table"}).
Blood pressure
--------------
Animal studies provide strong evidence that blood pressure is raised in offspring of mothers who are exposed to diet restriction during pregnancy. Inadequate nutrition is postulated to reduce the size and number of nephrons, thereby restricting adult renal functional capacity.[@bib96; @bib97; @bib98] Early nutrition can also affect the renin-angiotensin system,[@bib99; @bib100] exposure to glucocorticoids,[@bib101] and arterial distensibility,[@bib102; @bib103] and it has indirect effects on blood pressure through body composition.
Evidence for an association of maternal diet during pregnancy with raised blood pressure in later life is sparse. An effect of macronutrient imbalance is suggested in European cohorts[@bib104; @bib105; @bib106] and in one study of adolescents in low-income and middle-income countries,[@bib107] but results differ. Maternal calcium supplementation can reduce offspring blood pressure, as shown in a trial in Argentina.[@bib108] Low maternal fat stores or inadequate pregnancy weight gain is related to elevated offspring blood pressure in Jamaican children[@bib109; @bib110] and Filipino adolescents,[@bib107] but there is little evidence for adults in low-income and middle-income countries.
Many reviews and meta-analyses relate birthweight to adult blood pressure.[@bib4; @bib111; @bib112; @bib113; @bib114; @bib115; @bib116] Across a wide range of birthweights, most studies report an inverse association of birthweight to systolic blood pressure and hypertension prevalence in later life as well as weaker, less consistent inverse associations with diastolic blood pressure. Effects can amplify with age.[@bib117] Large studies tend to find less significant effects than do small studies.[@bib113] The association of birthweight with later blood pressure strengthens when adjusted for adult body-mass index, suggesting a role for postnatal growth.[@bib4; @bib84; @bib118; @bib119] Individuals at highest risk are those with intrauterine growth restriction but a high body-mass index in adulthood. A study of blood pressure in adults from Shanghai showed a U-shaped relation with birth weight, emphasising the importance of examining non-linear relations.[@bib66]
In Beijing adults,[@bib81] an increase of 1 kg in birthweight was associated with −2·9 mm Hg systolic and −1·7 mm Hg diastolic blood pressure after adjustment for adult body-mass index. Much the same findings were reported for Australian Aboriginals.[@bib120] By contrast, studies from India[@bib93; @bib121] and Guatemala[@bib82] showed no inverse relation of birthweight to adult blood pressure. In India, birthlength was positively associated with adult systolic blood pressure and left ventricular mass,[@bib121] and in the Guatemala trial birthweight was positively associated with systolic and diastolic blood pressure in the daughters, but not sons, of women taking nutrition supplements.[@bib82]
A systematic review of 23 studies recorded a positive association between rapid postnatal growth or weight gain and later blood pressure, but no studies included adults in low-income and middle-income countries.[@bib113] The timing of compensatory growth is important. There is no evidence that rapid infant weight gain increases adult blood pressure. Conversely, adults in Hong Kong with large increases in ponderal index during infancy had lower blood pressure,[@bib122] and male Filipino adolescents with higher weight and height velocity in infancy had decreased risk of high blood pressure.[@bib123]
In our new analyses, data for systolic and diastolic blood pressure were available for all five cohorts. Because both sets of results were almost identical, we present only those for systolic blood pressure. Except for South Africa, adjustment for confounders other than adult body-mass index and height did not produce substantial changes in the effect estimates ([webtables 7a and b](#sec1){ref-type="sec"}, [figure 7](#fig7){ref-type="fig"}). The adjusted results differed across sites. In the pooled analyses, weight, height, and body-mass-index-for-age at 2 years were positively associated with systolic blood pressure.
Further adjustment for adult body-mass index and height led to important changes in the coefficients for birthweight ([table 3](#tbl3){ref-type="table"}), which became negative in most countries. This pattern was also noted, albeit to a lesser extent, for anthropometric indices measured at 2 years, especially weight-for-age and body-mass-index-for-age.
Cardiovascular disease
----------------------
The possible biological mechanisms underlying associations between undernutrition and cardiovascular disease are similar to those involved in the aetiology of high blood pressure, lipids, and diabetes.
Several studies in high-income countries have shown that birthweight is inversely associated with the risk of coronary heart disease[@bib124] and stroke.[@bib125; @bib126; @bib127] The hazard ratio for coronary heart disease in the Helsinki cohort study was 3·63 in men who weighed less than 2·5 kg at birth compared with those weighing more than 4·0 kg. Lower birthweight has also been associated with increased carotid intima media thickness, reduced arterial compliance, and impaired endothelial function, which are all considered to be precursors of cardiovascular disease.[@bib127] Evidence from low-income and middle-income countries is limited to one study from India;[@bib121; @bib128] prevalence of coronary heart disease was inversely related to birthweight after adjustment for adult body-mass index (14% in men and women older than 45 years weighing \<5 lbs \[2·27 kg\] compared with 4% for those weighing \>7 lbs \[3·18 kg\] at birth). Arterial compliance was unrelated to birthweight.
A systematic review concluded that lower infant weight is associated with an increased risk of coronary heart disease in men.[@bib95] Shorter childhood height, but accelerated childhood weight gain, are associated with increased risk of cardiovascular disease.[@bib125; @bib126] Several studies show an increased risk of cardiovascular disease in shorter men and women; however, no studies were identified from low-income and middle-income countries.
Lung function
-------------
Lung architecture develops in utero and during the first 2--3 years of life.[@bib129] Early impairment of nutrition or oxygen availability can permanently damage lung structure and function.[@bib130] Forced expiratory volume in 1 second (FEV~1~) and forced vital capacity show pulmonary development and have been used as outcomes in several studies of early determinants.
A meta-analysis of eight studies (six from Europe), showed positive associations between birthweight and FEV~1~ after adjustment for age, smoking, and height.[@bib131] The two non-European studies included a retrospective cohort of men and women aged 38--59 years from India, in whom mean FEV~1~ and forced vital capacity were positively associated with birthweight irrespective of smoking; however, this study did not adjust for socioeconomic status.[@bib132] In the Pelotas cohort in Brazil, both indicators were lowest in 18-year-olds with low birthweight, especially those with intrauterine growth restriction, but the effect disappeared after adjustment for socioeconomic and gestational confounding factors.[@bib133]
Immune function
---------------
Studies from The Gambia note that individuals born in the hungry season show immune system changes---suggesting lower thymic output and reduced cellular and humoral responses---that might lead to long-term programming effects.[@bib134; @bib135]
In Pakistani adults[@bib136] and Filipino adolescents,[@bib137] antibody response to selected vaccines was lower in people who were small at birth than in those with a birthweight of 2500 g or more. A Gambian study showed that young adults born in the annual hungry season were substantially more likely to die from infections than were those born the rest of the year.[@bib138; @bib139] This finding was not confirmed in other settings with similar seasonal variability and high adult mortality because of infectious diseases,[@bib140; @bib141] nor in the Dutch famine study in 1944.[@bib142] Further studies are needed to establish the clinical significance of these findings for adults.
Cancers
-------
Unlike other outcomes considered here, cancers are associated with larger size in early life, possibly reflecting increased exposure to growth factors before or after birth, or both.[@bib143; @bib144; @bib145; @bib146] Most of the published work relates to breast cancer.
In high-income countries, studies have shown consistent positive association between birthweight and premenopausal breast cancer.[@bib143; @bib144; @bib145; @bib146] The risk typically increases by 20--40% from lowest to highest birthweight categories. Much the same associations were reported for prostate, haemopoietic, and colorectal cancers. Data from low-income and middle-income countries are scarce. A small study in China showed no association between birthweight and breast cancer,[@bib147] although in Poland, women of higher birthweight were at increased risk.[@bib148]
Although data are scarce, no associations have been reported between weight in infancy and cancers.[@bib95] Single studies have suggested that higher energy intake in childhood is associated with increased cancer risk, and famine exposure is protective.[@bib149] However, there is no convincing evidence that higher bodyweight in childhood predicts cancer in later life; in fact some trials have suggested that the opposite notion could be true.[@bib143; @bib144; @bib145] There are no data from low-income and middle-income countries to date. Studies from high-income countries have shown that taller adults have an increased risk of several cancers; however, the Chinese study showed no association for breast cancer.[@bib147]
Bone mass, fracture risk, and osteoporosis
------------------------------------------
Bone mass is a composite measure of skeletal size and mineral density. It peaks in young adulthood and subsequently decreases, resulting in a heightened risk of osteoporosis and bone fractures in old age. Bone mass in elderly people results from the rate of mineral loss and the mass accumulated during skeletal growth, which in turn depends on dietary calcium and vitamin D status.
Maternal calcium intake and vitamin D status in pregnancy are positively related to bone mass in children.[@bib150] No studies have examined adult outcomes.
Short birthlength is associated with an increased risk of bone fractures in adults.[@bib150] Positive correlations between birthweight or weight in infancy and adult bone-mineral content or density suggest that fetal and infant growth make important contributions to adult bone mass.[@bib150] Correlations are stronger for bone-mineral content than for density, and are reduced after adjustment for adult height, indicating that early weight predicts adult bone mass through its effect on skeletal size. A study from Finland showed higher risk of hip fracture in adults who grew rapidly from birth to 7 years and slowly from 7 to 15 years.[@bib150]
Mental illness
--------------
Specific forms of mental illness are thought to be affected by adverse intrauterine experience, including maternal undernutrition. Alterations in brain development, occurring sometime in midgestation, can precipitate evolving malfunction that manifests in early adulthood. The neurodevelopmental hypothesis is supported by significant changes in the size and structure of features of the brain in some adults diagnosed with schizophrenia. Other effects of prenatal undernutrition, such as changes in arousal and sleep waves, are consistent with schizophrenia.[@bib151] The strong link between poverty and mental health[@bib152] can be partly explained by nutritional factors.
Studies investigating the Dutch Famine report more than a two-fold increase in risk for schizophrenia associated with malnutrition in midgestation.[@bib153] A very severe famine in China in 1958--61 indicated a similar level of risk of schizophrenia in a low-income or middle-income setting.[@bib154] Studies of the Chinese example suggest that an increased risk of mental illness is robustly associated with prenatal exposure to famine.[@bib155] Bennet and Gunn state that "nutritional inadequacy, in one form or another is one of the largest single non-genetic contributors to mental retardation and aberrant neural development".[@bib151]
Several cohort studies have reported associations between low birthweight and depression in men, but not in women,[@bib36] also between infant size and depression in both men and women, after adjustment for socioeconomic status, and with suicide in men.[@bib95] We identified no studies from low-income and middle-income countries.
Discussion
==========
[Table 4](#tbl4){ref-type="table"} summarises the review of published data and our new analyses, restricted to anthropometric indicators of undernutrition ([panel 2](#box2){ref-type="boxed-text"}). We provide strong evidence that adequate nutrition in utero and in the first 2 years of life is essential for formation of human capital. Undernourished children are more likely to become short adults, to have lower educational achievement, and to give birth to smaller infants. Undernutrition is also associated with lower economic status in adulthood. At present our cohorts are too young to assess the association between undernutrition and life expectancy, but in view of the direct association between longevity and schooling,[@bib159] such an association will probably become apparent in the long term. Because of the major importance of nutrition for human capital, the amount of research on this issue is remarkably small. Areas in which further research is particularly needed are listed in [panel 3](#box3){ref-type="boxed-text"}.
The effect of undernutrition spans at least three generations, as suggested by the small but significant association between grandmother\'s height and birthweight of children born to women from the five cohorts. Because of their fairly small magnitude, intergenerational effects do not preclude achievement of progress by acting only on the present generation.
The results of outcomes related to chronic disease were not so straightforward ([table 4](#tbl4){ref-type="table"}). Adult body-mass index seems to be strongly affected by the childhood indices related to weight, and to a lesser extent by height-for-age. Because body-mass index includes fat and lean mass, its associations with early weight and height might have different biological implications. Glucose concentrations were not associated with any of the exposures, but it should be noted that participants in the five cohorts are fairly young and that a post-glucose-load concentration was available in only one cohort. In high-income countries, the association of lower birthweight with raised glucose concentration is seen mainly with post-glucose-load values. Systolic and diastolic blood pressure were positively associated with childhood weight and height, and to a lesser extent to body-mass-index-for-age, but these associations were small and their clinical relevance is questionable. Taken together, our results show weaker associations between size at birth or in infancy with outcomes related to chronic disease than do those arising from cohorts in developed countries. In addition to the young age of our cohorts, other factors might have a role, including the fact that the causes of low birthweight are different and there is less catch-up growth compared with developed settings, and that some of our cohorts were not undergoing the nutrition transition.
We analysed five long running prospective cohorts in low-income and middle-income countries in a similar way. The consistency of most results is remarkable, considering that study sites are located in South and Central America, sub-Saharan Africa, and south and east Asia. Because analyses were defined a priori, our results are not affected by publication bias.
There were substantial increases in the coefficients after adjustment for adult body-mass index and height. In earlier analyses related to the Barker hypothesis, adjustment for present size was a standard procedure, but this practice has been challenged.[@bib84] Our reviews of studies from low-income and middle-income countries on lipid profiles, diabetes, blood pressure, and cardiovascular disease showed that the negative effects of undernutrition often only become apparent---or at least were strengthened---after such adjustment. If an early weight and present weight or body-mass index are included in the same regression equation, the coefficient associated with the early weight measure will become negative whenever weight gain is positively associated with the outcome. For example, a negative association with birthweight that becomes apparent only when adult body-mass index is included in the statistical model does not suggest that low birthweight itself is a risk factor; in fact, postnatal excessive weight gain might have a large role.[@bib70; @bib84; @bib95; @bib119]
For the outcomes for which no new data are presented, there is insufficient evidence linking undernutrition to long-term changes in immune function or blood lipids, or in indicators related to osteoporosis. Birthweight is positively associated with lung function, and there is some evidence that undernutrition might contribute to mental illness. By contrast with these findings (ie, showing detrimental effects of undernutrition), studies suggest a positive association between birthweight and the incidence of some cancers.
A recent symposium[@bib160] addressed the contrasting perspectives of auxology and biomedicine---"poor growth is poor health"---and evolutionary biology and anthropology---"poor growth is adaptive". The evidence for the biomedical stance is overwhelming and recognised by the symposium participants, but the two approaches are not incompatible. In response to poor nutrient availability at the cellular level, vital functions are preserved, linear growth is stopped, and muscle and fat can be metabolised for continued function. Thus poor growth can be a survival strategy. However, the evidence that growth failure has a huge cost is overwhelming: compared with people who grow well, there is increased susceptibility to infections and greater mortality[@bib1] and losses in human capital in survivors. A population of stunted people will indeed have lower nutritional requirements than will a population with unrestricted growth, which might be seen as an adaptation; however, such a population will be less likely to be competitive in the modern world because of reduced human capital.
Rapid weight gain is especially relevant in low-income and middle-income countries that are undergoing rapid transition and facing an epidemic of overweight and obesity. The long-term effects of early undernutrition might be compounded by the adoption of diets and lifestyles of developed countries.[@bib134] A baby of low birthweight, who is stunted and underweight in infancy and gains weight rapidly in childhood and adult life, can represent a worst-case scenario for cardiovascular and metabolic disease.[@bib10; @bib134; @bib161; @bib162] However, rapid weight gain in infancy is associated with lower morbidity and mortality in low-income and middle-income settings,[@bib1; @bib163] and as shown above, bodysize at 2 years of age is clearly associated with enhanced human capital. Although these are sufficient reasons for strong efforts in the prevention of undernutrition, attention should also be given to preventing excessive weight gain after infancy.
To design evidence-based policies, the potential hazards of rapid weight gain in different age ranges should be established. There is growing evidence that a high birthweight[@bib64] and weight gain in infancy lead primarily to accumulation of lean body mass, whereas gaining weight later in childhood is more likely to result in accumulation of fat mass.[@bib9; @bib22; @bib65; @bib164] A recent meta-analysis centred on studies from high-income countries concluded that "there is insufficient evidence to recommend prevention of adult disease through strategies to alter infant growth."[@bib95] Therefore, present evidence does not accord with limiting weight gain in the first year of life, and suggests that rapid weight gain becomes hazardous only later in childhood. Further research is needed to establish the exact age when rapid weight gain does more harm than good.
The first article in this Series proposed stunting as a better overall indicator of undernutrition than underweight.[@bib1] In countries undergoing the nutrition transition, monitoring length-for-age and weight-for-length in young children has been argued to be more appropriate than monitoring weight-for-age,[@bib165] because weight gain can reflect children becoming taller, fatter, or both. Our findings support this argument. Height-for-age at 2 years was more closely related to outcomes for human capital than birthweight, weight-for-age, or body-mass-index-for-age. Body-mass-index-for-age was not an important predictor of human capital, although it is highly predictive of adult body-mass index. Countries undergoing the nutrition transition should consider the advantages of assessing height-for-age and body-mass-index-for-age, in view of their different predictive values.
Because of the observational nature of our analyses, the possibility of residual confounding cannot be ruled out. However, that adjustment for confounders, including socioeconomic indicators, made little difference to estimates of effect size is reassuring. In the one trial included in our analysis, exposure to a nutritious supplement during pregnancy and early childhood, compared with exposure to low-energy supplement, led to greater adult height, schooling (women only), improved scores on tests of intelligence and reading, greater income, and better growth of the next generation.[@bib31; @bib38; @bib48; @bib57; @bib166; @bib167]
Our results strongly suggest that undernutrition leads to long-term impairment. This evidence, combined with the well-known short-term effects of undernutrition, is sufficient for giving the prevention of undernutrition high priority in national health, education, and economic agendas in low-income and middle-income countries.[@bib45; @bib168] At the same time as investments are made against undernutrition, middle-income countries undergoing the nutrition transition should also address the negative consequences of rapid weight gain, especially in later childhood.
Search strategy and selection criteria
======================================
14 adult outcomes were selected: height; achieved schooling and educational performance; income and assets; birthweight in the offspring; body-mass index, body composition, and obesity; blood lipids; insulin resistance and type 2 diabetes; blood pressure; cardiovascular disease; lung function; immune function; cancers; bone mass, fracture risk, and osteoporosis; and mental illness. Exposure variables were measured during pregnancy (maternal height and weight before pregnancy, weight gain, micronutrient status and diet), at birth (weight, length, ponderal index, intrauterine growth restriction), and at 2 years of age (stunting, wasting, underweight). Searches of published work were undertaken in the Medline, Embase, CINAHL, EconLit, Psychinfo, and PsychArticles databases, with all possible combinations of exposures and outcomes, which identified more than 15 000 original articles and 700 reviews. The search was narrowed down to articles from low-income and middle-income countries in which outcomes were measured in adulthood or late adolescence. We identified 28 relevant articles originating from populations in low-income and middle-income countries. We excluded studies with low statistical power or poor methodological quality. Information from high-income countries was summarised by selecting high-quality review articles, and was complemented by original research articles if necessary. We complemented the search by contacting investigators involved in long-term cohort studies in low-income and middle-income countries to identify relevant original or review articles and book chapters, and by searching our own personal files.
Web Extra Material {#sec1}
==================
Webfigure 1a-fEffect of maternal height on attained height in adulthood -- meta-analyses of four studies stratified by sex.P value \<0.001 (random effects)Effect of birthweight on attained height in adulthood -- meta-analyses of five studies stratified by sex.P value \<0.001 (fixed effects)Effect of intrauterine growth retardation on attained height in adulthood -- meta-analyses of five studies stratified by sex.P value\<0.001 (fixed effects)Effect of weight for age Z-score at 2 years on attained height in adulthood -- meta-analyses of five studies stratified by sex.P value \<0.001 (random effects)Effect of height for age Z-score at 2 years on attained height in adulthood -- meta-analyses of five studies stratified by sex.P value \<0.001 (fixed effects)Effect of body mass index for age Z-score at 2 years on attained height in adulthood -- meta-analyses of five studies stratified by sex.P value = 0.423 (random effects) Webfigure 2a-fEffect of maternal height on schooling in adulthood -- meta-analyses of three studies stratified by sex.P value\<0.001 (fixed effects)Effect of birthweight on schooling in adulthood -- meta-analyses of four studies stratified by sex.P value\<0.001 (fixed effects)Effect of intrauterine growth retardation on schooling in adulthood -- meta-analyses of four studies stratified by sex.P value\<0.001 (fixed effects)Effect of weight for age Z-score at 2 years on schooling in adulthood -- meta-analyses of four studies stratified by sex.P value\<0.001 (fixed effects)Effect of height for age Z-score at 2 years on schooling in adulthood -- meta-analyses of four studies stratified by sex.P value \<0.001 (fixed effects)Effect of body mass index for age Z-score at 2 years on schooling in adulthood -- meta-analyses of four studies stratified by sex.P value = 0.019 (random effects) Webfigure 3a-fEffect of maternal height on body mass index in adulthood -- meta-analyses of four studies stratified by sex.P value = 0.092 (fixed effects)Effect of birthweight on body mass index in adulthood -- meta-analyses of five studies stratified by sex.P value\<0.001 (fixed effects)Effect of intrauterine growth retardation on body mass index in adulthood -- meta-analyses of five studies stratified by sex.P value\<0.001 (fixed effects)Effect of weight for age Z-score at 2 years on body mass index in adulthood -- meta-analyses of five studies stratified by sex.P value\<0.001 (random effects)Effect of height for age Z-score at 2 years on body mass index in adulthood -- meta-analyses of five studies stratified by sex.P value\<0.001 (fixed effects)Effect of body mass index for age Z-score at 2 years on body mass index in adulthood -- meta-analyses of five studies stratified by sex.P value\<0.001 (random effects) Webtable 1a-bAttained height (cm) for males in the five study sites, according to indicators of maternal and child undernutrition: regression analyses.Attained height (cm) for females in the five study sites, according to indicators of maternal and child undernutrition: regression analyses. Webtable 2a-bSchooling (number of years completed with approval) for males in the five study sites, according to indicators of maternal and child undernutrition: regression analyses.Schooling (number of years completed with approval) for females in the five study sites, according to indicators of maternal and child undernutrition: regression analyses. Webtable 3a-bAnnual income (log US\$) for males in Brazil and Guatemala, and number of assets in India, according to indicators of maternal and child undernutrition: regression analyses. No information available for Philippines and South Africa, where most study subjects are not yet financially independent.Annual income (log US\$) for females in Brazil and Guatemala, and number of assets in India, according to indicators of maternal and child undernutrition: regression analyses. No information available for Philippines and South Africa, where most study subjects are not yet financially independent. Webtable 4Birthweight of the first offspring (g) for females in four study sites, according to indicators of maternal and child undernutrition: regression analyses. No information available for South Africa, where the number of births was very small. Webtable 5a-bBody mass index (kg/m^2^) for males in the five study sites, according to indicators of maternal and child undernutrition: regression analyses.Body mass index (kg/m^2^) for females in the five study sites, according to indicators of maternal and child undernutrition: regression analyses. Webtable 6a-bGlucose (log~e~ mmol/L) for males in four study sites, according to indicators of maternal and child undernutrition: regression analyses. No data available from South Africa.Glucose (log~e~ mmol/L) for females in four study sites, according to indicators of maternal and child undernutrition: regression analyses. No data available from South Africa. Webtable 7a-bSystolic blood pressure (mm/Hg) for males in four study sites, according to indicators of maternal and child undernutrition: regression analyses.Systolic blood pressure (mm/Hg) for females in the five study sites, according to indicators of maternal and child undernutrition: regression analyses.
Acknowledgments
===============
Funding for the preparation of the Series was provided by the Bill & Melinda Gates Foundation. Meetings were hosted by the UNICEF Innocenti Research Centre and the Rockefeller Foundation Bellagio Conference Center. Analyses in this paper were made possible by a grant by the Wellcome Trust of the UK.The sponsors had no role in the analysis and interpretation of the evidence nor in writing the report and the decision to submit for publication. Jean-Pierre Habicht critically reviewed the manuscript. We thank the following colleagues from each site---Guatemala: Rafael Flores, Usha Ramakrishnan, Aryeh Stein, and Kathryn Yount of Emory University; Ruben Grajeda, Paul Melgar, Manuel Ramirez-Zea, Humberto Mendez, and Luis Fernando Ramirez of INCAP; Jere Behrman of the University of Pennsylvania; John Hoddinott, Agnes Quisumbing, and Alexis Murphy of IFPRI; and John Maluccio of Middlebury College. Cebu: Socorro A Gultiano, Josephine Avila, and Lorna Perez of Office of Population Studies Foundation, University of San Carlos, Cebu, Philippines; Christopher Kuzawa and Thomas W McDade, Northwestern University. Pelotas: Fernando Barros, Bernardo Horta, and Denise Gigante of the Universidade Federal de Pelotas, and Rosangela Lima of the Universidade Católica de Pelotas. India: Santosh K Bhargava of Sunder Lal Jain Hospital. The original cohort study was funded by the US National Center for Health Statistics and the Indian Council of Medical Research. Soweto: John Pettifor and Stella Fleetwood of the University of Witwatesrand. We thank Mario Azevedo (Universidade Federal de Pelotas) for preparation of tables, figures, and meta-analyses; and Shane Norris (University of Witwatersrand), Clive Osmond and Shirin Wadia (University of Southampton), Meng Wang (Emory University) for data analyses. Finally, we would like to acknowledge funding sources of each individual study: Wellcome Trust (Pelotas and Soweto), US National Institutes of Health and the US National Science Foundation (Guatemala), British Heart Foundation, the Medical Research Council UK, and the Indian Council of Medical Research (India), Human Sciences Research Council, South African Medical Research Council, the Mellon Foundation, the South-African Netherlands Programme on Alternative Development and the Anglo American Chairman\'s Fund (Soweto), Ford Foundation, USAID, The World Bank, Nestle Coordinating Center for Nutrition Research (Cebu).
CGV convened the working group, and conceptualised and coordinated the preparation of the paper. PCH led the analyses. Primary responsibility for specific topics were as follows: height and economic productivity (RM); education and mental health (LR); intergenerational effects, lipids, and immunity (CGV); body composition and blood pressure (LA); and diabetes, cardiovascular disease, cancer, and bone health (CF and HSS). All authors provided original data and contributed to the final paper.
Series steering committee---Robert E Black (Johns Hopkins Bloomberg School of Public Health, USA), Zulfiqar A Bhutta (Aga Khan University, Pakistan), Jennifer Bryce (Johns Hopkins Bloomberg School of Public Health, USA), Saul S Morris (London School of Hygiene and Tropical Medicine, UK), Cesar G Victora (Federal University of Pelotas, Brazil).
Other members---Linda Adair (University of North Carolina, USA), Tahmeed Ahmad (ICDDR,B, Bangladesh), Lindsay H Allen (USDA ARS Western Human Nutrition Research Center, USA), Laura E Caulfield (Johns Hopkins Bloomberg School of Public Health), Bruce Cogill (UNICEF, USA), Denise Coitinho (WHO, Switzerland), Simon Cousens (London School of Hygiene and Tropical Medicine, UK), Ian Darnton-Hill (UNICEF, USA), Mercedes de Onis (WHO, Switzerland); Kathryn Dewey (University of California, Davis, USA), Majid Ezzati (Harvard School of Public Health, USA), Caroline Fall (University of Southhampton, UK), Elsa Giugliani (Federal University of Rio Grande de Sul, Brazil), Batool A Haider (Aga Khan University, Pakistan), Pedro Hallal (Federal University of Pelotas, Brazil), Betty Kirkwood (London School of Hygiene and Tropical Medicine, UK), Reynaldo Martorell (Emory University, Rollins School of Public Health, USA), Colin Mathers (WHO, Switzerland), David Pelletier (Cornell University, USA), Per Pinstrup-Andersen (Cornell University, USA), Linda Richter (Human Sciences Research Council, South Africa), Juan A Rivera (Mexico National Institute of Public Health), Harshpal Singh Sachdev (Sitaram Bhartia Institute of Science and Research, India), Meera Shekar (World Bank, USA), Ricardo Uauy (Institute of Nutrition, Chile).
We declare that we have no conflict of interest.
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Basic characteristics of the five cohort studies included in the new analyses
**Design** **Year of cohort recruitment** **Age at recruitment** **Initial sample** **Age at last visit (years)** **Number examined in last visit** **Attrition rate** **Infant mortality (per 1000)** **Comments**
--------------------------- -------------------- -------------------------------- ------------------------ -------------------- ------------------------------- ----------------------------------- ---------------------------------------- -------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Brazil (Pelotas) Prospective cohort 1982 Birth 5914 21--23 4297 23%[\*](#tbl1fn1){ref-type="table-fn"} 36 All children born in the city\'s maternity hospitals (\>99% of all births) during 1982 were enrolled. All social classes included
Guatemala (four villages) Community trial 1969--77 Birth--7 years 2392 26--41 1571 23%[†](#tbl1fn2){ref-type="table-fn"} 75 Intervention trial with two communities receiving high-energy and protein supplement and two control villages. All children younger than 7 years in 1969 and all born during 1969--77 were enrolled and followed up until 7 years of age or until the study ended in 1977. Furthermore, data were obtained for mothers during pregnancy and breast-feeding periods
India (New Delhi) Prospective cohort 1969--72 Before pregnancy 8181 26--32 1583 68%[‡](#tbl1fn3){ref-type="table-fn"} 47 All married women living in a defined area of the city were recruited and followed up. Pregnancies were identified, and neonates were enrolled and followed up. Primarily middle-class sample
Philippines (Cebu) Prospective cohort 1983--84 Gestation 3080 21·4 2032 34% 51[§](#tbl1fn4){ref-type="table-fn"} Pregnant women living in 33 neighbourhoods selected by random; first data collection at 30 weeks\' gestation. All social classes included
South Africa (Soweto) Prospective cohort 1990 Gestation 3273 15 2100 22% 27 Pregnant women with a gestational age of 26--32 weeks living in a defined urban geographical area. Predominantly poor, black sample
Participants known to have died were regarded as having been traced; those who moved out of the study area were regarded as lost to follow-up.
Excludes participants who were no longer living in Guatemala and regards those known to have died as having been traced.
Includes participants known to have died and those migrated from the study area.
Infant mortality rate when survey was initiated, based on 1983 Demographic and Health Survey.
######
Exposure and outcome variables, by study site and sex
**Brazil (Pelotas)** **Guatemala (4 villages)** **India (New Delhi)** **Philippines (Cebu)** **South Africa (Soweto)**
--------------------------------------------------------------------- ---------------------- ---------------------------- ----------------------- ------------------------ ----------------------------------------- ----------------------------------------- -------------------- -------------------- -------------------- --------------------
**Exposure variables**
Maternal height (cm) 156·5 (6·2) 156·4 (5·9) 149·1 (5·3) 149·0 (5·2) N/A N/A 150·6 (5·0) 150·5 (5·0) 158·7 (11·2) 158·5 (6·6)
Birthweight (kg) 3·25(0·57) 3·13(0·55) 3·10(0·51) 3·00(0·50) 2·89(0·44) 2·79(0·38) 3·03(0·43) 2·98(0·41) 3·13(0·51) 3·04(0·50)
Birthweight (\<2500 g) 8·0% (7·0--9·0) 10·1% (9·0--11·2) 8·8% (6·4--11·2) 10·6% (7·8--13·4) 16·6% (14·0--19·2) 19·9% (16·7--23·3) 10·8% (7·4--10·9) 9·2% (8·8--12·8) 9·1% (7·5--10·7) 11·4% (9·6--13·2)
IUGR (%) 15·3% (13·9--16·7) 14·4% (13·0--15·8) 34·0% (29·4--38·6) 27·9% (23·2--32·6) 39·8% (36·2--43·4) 40·0% (35·7--44·3) 22·3% (20·2--24·3) 20·1% (18·0--22·2) 15·1% (13·1--17·1) 12·7% (10·9--14·5)
Weight-for-age[\*](#tbl2fn1){ref-type="table-fn"} (*Z* scores) 0·05(1·13) 0·14(1·03) −1·73(0·98) −1·73(1·01) −1·48(1·07) −1·41(1·08) −1·68(0·96) −1·68(0·99) −0·54(1·32) −0·34(1·19)
Weight-for-age[\*](#tbl2fn1){ref-type="table-fn"} (\<−2 *Z* scores) 3·6% (2·9--4·3) 2·6% (2·0--3·2) 35·6% (31·4--39·8) 37·9% (33·3--42·5) 32·3% (29·1--35·5) 27·0% (23·4--30·6) 35·3% (32·4--38·2) 36·6% (33·5--39·8) 12·2% (9·5--14·9) 8·0% (5·9--10·2)
Height-for-age[\*](#tbl2fn1){ref-type="table-fn"} (*Z* scores) −0·78(1·28) −0·61(1·20) −3·26(1·10) −3·15(1·01) −1·97(1·18) −1·90(1·12) −2·59 (1·12) −2·50 (1·10) −1·43 (1·31) −1·16 (1·19)
Height-for-age[\*](#tbl2fn1){ref-type="table-fn"} (\<−2*Z* scores) 16·3% (14·9--17·7) 11·6% (10·3--12·9) 87·4% (84·4--90·4) 86·3% (83·0--89·6) 49·4% (46·0--52·8) 43·4% (39·4--47·4) 69·0% (66·2--68·9) 65·6% (62·5--68·9) 29·9% (26·1--33·7) 22·9% (19·5--26·3)
**Outcomes (adolescents and adults)**
Height (cm) 173·7 (6·9) 160·7 (6·2) 162·8 (6·1) 150·7 (5·6) 169·7 (6·3) 154·9 (5·7) 163·1 (5·9) 151·2 (5·5) 166·3 (8·1) 158·7 (6·2)
Attained schooling (years) 9·0 (3·2) 9·8 (3·1) 5·4 (3·5) 4·5 (3·2) 13·1 (3·4) 13·9 (3·1) 9·9 (3·4) 11·2 (2·8) 9·6 (3·7) 10·1 (0·9)
Monthly income (log US\$)[†](#tbl2fn2){ref-type="table-fn"} 5·1 (0·7) 4·8 (0·7) 5·3 (0·9) 3·7 (1·8) 17·2%[‡](#tbl2fn3){ref-type="table-fn"} 18·7%[‡](#tbl2fn3){ref-type="table-fn"} N/A N/A N/A N/A
Offspring birthweight (kg) 3·16(0·63) 3·09(0·56) 2·94(0·45) 2·93(0·45) 2·82(0·50) 2·85(0·55) N/A 2·95(0·52) N/A N/A
BMI (kg/m^2^) 23·8 (4·1) 23·5 (4·6) 24·7 (3·6) 26·9 (4·8) 24·9 (4·3) 24·6 (5·1) 21·0 (3·1) 20·2 (3·1) 19·7 (3·4) 22·1 (4·4)
BMI (≥25 kg/m^2^) 30·6% (28·7--32·5) 27·0% (25·1--28·9) 41·1% (37·2--45·0) 62·3% (58·7--65·9) 47·0% (43·7--50·3) 45·4% (41·6--49·3) 7·5% (5·9--9·1) 9·7% (8·0--11·5) 12·8% (10·4--15·2) 29·5% (26·4--32·6)
BMI (≥30 kg/m^2^) 7·5% (6·4--8·6) 9·1% (7·9--10·3) 8·9% (6·7--11·1) 23·9% (20·7--27·1) 9·5% (7·6--11·4) 13·1% (10·5--15·8) 1·1% (0·4--1·7) 2·0% (1·2--2·9) 3·6% (2·3--4·9) 9·1% (7·1--11·1)
Plasma glucose (mmol/L)[§](#tbl2fn4){ref-type="table-fn"} 5·54(0·83) 5·27(0·79) 5·17 (0·73) 5·27 (1·59) 5·37 (1·21) 5·29(1·18) 5·66(0·52) 5·52 (0·51) N/A N/A
Systolic blood pressure (mm Hg) 123·5 (14·4) 111·3 (13·0) 116·8 (11·4) 108·5 (13·0) 118·3 (11·3) 106·7 (11·0) 111·8 (10·8) 99·3 (9·9) 113·4 (25·3) 108·8 (19·7)
Number of participants[¶](#tbl2fn5){ref-type="table-fn"} 445--3035 843--2873 348--921 356--878 719--876 513--626 912--1079 762--953 558--1184 577--1251
Data are mean (SD) or prevalence (95% CI).
IUGR=intrauterine growth restriction. BMI=body-mass index. N/A=not available.
At roughly 2 years of age.
Geometric mean and SD.
Percentage in the highest quintile of income based on assets score for the Delhi cohort.
Geometric mean and SD of fasting glucose, except for Brazil where a non-fasting sample was obtained.
Smallest and largest number of participants with available data for the variables under study. For the Delhi cohort, these sample sizes refer to participants for whom complete information is available about occupation of father when the participant was a child, and adult age and BMI. First offspring birthweight is excluded from these values; the sample sizes for this variable are 231 for men and 295 for women.
######
Summary of the pooled adjusted results from the five cohort studies: height, schooling, income/assets, offspring birthweight, body-mass index, blood pressure, and glucose concentration[¶](#tbl3fn5){ref-type="table-fn"}
**Males** **Females** **Both sexes**
--------------------------------------------------------------------------------- --------------------------- ------------- --------------------------- ---------- -------- ----------
**Height (cm)**
Maternal height[†](#tbl3fn2){ref-type="table-fn"} (cm) 0·47 (0·16 to 0·59) \<0·0001 0·51 (0·46 to 0·54) \<0·0001 0·50 \<0·0001
Birthweight (kg) 3·25 (2·72 to 4·19) \<0·0001 3·25 (3·06 to 3·64) \<0·0001 3·25 \<0·0001
IUGR (yes/no) −2·17 (−3·32 to −1·44) \<0·0001 −2·32 (−2·60 to −1·78) \<0·0001 −2·24 \<0·0001
WAZ at 2 years (*Z* score) 2·75 (1·83 to 2·86) \<0·0001 2·63 (1·73 to 2·81) \<0·0001 2·69 \<0·0001
HAZ at 2 years (*Z* score) 3·26 (3·13 to 3·31) \<0·0001 3·22 (2·92 to 3·50) \<0·0001 3·24 \<0·0001
**Schooling (years)**
BAZ at 2 years (*Z* score) 0·20 (−1·39 to 0·51) 0·03 0·17 (−0·39 to 0·40) 0·08 0·18 0·06
Maternal height[†](#tbl3fn2){ref-type="table-fn"} (cm) 0·02 (0·00 to 0·07) 0·04 0·02 (0·01 to 0·06) \<0·0001 0·02 \<0·0001
Birthweight (kg) 0·39 (0·16 to 0·48) \<0·0001 0·25 (−0·06 to 0·68) \<0·0001 0·30 \<0·0001
IUGR (yes/no) −0·18 (−0·39 to 0·16) 0·10 −0·25 (−0·52 to 0·28) 0·003 −0·23 0·001
WAZ at 2 years (*Z* score) 0·51 (0·21 to 0·59) \<0·0001 0·52 (−0·02 to 0·57) \<0·0001 0·52 \<0·0001
HAZ at 2 years (*Z* score) 0·48 (0·32 to 0·51) \<0·0001 0·53 (0·03 to 0·56) \<0·0001 0·50 \<0·0001
BAZ at 2 years (*Z* score) 0·09 (−0·57 to 0·37) 0·51 0·16 (−0·03 to 0·33) \<0·0001 0·16 0·02
**Birthweight of the first offspring**[‡](#tbl3fn3){ref-type="table-fn"}**(g)**
Maternal height[†](#tbl3fn2){ref-type="table-fn"} (cm) 7·0 (2·5 to 11·9) 0·02
Birthweight (kg) 208·0 (190 to 294) \<0·0001
IUGR (yes/no) −126·7(−174 to −44) 0·002
WAZ at 2 years (*Z* score) 74·7 (31 to 94) \<0·0001
HAZ at 2 years (*Z* score) 78·5 (43 to 98) \<0·0001
BAZ at 2 years (*Z* score) 14·5 (−2 to 39) 0·37
**Body-mass index (kg/m^2^)**
Maternal height[†](#tbl3fn2){ref-type="table-fn"} (cm) 0·01 (−0·01 to 0·05) 0·15 0·01 (0·00 to 0·02) 0·39 0·01 0·09
Birthweight (kg) 0·71 (0·01 to 1·02) \<0·0001 1·13 (0·91 to 2·21) \<0·0001 0·87 \<0·0001
IUGR (yes/no) −0·50 (−0·82 to 0·03) \<0·0001 −0·76 (−1·42 to −0·38) \<0·0001 −0·60 \<0·0001
WAZ at 2 years (*Z* score) 0·90 (0·39 to 1·26) \<0·0001 0·95 (0·66 to 1·35) \<0·0001 0·92 \<0·0001
HAZ at 2 years (*Z* score) 0·42 (0·06 to 0·63) \<0·0001 0·38 (0·13 to 0·84) \<0·0001 0·40 \<0·0001
BAZ at 2 years (*Z* score) 0·74 (0·33 to 1·13) \<0·0001 0·93 (0·68 to 1·14) \<0·0001 0·81 \<0·0001
**Glucose concentration**[‡](#tbl3fn3){ref-type="table-fn"}**(log/mmol/L)**
Maternal height[†](#tbl3fn2){ref-type="table-fn"} (cm) 0·067 (0·033 to 0·182) 0·11 −0·011 (−0·113 to 0·082) 0·81 0·031 0·31
Adjusted maternal height[§](#tbl3fn4){ref-type="table-fn"} (cm) 0·034 (−0·019 to 0·184) 0·45 0·005 (−0·109 to 0·104) 0·92 0·020 0·56
Birthweight (kg) −0·001 (−0·018 to 0·004) 0·84 −0·009 (−0·012 to −0·005) 0·08 −0·004 0·18
Adjusted birthweight[§](#tbl3fn4){ref-type="table-fn"} (kg) −0·005 (−0·028 to−0·002) 0·28 −0·013 (−0·024 to −0·010) 0·01 −0·009 0·01
IUGR (yes/no) −0·006 (−0·016 to −0·003) 0·30 −0·005 (−0·028 to 0·006) 0·36 −0·005 0·17
Adjusted IUGR[§](#tbl3fn4){ref-type="table-fn"} (yes/no) −0·004 (−0·020 to 0·000) 0·43 −0·003 (−0·020 to 0·014) 0·65 −0·004 0·38
WAZ at 2 years (*Z* score) 0·001 (−0·007 to 0·014) 0·65 −0·002 (−0·011 to 0·000) 0·38 0·000 0·79
Adjusted WAZ at 2 years[§](#tbl3fn4){ref-type="table-fn"} (*Z* score) −0·005(−0·010 to 0·006) 0·05 −0·005 (−0·019 to−0·002) 0·05 −0·005 0·005
HAZ at 2 years (*Z* score) 0·003 (−0·004 to 0·015) 0·15 −0·002 (−0·010 to 0·005) 0·26 0·000 0·76
Adjusted HAZ at 2 years[§](#tbl3fn4){ref-type="table-fn"} (*Z* score) −0·002 (−0·008 to 0·010) 0·50 −0·004 (−0·016 to −0·002) 0·13 −0·003 0·13
BAZ at 2 years (*Z* score) −0·001 (−0·003 to 0·005) 0·69 0·000 (−0·013 to 0·003) 0·92 −0·001 0·72
Adjusted BAZ at 2 years[§](#tbl3fn4){ref-type="table-fn"} (*Z* score) −0·003 (−0·006 to 0·005) 0·16 −0·004 (−0·018 to −0·001) 0·09 −0·004 0·03
**Systolic blood pressure (mm Hg)**
Maternal height[†](#tbl3fn2){ref-type="table-fn"} (cm) 0·10 (0·04 to 0·19) 0·03 0·06 (0·02 to 0·24) 0·10 0·08 0·07
Adjusted maternal height[§](#tbl3fn4){ref-type="table-fn"} (cm) −0·01 (−0·10 to 0·04) 0·85 −0·04 (−0·09 to 0·10) 0·38 −0·02 0·45
Birthweight (kg) −0·54 (−0·86 to 1·24) 0·18 0·11 (−0·51 to 3·16) 0·79 −0·22 0·43
Adjusted birthweight[§](#tbl3fn4){ref-type="table-fn"} (kg) −2·04 (−3·81 to −0·28) \<0·0001 −1·46 (−1·82 to 0·03) \<0·0001 −1·76 \<0·0001
IUGR (yes/no) −0·26 (−1·76 to 3·28) 0·58 −0·03 (−1·40 to 1·17) 0·95 −0·16 0·65
Adjusted IUGR[§](#tbl3fn4){ref-type="table-fn"} (yes/no) 0·68 (−0·57 to 6·77) 0·13 0·93 (−0·87 to 1·78) 0·05 0·79 0·02
WAZ at 2 years (*Z* score) 0·98 (0·55 to 1·86) \<0·0001 0·68 (−0·07 to 1·70) \<0·0001 0·83 \<0·0001
Adjusted WAZ at 2 years[§](#tbl3fn4){ref-type="table-fn"} (*Z* score) −0·72 (−1·10 to −0·30) 0·001 −0·45 (−0·92 to 0·72) 0·039 −0·59 \<0·0001
HAZ at 2 years (*Z* score) 0·96 (0·62 to 2·93) \<0·0001 0·61 (−0·17 to 2·09) 0·001 0·79 \<0·0001
Adjusted HAZ at 2 years[§](#tbl3fn4){ref-type="table-fn"} (*Z* score) −0·08 (−0·96 to 0·53) 0·68 −0·02 (−1·67 to 2·67) 0·92 −0·05 0·71
BAZ at 2 years (*Z* score) 0·27 (−1·02 to 0·98) 0·16 0·30 (−0·02 to 0·65) 0·13 0·29 0·04
Adjusted BAZ at 2 years[§](#tbl3fn4){ref-type="table-fn"} (*Z* score) −0·76 (−1·26 to −0·22) \<0·0001 −0·48 (−1·19 to 0·11) 0·01 −0·63 \<0·0001
WAZ=weight-for-age *Z* score. HAZ=height-for-age *Z* score. BAZ=body-mass-index-for-age *Z* score. IUGR=intrauterine growth restriction.
Data are adjusted coefficients from linear regression analyses, using all exposures as continuous variables, except IUGR, which was included in the model as a dummy variable (0=no; 1=yes).
Information about maternal height not available for India.
Glucose and offspring birthweight not available for South Africa.
Additional adjustment for adult BMI and height.
Adjusted for individual\'s age when the outcome variables were measured, years of schooling completed by the mother (in India, by the father), and a measure of early childhood socioeconomic status.
######
Summary of the evidence, particularly from low-income and middle-income settings, on the associations between maternal and child undernutrition and adult exposures
**Maternal size and nutrition** **Size of newborn baby** **Infant and child size and growth**
---------------------------------------------------- ---------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
**Height**
Published work Insufficient evidence Strong, positive Strong, positive
New analysis Consistent association with maternal height Positive association with birthweight and negative association with IUGR Strong associations with height for age and weight-for-age; no association with BMI-for-age
**Achieved schooling and educational performance**
Published work Insufficient evidence Weak, positive Strong, positive
New analysis Weak positive association with maternal height Strong positive association with birthweight; negative association with IUGR Strong positive association with height and weight-for-age; weak association with BMI-for-age
**Income and wealth**
Published work Insufficient evidence Indirect evidence, mediated through schooling and adult size Indirect evidence, mediated through schooling and adult size
New analysis No association with maternal height Positive association with birthweight; negative association with IUGR in two of three countries. Positive association with height and weight-for-age; no association with BMI-for-age
**Bodysize of offspring**
Published work Insufficient evidence Strong, positive Strong, positive
New analysis Weak direct association between maternal height and birthweight of their grandchildren Strong positive association of maternal and offspring birthweight; inverse association between maternal IUGR and offspring birthweight Positive associations between weight and height-for-age---but not BMI-for-age---with birthweight of the offspring
**BMI, body composition, and obesity**
Published work Insufficient evidence Strong, positive with lean body mass; no clear association with fat mass Positive association between large infant size and both lean and fat mass
New analysis No association with maternal height Strong positive association with birthweight and negative association with IUGR Strong positive association with BMI-for-age and weight-for-age; weak positive association with height-for-age
**Insulin resistance and type 2 diabetes**
Published work Inconsistent Weak, inverse (low birthweight associated with higher risk)[\*](#tbl4fn1){ref-type="table-fn"} Strong evidence that rapid weight gain increases risk of diabetes
New analysis No association with maternal height No association with birthweight except when adult BMI was adjusted for, when an inverse association became apparent No association with height-for-age. Negative associations with weight and BMI-for-age after adjustment for adult BMI and height
**Blood pressure**
Published work Weak, inconsistent Moderate, negative Strong positive, synergistic with small newborn size
New analysis No association No consistent association with birthweight except when adult BMI was adjusted for, when an inverse association became apparent Positive association with weight and height-for-age, and to a lesser extent with BMI-for-age. Associations tended to become negative after adjustment for adult BMI and height
**Cardiovascular disease**
Published work Insufficient evidence Little evidence of a negative association after adjustment for adult size[†](#tbl4fn2){ref-type="table-fn"} Evidence for an association between small size---especially when followed by rapid weight gain---and cardiovascular disease, but no studies from low-income and middle-income countries
**Lung function**
Published work Insufficient evidence Strong, positive Insufficient evidence
**Immune function**
Published work Inconsistent Inconsistent Insufficient evidence
**Blood lipids**
Published work Insufficient evidence Evidence of no association Inconsistent
**Cancers**
Published work Insufficient evidence Studies from high-income countries show evidence of a positive association for some cancers, confirmed in one of only two studies identified from low-income and middle-income countries Inconsistent
**Bone mass, fracture risk, and osteoporosis**
Published work Insufficient evidence Insufficient evidence[‡](#tbl4fn3){ref-type="table-fn"} Insufficient evidence
**Mental illness**
Published work Little evidence between intrauterine exposure to famine and schizophrenia Little evidence of inverse association between birthweight, depression, and suicide Insufficient evidence
BMI=body-mass index. IUGR=intrauterine growth restriction.
In most studies from high-income countries, inverse associations are reported.
Not true for studies from high-income settings, where inverse associations are noted (no adjustment for adult size).
Studies from high-income countries show consistent associations between birthweight and adult bone mass.
###### Exposure variables and adult outcomes that were assessed
**Exposure variables**
•Maternal height (cm): measured by the study teams during pregnancy or soon after delivery. No data were available for India•Birthweight (kg): measured by the research teams except in South Africa where they were obtained from reliable birth records.[@bib13] In Cebu (the Philippines), data for birthweight include interviewer-measured data (60%) and hospital records•Intrauterine growth restriction: gestational age was calculated from the date of the last menstrual period except in Cebu, in which the Ballard scores[@bib14] were used for all infants with low birthweight or whose mothers had pregnancy complications. Intrauterine growth restriction was defined as a birthweight for gestational age below the tenth percentile of the sex-specific Williams reference curves[@bib15]•Height-for-age or length-for-age (*Z* scores): children were measured by the research teams at around 2 years of age, and their height (in South Africa) or recumbent length (other sites) were converted into *Z* scores with the WHO Growth Standards.[@bib16] Stunting was defined as being less than the *Z* score cutoff of −2•Weight-for-age and body-mass-index-for-age (*Z* scores): defined as above. Underweight and wasting were defined by the *Z* score cutoff of −2
**Adult and adolescent outcomes**
•Height (cm): measured by the study teams•Achieved schooling/education (years): number of years completed with approval•Income or assets: personal income was measured in local currency in Brazil and Guatemala and expressed in US dollars. Individuals with no income---mostly young adults living with their families or housewives (36% in Brazil and 13% in Guatemala)---were excluded from the analyses. Data from the Philippines and Soweto (South Africa) were not included because few adolescents had independent incomes. In India, household assets were recorded•Offspring birthweight (g): In Brazil and India, data were obtained from birth records or if unavailable by maternal recall; measured by the research team in Guatemala; and by maternal recall in the Philippines•Body-mass index (kg/m^2^): measured by the study teams•Blood glucose concentration (mmol/L): fasting glucose concentrations were measured in Guatemala and the Philippines. In Brazil, only non-fasting concentrations were available. In India, fasting concentrations and 120-min results from glucose tolerance tests were obtained. This information is not yet available for South Africa. To correct for the skewed distribution in some sites, we used a natural logarithmic transformation•Systolic blood pressure (mm Hg): measured by the research team in all sites. In Brazil, South Africa, and India, we used the average of two values taken on the same day. In the Philippines and Guatemala, three measures were averaged
###### What this paper does not cover
This paper addresses maternal and child undernutrition through the use of anthropometric indicators. There are other dimensions of undernutrition that are equally important. These include micronutrient deficiencies---eg, iodine, iron, vitamin A, and calcium---which might lead to long-term consequences. An earlier *Lancet* Series addressed the long-term consequences of iodine and zinc deficiency on intellectual development,[@bib156] and these deficiencies were incorporated in the estimates of burden of diseases included in the first paper in this Series.[@bib1]
Breastfeeding can also have long-term health consequences. A recent series of systematic reviews addressed its association with body-mass index, blood pressure, diabetes and related indicators, blood lipids, and schooling.[@bib86]
Two important studies on the effects of short exposures to malnutrition during famines in Europe---the Dutch famine[@bib157; @bib158] and Leningrad siege studies---were cited only when evidence from low-income and middle-income countries was very scarce. Although these investigations provide unique information about crucial periods when undernutrition is likely to have lasting effects, they were deemed not to be representative of the situation in such countries when undernutrition acts throughout longer time periods including pregnancy, infancy, and childhood.
###### Areas for future research
•Association between rapid weight and length gain at different age intervals in infancy and childhood with human capital and outcomes related to chronic disease, to define the age after which rapid growth should be avoided•Long-term effects of weight gain in late childhood stratified in previously stunted and non-stunted children, and for children with and without intrauterine growth restriction•Long-term effects of micronutrient deficiencies in childhood•Association between undernutrition and long-term changes in immune function, blood lipids, osteoporosis, and mental illness•Improved quantification of the economic effect of undernutrition on adult productivity•Interactions between genes and environmental factors in long-term outcomes
[^1]: Members listed at end of paper
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Shaquille O'Neal put his poker face to the test in a new promotional video for Omaze.
The NBA Hall of Famer has teamed up with the online fundraising platform to give fans the chance to win a trip to Las Vegas to watch him DJ and even play a few hands of poker. Proceeds from the campaign will support the Sager Strong Foundation, which funds research and clinical trials for leukemia and other blood cancers.
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Scott wins Australian PGA after storm delay
GOLD COAST, Australia — Adam Scott shot a 4-under 67 to win the storm-delayed Australian PGA by four strokes on Sunday.
Scott and playing partner Rickie Fowler marked their balls on the 12th fairway after a severe storm warning suspended play with Scott holding a one-shot lead.
When Scott returned, his iron shot from the fairway nearly holed out for an albatross and he made the 1-foot eagle putt.
Scott was 4 under in his seven holes after the weather suspension. Fowler finished second with a 68.
Making his first appearance back in Australia since his April win at The Masters, Scott finished with a 14-under 270 at Royal Pines.
Scott joins Greg Norman, Craig Parry, Peter Lonard, Robert Allenby and Peter Senior as the only Australian golfers to add the Joe Kirkwood Cup for winning the Australian PGA to the Australian Open and Australian Masters titles in their careers. Those three tournaments are considered the Australian majors.
Scott's shot on the 12th came on a 4-iron from 266 yards.
"I came out and knew I had to do something great to win this," Scott said. "It's been an incredible year since April, and so great to come home. I've had a great week."
Fowler said the storm suspension hurt him.
"I had some good momentum going up until we had the rain delay," Fowler said. "I got to within one and then he came out swinging.
"He made some great swings coming down that last stretch. So it's a little tough to catch a guy when he's making an eagle and a couple of birdies."
Scott moves on to Royal Melbourne next week to defend his Australian Masters title. Then he will play with Jason Day on the Australian team at the World Cup, also at Royal Melbourne, then will play at the Australian Open at Royal Sydney a week later.
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Skin graft meshing, over-meshing and cross-meshing.
Split skin grafts (SSGs) are often meshed to increase their size and allow exudate to escape. We investigated the expansion obtained with meshing, and the possibility of re-meshing skin that has already been meshed ("overmeshing"). Both useful and inadvisable permutations are illustrated. Thin porcine SSGs were sideways meshed, or meshed with ratios of 1.5:1 and 3:1. Subsequently samples were over-meshed in a variety of ratios and directions. All grafts were maximally expanded and their areas calculated. Meshed skin did not expand as much as suggested by the ratios displayed on dermacarriers. A 1:1.5 dermacarrier produced an area expansion of 1.36×, and a 1:3 meshing apparatus produced only a 1.80×area expansion. Several combinations of twice-meshed SSGs maintained integrity as long as over-meshing was done in the axis of initial meshing. Up to 2.3×expansion was obtained, by following a 1:1.5 mesh with a 1:3 mesh. We term this procedure as "overmeshing". Re-meshing in a direction orthogonal to initial meshing (cross meshing) cut the skin into small pieces. Over-meshing a SSG can allow considerable further expansion, facilitating overgrafting of donor sites or simply increasing the area that can be covered with the existing harvested skin.
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Sign up to get our new weekly column as a newsletter. We're looking back at the strongest, smartest opinion takes of the week from CNN and other outlets.
That was the advice of CNN legal analystafter Robert Mueller delivered his report examining Russian interference in the 2016 election to Attorney General William Barr on Friday. "A major milestone," wrote Honig. "But it is the calm; the storm lies ahead." Get ready, he warned, for a "multifront legal and political battle that will test fundamental notions of due process, executive authority and separation of powers."
Former FBI Directoroutlined Thursday in an op-ed for The New York Times what he hopes to see in the report: "a demonstration to the world -- and maybe most of all to our president and his enablers -- that the United States has a justice system that works."
As the nation waited to find out what's actually in the document, issued a reminder of the "damage that the investigation has already inflicted" -- including five high-level officials and Trump associates who have been "convicted or pleaded guilty, most of them after lying about their interaction with Russians."
The Conways aren't exactly "Love's Labour's Lost," but...
Bill Carter said the ongoing marital saga managed to be resonant of "King Lear" and yet George Conway has been attacking Donald Trump on Twitter for months. He took aim again this week, this time at the President's mental state, and Conway's wife (and Trump's adviser) Kellyanne, decided to take sides -- and not with the guy with whom she shares a last name.said the ongoing marital saga managed to be resonant of "King Lear" and yet too obvious a comedy for the professionals: "If some writer at 'SNL' doesn't come up with a sketch that shows the Conways' conversations over things like kids' playdates and family vacation plans devolving into the pattern we often see in Kellyanne's arguments with (CNN's Chris) Cuomo, it will only be because the idea may be too obvious to be funny."
Why can't Donald Trump let John McCain rest in peace?
Julia Reinstein: "Trump got dunked on by the National Cathedral. Yes, the National Cathedral." Trump himself took trolling up a notch by mixing it up with a dead man ... and a cathedral. After years of feuding with Sen. John McCain -- who died last August -- Trump mystifyingly revived the rancor on Twitter, and complained during a speech Wednesday: "I gave him the kind of funeral that he wanted, which as President I had to approve. I don't care about this. I didn't get thank you." In response, the National Cathedral in Washington -- site of McCain's services -- clapped back in a statement that produced a slew of incredulous headlines, like this one from Buzzfeed's: "Trump got dunked on by the National Cathedral. Yes, the National Cathedral."
Richard Cherwitz wrote that such messages are John Kirby The senator's widow, Cindy McCain, tweeted a photo of a horrific message sent to her by a stranger in the wake of Trump's tweets. Communications professorwrote that such messages are an ominous partial index of the toll Trump's discourse has taken. Retired Navy Rear Adm. addressed Trump himself: "With all due respect, sir, you need to stop railing against John McCain. It's beneath the office to which the American people elected you. And, quite frankly, it's beneath every measure of common decency."
Michael D'Antonio something "is terribly wrong" with Trump. His chief of staff, Mick Mulvaney, felt compelled to deny on television that his boss is a white supremacist, D'Antonio noted. Trump has become "a President whose behavior is so troll-like that Americans have come to expect him to act more like an out-of-control Reddit commenter than a chief executive of the United States." suggested something "is terribly wrong" with Trump. His chief of staff, Mick Mulvaney, felt compelled to deny on television that his boss is a white supremacist, D'Antonio noted. Trump has become "a President whose behavior is so troll-like that Americans have come to expect him to act more like an out-of-control Reddit commenter than a chief executive of the United States."
The March Madness of Me, Me, Me
Victor Davis Hanson. He offered 10 reasons they like him anyway -- among them, he wrote, Trump's transformative leadership amid record low rates of peacetime unemployment. Few would accuse Donald Trump of modesty. But progressives are way off base if they think his supporters care about that, wrote. He offered 10 reasons they like him anyway -- among them, he wrote, Trump's transformative leadership amid record low rates of peacetime unemployment.
Kara Alaimo observed that he had a point, but Rep. Devin Nunes (R-CA) filed a defamation suit against Twitter this week for, among other things, allowing users to post insulting tweets about him.observed that he had a point, but was missing a bigger one . "Nunes is right that online abuse is a big problem. But rather than seeking millions of dollars for himself, he should use his power as a member of Congress to pursue laws that compel social platforms and law enforcement bodies to take action to help all victims of online hate -- most of whom are much more vulnerable than he is."
More Democrats on the merry-go-round
The week brought a flurry of activity in the emerging battle royale for the 2020 Democratic nomination. After months of campaigning, Sen. Kirsten Gillibrand officially declared her candidacy, South Bend, Ind. Mayor Pete Buttigieg emerged as a dark horse sweetheart and Beto O'Rourke showed he could run with the big dogs (i.e., Bernie Sanders) when it comes to fundraising.
Paul Waldman in The Washington Post, as they "have fundamentally different ideas about how Democrats can win elections:" Biden wants to persuade GOP-leaning voters; Abrams' wants to mobilize Democratic-leaning voters. The big buzz, however, hovered around Joe Biden, and the rumors that he would soon announce his candidacy AND a running mate: possibly former Georgia gubernatorial candidate and political dynamo Stacey Abrams. Biden and Abrams would be an "odd pairing," reflectedin The Washington Post, as they "have fundamentally different ideas about how Democrats can win elections:" Biden wants to persuade GOP-leaning voters; Abrams' wants to mobilize Democratic-leaning voters.
Jill Filipovic of Warren's performance at a CNN town hall Monday night. She nailed it, wrote Filipovic. "The question now isn't her skill, style or substance." It's whether the media will give a "steady, competent woman her due." Meanwhile, Sen. Elizabeth Warren, "even though she's not getting the breathless headlines of the B-boys -- Beto O'Rourke, Bernie Sanders, Joe Biden and Pete Buttigieg," is "adeptly setting the bar for every other candidate in this race," assessed of Warren's performance at a CNN town hall Monday night. She nailed it, wrote Filipovic. "The question now isn't her skill, style or substance." It's whether the media will give a "steady, competent woman her due."
Jamelle Bouie in The New York Times. He agreed with novelist James Michener, who as an elector in 1968 called the Electoral College a "time bomb lodged near the heart of the nation." Warren made news Monday night when she suggested getting rid of the Electoral College. It's an idea worth considering, wrote in The New York Times. He agreed with novelist James Michener, who as an elector in 1968 called the Electoral College a "time bomb lodged near the heart of the nation."
Tom Wyler. "Don't kill the Electoral College. Just make it work better" -- by doing away with a winner-take-all approach in favor of allocating electoral votes on a proportional basis. Not so fast , said senior Obama administration official. "Don't kill the Electoral College. Just make it work better" -- by doing away with a winner-take-all approach in favor of allocating electoral votes on a proportional basis.
Another smart take:
Jen Psaki: What John Hickenlooper has to do to win --
Say their names
As New Zealand and the world continued to mourn the 50 victims of the recent mosque attacks, a new resolve took shape: focus on the fallen, not the gunman. "You will never hear me mention his name," vowed Prime Minister Jacinda Ardern.
Khaled Beydoun posted a widely shared Twitter thread featuring the lives and stories of the many individuals shot dead at prayer. He Law professorposted a widely shared Twitter thread featuring the lives and stories of the many individuals shot dead at prayer. He explained in an op-ed: "For far too long, American audiences have been largely unsympathetic to slain Muslims. ... Saying their names, and telling their stories as best I could ... immersing myself in learning about people, who were killed for adhering to my very faith, was an emotional journey like no other."
Igor Volsky and trauma surgeon (and gun violence survivor) Joseph Sakran were encouraged by Ardern's other words -- "our gun laws will change" -- Advocateand trauma surgeon (and gun violence survivor)were encouraged by Ardern's other words -- "our gun laws will change" -- which went beyond the typical American "thoughts and prayers." "Rather than stereotyping gun owners into good guys and bad guys," they wrote, the public health approach recognizes that firearms are dangerous and should be hard to get.
We asked how you feel about the college admissions scandal. Your stories were incredible
CNN Opinion asked readers to share their stories in the wake of the admissions scandal. From more than 400 responses, Jhodie-Ann Williams, Kirsi Goldynia and I curated a remarkable cohort of stories. Christian Badillo, a Stanford senior, who is the first person from his Chicago public high school to be admitted to the university, saw the alleged scheme as a "slap in the face to the American dream." High school senior Mick Hashimoto said of his peers -- many of whom are waiting this month to hear back from colleges -- "We are frustrated with what America has become."
And artist Aimee Manion wrote that college felt like a bait and switch; on the far side of it, "student loan debt shaped the course of my life." Read them all here
Another smart take:
John MacIntosh: The corrupting influence of college sports --
Health is the key to Africa's economic growth
Paul Kagame and billionaire philanthropist Bill Gates Rwandan Presidentand billionaire philanthropist sounded out the clear link for Africa's growing population between economic growth and greater investment in health care there: Every vaccination is "like a shot of adrenaline into the heart of the economy." In Rwanda, which has been working toward universal health care for its citizens since the mid-2000s, the country's GDP growth bears this connection out, they wrote.
More smart takes:
Nisha Jogia Soni: What raising a child with Down syndrome really means --
Dumbledore's love dares to speak its name -- and it's about time
J.K. Rowling set the global community of Harry Potter fans on red alert with a recent interview in which she described Albus Dumbledore's relationship with the dark wizard Gellert Grindelwald as "incredibly intense" and "passionate." Putting out an important gay romance like this one "as an afterthought ... feels like a cop-out," opined Holly Thomas. "How wonderful it would have been for millions of children to have known that Dumbledore was gay from the beginning of the series -- and to have grown up with that knowledge woven into the books."
"The books can't be rewritten" for a more socially aware time, she wrote . "The best hope ... might be for any current or future children's authors to include clear LGBTQ narratives as par for the course, and for those stories to become as beloved, and as influential, as 'Harry Potter.'"
Don't miss these
Nic Robertson: The UK might be hacking off its constitutional limbs --
Juliette Kayyem and Monica Medina: Why women should be required to register for the draft --and
Gavin Newsom: Why I put a freeze on the death penalty --
Kate Maltby: Saudi Arabia and Iran share a mutual disdain for women who speak up --
Carl Safina: A dead whale containing 90 pounds of plastic is message in a bottle --
Sign up to get this weekly column as a newsletter.
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Prognostic role of chemotherapy-induced nausea and vomiting in recurrent ovarian cancer patients: results of an individual participant data meta-analysis in 1213.
The aim of this study was to analyze the potential impact of chemotherapy-induced nausea and vomiting (CINV) on dose reductions, discontinuation of chemotherapy, and survival. This study was designed as individual participant data meta-analysis with the original study data of three phase II/III trials that were conducted by the North-Eastern German Society of Gynecological Oncology (NOGGO) including 1213 patients with recurrent ovarian cancer. Logistic and Cox regression analyses were used to estimate odds and hazard ratios after adjusting for age, ECOG, amount of delivered cycles, amount of recurrences, and amount of comedications and study. The majority of patients developed nausea (58.1%) and almost one third experienced vomiting (31.0%). CINV was not associated with FIGO stage, grading, histology, and number of recurrences. The necessity of dose reduction and discontinuation of chemotherapy did not correlate to nausea and vomiting (p = 0.88, p = 0.39 and p = 0.25, p = 0.54 respectively). Progression-free survival was shorter in patients with grade III/IV nausea and vomiting (p = 0.02; hazard ratio (HR) for grade III/IV nausea 1.58, 95% CI 1.14-2.20, and p = 0.02; HR for grade III/IV vomiting 1.67, 95% CI 1.15-2.42 respectively). CINV grade III/IV was also associated with poorer overall survival (p < 0.001; HR for grade III/IV nausea 2.35, 95% CI 1.64-3.37, and p < 0.001; HR for grade III/IV vomiting 1.67, 95% CI 1.15-2.42 respectively). CINV is significantly associated with poorer prognosis in recurrent ovarian cancer patients while there was no correlation found with the necessity of dose reduction and prior discontinuation of treatment. This study underlines the importance of prevention and treatment of CINV as part of early best supportive care.
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fifths of a litre?
3600
Convert 26834.08 days to seconds.
2318464512
How many millilitres are there in 11.9476 litres?
11947.6
What is seven quarters of a millennium in years?
1750
How many micrometers are there in 6/5 of a centimeter?
12000
How many months are there in 3/5 of a decade?
72
How many millilitres are there in 7/2 of a litre?
3500
What is 7/2 of a litre in millilitres?
3500
What is 6/5 of a decade in months?
144
What is three eighths of a kilometer in meters?
375
How many centuries are there in 44945.83 years?
449.4583
How many years are there in 16215.051 months?
1351.25425
Convert 2454.147 kilograms to grams.
2454147
How many kilometers are there in 74074.69um?
0.00007407469
How many litres are there in 989.4619 millilitres?
0.9894619
Convert 730.2185 meters to millimeters.
730218.5
What is 3/5 of a microgram in nanograms?
600
How many centimeters are there in 0.881188 millimeters?
0.0881188
What is 308.473 centimeters in nanometers?
3084730000
What is 182.34108 months in decades?
1.519509
Convert 41477.37 centuries to millennia.
4147.737
What is seven eighths of a milligram in micrograms?
875
Convert 24204.48 days to hours.
580907.52
How many grams are there in 999.5691ng?
0.0000009995691
Convert 61390.35kg to tonnes.
61.39035
How many kilograms are there in five eighths of a tonne?
625
What is 36.58453l in millilitres?
36584.53
What is twenty-one halves of a litre in millilitres?
10500
What is 31/2 of a millennium in centuries?
155
What is 670.0896l in millilitres?
670089.6
What is 3/25 of a millimeter in micrometers?
120
What is 207.0663t in micrograms?
207066300000000
How many minutes are there in 3/40 of a week?
756
How many millilitres are there in 12.03142 litres?
12031.42
Convert 113776.41 months to decades.
948.13675
What is 40.80484 grams in tonnes?
0.00004080484
How many months are there in 1/6 of a century?
200
What is 0.3175691 decades in millennia?
0.003175691
How many millilitres are there in 3/25 of a litre?
120
What is seventy-four fifths of a micrometer in nanometers?
14800
How many seconds are there in 64.24089us?
0.00006424089
How many years are there in twenty-five quarters of a millennium?
6250
What is 243678.7 litres in millilitres?
243678700
Convert 600677.28 hours to weeks.
3575.46
Convert 669672.3 millennia to months.
8036067600
What is 6846.872 millilitres in litres?
6.846872
How many months are there in 630.3736 decades?
75644.832
Convert 7783.394l to millilitres.
7783394
What is 7/3 of a hour in minutes?
140
Convert 81374.75t to grams.
81374750000
Convert 596411.676 minutes to weeks.
59.167825
Convert 33443.7 years to centuries.
334.437
Convert 513.9119 millennia to centuries.
5139.119
What is 27/4 of a milligram in micrograms?
6750
What is one tenth of a tonne in kilograms?
100
What is five quarters of a year in months?
15
Convert 9.043643ml to litres.
0.009043643
How many micrograms are there in 65365.95t?
65365950000000000
What is 4.743084 centuries in millennia?
0.4743084
What is 2257.853 decades in months?
270942.36
How many hours are there in 27/4 of a day?
162
What is 3/10 of a centimeter in millimeters?
3
What is 12/25 of a minute in milliseconds?
28800
Convert 0.7753335 hours to days.
0.0323055625
How many millilitres are there in seventeen halves of a litre?
8500
How many months are there in 21/2 of a decade?
1260
What is twenty-one quarters of a minute in seconds?
315
What is seven eighths of a centimeter in micrometers?
8750
What is 13/5 of a decade in months?
312
How many litres are there in 7363.906ml?
7.363906
What is 6/5 of a kilogram in grams?
1200
How many weeks are there in 202983.396 hours?
1208.2345
How many centimeters are there in nine tenths of a meter?
90
How many millilitres are there in one tenth of a litre?
100
What is 3684.015ml in litres?
3.684015
What is 0.712227 nanoseconds in microseconds?
0.000712227
How many micrograms are there in 7.366495 tonnes?
7366495000000
How many meters are there in three fifths of a kilometer?
600
What is one fifth of a milligram in micrograms?
200
Convert 9699.478 grams to tonnes.
0.009699478
What is seven quarters of a microgram in nanograms?
1750
What is 4/3 of a week in hours?
224
What is 0.1378182um in millimeters?
0.0001378182
Convert 548.0974 millilitres to litres.
0.5480974
How many decades are there in fifty-four fifths of a millennium?
1080
Convert 1347381.54ms to days.
0.01559469375
What is 3.674581 nanograms in kilograms?
0.000000000003674581
What is fifty-four fifths of a centimeter in millimeters?
108
Convert 85944.23 hours to minutes.
5156653.8
What is 3.341563 millennia in decades?
334.1563
How many seconds are there in two ninths of a day?
19200
Convert 47.22081mg to kilograms.
0.00004722081
How many nanograms are there in 3/8 of a microgram?
375
How many years are there in thirty-seven fifths of a decade?
74
What is 3/40 of a week in minutes?
756
How many microseconds are there in 11/4 of a millisecond?
2750
How many tonnes are there in 3741.237mg?
0.000003741237
How many micrometers are there in 0.3347707 millimeters?
334.7707
What is 789.5456 centuries in years?
78954.56
What is eleven halves of a milligram in micrograms?
5500
What is 67/4 of a litre in millilitres?
16750
How many millilitres are there in 3/40 of a litre?
75
What is 970985.4km in nanometers?
970985400000000000
What is thirty-four fifths of a litre in millilitres?
6800
How many millilitres are there in 1/10 of a litre?
100
What is 7/8 of a decade in months?
105
What is 941.465 days in minutes?
1355709.6
What is 18958.3065us in weeks?
0.00000003134640625
What is 5/6 of a millennium in months?
10000
What is 5/28 of a week in hours?
30
How many years are there in 0.4801578 decades?
4.801578
Convert 6912.899cm to kilometers.
0.06912899
What is four fifteenths of a century in months?
320
How many centimeters are there in 42/5 of a meter?
840
Convert 0.2348708 meters to micrometers.
234870.8
What is 3/8 of a millennium in years?
375
Convert 37849.8 kilometers to centimeters.
3784980000
How many meters are there in seventeen quarters of a kilometer?
4250
What is 1/4 of a microgram in nanograms?
250
What is 0.1004725 decades in years?
1.004725
What is 8069.796 micrograms in tonnes?
0.000000008069796
How many meters are there in fifty-one halves of a kilometer?
25500
How many micrometers are there in 5919.814m?
5919814000
How many nanograms are there in 89449.1 grams?
89449100000000
What is 4.646153 kilometers in meters?
4646.153
How many milligrams are there in fourty-three halves of a gram?
21500
Convert 43.33755 centuries to decades.
433.3755
How many years are there in thirty-one halves of a millennium?
15500
Convert 870.8913 tonnes to grams.
870891300
Convert 1757589.3 seconds to minutes.
29293.155
What is 4251.287 milliseconds in seconds?
4.251287
How many minutes are there in 17/6 of a hour?
170
How many centimeters are there in 415.2142 micrometers?
0.04152142
How many decades are there in 10.0372 centuries?
100.372
What is 67131.13 millimeters in meters?
67.13113
What is 57.68307 litres in millilitres?
57683.07
What is 68450.6ug in tonnes?
0.0000000684506
Convert 749.4478m to millimeters.
749447.8
What is 60345.87km in millimeters?
60345870000
Convert 0.1409845mm to kilometers.
0.0000001409845
Convert 253985.85 minutes to days.
176.3790625
How many decades are there in 30.77401 centuries?
307.7401
Convert 1952.002 decades to months.
234240.24
How many milligrams are there in 189.8284t?
189828400000
Convert 54.2873 grams to tonnes.
0.0000542873
How many nanometers are there in three eighths of a micrometer?
375
What is 1420.954 centuries in millennia?
142.0954
Convert 21882.58 kilometers to nanometers.
21882580000000000
How many years are there in seventeen quarters of a millennium?
4250
What is 23.432268 months in decades?
0.1952689
Convert 1914.217kg to grams.
1914217
What is 245.0819kg in micrograms?
245081900000
How many millilitres are there in 11/10 of a litre?
1100
What is 60.6998 nanograms in tonnes?
0.0000000000000606998
How many litres are there in 0.2700402ml?
0.0002700402
What is 118905.1 micrometers in centimeters?
11.89051
How many centimeters are there in 1/4 of a meter?
25
How many tonnes are there in 19.36297 grams?
0.00001936297
What
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Effect of tacrolimus on the excitatory synaptic transmission between the parallel fibers and pyramidal cells in the rat dorsal cochlear nucleus.
The immunosuppressive drug tacrolimus has several effects on the central nervous system. Besides its protective effect in hearing deficiencies, it is also considered to be able to cause tinnitus. In the present work, we attempted to describe its effects on a characteristic synapse of the auditory system that may be involved in the pathogenesis of tinnitus. Slices of the dorsal cochlear nucleus (200 microm thick) were prepared from 9- to 14-day-old Wistar rats. In response to stimulation targeting the superficial layer of the nucleus, we recorded excitatory postsynaptic currents (EPSCs) developing in the cell bodies of the pyramidal neurons using whole-cell voltage clamps. Inhibitory synaptic activity was inhibited by the application of bicuculline and strychnine. Short-term plasticity was investigated using high-frequency stimulation (50 Hz). Unambiguous identification of the investigated neurons was ensured by employing biocytin in the pipette solution, which allowed the confocal reconstruction of the cells after the functional measurements. A concentration of 1 micromol/L tacrolimus was applied extracellularly. Tacrolimus effectively and reversibly inhibited glutamatergic neurotransmission in the investigated synapse from -145 +/- 26 pA to -55 +/- 15 pA (n = 7; P = .00928). In contrast, EPSC amplitudes without failures were not significantly reduced (from -153 +/- 26 pA to -131 +/- 23 pA) in the presence of tacrolimus, but there were increased failure numbers of synaptic transmission. These data suggested that application of tacrolimus produced a combined pre- and postsynaptic inhibition. Tacrolimus affected short-term synaptic plasticity in the rat dorsal cochlear nucleus. It was also capable of inhibiting the glutamatergic neurotransmission. These effects suggested that tacrolimus may have neuroprotective effects in this structure.
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Outcomes of patients admitted to the intensive care unit with idiopathic pulmonary fibrosis.
To evaluate outcomes of patients admitted to an intensive care unit with idiopathic pulmonary fibrosis (IPF) and acute respiratory deterioration. Retrospective cohort study. University-affiliated, tertiary adult ICU. All patients admitted to the ICU between January 1996 and December 2006 with an established diagnosis of IPF were identified from review of case notes, ICU charts and electronic hospital records. Patient demographics, ICU investigation and treatment profiles were characterised; final follow-up was electronically from the State Registry. Primary study end-point was survival from ICU admission until December 2007; secondary end-points were survival from diagnosis and from first respiratory hospital admission. 24 patients were identified with IPF, diagnosed by lung biopsy (8) and by clinical criteria; 21 patients were admitted with acute respiratory failure, and three postoperatively. Mean age was 66 (SD, 16) years, mean APACHE III score was 82 (SD, 37), and 14 were men. Admission diagnoses were acute exacerbation of IPF (8), pneumonia (10), acute heart failure (3) and postoperative (3). All patients received broad-spectrum antibiotics, and 17 continued to receive corticosteroids prescribed previously. Nineteen patients were mechanically ventilated for a mean of 19.1 days (SD, 25.3); 13 of 19 patients had non-invasive ventilation before mechanical ventilation, and four received only non-invasive ventilation. Sixteen mechanically ventilated patients died in the ICU, another six died in hospital (2-30 days after ICU discharge); and two were discharged home. Median survival (95% CI) was 16 (9-19) days from ICU admission; 55 (18-284) days from first respiratory admission; and 1.05 (0.34-1.75) years from IPF diagnosis. Outcomes of patients with IPF admitted to the ICU are poor. Indications for mechanical ventilation appear uncertain.
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Let’s be honest: dating is one of life’s most difficult adventures. Sure, it can be a lot of fun, but it’s also often fraught with anxiety, insecurity, and doubt. Despite all its uncertainties, the pleasures and rewards of dating are more than worth it. Dating, like any other social situation, can be extra stressful for people with ADD or ADHD. For any of you single readers out there, here are a few tips for dating with ADD/ADHD.
Choose The Right Activities
When planning your date, suggest the types of activities in which you flourish. Avoid theater performances or poetry readings if you know those types of static activities are likely to make your mind wander. Instead, suggest a physical activity like a hike or a tennis game. These active date ideas will boost your energy and improve your focus. Plus, suggesting a unique activity is a great way of expressing your personality to your date.
Educate Your Date
Chances are your date may not be familiar with the signs and symptoms of ADD/ADHD. Without overwhelming them with too much info right out of the gate, find small opportunities to educate them. Understanding is key to acceptance, so give your date a head start by helping them see the world through your eyes.
Take It Slow
People with ADD/ADHD can be prone to impulsiveness. In romantic situations, that impulsiveness often leads to relationships that move a little too quickly. Moving too fast is a well-known dating red-flag, so make extra effort to take it slow. Ask yourself if you’re truly ready to make the next step in your relationship before diving in without thinking.
Dating is a highly personal experience and there is no one-size-fits-all solution for everyone. Working with a coach can help you figure out the exact strategies and tools which will improve your individual dating life. Working with an objective third-party offers the exact amount of tailored support you need to make your next relationship last a lifetime.
Whether you’re looking for long-term romance or for the fun of a fling, these tips for dating with ADD/ADHD will help you find the relationship you’ve been looking for.
Are you ready for personalized support? Get all the details on coaching here.
Ready to take action and use these tips in your dating life? My free checklist can help!
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A Biography of Alexander Hamilton (1755-1804)
The Quasi War with Adams (1789-1800)
Meanwhile, Adams was nourishing a healthy dislike for Hamilton. It
seemed that everywhere Adams turned, the Federalist party leader was
behind the scenes undercutting his political ambitions. Hamilton, to
whom Adams contemptuously referred as "his puppyhood," had maneuvered
electoral votes in the 1789 election so that Adams would not accidentally
become president over Washington, a position which Adams had felt himself
equally deserving. In the election of 1796, knowing Adams' unpopularity
and the need for a southern Federalist on the ticket, Hamilton had
preferred Charles Pinckney as the party candidate. As votes were not at
that time distinguished between presidential and vice presidential
candidates, electors' votes had to be cast strategically to ensure that
the right man got the top spot. Hamilton had directed Federalist
electors to vote equally for Adams and the southerner, which could easily
have derailed Adams' bid for the executive. Hamilton's strategy was not
directly aimed against Adams at that point, but was calculated to win
southern support for the Federalists, and to lessen Jefferson's chances
for the presidency. Nevertheless, Adams deeply resented Hamilton's
meddlings in his political career, and was equally incensed when, after
the finally ascended to the presidency, Hamilton sent him unsolicited
recommendations on foreign policy issues.
As inspector general, Hamilton found himself in a disappointingly
familiar position having to plead and prod the government into providing
for a neglected army: "Symptoms bordering on mutiny for the want of pay
have been reported to me . . . And discontents less turbulent have been
communicated from several other quarters."
Subsequent events soon ended the annoyance. In February of 1799, Adams
abruptly decided to send a peace emissary to Paris, canceling out his
earlier pledge not to send another minister to France after the
indignities of the XYZ affair. Before the mission got underway, word of
the overthrow of the Directory by Napoleon reached American shores.
Hamilton, Pinckney, and other Federalists advised Adams to delay the
mission until further reports of the situation in France were heard.
Adams, who had begun to suspect a "plot" involving Hamilton and his
supporters to influence negotiations with France, dismissed McHenry in a
rage, and resolved to send the peace envoy regardless of the opinions of
other Federalists. Adams' decision dealt a blow to party unity--the
chief executive was now at odds with the rest of the Federalists. With
the peace mission underway, the Quasi War with France diminished, soon
thereafter, Adams ordered the army disbanded; and Hamilton resigned as
inspector general in July of 1800.
People vs Croswell (February 1804)
When he ascended to the presidency, it was Thomas Jefferson's turn to
feel the sting of printed venom. In 1803, rankled by attacks in
Federalist papers, Jefferson decided to make use of the Sedition Act to
"restore the integrity of the press." Toward that end, he wrote to
Republican governors instructing them to initiate selective prosecutions
of Federalist newspaper publishers who were printing anti-administration
pieces.
Harry Croswell of Hudson New York, the publisher of a small paper called
The Wasp, was one of Jefferson's victims. Croswell was indicted for
seditious libel against president Thomas Jefferson after running a story
reporting that Jefferson had paid newspaper publisher James Callender to
run pieces hostile to the Washington administration. After a request to
introduce the truth of the story as a defense was denied, Croswell was
found guilty by the New York Court of General Sessions.
Croswell appealed to the New York Supreme Court, and enlisted the help of
attorney extraordinaire Alexander Hamilton, who, overwhelmed with other
cases, had been unable to take the Croswell case the first time around.
Hamilton at first tried to chase down James Callender to appear as a
witness for the defense, but Callender was found face down in a puddle,
suspiciously dead.
People vs Croswell , considered among Hamilton's finest courtroom
performances, played to a standing room only crowd. It was a
precedent-setting case having the possibility of changing New York law to
allow truth as a defense against libel charges. In a six-hour closing
argument, Hamilton passionately defended the freedom of the press,
likening the current trial to cases brought by the infamous British Star
Chamber, which body was "cruel" and "tyrannical," and robbed the people
of their liberty. Liberty of the press must be defended, Hamilton
argued, when the truth is reported with good motives, regardless of the
target.
After the trial the attorney for the prosecution, Ambrose Spencer, said
of Hamilton: "In power of reasoning, Hamilton was the equal of Webster;
and more than this can be said of no man." In spite of his stellar
performance, however, Hamilton was not able to overturn the initial
verdict. The defeat was extremely disappointing to him. Unfortunately,
Hamilton did not live long enough to see his arguments revived and
transformed into a law in 1805 permitting truth to be used as a defense
in cases of libel. The law was further enshrined as an article in the
New York state constitution sixteen years later.
|
{
"pile_set_name": "Pile-CC"
}
|
Peroxynitrite formation from the simultaneous reduction of nitrite and oxygen by xanthine oxidase.
One electron reductions of oxygen and nitrite by xanthine oxidase form peroxynitrite. The nitrite and oxygen reducing activities of xanthine oxidase are regulated by oxygen with K(oxygen) 26 and 100 microM and K(nitrite) 1.0 and 1.1 mM with xanthine and NADH as donor substrates. Optimal peroxynitrite formation occurs at 70 microM oxygen with purine substrates. Kinetic parameters: V(max) approximately 50 nmol/min/mg and K(m) of 22, 36 and 70 microM for hypoxanthine, pterin and nitrite respectively. Peroxynitrite generation is inhibited by allopurinol, superoxide dismutase and diphenylene iodonium. A role for this enzyme activity can be found in the antibacterial activity of milk and circulating xanthine oxidase activity.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
HNLMS Schorpioen
HNLMS Schorpioen is a monitor built in France for the Royal Netherlands Navy in the 1860s. These new ships were equipped with heavy rifled guns, and a heavy armor. The hull had an armor plated belt of and the gun turret, housing the two guns, had almost of armor.
She came from the building yard with two tripod masts and able to employ about of sails, but she proved to be a difficult sailing ship and some years later the yards, masts and the sails were removed. As with her huge steam engines gave her a maximum speed of . Her striking weapon was the pointed ram bow, slightly different from Buffels, but she never ever used this overestimated weapon.
Service record
As with Buffel, her record is not very impressive. In 1886 Schorpioen was hit in the stern quarter by a paddle steam tugboat in the harbor of Den Helder and sank in two hours. It was possible to raise and repair her. In 1906 she completed her role as an operational warship and was transformed into an accommodation ship.
At the beginning of World War II, she fell into German hands, was towed to Germany, and served there as a lodging - and storage ship. After the war, in 1947 she was found in Hamburg, Germany and towed back to Den Helder; again to become a lodging ship, first in Amsterdam and later in Den Helder where she became the barracks for the Dutch WRNS. In 1982, after decommissioning, she was bought by a private foundation that was established to transform her into a floating museum in Middelburg, in the southern part of the country. Seven years later, after a complete renovation, she opened her doors to visitors, as a museum ship.
In 1995, the Royal Netherlands Navy re-acquired the ship and put her under the supervision of the Dutch Navy Museum in Den Helder where she is now the third, and largest, vessel on display. In May 2000, after a renovation period of eighteen months to restore her to her former glory, the ship was opened to visitors.
See also
List of museum ships
Notes
References
External links
Photo-collection on Dutch ironclads
HMLMS Schorpioen at Dutch Naval Museum
HNSA Ship Page: HMLMS Schorpioen
Category:19th-century naval ships of the Netherlands
Category:Naval ships of the Netherlands captured by Germany during World War II
Category:Museum ships in the Netherlands
Category:1868 ships
Category:Schorpioen-class monitors
Category:Ships built in France
|
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Yago Pikachu
Glaybson Yago Souza Lisboa (born 5 June 1992), known as Yago Pikachu, is a Brazilian footballer who plays for Vasco da Gama as either a right back or a midfielder.
Club career
Paysandu
Born in Belém, Pará, Yago Pikachu joined Paysandu's youth setup in 2005 at the age of 13, after starting it out at Tuna Luso. He earned the nickname Pikachu for his short stature and speed. After being promoted to the main squad, he made his senior debut on 14 January 2012, starting in a 1–2 Campeonato Paraense home loss against Cametá.
Yago Pikachu scored his first senior goal on 25 January, netting the first in a 1–2 away loss against Águia de Marabá. He finished the tournament with four goals, and also scored regularly in the year's Série C, as his side returned to Série B after six years.
Yago Pikachu made his debut in the second division on 25 May 2013, starting in a 1–1 home draw against ASA. He scored his first goal in the category six days later, netting the first against América-RN which ended in the same scoreline.
Despite scoring nine goals, Yago Pikachu could not avoid his team's relegation as it finished 18th. He again helped the side in its promotion the following year, contributing with four goals in 22 matches.
On 12 June 2015 Yago Pikachu scored an olympic goal in a 2–0 away win against ABC. He completed 200 games for Paysandu on 15 August, but in a 3–1 home win against Oeste.
Vasco da Gama
On 16 December 2015, Yago Pikachu signed a three-year deal with fellow second tier club Vasco da Gama. Mainly used as a substitute in the midfield during the year, he contributed with three goals in 27 matches as his side achieved promotion to Série A.
Yago Pikachu made his top tier debut on 14 May 2017, starting in a 4–0 away loss against Palmeiras. Seven days later he scored his first goal in the division, netting the opener in a 2–0 home win against Bahia. He completed the 2017 season with two goals in 27 games.
Career statistics
Honours
Paysandu
Campeonato Paraense: 2013
Vasco da Gama
Campeonato Carioca: 2016
Individual
Campeonato Carioca Team of the year: 2018
References
External links
Category:1992 births
Category:Living people
Category:Sportspeople from Belém
Category:Brazilian footballers
Category:Association football fullbacks
Category:Association football midfielders
Category:Campeonato Brasileiro Série A players
Category:Campeonato Brasileiro Série B players
Category:Campeonato Brasileiro Série C players
Category:Paysandu Sport Club players
Category:CR Vasco da Gama players
|
{
"pile_set_name": "Wikipedia (en)"
}
|
Q:
gitolite installation issue
Has any one tryied the easy install option of gitolite?
I am trying to install gitolite from my windows (workstation ) to a solaris box.
[command used to install]
./gl-easy-install -q git sjcfsap1 git
The command breaks at the following place .
*Y*ou are logging into system : [gitserver]
cloning gitolite-admin repo...
Initialized empty Git repository in c:/Documents and Settings/chandve/gitolite-a
dmin/.git/
Password:
fatal: 'gitolite-admin' does not appear to be a git repository
fatal: The remote end hung up unexpectedly**
Has any one encountered this issue?
Do you think gitolite is worth this effort? I am looking to evaluate ACL for Git.
Thanks for your response in advance.
[The complete command execution log below]
CHANDVE@CHANDVE /c/git/repos/gitolite/src (master)
$ ./gl-easy-install git sjcfsap1 git
------------------------------------------------------------------------
you are upgrading v1.5.3-13-g20c2e1a to v1.5.3-13-g20c2e1a
Note: getting '(unknown)' for the 'from' version should only happen once.
Getting '(unknown)' for the 'to' version means you are probably installing
from a tar file dump, not a real clone. This is not an error but it's nice to
have those version numbers in case you need support. Try and install from a
clone
...press enter to continue or Ctrl-C to bail out
------------------------------------------------------------------------
the next command will create a new keypair for your gitolite access
The pubkey will be /c/Documents and Settings/chandve/.ssh/git.pub. You will hav
e to choose a
passphrase or hit enter for none. I recommend not having a passphrase for
now, *especially* if you do not have a passphrase for the key which you are
already using to get server access!
Add one using 'ssh-keygen -p' after all the setup is done and you've
successfully cloned and pushed the gitolite-admin repo. After that, install
'keychain' or something similar, and add the following command to your bashrc
(since this is a non-default key)
ssh-add $HOME/.ssh/git
This makes using passphrases very convenient.
...press enter to continue or Ctrl-C to bail out
------------------------------------------------------------------------
Hmmm... pubkey /c/Documents and Settings/chandve/.ssh/git.pub exists; should I j
ust (re-)use it?
IMPORTANT: once the install completes, *this* key can no longer be used to get
a command line on the server -- it will be used by gitolite, for git access
only. If that is a problem, please ABORT now.
doc/6-ssh-troubleshooting.mkd will explain what is happening here, if you need
more info.
...press enter to continue or Ctrl-C to bail out
------------------------------------------------------------------------
your $HOME/.ssh/config already has settings for gitolite. I will assume
they're correct, but if they're not, please edit that file, delete that
paragraph (that line and the following few lines), Ctrl-C, and rerun.
In case you want to check right now (from another terminal) if they're
correct, here's what they are *supposed* to look like:
host gitolite
user git
hostname sjcfsap1
port 22
identityfile ~/.ssh/git
...press enter to continue or Ctrl-C to bail out
gitolite.pm 100% 26KB 26.3KB/s 00:00
gl-auth-command 100% 8319 8.1KB/s 00:00
gl-compile-conf 100% 26KB 25.6KB/s 00:00
gl-conf-convert 100% 2325 2.3KB/s 00:00
gl-easy-install 100% 23KB 23.2KB/s 00:00
gl-emergency-addkey 100% 1295 1.3KB/s 00:00
gl-install 100% 4087 4.0KB/s 00:00
gl-setup 100% 3081 3.0KB/s 00:00
gl-system-install 100% 1814 1.8KB/s 00:00
gl-tool 100% 2145 2.1KB/s 00:00
output.txt 100% 60KB 60.2KB/s 00:00
sshkeys-lint 100% 2962 2.9KB/s 00:00
example.conf 100% 12KB 12.1KB/s 00:00
example.gitolite.rc 100% 8390 8.2KB/s 00:00
VERSION 100% 19 0.0KB/s 00:00
0-INSTALL.mkd 100% 12KB 11.6KB/s 00:00
1-migrate.mkd 100% 3569 3.5KB/s 00:00
2-admin.mkd 100% 9063 8.9KB/s 00:00
3-faq-tips-etc.mkd 100% 29KB 29.0KB/s 00:00
4-wildcard-repositories.mkd 100% 12KB 11.8KB/s 00:00
5-delegation.mkd 100% 6143 6.0KB/s 00:00
6-ssh-troubleshooting.mkd 100% 19KB 19.5KB/s 00:00
7-install-transcript.mkd 100% 8372 8.2KB/s 00:00
9-gitolite-and-ssh.mkd 100% 7798 7.6KB/s 00:00
9-packaging.mkd 100% 2257 2.2KB/s 00:00
9-uninstall.mkd 100% 2791 2.7KB/s 00:00
admin-defined-commands.mkd 100% 9700 9.5KB/s 00:00
big-config.mkd 100% 6469 6.3KB/s 00:00
CHANGELOG 100% 3873 3.8KB/s 00:00
COPYING 100% 18KB 17.9KB/s 00:00
hook-propagation.mkd 100% 7654 7.5KB/s 00:00
overkill.mkd 100% 2059 2.0KB/s 00:00
progit-article.mkd 100% 12KB 12.5KB/s 00:00
report-output.mkd 100% 1818 1.8KB/s 00:00
shell-games.mkd 100% 3363 3.3KB/s 00:00
gitolite-hooked 100% 0 0.0KB/s 00:00
update 100% 4728 4.6KB/s 00:00
post-update 100% 943 0.9KB/s 00:00
------------------------------------------------------------------------
the gitolite rc file needs to be edited by hand. The defaults are sensible,
so if you wish, you can just exit the editor.
Otherwise, make any changes you wish and save it. Read the comments to
understand what is what -- the rc file's documentation is inline.
Please remember this file will actually be copied to the server, and that all
the paths etc. represent paths on the server!
...press enter to continue or Ctrl-C to bail out
------------------------------------------------------------------------
Oh hey... you already had a '.gitolite.rc' file on the server.
Let's see if we can use that instead of the default one...
...press enter to continue or Ctrl-C to bail out
.gitolite.rc 100% 8390 8.2KB/s 00:00
------------------------------------------------------------------------
ignore any 'please edit this file' or 'run this command' type lines in the
next set of command outputs coming up. They're only relevant for a manual
install, not this one...
...press enter to continue or Ctrl-C to bail out
*** WARNING ***: looks like an upgrade... ignoring argument 'git'
/export/home/git/repositories already exists
/export/home/git/.gitolite already exists
/export/home/git/.gitolite/conf already exists
/export/home/git/.gitolite/doc already exists
/export/home/git/.gitolite/keydir already exists
/export/home/git/.gitolite/logs already exists
/export/home/git/.gitolite/src already exists
/export/home/git/.gitolite/hooks already exists
/export/home/git/.gitolite/hooks/common already exists
/export/home/git/.gitolite/hooks/gitolite-admin already exists
copying post-update hook to gitolite-admin repo...
Pseudo-terminal will not be allocated because stdin is not a terminal.
stty: : Invalid argument
You are logging into system : sjcfsap1
/export/home/git/repositories already exists
/export/home/git/.gitolite already exists
/export/home/git/.gitolite/conf already exists
/export/home/git/.gitolite/doc already exists
/export/home/git/.gitolite/keydir already exists
/export/home/git/.gitolite/logs already exists
/export/home/git/.gitolite/src already exists
/export/home/git/.gitolite/hooks already exists
/export/home/git/.gitolite/hooks/common already exists
/export/home/git/.gitolite/hooks/gitolite-admin already exists
copying post-update hook to gitolite-admin repo...
------------------------------------------------------------------------
now we will clone the gitolite-admin repo to your workstation and see if it
all hangs together. We'll do this in your $HOME for now, and you can move
it elsewhere later if you wish to.
...press enter to continue or Ctrl-C to bail out
Initialized empty Git repository in c:/Documents and Settings/chandve/gitolite-a
dmin/.git/
Password:
Password:
fatal: 'gitolite-admin' does not appear to be a git repository
fatal: The remote end hung up unexpectedly
A:
This can occur if on the server, the git user has a key in ~/.ssh/authorized_keys for the remote user that is not prefixed with the command variable:
% cat ~/.ssh/authorized_keys
ssh-rsa ...... user@host
# gitolite start
command="/home/gituser/.... user@host
# gitolite end
%
Just remove the first line and you're good to go.
A:
I did precisely the same installation (Windows to Solaris), and it is worth it.
I did it:
from a git bash session (not a DOS session),
with $HOME correctly set (i.e. referencing a directory where my .ssh public/private keys are stored, including the one for the user present on the Solaris server side)
|
{
"pile_set_name": "StackExchange"
}
|
Compensated pathogenic deviations.
Deleterious or 'disease-associated' mutations are mutations that lead to disease with high phenotype penetrance: they are inherited in a simple Mendelian manner, or, in the case of cancer, accumulate in somatic cells leading directly to disease. However, in some cases, the amino acid that is substituted resulting in disease is the wild-type native residue in the functionally equivalent protein in another species. Such examples are known as 'compensated pathogenic deviations' (CPDs) because, somewhere in the second species, there must be compensatory mutations that allow the protein to function normally despite having a residue which would cause disease in the first species. Depending on the nature of the mutations, compensation can occur in the same protein, or in a different protein with which it interacts. In principle, compensation can be achieved by a single mutation (most probably structurally close to the CPD), or by the cumulative effect of several mutations. Although it is clear that these effects occur in proteins, compensatory mutations are also important in RNA potentially having an impact on disease. As a much simpler molecule, RNA provides an interesting model for understanding mechanisms of compensatory effects, both by looking at naturally occurring RNA molecules and as a means of computational simulation. This review surveys the rather limited literature that has explored these effects. Understanding the nature of CPDs is important in understanding traversal along fitness landscape valleys in evolution. It could also have applications in treating diseases that result from such mutations.
|
{
"pile_set_name": "PubMed Abstracts"
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|
Hi there, i am a young developer and i'm glad to share with new my new app, Galaxy Sensors, it uses sensors built-in our Note3 to show temperature, humidity, light, pressure and height, i also developed a simple widget to show the temperature for our home screen, i'm planning to add other widget as soon as i have time to do it, i will leave you the link to the play store, a shor changelog of the last version and a few screenshots, thanks1.1 added Google Analytics1.2 added translation in:-Italian-English-French-German-Portoguese-Russian-Spanish1.2.1 fixed an orientation bug1.3 added icons1.3.1 bug fix1.3.2 finally aviable first widget1.3.3 added share functionality, fixed a bug with translation1.3.4 fixed russian, widget 2x11.3.5 added imperial system ON/OFF menu option1.3.6 fixed some translation, added version number, added option to change font1.3.7 added inHg to imperial system1.4 fixed widget, added notification, new accuracy (0s: Low -15s: Medium -45s: High)
|
{
"pile_set_name": "OpenWebText2"
}
|
Slideshow ( 10 images )
TOKYO (Reuters) - A powerful typhoon was approaching Tokyo on Wednesday evening, threatening Pacific coastal regions to the northeast of the capital with heavy rains and high winds, leading to flight cancellations and evacuation advisories in some areas.
The center of typhoon “Shanshan”, a Chinese girl’s name, was located 200 km (125 miles) southeast of Tokyo as of 9:00 p.m. (8.00 a.m. ET), and is expected to move north along the east coast of Japan’s main island on Thursday, possibly snarling the morning rush hour.
The Japan Meteorological Agency warned that Tokyo and surrounding areas could get as much as 300 mm (12 inches) of rain in the 24 hours to 6:00 p.m. on Thursday, with winds gusting as high as 180 kmh (111 mph).
Shanshan is expected to move slowly, meaning heavy rain may fall in one area for an extended period, the agency said.
The city of Mobara, east of Tokyo, issued an evacuation advisory for its entire population of about 90,000 people.
Several other municipalities near Tokyo also issued evacuation advisories for some residents, bringing the total number of people affected to more than 100,000, according to public broadcaster NHK.
NHK also said airlines had canceled more than 160 flights.
The western Japan regions hit by deadly floods in July look set to be spared any damage from the typhoon as it winds its way up the northeastern coast.
Japan has experienced one weather disaster after another since the start of July, including a record-breaking heatwave that saw temperatures surge to 41.1 Celsius (106 Fahrenheit) and had killed at least 132 people as of August 5.
|
{
"pile_set_name": "OpenWebText2"
}
|
Analysis of behavioral and hippocampal variation in congenic albino and pigmented BALB mice.
Mice of the BALB/c strain are widely used in behavioral research in spite of the albino condition, which can obscure brain-behavior relationships. We have developed a pigmented BALB strain, congenic to BALB/c, which could be more appropriate for neurogenetic studies that aim at identifying the effects of neurological mutations on behavior. Comparison of inbred albino and pigmented congenic BALB arising from the same litters provides a valuable tool for detecting the consequences of the albino mutation on behavioral performances. Preliminary results presented here show that the albino condition does not interfere with the development and patterns of connectivity of mossy fibers in the hippocampus. On the other hand, obvious coat color-linked differences appear for locomotor activity and defecation scores in the open field, pigmented mice being unexpectedly less active and more reactive than albino, as if better vision increased their reactions to a novel, anxiogenic environment. Finally, pigmented mice do not show better performances in the radial maze, which confirms that the inability of BALB mice for spatial learning in a highly demanding version of this task cannot be attributed to their inability to process visual information.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
Twitter Launches Proper ‘Lights Out’ Dark Mode
By Adnan Farooqui on 03/28/2019 14:44 PDT
Twitter is finally rolling out a proper dark mode for its mobile app. The company today announced that the proper battery-saving dark mode dubbed “lights out” is rolling out right away. This has been one of the most requested features from users and it’s good to see that Twitter is doing something with all of that feedback.
Advertising
Many app developers are actively building proper dark modes into their apps as most flagship smartphones now ship with OLED displays, this includes the new iPhones as well. The dark mode can make a noticeable difference in the power consumption of such displays and can thus prolong the handset’s battery life.
Twitter also points out that a proper black background also helps reduce eye strain particularly when the user is looking at their phone in the dark. That’s something a lot of us tend to do before going to sleep every night.
It’s pertinent to mention here that the lights out dark mode for Twitter’s mobile app is currently rolling out for iOS only. The company hasn’t said at this point in time when the Android version of the app will get it. Twitter hasn’t provided any time frame in which we can expect the mode to come to Android.
|
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"pile_set_name": "Pile-CC"
}
|
Remove “Edit With Paint 3D” Option From Context Menu In Windows 10
In Creators Update and above versions of Windows 10, there is a new option in the file context menu called Edit with Paint 3D for image file formats. The Edit with Paint 3D opens the image file in Paint 3D app.
Edit with Paint 3D option in right-click menu
As you might have observed by now, the Edit with Paint 3D context menu option appears only when you right click on a picture file. In other words, the option appears when you right-click on JPEG, BMP, PNG, GIF, TIF, and TIFF image file types.
The Edit with Paint 3D option is added by an app called Paint 3D app. If you don’t know, the Paint 3D app is introduced with Creators Update for Windows 10. Although the Paint 3D is an alternative and update to the classic Paint program, the classic Paint program continues to be the part of Windows 10.
The new Paint 3D app is designed to help users create 3D objects using regular keyboards, mouse, touch screen and stylus. You can open regular pictures with Paint 3D app and create 3D objects out of it.
The Paint 3D is certainly a step ahead of the classic Paint program, but there are many users who use third-party image editing tools like Paint.net to get their job done.
If you use the built-in classic Paint or a third-party image editing tool, you might want to remove the Edit with Paint 3D option from the context menu in Windows 10.
Follow the instructions mentioned in one of the given below methods to remove Edit with Paint 3D option from right-click of Windows 10.
Step 3: Under the Shell key, you should see 3D Edit key. Right-click on the 3D Edit key and then click Delete option to delete the key. This will remove the Edit with Paint 3D option for BMP image files. You need to do the same for all image file types.
Step 4: Next, navigate to the following keys one after another. Look for 3D Edit key and delete the same.
|
{
"pile_set_name": "Pile-CC"
}
|
This US Firm Wants to Help Build China’s Surveillance State
In a nondescript office tower a mile from the Las Vegas Strip, two women toil in a windowless room crammed with bikinis in every size, style, and hue. It’s the stockroom of Bikini.com, an online swimwear store. Down the hall, colleagues are working to break into China’s red-hot market for surveillance software powered by artificial intelligence.
Bikini.com is owned by Remark Holdings, a small public company with Hollywood producer Brett Ratner on its board and financial ties to TV’s Dr. Mehmet Oz. Remark’s leaders are trying to transform the unprofitable, debt-loaded website operator into a provider of corporate AI technology in Asia, particularly China. Remark’s business and share price are struggling, but its peculiar AI project has made some progress.
In March, Remark said it had signed a deal with a Thai conglomerate that operates more than 10,000 7-Eleven stores in Thailand, among many other businesses. Charoen Pokphand Group hopes to recognize the faces of customers for loyalty programs, and of shoplifters for security purposes, according to Athikom Asvanund, an executive who advises CP Group’s chairman, Soopakij Chearavanont. In a statement, Chearavanont says Remark’s technology could also help Chinese insurance giant Ping-An, in which CP owns a stake, with tasks like processing claims.
China is the main focus of Remark’s AI project. The company has several subsidiaries in the country, where engineers are cheap and work six days a week. One subsidiary built technology for use by police in China’s fifth largest city, Hangzhou, that analyzes surveillance video to identify motorcycles driving on streets where they are banned. Remark also is helping a Chinese supermarket group identify frequent shoppers through facial recognition software. Remark CEO Shing Tao, a cheery native New Yorker, says his company is using the technology to clock in workers and prevent them from working double shifts at Chinese construction sites, and that he’s angling for police contracts that will use the technology to spot fugitives in public.
Remark is trying to tap into China’s seemingly endless appetite for surveillance, for both security and commercial ends. A national strategy released last year declared the country will rival the US in AI by 2020. Rapid adoption of facial recognition in China means your physiognomy can now get you cash from an ATM—or plucked from a concert crowd of 20,000 by local police, as one man suspected of stealing potatoes learned in May. Tao says the country’s openness to the technology and more lax approach to privacy make it a logical target for Remark. “China is the low-hanging fruit,” he says. “They really understand and accept what AI is, and they’re ready to go.”
Remark is tiny compared with the giant US tech companies at the forefront of AI research; its AI push is built on a shoestring. Remark reported $70 million in revenue last year, mostly from its travel business; that’s less than Google generates on an average day. Remark’s chief technology officer, Jason Wei, says his developers in China lean heavily on open source tools released by Google and academics, and honed their facial recognition software in part with photos scraped from Chinese and US social media sites including Facebook.
That’s not exactly a recipe for world-beating AI technology. Remark’s AI offerings haven’t netted the revenue Tao told investors they would, and the company’s share price has slid 70 percent this year. US sanctions and China’s thriving ecosystem of domestic AI providers also pose challenges to Remark’s efforts to build a business in the country. Asked about Remark, Hao Lu, chief innovation officer at Yitu Technology, a leading facial recognition startup, had never heard of the company or its Chinese brand.
Remark created software to watch over restaurant kitchens and log instances of workers removing hats or face masks.
Courtesy of Shing Tao
Still, the notion that a small-time website operator is building AI offerings shows how quickly advances in areas such as image recognition spread, with the help of open source software. Four years ago, it would have been implausible for a small company with few technology chops to create tools capable of recognizing faces or objects such as motorcycles. Now, a developer without machine learning experience can cobble together a system that detects some common objects reasonably well in four months, says Reza Zadeh, founder of Palo Alto video recognition startup Matroid. Such software wouldn’t be easy for customers to use or competitive with more sophisticated products like Matroid’s, but it might work well enough to win a deal. “That’s the stuff you will see startups that are inexperienced try to peddle,” says Zadeh, who is also an adjunct professor at Stanford.
Smaller players like Remark may feel freer to take AI technology places that companies with more name recognition can’t, or won’t. Google and Microsoft both have AI research labs in China, but it’s hard to imagine them or other leading US software companies bidding for police facial recognition contracts there. Google, for example, recently pledged not to renew a Pentagon contract in which it applied machine learning to drone imagery after protests from its employees. Asked whether he has qualms about working with Chinese authorities, Tao says he simply wants to help customers operate more effectively, whether they’re in retail or enforcing local laws. “We’re not breaking the rules,” he adds.
How Stuff Works
Remark didn’t start as a tech company. It was created in 2006 as a spinout from Discovery Communications called How Stuff Works International, or HSWI, to market versions of the popular explanation site in emerging markets. When that business proved less lucrative than hoped, HSWI in 2009 cofounded an online health site called ShareCare, alongside partners including the founder of WebMD, Dr. Oz, and Oprah Winfrey’s production company. Remark still owns 5 percent. In 2011, HSWI changed its name to Remark Media, and started a broader expansion, acquiring Bikini.com, and later Vegas.com, which offers hotel and show bookings.
The acquisitions bolstered Remark’s revenue, but Tao worried media and ecommerce were threatened by growing technology companies. He was named CEO in 2012 after a stint on Remark’s board; previously, he had worked as an investor on deals involving Taiwanese technology companies, and sat on the board of Playboy Enterprises. “It was very clear that we needed to have some type of technology, some type of edge, that no one could compete with,” recalls Tao.
Tao turned to Wei, now the CTO, to assess what kind of technology a company with minimal technology expertise might develop. Wei had been brought in to improve Bikini.com’s publishing system, but previously worked at Toshiba and founded a virtual-world startup.
Wei tinkered with making a wearable camera for pets—tested on Tao’s dog—and a device to prevent texting and driving. Neither seemed promising, and engineering costs mounted. Wei estimates his explorations burned through more than $100,000 in two months. “We decided, OK, maybe we should try China, because in Chengdu that much money probably can last us for a year,” he says.
In Chengdu, Wei assembled software engineers to build a social-media analysis service for marketers. The software skirted obstacles to scraping put in place by social networks and collected public updates and photos from networks such as Weibo and Facebook. The goal was to identify accounts belonging to the same person, and index them by subject and location. Wei says names and identifying personal information such as phone numbers were scrubbed to protect privacy.
That project led Remark to the AI technology taking off in Silicon Valley. Wei studied how a technique called deep learning had recently made computers much better at classifying images. He borrowed ideas and open source code from companies such as Google and leading academics. He describes University of Oxford professor Andrew Zisserman, who also works with Alphabet, as his team’s “hero” for releasing ready-to-use deep learning models that can recognize objects and faces in photos. “Through the pictures, through facial recognition, we’re able to put a lot of pieces together,” Wei explains.
Remark launched its social media analytics service under the brand KanKan, or see and explore in Mandarin. Clients included Aston Martin’s ad agency in China, according to Tao. He also changed his company’s name to Remark Holdings, and began pitching its image processing software to companies and public agencies in Asia. “We’d built up a strong base of data, and during this time the costs of AI kind of came down,” says Tao.
Tracking Faces
At Remark’s offices in Las Vegas, Wei eagerly connects the feed from the boardroom’s videoconferencing system to his team’s software. In one mode, the software draws boxes around each face in the room, moving as the person moves. In another it traces the movement of people’s limbs, and correctly says that a WIRED reporter wears glasses and is between 30 and 40 years old. Wei says another piece of his team’s software can determine dozens of facial expressions, although many with only low accuracy. “Basic ones like a smile, crying, angry, nervous—these are useful enough for retail stores to determine if their customers are happy or an employee is doing the proper job,” he says.
Wei also played video from a camera mounted above six busy workers in a bustling restaurant kitchen. Digital red boxes tracked the faces of two workers not wearing face masks. He said the software was developed to bid for a pilot project in Shanghai—similar to one described in a report from state-owned Chinese media—in which authorities installed cameras in restaurant kitchens that automatically alerted city inspectors to breaches of food safety rules. In a nearby meeting room, Wei showed off black metal cases housing computing boards from graphics chipmaker Nvidia, whose powerful chips have become central to major AI projects, and security cameras from Hikvision, a leading video surveillance company partly owned by the Chinese government. Remark installs its software on the computers, which are then hooked up to cameras, Wei says. He described a test of Remark’s facial recognition technology in which it correctly spotted staff mingling with crowds on the Vegas strip.
All that technology hasn’t boosted Remark’s finances as much as Tao projected. In March, he told investors that KanKan would contribute $50 million in revenue in 2018. Through the first six months of the year, Remark’s technology business generated just $4.6 million in revenue, according to a company filing.
“It’s an impossible story,” says Anne Stevenson-Yang, cofounder of Beijing-based financial research firm J Capital Research, who issued two trenchant research notes about Remark’s AI dreams this year. They describe her failure to confirm contracts Remark claims to have with Chinese banks. Her conclusion: The company’s technology is minimal and wildly oversold. “It’s to pump the stock and sell the stock, that’s all,” she adds. J Capital’s webpage for her Remark reports notes that the company’s clients may be shorting Remark’s stock.
Tao says Remark’s AI revenue hasn’t met his expectation because contracts took longer to complete than expected, and increased government scrutiny on banks derailed projects in which Remark helped with credit checks. He told investors last year that the Shanghai restaurant system was destined for 2,000 restaurants in a deal worth “seven figures,” but now says it has been delayed by city bureaucracy.
Tao showed WIRED a memorandum of understanding between Remark and supermarket operator Beijing Hualian for technology to track shoppers that mentions facial recognition. Other contracts show a Remark subsidiary pledging to provide the restaurant observation system to a Shanghai company working with the city’s Jing’an District, and the motorcycle detection system for use by police in Hangzhou. Tao says it covers more than a dozen intersections, and automatically flags images of offending vehicles. He shrugs off J Capital’s reports, saying his business partners shouldn’t be expected to reveal all to nosy analysts, and that accusations he misled investors don’t make sense. “Why would we put our core business at risk?” Tao asks. He points to Remark’s appearance on leaderboards ranking the accuracy of facial recognition software hosted by academics at the state universities of Massachusetts and Washington, although neither independently verify the code behind results submitted by participants.
Facial recognition was a hot topic in China’s canal-crossed historic town of Wuzhen last week, at the annual World Internet Conference. China’s government uses the event to project a picture of digital innovation—within carefully defined political bounds.
Last year, Apple CEO Tim Cook and Google CEO Sundar Pichai each gave keynotes. This year, under the pall of the Trump trade war, the top American CEO attending was Steve Mollenkopf of Qualcomm. Remark was present, hosting a booth on the expo floor. On Thursday, the company tweeted a photo of Tao presenting the KanKan AI platform on stage. A few hours earlier, Tao reflected on China’s openness to AI and the opportunities for Remark, if it can deliver technology that works. “AI is transforming the world, and China is leading the world on adoption of this technology,” he said.
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---
abstract: 'In this paper, we determine the relative rank of the semigroup $\T(X,Y)$ of all transformations on a finite chain $X$ with restricted range $Y\subseteq X$ modulo the set $\OP(X,Y)$ of all orientation-preserving transformation in $\T(X,Y)$. Moreover, we state the relative rank of the semigroup $\OP(X,Y)$ modulo the set $\O(X,Y)$ of all order-preserving transformations in $\OP(X,Y)$. In both cases we characterize the minimal relative generating sets.'
author:
- |
Ilinka Dimitrova\
*Faculty of Mathematics and Natural Science*\
*South-West University “Neofit Rilski”*\
*2700 Blagoevgrad, Bulgaria*\
*e-mail: ilinka\_dimitrova@swu.bg*\
\
Jörg Koppitz\
*Institute of Mathematics and Informatics*\
*Bulgarian Academy of Sciences*\
*1113 Sofia, Bulgaria*\
*e-mail: koppitz@math.bas.bg*
title: On relative ranks of finite transformation semigroups with restricted range
---
*Key words:* transformation semigroups with restricted range, order-preserving transformations, orientation-preserving transformations, relative rank, relative generating sets.
2010 Mathematics Subject Classification: 20M20\
Introduction and Preliminaries
==============================
Let $S$ be a semigroup. The *rank* of $S$ (denoted by $\rank S$) is defined to be the minimal number of elements of a generating set of $S$. The ranks of various well known semigroups have been calculated [@GH; @GH1; @Howie; @HMcF]. For a set $A \subseteq S$, the *relative rank* of $S$ modulo $A$, denoted by $\rank (S : A)$, is the minimal cardinality of a set $B\subseteq S$ such that $A \cup B$ generates $S$. It follows immediately from the definition that $\rank (S : \emptyset) = \rank S$, $\rank ( S : S) = 0$, $\rank (S : A ) = \rank (S : \langle A \rangle )$ and $\rank (S : A) = 0$ if and only if $A$ is a generating set for $S$. The relative rank of a semigroup modulo a suitable set was first introduced by Ruškuc in [@Ruskuc] in order to describe the generating sets of semigroups with infinite rank. In [@HRH], Howie, Ruškuc, and Higgins considered the relative ranks of the monoid $\T(X)$ of all full transformations on $X$, where $X$ is an infinite set, modulo some distinguished subsets of $\T(X)$. They showed that $\rank (\T(X) : \S(X)) = 2$, $\rank (\T(X) : \E(X)) = 2$ and $\rank (\T(X) : J) = 0$, where $\S(X)$ is the symmetric group on $X$, $\E(X)$ is the set of all idempotent transformations on $X$ and $J$ is the top $\mathcal{J}$-class of $\T(X)$, i.e. $J=\{\alpha\in\T(X) : |X\alpha|=|X|\}$. But also if the rank is finite, the relative rank gives information about the generating sets. In the present paper, we will determine the relative rank for a particular semigroup of transformations on a finite set.
Let $X$ be a finite chain, say $X=\{1<2<\cdots <n\}$, for a natural number $n$. A transformation $\alpha \in \T(X)$ is called *order-preserving* if $x\le y$ implies $x\alpha\le y\alpha$, for all $x,y\in X$. We denote by $\O(X)$ the submonoid of $\T(X)$ of all order-preserving full transformations on $X$. The relative rank of $\T(X)$ modulo $\O(X)$ was considered by Higgins, Mitchell, and Ruškuc in [@HMR]. They showed that $\rank(\T(X) : \O(X)) = 1$, when $X$ is an arbitrary countable chain or an arbitrary well-ordered set, while $\rank(\T(\R) : \O(\R))$ is uncountable, by considering the usual order of the set $\R$ of real numbers. In [@DFK], Dimitrova, Fernandes, and Koppitz studied the relative rank of the semigroup $\O(X)$ modulo $J=\{\alpha\in\O(X) : |X\alpha|=|X|\}$, for an infinite countable chain $X$. We say that a transformation $\alpha \in\T(X)$ is *orientation-preserving* if there are subsets $X_{1},X_{2}\subseteq X$ with $\emptyset \neq X_{1}<X_{2}$, (i.e. $x_{1}<x_{2}$ for $x_{1}\in X_{1}$ and $x_{2}\in X_{2}$), $X=X_{1}\cup X_{2}$, and $x\alpha \leq y\alpha$, whenever either $(x,y)\in X_{1}^{2}\cup X_{2}^{2}$ with $x\leq y$ or $(x,y)\in X_{2}\times X_{1}$. Note that $X_{2}=\emptyset$ provides $\alpha \in \O(X)$. We denote by $\OP(X)$ the submonoid of $\T(X)$ of all orientation-preserving full transformations on $X$. An equivalent notion of an orientation-preserving transformation was first introduced by McAlister in [@McA] and, independently, by Catarino and Higgins in [@CH]. It is clear that $\O(X)$ is a submonoid of $\OP(X)$, i.e. $\O(X)\subset \OP(X)\subset \T(X)$. It is interesting to note that the relative rank of $\T(X)$ modulo $\OP(X)$ as well as the relative rank of $\OP(X)$ modulo $\O(X)$ is one (see [@CH; @HRH]), but the situation will change if one considers transformations with restricted range.
Let $Y=\{a_{1}<a_{2}<\cdots <a_{m}\}$ be a nonempty subset of $X$, for a natural number $m\leq n$, and denote by $\T(X,Y)$ the subsemigroup $\{\alpha \in \T(X) : X \alpha \subseteq Y\}$ of $\T(X)$ of all transformations with range (image) restricted to $Y$. The set $\T(X,Y)$ coincides with $\T(X)$, whenever $Y=X$ (i.e. $m=n$). In 1975, Symons [@Symons] introduced and studied the semigroup $\T(X,Y)$, which is called semigroup of transformations with restricted range. Recently, the rank of $\T(X,Y)$ was computed by Fernandes and Sanwong in [@FS]. They proved that the rank of $\T(X,Y)$ is the Sterling number $S(n,m)$ of second kind with $\left\vert X\right\vert =n$ and $\left\vert Y\right\vert =m$. The rank of the order-preserving counterpart $\O(X,Y)$ of $\T(X,Y)$ was studied in [@FHQS1] by Fernandes, Honyam, Quinteiro, and Singha. The authors found that $\rank\O(X,Y)=\left(
\begin{array}{c}
n-1 \\
m-1\end{array}\right) +\left\vert Y^{\#}\right\vert,$ where $Y^{\#}$ denotes the set of all $y\in Y$ with one of the following properties: (i) $y$ has no successor in $X$; (ii) $y$ is no successor of any element in $X$; (iii) both the successor of $Y$ and the element whose successor is $y$ belong to $Y$. Moreover, the regularity and the rank of the semigroup $\OP(X,Y)$ were studied by the same authors in [@FHQS2]. They showed that $\rank\OP(X,Y)=\left(
\begin{array}{c}
n \\
m
\end{array}\right)$. In [@TK], Tinpun and Koppitz studied the relative rank of $\T(X,Y)$ modulo $\O(X,Y)$ and proved that $\rank(\T(X,Y):\O(X,Y))=
S(n,m)-
\left(
\begin{array}{c}
n-1 \\
m-1
\end{array}
\right) + a$, where $a \in \{0,1\}$ depending on the set $Y$. In this paper, we determine the relative rank of $\OP(X,Y)$ modulo $\O(X,Y)$ as well as the relative rank of $\T(X,Y)$ modulo $\OP(X,Y)$.
Let $\alpha \in \T(X,Y)$. The kernel of $\alpha$ is the equivalence relation $\ker\alpha $ with $(x,y)\in \ker\alpha $ if $x\alpha
=y\alpha$. It corresponds uniquely to a partition on $X$. This justifies to regard $\ker \alpha $ as a partition on $X$. We will call a block of this partition as $\ker\alpha$-class. In particular, the sets $x\alpha^{-1}=\{y\in X:y\alpha =x\}$, for $x\in X\alpha$, are the $\ker\alpha$-classes. We say that a partition $P$ is a subpartition of a partition $Q$ of $X$ if for all $p\in P$ there is $q\in Q$ with $p\subseteq q$. A set $T\subseteq X$ with $\left\vert T\cap x\alpha^{-1}\right\vert =1$, for all $x\in X\alpha$, is called a transversal of $\ker\alpha$. Let $A\subseteq X$. Then $\alpha |_{A}:A\rightarrow Y$ denotes the restriction of $\alpha$ to $A$ and $A$ will be called convex if $x<y<z$ with $x,z\in A$ implies $y\in A$.
Let $l\in \{1,\ldots ,m\}$. We denote by $\mathcal{P}_{l}$ the set of all partitions $\{A_{1},\ldots,A_{l}\}$ of $X$ such that $A_{2}<A_{3}<\cdots
<A_{l}$ are convex sets (if $l>1$) and $A_{1}$ is the union of two convex sets with $1,n\in A_{1}.$ Further, let $\mathcal{Q}_{l}$ be the set of all partitions $\{A_{1},\ldots,A_{l}\}$ of $X$ such that $A_{1}<A_{2}<\cdots <A_{l}$ are convex and let $\mathcal{R}_{l}$ be the set of all partitions of $X$, which not belong to $\mathcal{Q}_{l} \cup \mathcal{P}_{l}$. We observe that $\ker \beta \in \mathcal{Q}_{l} \cup \mathcal{P}_{l}$, whenever $\beta\in \OP(X,Y)$ with $|X\beta|=l$. In particular, $\ker \beta \in \mathcal{Q}_{l}$, whenever $\beta \in \O(X,Y)$.
Let us consider the case $l=m>1$. For $P\in \mathcal{P}_{m}$ with the blocks $A_{1}$,$A_{2}<\cdots <A_{m}$, let $\alpha _{P}$ be the transformation on $X$ defined by $$x\alpha_{P}:=a_{i}, \text{ whenever } x\in A_{i} \text{ for } 1\leq i\leq m$$ in the case $1\notin Y$ or $n\notin Y$ and $$x\alpha_{P}:=\left\{\begin{array}{ll}
a_{i+1}, & \text{if } x\in A_{i} \text{ for } 1\leq i<m \\
a_{1} & \text{if } x\in A_{m}
\end{array}\right.$$ in the case $1,n\in Y$. Clearly, $\ker \alpha _{P}=P$. With $X_{1}=\{1,\ldots ,\max A_{m}\}$, $X_{2}=\{\max A_{m}+1,\ldots ,n\}$ in the case $1\notin Y$ or $n\notin Y$ and $X_{1}=\{1,\ldots ,\max A_{m-1}\}$, $X_{2}=\{\max A_{m-1}+1,\ldots ,n\}$ in the case $1,n\in Y$, where $\max A_{m}$ ($\max A_{m-1}$) denotes the greatest element in the set $A_{m}$ ($A_{m-1}$, respectively), we can easy verify that $\alpha _{P}$ is orientation-preserving.
Further, let $\eta \in \T(X,Y)$ be defined by $$x\eta :=\left\{
\begin{array}{ll}
a_{i+1} & \mbox{if }~~ a_{i}\leq x<a_{i+1}\mbox{ for }1\leq i<m \\
a_{1} & \mbox{if }~~ x=a_{m} \\
a_{\Gamma} & \mbox{otherwise}
\end{array}\right. ~~\mbox{ with }~~ \Gamma :=\left\{
\begin{array}{ll}
1 & \mbox{if }~~ 1\notin Y \\
2 & \mbox{otherwise,}
\end{array}
\right.$$ in the case $1\notin Y$ or $n\notin Y$ and $$x\eta :=\left\{
\begin{array}{lll}
a_{i+1} & \text{if} & a_{i}\leq x<a_{i+1},~~ 1\leq i<m \\
a_{1}=1 & \text{if} & x = a_{m}=n
\end{array}\right.$$in the case that $1,n\in Y$. Notice that $P_0 :=\ker \eta \in \mathcal{P}_{m}$ if $1\notin Y$ or $n\notin Y$ and $\ker \eta \in \mathcal{Q}_{m}$ if $1,n\in Y$. In fact, $\eta \in \OP(X,Y)$ with $X_{1}=\{1,2,\ldots,a_{m}-1\}$ and $X_{2}=\{a_{m},a_{m}+1,\ldots,n\}$. Moreover, $\eta |_{Y}$ is a permutation on $Y$, namely $$\eta |_{Y}=\left(
\begin{array}{cccc}
a_{1} & \ldots & a_{m-1} & a_{m} \\
a_{2} & \cdots & a_{m} & a_{1}\end{array}\right).$$ We will denote by $\S(Y)$ the set of all permutations on $Y$. Note, $\beta \in \O(X,Y)$ implies that either $\beta|_{Y}$ is the identity mapping on $Y$ or $\beta|_{Y} \notin \S(Y)$.
The relative rank of $\OP(X,Y)$ modulo $\O(X,Y)$
================================================
In this section, we determine the relative rank of $\OP(X,Y)$ modulo $\O(X,Y)$. A part of these results were presented at the 47-th Spring Conference of the Union of Bulgarian Mathematicians in March 2018 and are published in the proceedings of this conference [@DKT].
If $m=1$ then $\OP(X,Y)$ is the set of all constant mappings and coincides with $\O(X,Y)$, i.e. $\rank(\OP(X,Y):\O(X,Y))=0$. So, we admit that $m>1$.
First, we will show that $$\mathcal{A}:=\{\alpha_{P}: P\in \mathcal{P}_{m}\}\cup \{\eta\}$$ is a relative generating set of $\OP(X,Y)$ modulo $\O(X,Y)$. Notice that $\eta=\alpha_{P_0}$ if $1\notin Y$ or $n\notin Y$.
\[le1\] For each $\alpha \in \OP(X,Y)$ with $\rank\alpha =m$, there is $\widehat{\alpha }\in \{\alpha _{P}: P\in \mathcal{P}_{m}\} \cup \O(X,Y)$ with $\ker \alpha =\ker \widehat{\alpha }$.
Let $\alpha \in \OP(X,Y)$ and let $X_{1},X_{2}\subseteq X$ as in the definition of an orientation-preserving transformation. If $X_{2}=\emptyset$ then $\alpha \in \O(X,Y)$. Suppose now that $X_{2}\neq \emptyset $ and let $X_{1}\alpha =\{x_{1}<\cdots <x_{r}\}$ and $X_{2}\alpha =\{y_{1}<\cdots
<y_{s}\}$ for suitable natural numbers $r$ and $s$. We observe that $X_{1}\alpha $ and $X_{2}\alpha $ have at most one joint element (only $x_{1}=y_{s}$ could be possible). If $x_{1}\neq y_{s}$ then $\ker \alpha =\{x_{1}\alpha
^{-1}<\cdots <x_{r}\alpha ^{-1}<y_{1}\alpha ^{-1}<\cdots <y_{s}\alpha
^{-1}\}=\ker \widehat{\alpha }$ with $\widehat{\alpha }=\left(
\begin{array}{cccccc}
x_{1}\alpha ^{-1} & \cdots & x_{r}\alpha ^{-1} & y_{1}\alpha ^{-1} & \cdots
& y_{s}\alpha ^{-1} \\
a_{1} & \cdots & a_{r} & a_{r+1} & \cdots & a_{r+s}\end{array}\right) \in \O(X,Y)$. If $x_{1}=y_{s}$ then $1,n\in x_{1}\alpha ^{-1} =
y_{s}\alpha ^{-1}$ and $\ker \alpha = \ker \alpha_P$ with $P = \{x_{1}\alpha ^{-1}, x_{2}\alpha ^{-1}<\cdots <x_{r}\alpha^{-1}<y_{1}\alpha ^{-1}<\cdots <y_{s-1}\alpha ^{-1}\}\in \mathcal{P}_{m}$.
\[le2\] $\OP(X,Y)=\left\langle \O(X,Y),\mathcal{A}\right\rangle $.
Let $\beta \in \OP(X,Y)$ with $\rank\beta =m$. Then there is $\theta \in
\{\alpha _{P}:P\in \mathcal{P}_{m}\}\cup \O(X,Y)$ with $\ker \beta =\ker
\theta$ by Lemma \[le1\]. In particular, there is $r\in \{0,\ldots ,m-1\}$ with $a_{1}\theta ^{-1}=a_{r+1}\beta ^{-1}$. Then it is easy to verify that $\beta
=\theta \eta ^{r}$, where $\eta ^{0}=\eta ^{m}$. Admit now that $i=\rank\beta <m$. Suppose that $\ker \beta \in \mathcal{P}_{i}$, say $\ker \beta =\{A_{1},A_{2}<\cdots <A_{i}\}$ with $1,n\in A_{1}$. Then there is a subpartition $P'\in \mathcal{P}_{m}$ of $\ker\beta$. We put $\theta =\alpha _{P'}$, $a=\min X\beta$, and let $T$ be a transversal of $\ker \theta$. In particular, we have $Y=\{x(\theta
|_{T})\eta ^{k}:x\in T\}$ for all $k\in \{1,\ldots ,m\}$. Since both mappings $\theta |_{T}:T\rightarrow Y$ and $\eta |_{Y}:Y\rightarrow Y$ are bijections, there is $k\in \{1,\ldots ,m\}$ with $a_{1}((\theta |_{T})\eta
^{k})^{-1}\beta =a$ and $a_{1}((\theta |_{T})\eta ^{k+1})^{-1}\beta \neq a$. Moreover, since $(\theta |_{T})\eta^{k}$ is a bijection from $T$ to $Y$ and both transformations $\theta \eta^{k}$ and $\beta $ are orientation-preserving, it is easy to verify that $f^{\ast }=((\theta |_{T})\eta ^{k})^{-1}\beta $ can be extended to an orientation-preserving transformation $f$ defined by $$xf=\left\{
\begin{array}{lll}
a_{1}f^{\ast } & \text{if} & x<a_{1} \\
a_{i}f^{\ast } & \text{if} & a_{i}\leq x<a_{i+1},~~ 1\leq i<m \\
a_{m}f^{\ast } & \text{if} & a_{m}\leq x,
\end{array}\right.$$ i.e. $f$ and $f^{\ast }$ coincide on $Y$. Moreover, $a_{1}f=a_{1}f^{\ast }=a_{1}((\theta |_{T})\eta ^{k})^{-1}\beta =a$. In order to show that $f$ is order-preserving, it left to verify that $nf\neq a$. Assume that $nf=a$, where $n\geq a_{m}$. Then $nf=a_{m}f^{\ast }=a_{m}f$, i.e. $(n,a_{m})\in \ker f$ and $n\eta =a_{m}\eta =a_{1}$. So, there is $x^{\ast }\in T$ such that $x^{\ast }((\theta |_{T})\eta ^{k})=a_{m}$, i.e. $x^{\ast }=a_{m}((\theta |_{T})\eta ^{k})^{-1}$. Now, we have $a=nf=a_{m}f^\ast=a_{m}((\theta |_{T})\eta ^{k})^{-1}\beta =a_{m}(\eta
^{k}|_Y)^{-1}(\theta |_{T})^{-1}\beta =a_{1}(\eta|_Y)^{-1}(\eta ^{k}|_Y)^{-1}(\theta
|_{T})^{-1}\beta =a_{1}((\theta |_{T})\eta ^{k+1})^{-1}\beta \neq a$, a contradiction.\
Finally, we will verify that $\beta =\theta \eta ^{k}f\in
\left\langle \O(X,Y),\mathcal{A}\right\rangle $. For this let $x\in X$. Then there is $\widetilde{x}\in T$ such that $(x,\widetilde{x})\in $ $\ker \beta $. So, we have $x\theta \eta ^{k}f=x\theta \eta ^{k}f^{\ast }=\widetilde{x}\theta \eta
^{k}((\theta |_{T})\eta ^{k})^{-1}\beta =\widetilde{x}\beta =x\beta $. Suppose now that $\ker \beta \notin \mathcal{P}_{i}$ and thus, $\ker \beta \in \mathcal{Q}_{i}$. Let $X\beta =\{b_{1},\ldots b_{i}\}$ such that $b_{1}\beta ^{-1}<\cdots <b_{i}\beta ^{-1}
$. Then we define a transformation $\varphi $ by $x\varphi =a_{j}$ for all $x\in b_{j-1}\beta ^{-1}$ and $2\leq j\leq i+1$. Clearly, $\varphi \in \O(X,Y)$. Further, we define a transformation $\nu \in \T(X,Y)$ by $$x\nu =\left\{
\begin{array}{ll}
b_{j-1} & \text{if } a_{j}\leq x < a_{j+1},~~ 2\leq j\leq i \\
b_{i} & \text{otherwise.}
\end{array}\right.$$ Since $\beta $ is orientation-preserving, there is $k\in
\{1,\ldots ,i\}$ such that $k=i$ or $b_{1}<\cdots <b_{k-1}>b_{k}<\cdots
<b_{i}$. Then $X_{1}=\{a_{1},\ldots ,a_{k+1}-1\}$ and $X_{2}=\{a_{k+1},
\ldots ,n\}$ gives a partition of $X$ providing that $\nu $ is orientation-preserving. Clearly, $\rank\nu =i$ and $1\nu =n\nu =b_{i}$. Thus, it is easy to verify that $\ker \nu \in \mathcal{P}_{i}$. Hence, $\nu
\in \left\langle \O(X,Y),\mathcal{A}\right\rangle $ by the previous case and it remains to show that $\beta =\varphi \nu \in \left\langle \O(X,Y),\mathcal{A}\right\rangle$. For this let $x\in X$. Then $x\in b_{j}\beta ^{-1}$ for some $j\in
\{1,\ldots ,i\}$, i.e. $x\varphi \nu =a_{j+1}\nu=b_{j}=x\beta $.
\
The previous proposition shows that $\mathcal{A}$ is a relative generating set for $\OP(X,Y)$ modulo $\O(X,Y)$. It remains to show that $\mathcal{A}$ is of minimal size.
\[le3\] Let $B\subseteq \OP(X,Y)$ be a relative generating set of $\OP(X,Y)$ modulo $\O(X,Y)$. Then $\mathcal{P}_{m}\subseteq \{\ker \alpha :\alpha \in B\}$.
Let $P\in \mathcal{P}_{m}$. Since $\alpha _{P}\in \OP(X,Y)=\left\langle
\O(X,Y),B\right\rangle $, there are $\theta _{1}\in \O(X,Y)\cup B$ and $\theta
_{2}\in \OP(X,Y)$ with $\alpha _{P}=\theta _{1}\theta _{2}$. Because of $\rank\alpha _{P}=m$, we obtain $\ker \alpha _{P}=\ker \theta _{1}$. Since $1\alpha _{P}=n\alpha _{P}$, we conclude that $\theta _{1}\notin \O(X,Y)$, i.e. $\theta _{1}\in B$ with $\ker \theta _{1}=\ker \alpha _{P}=P$.
\
In order to find a formula for the number of elements in $\mathcal{P}_{m}$, we have to compute the number of possible partitions of $X$ into $m+1$ convex sets. This number is $\left(
\begin{array}{c}
n-1 \\
m\end{array}\right)$. Thus, we have
\[re1\] $\left\vert \mathcal{P}_{m}\right\vert =\left(
\begin{array}{c}
n-1 \\
m
\end{array}
\right)$.
Now, we are able to state the main result of the section. The relative rank of $\OP(X,Y)$ modulo $\O(X,Y)$ depends of the fact whether both $1$ and $n$ belong to $Y$ or not.
\[th5\] For each $1 < m < n \in \mathbb{N}$,
1. $\rank(\OP(X,Y):\O(X,Y))=\left(
\begin{array}{c}
n-1 \\
m\end{array}\right)$ if $1\notin Y$ or $n\notin Y$;
2. $\rank(\OP(X,Y):\O(X,Y))=1+\left(
\begin{array}{c}
n-1 \\
m\end{array}\right)$ if $\{1,n\}\subseteq Y$.
1\. Note that $\ker \eta \in \mathcal{P}_{m}$ and $\eta = \alpha_{P_0}$. Hence, the set $\mathcal{A}=\{\alpha_{P}:P\in \mathcal{P}_{m}\}$ is a generating set of $\OP(X,Y)$ modulo $\O(X,Y)$ by Proposition \[le2\], i.e. the relative rank of $\OP(X,Y)$ modulo $\O(X,Y)$ is bounded by the cardinality of $\mathcal{P}_{m}$, which is $\left(
\begin{array}{c}
n-1 \\
m\end{array}\right)$ by Remark \[re1\]. But this number cannot be reduced by Lemma \[le3\].\
\
2. Let $B\subseteq \OP(X,Y)$ be a relative generating set of $\OP(X,Y)$ modulo $\O(X,Y)$. By Lemma \[le3\], we know that $\mathcal{P}_{m}\subseteq \{\ker \alpha
:\alpha \in B\}$. Assume that the equality holds. Note that $\ker \eta \in \mathcal{Q}_{m}$ and $\eta$ is not order-preserving. Hence, there are $\theta _{1},\ldots ,\theta _{l}\in
\O(X,Y)\cup B$, for a suitable natural number $l$, such that $\eta
=\theta _{1}\cdots \theta _{l}$. From $\rank\eta =m$, we obtain $\ker \theta
_{1}=\ker \eta $ and $\rank\theta _{i}=m$ for $i\in \{1,\ldots ,l\}$ and thus, $\{1,n\}\subseteq Y$ implies $(1,n)\notin \ker \theta _{i}$ for $i \in
\{2,\ldots ,l\}$. This implies $\theta _{2},\ldots ,\theta _{l}\in \O(X,Y)$. Since $\ker \theta _{1}=\ker \eta \notin \mathcal{P}_{m}$, we get $\theta
_{1}\in \O(X,Y)$, and consequently, $\eta =\theta _{1}\theta _{2}\cdots
\theta _{l}\in \O(X,Y)$, a contradiction. So, we have verified that $\left\vert \mathcal{P}_{m}\right\vert <\left\vert B\right\vert $, i.e. the relative rank of $\OP(X,Y)$ modulo $\O(X,Y)$ is greater than $\left(
\begin{array}{c}
n-1 \\
m\end{array}\right) $. But it is bounded by $1+\left(
\begin{array}{c}
n-1 \\
m\end{array}\right)$ due to Proposition \[le2\]. This proves the assertion.
\
We finish this section with the characterization of the minimal relative generating sets of $\OP(X,Y)$ modulo $\O(X,Y)$. We will recognize that among them there are sets with size greater than $\rank(\OP(X,Y):\O(X,Y))$.
Let $B\subseteq \OP(X,Y)$. Then $B$ is a minimal relative generating set of $\OP(X,Y)$ modulo $\O(X,Y)$ if and only if for the set $\widetilde{B}=\{\beta
\in B:\ker \beta \in \mathcal{Q}_{m}\} \subseteq B$ the following three statements are satisfied:$(i)$ $\mathcal{P}_{m} \subseteq \{\ker \beta :\beta \in B\setminus \widetilde{B}\}$,$(ii)$ $|B\setminus \widetilde{B}| = |\mathcal{P}_{m}|$, $(iii)$ $\eta |_{Y}\in \left\langle \beta |_{Y}:\beta \in B\right\rangle $ but $\eta |_{Y}\notin \left\langle \beta |_{Y}:\beta \in B\setminus \{\gamma
\}\right\rangle $ for any $\gamma \in \widetilde{B}$.
Suppose that the conditions $(i) - (iii)$ are satisfied for $\widetilde{B}=\{\beta \in B:\ker\beta \in \mathcal{Q}_{m}\}$. We will show that $\mathcal{A} \subseteq \left\langle \O(X,Y),B \right\rangle$. Let $\alpha \in \mathcal{A}\setminus\{\eta\}$. Then there is a partition $P = \{A_{1},A_{2}<\cdots<A_{m}\}\in \mathcal{P}_{m}$ such that $$\alpha = \alpha_{P}=\left(
\begin{array}{cccc}
A_{1} & A_{2} & \cdots & A_{m} \\
a_{1} & a_{2} & \cdots & a_{m}\end{array}\right), \mbox{ if } 1 \notin Y \mbox{ or } n \notin Y,$$ or $$\alpha = \alpha_{P}=\left(
\begin{array}{ccccc}
A_{1} & A_{2} & \cdots & A_{m-1} & A_m\\
a_{2} & a_{3} & \cdots & a_{m} & a_1
\end{array}
\right), \mbox{ if } 1, n \in Y.$$ Notice that in the latter case $a_1 = 1$ and $a_m = n$.\
Further, from $(i)$ it follows that there is $\beta \in B$ with $\ker\beta =\ker\alpha_P$, i.e. $\beta = \alpha_P$ or $$\beta =\left(
\begin{array}{ccccccc}
A_{1} & A_{2} & \cdots & A_{m-i+1} & A_{m-i+2} & \cdots & A_{m} \\
a_{i} & a_{i+1} & \cdots & a_{m} & a_{1} & \cdots & a_{i-1}\end{array}\right)$$ for some $i\in \{3,\ldots,m\}$. It is easy to verify that $\alpha_{P}=\beta^{k}\in \left\langle
B\right\rangle$, for a suitable natural number $k$. Hence, $\{\alpha_{P}: P \in \mathcal{P}_{m}\} \subseteq \left\langle\O(X,Y),B \right\rangle$. Further, $\ker \eta \in \mathcal{P}_{m}$, whenever $1\notin Y$ or $n\notin Y$, and $\ker \eta \in \mathcal{Q}_{m}$ otherwise. Thus, there is $\delta \in \left\langle \O(X,Y), B \right\rangle $ with $\ker \delta
=\ker \eta$. Then we obtain as above that $\eta =\delta^{l}\in \left\langle \O(X,Y),B \right\rangle$, for a suitable natural number $l$. Consequently, $\left\langle
\O(X,Y),\mathcal{A}\right\rangle \subseteq \left\langle \O(X,Y),B \right\rangle$. By Proposition \[le2\], we obtain $\OP(X,Y)=\left\langle \O(X,Y),B \right\rangle$. The generating set $B$ is minimal by properties $(i)$ and $(ii)$ together with Lemma \[le3\] and by the property $(iii)$ of $\widetilde{B}$.
Conversely, let $B$ be a minimal relative generating set of $\OP(X,Y)$ modulo $\O(X,Y)$. By Lemma \[le3\], there is a set $\overline{B}\subseteq B$ such that $\mathcal{P}_{m}=\{\ker \beta :\beta \in \overline{B}\}$ and $\left\vert
\overline{B}\right\vert =\left\vert \mathcal{P}_{m}\right\vert$. Since $\OP(X,Y) = \left\langle \O(X,Y),B \right\rangle$, there are $\beta _{1},\ldots ,\beta _{k}\in \O(X,Y)\cup B$ such that $\eta =\beta
_{1}\cdots \beta _{k}$. Without loss of generality, we can assume that there is not $\gamma \in \{\beta _{i}:1\leq i\leq k$, $\ker \beta
_{i}\in \mathcal{Q}_{m}\}=: \widehat{B}$ such that $\eta$ is a product of transformations in $\overline{B}\cup (\widehat{B}\setminus \{\gamma \})$. In the first part of the proof, we have shown that $\overline{B}\cup \widehat{B}$ is a relative generating set of $\OP(X,Y)$ modulo $\O(X,Y)$. Because of the minimality of $B$, we have $B=\overline{B}\cup \widehat{B}$, where $\{\ker
\beta :\beta \in B\setminus \widehat{B}\}\supseteq\mathcal{P}_{m}$, $|B\setminus\widehat{B}| = |\overline{B}| = |\mathcal{P}_{m}|$ and $\eta |_{Y}\in
\left\langle \beta |_{Y}:\beta \in B\right\rangle$ but $\eta |_{Y}\notin
\left\langle \beta |_{Y}:\beta \in B\setminus \{\gamma \}\right\rangle $ for any $\gamma \in \widehat{B}$.
\
In particular, for the relative generating sets of minimal size we have
$B\subseteq \OP(X,Y)$ is a relative generating set of $\OP(X,Y)$ modulo $\O(X,Y)$ of minimal size if and only if $|\widetilde{B}| = 1$ if $1,n \in Y$ and $\widetilde{B} = \emptyset$, otherwise.
The relative rank of $\T(X,Y)$ modulo $\OP(X,Y)$
================================================
In this section, we determine the relative rank of $\T(X,Y)$ modulo $\OP(X,Y)$ and characterize all minimal relative generating sets of $\T(X,Y)$ modulo $\OP(X,Y)$. Since $\O(X,Y)\leq \OP(X,Y)$, we see immediately that $\rank(\T(X,Y):\OP(X,Y))\leq S(n,m)-\left(
\begin{array}{c}
n-1 \\
m-1\end{array}\right) +1$. First, we state a sufficient condition for a set $B\subseteq
\T(X,Y)$ to be a relative generating set of $\T(X,Y)$ modulo $\OP(X,Y)$.
\[le7\] Let $B\subseteq \T(X,Y)$. If $\mathcal{R}_{m}\subseteq \{\ker \beta :\beta\in B\}$ and $\S(Y)\subseteq \left\langle \{\beta|_{Y}:\beta \in B\},\eta|_{Y}\right\rangle $ then $\left\langle \OP(X,Y),B\right\rangle =\T(X,Y)$.
Let $\gamma \in \T(X,Y)$ with $\rank \gamma =k \leq m$. We will consider two cases.
*Case 1.* Suppose that $\ker \gamma \in \mathcal{R}_{k}$. Then $\ker \gamma$ contains a non-convex set which cannot be decomposed into two convex sets, which contain $1$ and $n$, respectively. Since $k\leq m$, we can divide the partition $\ker \gamma$ into a partition $P\in \mathcal{R}_{m}$ such that $P$ contains a non-convex set which cannot be decomposed into two convex sets, which contain $1$ and $n$, respectively (if $k=m$ then we put $P=\ker \gamma$). Since $\mathcal{R}_{m}\subseteq \{\ker
\beta :\beta \in B\}$, there is $\lambda \in B$ with $\ker \lambda = P$. It is clear that $X\lambda = Y$.\
Further, let $X\gamma = \{y_1 < y_2 < \cdots < y_k\}$ and define the sets $$A_i = \{x \in Y : x\lambda^{-1} \subseteq y_i\gamma^{-1}\}$$ for $i = 1,\ldots,k$. It is clear that $\{A_1, A_2, \ldots, A_k\}$ is a partition of $Y$. Moreover, let $\{C_1 < C_2 < \cdots < C_k\} \in \mathcal{Q}_k$ be a partition of $X$ such that $|C_i \cap Y| = |A_i|$ for all $i = 1,\ldots,k$. Let $A_i = \{a_{i_1} < a_{i_2} < \cdots < a_{i_{t_i}}\}$ and $C_i \cap Y = \{c_{i_1} < c_{i_2} < \cdots < c_{i_{t_i}}\}$ with $t_i \in \{1, \ldots, m\}$ for $i \in \{1, \ldots, k\}$. We define a bijection $$\sigma: \bigcup_{i=1}^k A_i = Y \longrightarrow \bigcup_{i=1}^k (C_i \cap Y) = Y$$ on $Y$ with $a_{i_l}\sigma = c_{i_l}$, for $l = 1,\ldots,t_i$ and $i = 1,\ldots,k$. Since $\sigma \in \S(Y)$ and $\S(Y)\subseteq \left\langle \{\beta|_{Y}:\beta \in B\},\eta|_{Y}\right\rangle$ there is $\mu \in \langle B, \eta\rangle$ with $\mu|_Y = \sigma$.\
Finally, we define a transformation $\nu \in \O(X,Y) \subseteq \OP(X,Y)$ with $\ker \nu = \{C_1 < C_2 < \cdots < C_k\}$ and $x\nu = y_i$ for all $x \in C_i$ and $i = 1,\ldots,k$.\
Therefore, we have $\lambda, \mu, \nu \in \left\langle \OP(X,Y),B\right\rangle$ and it remains to show that $\gamma = \lambda\mu\nu$, i.e. $\gamma \in \left\langle \OP(X,Y),B\right\rangle$. Let $x \in X$. Then $x\gamma = y_i$ for some $i \in \{1,\ldots,k\}$ and we have $$x\gamma = y_i \Rightarrow x\lambda = z \in A_i \Rightarrow z\mu = u \in C_i \cap Y \Rightarrow u\nu = y_i.$$ Hence, $x\gamma = y_i = x(\lambda\mu\nu)$ and we conclude $\gamma = \lambda\mu\nu$.
*Case 2.* Suppose that $\ker \gamma \notin \mathcal{R}_{k}$, i.e. $\ker \gamma \in \mathcal{Q}_{k}\cup \mathcal{P}_{k}$ and there is $\rho_{1}\in \OP(X,Y)$ with $\ker\rho_{1}=\ker \gamma$. Further, there is a partition $P = \{D_{y} : y \in X\rho_{1}\} \in \mathcal{R}_{k}$ such that $y\in D_{y}$, for all $y\in X\rho_{1}$. Then we define a transformation $\rho_{2} : X \rightarrow X\gamma$ with $\ker\rho_{2} = P$ and $\{x\rho_2\} = y\rho_1^{-1}\gamma$ for all $x \in D_y$ and $y\in X\rho_{1}$. Since $\ker \rho_{1}=\ker \gamma$, the transformation $\rho_2$ is well defined and we have $\gamma = \rho_{1}\rho_{2}$. Moreover, $\rho_2 \in \left\langle \OP(X,Y),B \right\rangle$ by Case 1 (since $\ker \rho_2 \in \mathcal{R}_{k}$) and thus $\gamma =\rho_{1}\rho_{2}\in \left\langle \OP(X,Y),B \right\rangle$.
\[lenew\] $\left\langle \eta |_{Y}\right\rangle =\left\langle \left\{ \beta
|_{Y}:\beta \in \OP(X,Y)\right\} \right\rangle \cap \S(Y)$.
The inclusion $\left\langle \eta |_{Y}\right\rangle \subseteq \left\langle
\left\{ \beta |_{Y}:\beta \in \OP(X,Y)\right\} \right\rangle \cap \S(Y)$ is obviously. Let now $\beta \in \OP(X,Y)$ with $\beta |_{Y}\in \S(Y)$. Then there is $k\in \{1,\ldots ,m\}$ such that $$\beta =\left(
\begin{array}{cccccc}
A_{1} & \cdots & A_{m-k+1} & A_{m-k} & \cdots & A_{m} \\
a_{k} & \cdots & a_{m} & a_{1} & \cdots & a_{k-1}\end{array}\right)$$ with $\{A_{1},A_{2}<\cdots <A_{m}\} \in \mathcal{P}_{m} \cup \mathcal{Q}_{m}$ and $a_{i}\in A_i$ for $i\in \{1,\ldots ,m\}$ since $Y$ is a transversal of $\ker \beta $. Thus, $$\beta |_{Y}=\left(
\begin{array}{cccccc}
a_{1} & \cdots & a_{m-k+1} & a_{m-k} & \cdots & a_{m} \\
a_{k} & \cdots & a_{m} & a_{1} & \cdots & a_{k-1}\end{array}\right) =(\eta |_{Y})^{m-k+1}\in \left\langle \eta |_{Y}\right\rangle.$$ This shows that $\left\langle \left\{ \beta |_{Y}:\beta \in \OP(X,Y)\right\}
\right\rangle \cap \S(Y)\subseteq \{(\eta |_{Y})^{p}:p\in \mathbb{N}
\}=\left\langle \eta |_{Y}\right\rangle$.
The following lemmas give us necessary conditions for a set $B\subseteq
\T(X,Y)$ to be a relative generating set of $\T(X,Y)$ modulo $\OP(X,Y)$.
\[le8\] Let $B\subseteq \T(X,Y)\setminus \OP(X,Y)$ with $\left\langle \OP(X,Y),B\right\rangle =\T(X,Y)$. Then $\S(Y)\subseteq \left\langle \{\beta |_{Y}:\beta \in B\},\eta|_{Y}\right\rangle$.
Let $\sigma \in \S(Y)$. We extend $\sigma$ to a transformation $\gamma : X \rightarrow Y$, i.e. $\gamma|_{Y}=\sigma$. Hence, there are $\gamma_{1},\ldots,\gamma_{k}\in \OP(X,Y)\cup B$ (for a suitable natural number $k$) such that $\gamma=\gamma_{1}\cdots \gamma_{k}$. Since the image of any transformation in $\T(X,Y)$ belongs to $Y$, we have $\sigma =\gamma|_{Y}=\gamma_{1}|_{Y}\cdots \gamma_{k}|_{Y}$. Moreover, from $\sigma \in \S(Y)$, we conclude $\gamma_{i}|_{Y}\in \S(Y)$ for $1\leq i\leq k$. Let $\gamma_{i}\in \OP(X,Y)$ for some $i\in\{1,\ldots,k\}$. Then by Lemma \[lenew\] $$\gamma_{i}|_{Y}=\left(
\begin{array}{cccccc}
a_{1} & \cdots & a_{t} & a_{t+1} & \cdots & a_{m} \\
a_{m-t+1} & \cdots & a_{m} & a_{1} & \cdots & a_{m-t}\end{array}\right) \in \langle\eta |_{Y}\rangle$$ for a suitable natural number $t$. This shows $\sigma
\in \left\langle \{\beta |_{Y}:\beta \in B\},\eta |_{Y}\right\rangle$.
\[le9\] Let $B\subseteq \T(X,Y)\setminus \OP(X,Y)$ with $\left\langle \OP(X,Y),B\right\rangle =\T(X,Y)$. Then $\mathcal{R}_{m}\subseteq \{\ker \beta :\beta \in B\}$.
Assume that there is $P\in \mathcal{R}_{m}$ with $P \not\in \{\ker \beta :\beta \in B\}$. Let $\gamma \in \T(X,Y)$ with $\ker\gamma =P$. Then there are $\theta_{1}\in \OP(X,Y)\cup B$ and $\theta_{2}\in \T(X,Y)$ such that $\gamma = \theta _{1}\theta _{2}$. Since $\rank\gamma = m$, we obtain $\ker \gamma =\ker \theta_{1}= P$. Thus, $\theta_{1}\not\in B$, i.e. $\theta_{1}\in \OP(X,Y)$ and $\ker \theta_{1}\in \mathcal{Q}_{m}\cup \mathcal{P}_{m}$, contradicts $\ker \theta_{1} = P \in \mathcal{R}_{m}$.
\
Lemma \[le9\] shows that $\rank(\T(X,Y):\OP(X,Y))\geq \left\vert \mathcal{R}_{m}\right\vert $. We will verify the equality.
\[le10\] $\left\vert \mathcal{R}_{m}\right\vert = S(m,n)-\left(
\begin{array}{c}
n \\
m\end{array}\right)$.
The cardinality of the set $\mathcal{D}_{m}:=\mathcal{R}_{m}\cup \mathcal{P}_{m}$ was determined in [@TK]. The authors show that $\left\vert \mathcal{D}_{m}\right\vert
=S(m,n)-\left(
\begin{array}{c}
n-1 \\
m-1\end{array}\right)$. Because of $\mathcal{R}_{m}\cap \mathcal{P}_{m}=\emptyset$, we obtain $\mathcal{R}_{m}=\mathcal{D}_{m}\setminus \mathcal{P}_{m}$. Since $|\mathcal{P}_{m}| =\left(
\begin{array}{c}
n-1 \\
m
\end{array}
\right)$ (see Remark \[re1\]) it follows $\left\vert \mathcal{R}_{m}\right\vert =\left\vert \mathcal{D}_{m}\right\vert
-\left\vert \mathcal{P}_{m}\right\vert =S(m,n)-\left(
\begin{array}{c}
n-1 \\
m-1\end{array}\right) -\left(
\begin{array}{c}
n-1 \\
m\end{array}\right) =S(m,n)-\left(
\begin{array}{c}
n \\
m\end{array}\right)$.
\
Finally, we can state the relative rank of $\T(X,Y)$ modulo $\OP(X,Y)$.
\[th11\] $\rank(\T(X,Y):\OP(X,Y))=S(m,n)-\left(
\begin{array}{c}
n \\
m\end{array}\right)$.
If $m=1$ then $\T(X,Y)=\OP(X,Y)$, i.e. $\rank(\T(X,Y):\OP(X,Y))=0$. On the other hand, we have $S(1,n)=n=\left(
\begin{array}{c}
n \\
1\end{array}\right) $. Suppose now that $n\geq 2$. By Lemmas \[le9\] and \[le10\], we obtain $\rank(\T(X,Y):\OP(X,Y))\geq \left\vert
\mathcal{R}_{m}\right\vert =S(m,n)-\left(
\begin{array}{c}
n \\
m\end{array}\right) $. In order to prove the equality, we have to find a relative generating set $B$ of $\T(X,Y)$ modulo $\OP(X,Y)$ with $\left\vert
B \right\vert = |\mathcal{R}_{m}|$. We observe that for each $P \in \mathcal{R}_{m}$, there is $\beta_P \in \T(X,Y)$ with $\ker \beta_P = P$, which will be fixed. Let $\mathcal{B} := \{\beta_P : P \in \mathcal{R}_{m}\}$. If $m=2$ then $\mathcal{R}_{m}=\emptyset$ and $\S(Y)=\{\eta |_{Y},(\eta |_{Y})^{2}\} = \langle \eta |_{Y} \rangle$, obviously. If $m\geq 3$ then without loss of generality we can assume that there is $P'\in \mathcal{R}_{m}$ such that $Y$ is a transversal of $\ker \beta_{P'}$ and $\beta_{P'}|_{Y}=\left(
\begin{array}{ccccc}
a_{1} & a_{2} & a_{3} & \cdots & a_{m} \\
a_{2} & a_{1} & a_{3} & \cdots & a_{m}\end{array}\right)$. It is well known that $\S(Y)=\left\langle \beta_{P'}|_Y, \eta|_Y \right\rangle$. Hence, $\mathcal{B}$ is a relative generating set of $\T(X,Y)$ modulo $\OP(X,Y)$ by Lemma \[le7\]. Since $|\mathcal{B}| = |\mathcal{R}_{m}|$, we obtain the required result.
Now we will characterize the minimal relative generating sets of $\T(X,Y)$ modulo $\OP(X,Y)$. The minimal relative generating sets do not coincide with the relative generating sets of size $\rank(\T(X,Y):\OP(X,Y))$.
Let $B\subseteq \T(X,Y)$. Then $B$ is a minimal relative generating set of $\T(X,Y)$ modulo $\OP(X,Y)$ if and only if there is a set $\widetilde{B}\subseteq B$ such that the following three statements are satisfied:$(i)$ $\mathcal{R}_{m} \subseteq \{\ker \beta :\beta \in B\setminus \widetilde{B}\}$,$(ii)$ $|B\setminus \widetilde{B}| = |\mathcal{R}_{m}|$, $(iii)$ $\S(Y) \subseteq \left\langle \{\beta|_{Y}:\beta \in B\}, \eta|_{Y} \right\rangle$ but $\S(Y) \nsubseteq \left\langle \{\beta |_{Y}:\beta \in B\setminus \{\gamma\}\}, \eta|_{Y} \right\rangle$ for any $\gamma \in B$ with $\ker \gamma \in \{\ker \beta : \beta \in \widetilde{B}\}$.
Suppose that the conditions $(i) - (iii)$ are satisfied. Then by Lemma \[le7\] we have $\left\langle \OP(X,Y),B\right\rangle =\T(X,Y)$. It remains to show that $B$ is minimal. Assume that there is $\gamma
\in B$ such that $\left\langle \OP(X,Y),B\setminus \{\gamma \}\right\rangle
=\T(X,Y)$. Note that $\alpha \beta |_{Y}=\alpha |_{Y}\beta |_{Y}$ for all $\alpha ,\beta \in \T(X,Y)$. Hence, we can conclude that $\S(Y)\subseteq
\left\langle \left\{ \beta |_{Y}:\beta \in \T(X,Y)\right\} \right\rangle
\subseteq \left\langle \left\{ \beta |_{Y}:\beta \in \OP(X,Y)\cup (B\setminus
\{\gamma \})\right\} \right\rangle =\left\langle \left\{ \beta |_{Y}:\beta
\in B\setminus \{\gamma \}\right\} ,\eta |_{Y}\right\rangle $ by Lemma \[lenew\]. Hence, $\ker \gamma \notin \{\ker\beta :\beta \in \widetilde{B}\}$ by $(iii)$. This implies that $\gamma \in B\setminus \widetilde{B}$ and $|(B\setminus \widetilde{B})\setminus \{\gamma \}|<|\mathcal{R}_{m}|$ by $(ii)$, i.e. $\mathcal{R}_{m}\nsubseteqq \{\ker \beta :\beta \in (B\setminus \widetilde{B})\setminus \{\gamma \}\}$. Since $\ker\gamma \notin \{\ker \beta :\beta \in \widetilde{B}\}$, we have $\mathcal{R}_{m}\nsubseteqq \{\ker \beta :\beta \in (B\setminus \{\gamma \})\}$ and by Lemma \[le9\], we obtain that $\left\langle \OP(X,Y),B\setminus \{\gamma
\}\right\rangle \neq \T(X,Y)$, a contradiction. This shows that $B$ is a minimal relative generating set of $\T(X,Y)$ modulo $\OP(X,Y)$.
Conversely, let $B$ be a minimal relative generating set of $\T(X,Y)$ modulo $\OP(X,Y)$. We have $\mathcal{R}_{m}\subseteq
\{\ker \beta :\beta \in B\}$ and $\S(Y)\subseteq \left\langle \{\beta
|_{Y}:\beta \in B\},\eta |_{Y}\right\rangle $ by Lemma \[le9\] and Lemma \[le8\], respectively. Then there exists a set $\widetilde{B}\subseteq B$ with $|B\setminus \widetilde{B}| = |\mathcal{R}_{m}|$ and $\mathcal{R}_{m}\subseteq \{\ker \beta :\beta \in (B\setminus \widetilde{B})\}$. For the set $\widetilde{B}$, the conditions $(i)$ and $(ii)$ are satisfied. Assume now that there is $\gamma \in B$ with $\ker \gamma \in \{\ker \beta :\beta
\in \widetilde{B}\}$ such that $\S(Y)\subseteq \left\langle \{\beta
|_{Y}:\beta \in B\setminus \{\gamma\}\},\eta |_{Y}\right\rangle$. Then because of $\mathcal{R}_{m}\subseteq \{\ker \beta :\beta \in (B\setminus \{\gamma\})\}$, the set $B\setminus \{\gamma)$ is a relative generating set of $\T(X,Y)$ modulo $\OP(X,Y)$ by Lemma \[le7\]. This contradicts the minimality of $B$. Consequently, $(iii)$ is satisfied.
\
In particular, for the relative generating sets of minimal size we have
$B\subseteq \T(X,Y)$ is a relative generating set of $\T(X,Y)$ modulo $\OP(X,Y)$ of minimal size if and only if $\widetilde{B}=\emptyset$.
[99]{}
Catarino P. M., Higgins P. M., The monoid of orientation-preserving mappings on a chain, Semigroup Forum, 58 (1999), 190–206.
Dimitrova I., Fernandes V. H., Koppitz J., A note on generators of the endomorphism semigroup of an infinite countable chain, Journal of algebra and its applications, 16(2) (2017), 1750031.
Dimitrova I., Koppitz J., Tinpun K., On the relative rank of the semigroup of orientation-preserving transformations with restricted range, Proceedings of the 47-th Spring Conference of the Union of Bulgarian Mathematicians, (2018), 109–114.
Fernandes V. H., Honyam P., Quinteiro T. M., Singha B., On semigroups of endomorphisms of a chain with restricted range, Semigroup Forum, 89 (2014), 77–104.
Fernandes V. H., Honyam P., Quinteiro T. M., Singha B., On semigroups of orientation-preserving transformations with restricted range, Comm. Algebra, 44 (2016), 253–264.
Fernandes V. H., Sanwong J., On the rank of semigroups of transformations on a finite set with restricted range, Algebra Colloq., 21 (2014), 497–510.
Gomes G. M. S., Howie J. M., On the rank of certain semigroups of order-preserving transformations, Semigroup Forum, 51 (1992), 275–282.
Gomes G. M. S., Howie J. M., On the ranks of certain finite semigroups of transformations, Math. Proc. Cambridge Philos. Soc., 101 (1987), 395–403.
Higgins P. M., Mitchell J. D., Ruškuc N., Generating the full transformation semigroup using order preserving mappings, Glasgow Math. J., 45 (2003), 557–566.
Howie J. M., Fundamentals of semigroup theory, Oxford, Oxford University Press, 1995.
Howie J. M., McFadden R. B., Idempotent rank in finite full transformation semigroups, Proc. Royal Soc. Edinburgh, 114A (1990), 161–167.
Howie J. M., Ruškuc N., Higgins P. M., On relative ranks of full transformation semigroups, Comm. Algebra, 26 (1998), 733–748.
McAlister D., Semigroups generated by a group and an idempotent, Comm. in Algebra, 26 (1998), 515–547.
Ruškuc N., On the rank of completely 0-simple semigroups, Math. Proc. Cambridge Philos. Soc., 116 (1994), 325–338.
Symons J. S. V., Some results concerning a transformation semigroup, J. Austral. Math. Soc., 19 (1975), 413–425.
Tinpun K., Koppitz J., Relative rank of the finite full transformation semigroup with restricted range, Acta Mathematica Universitatis Comenianae, 85(2) (2016), 347–356.
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National Policy
The National Policy was a Canadian economic program introduced by John A. Macdonald's Conservative Party in 1876 and put into action in 1879. It called for high tariffs on imported manufactured items to protect the manufacturing industry, the building of the Canadian Pacific Railway, and the fostering of immigration to Western Canada. Macdonald campaigned on the policy in the 1878 election, and defeated the Liberal Party, which supported free trade. It lasted from 1879 until sometime in the early 1950s.
Usage
The term National Policy originally referred to a proposed raise in tariffs by the Macdonald-led Conservatives ("Tories") during the 1878 election campaign. Over time, the term became associated with the entire Tory platform for developing the economy, especially increased immigration to Western Canada and the development of the Canadian Pacific Railway's transcontinental line.
Manufacturers
Macdonald hoped that by creating a strong manufacturing base in Canada, the nation would become more secure and less reliant on the United States. He was also closely linked to the Montreal and Toronto business interests that would benefit from such a policy, and they played an important role in keeping the Tories in office until 1896.
Despite a brief experiment with free trade in the Canadian–American Reciprocity Treaty before Confederation, the Americans were intent on pursuing a strongly protectionist policy, with tariffs higher than Canada imposed under the National Policy.
With such high American tariffs, Canadian firms could not compete in the United States, but American firms could enter Canada. Canadian producers were particularly hurt by American producers dumping surplus goods in Canada to avoid lowering prices in the United States. Tariffs were put on goods coming into Canada, which made American goods more expensive.
The policy was introduced in the budget of March 14, 1879, and it created high tariffs on the import of most manufactured goods. At the same time, the tariffs on raw materials were lowered also to help manufacturers. The tariff was not as high as that in the United States, however. The Canadian government was dependent upon revenue from customs; an income tax had not yet been introduced, largely because it was feared that it would reduce immigration when Canada was already having difficulty attracting immigrants. Too high a tariff would have cut off almost all imports, thus depriving the government of revenue.
The policy quickly became one of the most central aspects of Canadian politics, and it played an important role in keeping the Tories in power until 1896, when Wilfrid Laurier and the Liberals campaigned on a promise to keep the National Policy in place. While many Liberals still supported free trade, the National Policy was too popular in Ontario and Quebec for it to end. When the Liberals campaigned on free trade in the 1911 election, they lost the election.
Unpopularity in the west
Although the policy was popular in central Canada, it was extremely unpopular in western Canada. This opposition to the National Policy played an important role in the rise of the Progressive Party of Canada in the 1920s. Its platform was entitled the "New National Policy", and it advocated free trade.
Dismantled by Liberals
The National Policy was slowly dismantled under the many years of Liberal rule under William Lyon Mackenzie King and Louis St. Laurent. At the same time, the United States was lowering its tariffs. Economic integration surged during World War II, and in 1965 the automobile industry in the two nations became fully integrated. However, complete free trade was not achieved until 1988 with the Canada–United States Free Trade Agreement brought in by Brian Mulroney's Progressive Conservative government.
Assessment
The assessment of the National Policy is mixed. In general, economists argue that it increased prices and lowered Canada's efficiency and ability to compete in the world. By not becoming merged into the larger, more efficient American economy, Canada built too many monopolistic firms and too many small inefficient factories with high prices for consumers. The overall impact was not large because the policy applied only to the manufacturing sector, which played a relatively small role, compared to agriculture, fishing, transportation, mining, lumbering and services, which were not affected by the National Policy. Historians tend to see the policy in a more positive light by viewing it as a necessary expense to create a unified nation independent of the United States.
In the years right after the policy was introduced, Canada experienced the same type of economic boom that many other nations experienced, as well as the construction of a manufacturing base and the development of the nation, which is generally what the Tories and economic nationalists use to justify the policy. However, Canada also suffered a net population outflow, as more people emigrated from Canada (usually to the United States) than arrived as immigrants.
Eden and Molot (1993) argue that there have been three national policies in Canada: the "National Policy" of defensive expansionism, 1867–1940; compensatory liberalism, 1941–81; and market liberalism, starting in 1982. The defensive expansion phase relied on the tariff, railway construction, and land settlement to build the country. The second national policy combined a commitment to the GATT system, Keynesian macroeconomic policies, and the construction of a domestic social welfare net. Current national policy relies on Canada-US free trade and NAFTA free trade, market-based policies, and fiscal restraint. They argue for a fourth policy called "strategic integration." It would consist of free trade, both external and internal; the building of a national telecommunications infrastructure based on the development and diffusion of information technologies; and human capital development.
See also
American System (economic plan), a similar policy used in the United States
Economic nationalism
Graham Fraser (industrialist)
Protectionism
Tariffs
References
Barber, Clarence L. "Canadian Tariff Policy" in Canadian Journal of Economics and Political Science, Vol. 21, No. 4 (Nov., 1955), pp. 513–530 explains the concept of the effective rate of protection in JSTOR
Eden, Lorraine and Molot, Maureen Appel. "Canada's National Policies: Reflections on 125 Years" Canadian Public Policy 1993 19(3): 232-251.
Fowke, Vernon C. The National Policy and the Wheat Economy (Toronto, 1957)
Fowke, V. C. "The National Policy-Old and New" Canadian Journal of Economics and Political Science, Vol. 18, No. 3 (Aug., 1952), pp. 271–286 in JSTOR
Fowke, Vernon C. "National Policy and Western Development in North America" Journal of Economic History, Vol. 16, No. 4 (Dec., 1956), pp. 461–479 in JSTOR
External links
The National Policy and Canadian Federalism
George Hoberg, "Canada and North American Integration"
Category:Economic history of Canada
Category:Economic nationalism
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1. Field of the Invention
The present invention relates to an image forming apparatus, an image forming method, and a computer-readable recording medium.
2. Description of the Related Art
There are conventionally-known image forming apparatuses that form images on a recording medium, such as sheet, by using colorless and transparent toner in addition to colored toner of CMYK, or the like. Furthermore, in order to utilize the above-described image forming apparatuses, there is a known technology for achieving visual surface effects by attaching control data to document data, such as “control code for providing predetermined glossy texture to the surface of an image although it is hard to be recognized as a pattern” or “control code for specifying a pattern that may be definitely recognized as a pattern”.
For example, there is a disclosed printing control device that applies a visual effect to a recording medium (see Japanese Patent Application Laid-open No. 2012-083736). Japanese Patent Application Laid-open No. 2012-083736 discloses the configuration of the printing control device that processes the gloss-control plate data that specifies the gloss control value for determining the type of surface effect to be applied and its area on the recording medium on a pixel by pixel basis.
However, according to the above-described conventional technology for applying visual surface effects, the control code, processed by a raster image processor (RIP), is replaced with a pattern. Therefore, if images are recorded after the document data is reduced in size, e.g., images are combined before they are formed on a recording medium, the pattern of the transparent toner is used without being reduced in size; therefore, there is a problem in that it is difficult to achieve the desired visual surface effect.
In view of the conventional problem, there is a need to provide an image forming apparatus, an image forming method, and a computer-readable recording medium having a computer program that make it possible to achieve the desired visual surface effect even in a case where an image is recorded on a recording medium after the document data is reduced or enlarged in size.
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Q:
Java bytecode with Jasmin: why is the message not printed on the screen?
I recently became interested in Java bytecode and I created the following Hello World program.
The "Hello World" is printed, however I can't figure out why "Creating awesome object" isn't printed. Can you help me figure out what I'm doing wrong?
.class public HelloWorld
.super java/lang/Object
.method public <init>()V
.limit stack 2
aload_0 ; push 'this' unto stack
invokespecial java/lang/Object/<init>()V ; invoke constructor
getstatic java/lang/System/out Ljava/io/PrintStream;
ldc "Creating awesome object!"
invokevirtual java/io/PrintStream/println(Ljava/lang/String;)V
return
.end method
.method public static main([Ljava/lang/String;)V
.limit stack 2
getstatic java/lang/System/out Ljava/io/PrintStream;
ldc "Hello world"
invokevirtual java/io/PrintStream/println(Ljava/lang/String;)V
return
.end method
A:
I don't know much about Java bytecode, but it seems to me you don't create an instance of HelloWorld in main. If you don't create an instance, the constructor does not get called, so there you have it. :)
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A van reportedly carrying gas cylinders has exploded after being driven into the Australian Christian Lobby headquarters in Canberra on Wednesday night, setting the building alight.
There were no injuries suffered from people inside the building but the driver is being treated for his injuries in hospital.
ACT Policing said the van was carrying gas cylinders which were exploded at approximately 10.45pm. The vehicle was destroyed and the two-storey office building, named Eternity House, was badly damaged by fire.
The police later said in a statement they had established the actions of the 35-year-old male driver "were not politically, religiously or ideologically motivated".
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Last night I attended a winter wedding in Karachi, Pakistan. There was singing and dancing and both men and women mingled together under a voluminous violet tent with strings of marigolds hanging down the poles. The men wore shalwar kurta with waistcoats and warm woollen shawls. The women wore brightly-colored shalwar kameezes, saris, and ghararas (long skirts), moving around the tent like glittering butterflies as Bollywood music thumped from the speakers around the dancefloor. Some members of the family had their heads covered in jewel-toned scarves that matched the colors of their clothes. One or two of the women wore their traditional dupattas easily over their heads. The majority of the women, though, wore their hair free, blow-dried into elaborate curls or straight curtains of silky dark tresses.
This is the Muslim country in which I was born and raised, and the scene refutes the results of the recent University of Michigan’s Institute for Social Research survey asking “What style of dress is appropriate for women in public?” The participants were given six headshots of brown women wearing various types of headgear, from most to least covered. Which is ridiculous, because everyone knows that at a Pakistani wedding the focus is on your clothes, shoes, jewelry and handbag. Nobody’s looking at your head unless you’ve actually decided to go punk and shave all your hair off.
The study found that few favored the type of burqa known colloquially as the “shuttlecock”, the blue bag with mesh over the eyes favored by the fashion-forward Taliban in Afghanistan. The slightly more liberated black burqa with matching face-veil garnered more support from their chic peers in Saudi Arabia. Most popular in this survey seemed to be a blood-circulation-cutting white hijab over a woman’s head, and only Lebanon favors godless women who don’t want to cover their hair at all (no surprise there, as Lebanon is considered as un-Islamic as you can get while still being Muslim).
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But while the researchers thought that they were perhaps uncovering a profound truth about Muslim opinion on women’s fashion, the survey provoked a degree of ridicule amongst Muslims on social media. What purpose did asking the question serve beyond a strange Orientalist obsession with what Muslim women wear? Who was answering it, men or women? And why should it matter so much what “people” think women “should” wear – can’t Muslim women decide for themselves what is appropriate without input from an anonymous group of participants from “around the world” (in truth seven Middle Eastern Muslim countries, as if Muslims don’t live anywhere else, like Europe, America, or Africa)?
The best response to it was blogger and satirist Karl Sharro’s parody survey by an Arab university asking “What style of dress is appropriate for American women?” Six women were presented wearing these styles of headdress:
If I were writing about this survey, I would ask, in a breathless headline worthy of the Daily Mail, “So, just why ARE people so obsessed with how Muslim women dress?” In the wedding I described above, nobody thought twice about what anyone had chosen to wear; even the young girl with the scandalously low-slung sari and the tight body sheathe sequinned top that revealed her midriff and bare shoulders flitted around at ease in the gathering -- the shameless hussy.
Growing up in Pakistan, I’d never seen anyone wear a hijab, and burqas were reserved for the very traditional women of my family who observed “purdah”, the separation of men and women first prescribed for the wives of the Prophet Mohammed and adopted by the female descendents of his family. It was only in the late 1980s that I saw my first hijab, worn by the mother of a Pakistani-American girl from Peoria, Illinois. Even the draconian years of Zia ul Haq’s Islamic dictatorship couldn’t make Pakistani women abandon their bouffant hairstyles and traffic-stopping golden “streaks”.
Saudi-Wahabi social influence filtered to Pakistan and much of the rest of the non-Arab world throughout the next two decades, thanks to a campaign that attempted to export the kingdom’s religio-social values to its would-be satellite states. Slowly, more and more women started to wear the black burqa and the tight hijab – not because they wanted to be pious, but because they wanted to emulate what suddenly seemed trendy amongst Gulf Arabs. The Iranian-style manteau and black scarf never caught on in Pakistan because being able to carry off the look requires the type of bold beauty that is the signature of Iranian women, while we Pakistanis prefer to rely on an amalgam of Bollywood, Gulf Arab, and our own indigenous traditions to make our fashion statements.
Which brings me to my point: Muslim women’s fashions have been interpreted and overanalyzed by the Western world as some sort of profound assertion of political identity or religious stance. Yes, there is an element of that in there, but the bigger truth is that Muslim women wear what they do, including what’s on their heads, because of how it makes them look and feel, just like all women around the world, and it takes on the cultural overtones of the milieu in which they live. There’s no need to survey this or pathologize it: there’s certainly no point in turning it into a value judgment. If people truly care about the autonomy and agency of Muslim women, as this survey seems to imply, they should just leave the warddrobe choices to Muslim women themeselves, and find a better medium through which to express their concern.
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Tokyo – Awesome/Crazy city
We are finally catching up to finish writing about our Japan experience… two big ones are missing, Tokyo, in this post, and Kyoto to come shortly… We got a chance to visit Tokyo twice during our stay in Japan. We spent one weekend there with a few of our friends who were visiting Japan, Annmarie, Trev and Torie. We also spent the last couple of days on the way out there. We got into Tokyo Station by Shinkansen (Bullet train) late on a friday afternoon. We really enjoyed the bullet train experience! Very comfortable and civilised, as you would expect Japan to be! When we made it in, we quickly went to drop our stuff at our hotel, the Comsoleil hotel. This is a pretty central location, with clean modern rooms, and not too expensive. After this we decided to go have a look for a famous Izakaya restaurant in the Yurakucho area… we never found it, but had a nice walk around the underworld of Tokyo. Dark streets and small night markets, full of people walking around, and even a few modern day “hostesses” welcoming businessmen to bars and restaurants. This little walk took us around the Ginza area as well. After a coupe hours walk we headed back to sleep as we were meeting the Aussie/American gang early in the morning.
Bar alley
Hostess going to work
Izakaya
On day 2 we started off by heading to Asakusa. This is a temple in the north east area of Tokyo. it was nice to see, but it was very full of tourists. Its worth it though!
The entrance to the Asakusa market
The main Asakusa temple
Make sure to wash your hands and mouth before entering!
Reading our fortune… it wasn’t great for most of us!
Random sightings in Asakusa, a group of drummers dressed as bullfighters
Random sightings in Asakusa, giant puppet
Another awesome Japanese drain cover
Here it really was quite interesting to see all the people walking around and the random group of drummer playing something similar to a Brazilian batucada, all dressed as bullfighters… only in Japan! Since we were in the area, we headed over towards the Akihabara area (the electronics and comics area). Here we made a quick stop for Trev to buys some fireworks, for which he got an awesome deal! Then, walking into Akihabara we ran into a small noodle shop in the street, and it was amazing! It was great that the 6 people in our group occupied the entire restaurant, so we had a very nice private meal!
Yummy Ramen
The place is ours
After this, we divided our efforts and went to a local “Maid Cafe”. This is a really strange experience… Basically, its a restaurant/dessert shop where all of the waitresses are dressed as prototypical maids complete with miniskirt and squeaky voices. Once there they “take you on a magical journey” where your imagination is the limit. It was all very weird, and even a little bit uncomfortable, specially when looking at the business men in suits looking at the young girls dressed as maids. It was really a strange experience!
our maid
The Girls
After this, we closed the day with an amazing dinner in the Roppongi area (the bar/party area) in a teppanyaki called OMAE XEX, very highly recommended! Definitely need a reservation here though.
Geisha serving sake
Our Chef
On the final day that weekend we decided to go to the west of the city and visit the Meiji Shrine. This is a beautiful temple in the middle of a park that was built by emperor Meiji in the late 19th century. Everything about this place is amazing. Its a truly beautiful shrine that you can not miss. We even got to witness a typical japanese wedding at the shrine!
The entrance to the Shrine with gigantic tori gates
Sake barrels given as a tribute to the emperor
Mari and I near the sake
The bride getting ready for the photo shoot
The wedding couple, including a scared groom
Trev and I hugging the gate
Once you exit Meiji, you come out at Harajuku train station. This is a place where if you get the right time (weekend in the later morning) you get to see the Harajuku girls, all dressed up. As you keep walking down this main street, you go into Omotesando, a nice shopping areas with lots of little streets and restaurants to visit. If you are in the mood to walk, you can even get on foot to Shibuya, which is the most famous crossing, where there are millions of people on the streets (if you have seen a movie where Tokyo appears, you have seen this).
Shibuya from ground level
Shibuya form above
Omotesando
After this, we went back to Kobe, but came back to Tokyo at the end of our trip, where we went to a few more places. In our return, we found we were running into one of the largest snow storms Tokyo had seen in over 30 years! It was beautiful though.
Tokyo tower in the snow
The imperial palace… so peaceful!
We got a chance to walk around the imperial palace and some shrines in the snow, and it was really nice as everything was very quiet and peaceful. it was also quite difficult to walk around! In this stop over in Tokyo, Mariana found an amazing Gyoza restaurant in Hrajuku that was delicious. Don’t miss going to Harajuku Gyoza Lou… don’t worry about the queue, it’ll probably go quickly and it’s worth it!
The guy is a gyoza machine
and we like it!
Keep them coming
When we were caught in the snow, we were looking for a restaurant and ran into this small place behind our hotel. The food was terrific (different types of skewers chosen by the chef), and while we had no clue what we would get, everything was a pleasant surprise. The waiter even braved the snow storm to get us a coke, as they didn’t have any… he ran to the nearest Family Mart! True Japanese hospitality. The snow storm resulted in us not being able to get to the airport, which meant an extra night in Tokyo…. but it included 5-6 hours in the train trying to get to the airport, then 12 hours of waiting there, an emergency hotel booking while running to the train, and begging and pleading to get a flight back home! It was absolute chaos!
The airport during a snowstorm – crowded!
It was all a magical and wonderful experience. People were so nice, and we really enjoyed our time here!
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Tell us a bit about you: where you live, how you got into writing/journalism and what sorts of things you typically cover.
I’ve been a journalist for 26 years, ever since graduating from college. I had hoped to get a Ph.D. in Brazilian history, but a friend who worked as the assistant to the late, great New York Times writer Johnny Apple invited me to a dinner party at Apple’s house. My friend was going to law school, and Apple needed a new assistant. I didn’t even know who he was — I’m from the West Coast and just happened to be in Washington for a brief stay. But we started talking, and he offered me the job. He told me my nice Oregon parents would be happier if I took a “real job” instead of worrying about me living on ramen for the next four years. (He definitely had a point!)
I loved the newsroom, the energy there, and just didn’t look back.
Since then I’ve covered a lot of things – crime in Baltimore in the late 1980s; the shift from communism to capitalism in Poland in the early 1990s; and basically since then, how health and health trends intersect with our particular culture. I’ve written two other books, including one that examines how our noses and scent affect our lives.
Where did you get the idea for this book and when?
I moved back to the East Coast from a six-year stay in Oregon in late 2008, just as the economy was tanking. Newspapers and magazines were laying people off, and it was really hard to find work. I had lunch with an acquaintance who is an editor at Simon & Schuster and all around us, women were drinking.
I drink, too, but drinking at lunch puts me out for the day. We started talking about women’s drinking habits, (and our own), and the cultural shift we’d seen around us. She suggested I look into it. The proposal hit her desk the same day as the news of a terrible accident in which a suburban mom killed herself and seven others when she had the equivalent of 10 shots of vodka in her system.
Was it a difficult book to sell to an agent or publisher?
No, because I was lucky to have already had her interest. I had written other books so already had an agent.
What were the most challenging aspects of reporting or researching the book?
At first I thought the book would be a straightforward trend book, about women drinking more than in previous generations, and why. But then I started researching how they got better if they got into trouble, and I found some really interesting new options. I hadn’t had exposure to harmful drinking in my life, and I assumed that the traditional 12-step methods we rely on in this country were effective. I was stunned to learn that they had a very low success rate and were designed by men, for men at a time when the knowledge of brain chemistry was at its infancy – and that it was used by the courts, employee assistance programs, and the medical establishment as a gold standard.
So digging into that was challenging – but fun. It’s always exciting to shift your thinking about something you’ve accepted, or taken for granted -– sort of like you did with “Malled.”
How did you research the book? Tell us where you went, who you spoke to, how you found sources.
At first I started looking into statistics, which as a reporter is the easiest starting place. Drunk driving among women was up; hospitalizations for alcohol overdosing were up among women; the number of older women who checked into rehab had spiked. The number of women who said they were regular drinkers was up.
Once I had those figures, I could sort of move backwards – contacting the researchers and interviewing them. Researchers typically know the others in their areas of expertise, and a lot of them are really generous. One man told me, “Oh, I’m nothing in this field – you should talk to so-and-so and so-and-so.” Those so-and-sos turned out to be amazing sources who were patient and funny and helpful, and pointed out where I had holes.
I also did a lot of searching online for women who would be willing to talk to me about their issues. It is a dicey thing to ask people to discuss a topic that is shameful or embarrassing to them, but I’m a good listener and sometimes that’s what people need. Talking helps a lot of us process our “stuff.”
How long did it take you, from signed contract to delivered manuscript?
Three years.
Was this faster or slower than you anticipated?
Much slower. I thought it would take me a year! That’s crazy.
What did you enjoy most about working on the book?
I loved learning about our history with alcohol, and how our habits have shifted so dramatically over the years. I loved meeting people, and making new friends, but I also loved diving into the history of why we treat alcohol so oddly in this country. We went from Martha Washington, whose collection of 500 recipes included 50 for boozy drinks, (plus some hangover cures), to wild-eyed prohibitionists to Girls Gone Wild.
What was the least fun part?
Some chapters were torture. Reducing the history was particularly hard for me, because I found it so fascinating. At one point, I had about six pages on how the women who crossed the Oregon Trail drank whiskey and wrote about how it helped calm their nerves and sadness in their diaries. My editor, God love her, wrote, “I know this is fascinating, but I think we could carve this down to a sentence or two.” What? All those diaries I read to a sentence? Sometimes you need cold water on your face to knock you to your senses.
Who do you see as readers for this book?
I think any woman who has ever thought twice about their drinking would be interested in this book, and anyone who has ever thought twice about the drinking of a woman they love would be interested in this book. I tried to bust a lot of myths. I also think it would be a good read for anyone interested in women’s history and women’s studies. It traces the arc of female power through our relationship to alcohol in ways that are quite surprising.
If you have written other books, how is this one different – in tone, content, approach?
This was much better conceived and executed than my other books, because it had a tighter focus. I used history as a guide, and medical research as a foundation, whereas my nose book was a sort of kooky history – cool stuff you didn’t know about your sense of smell, the history of Kleenex, nose jobs. My first book was a starter book, on interfaith marriage. It was too long and not focused enough.
What advice would you offer a would-be non-fiction author?
Develop a good working relationship with your editor. That is absolutely key. If you don’t see eye-to-eye from the beginning, you aren’t going to see eye-to-eye at the end. I’ve had a great experience this time with a patient, wise, and incredibly generous editor who helped reel me back in when I needed to be. I haven’t always had that experience. Chemistry matters. My best working relationships have always been with editors I really admire and love. In other words, don’t try to force something that isn’t there. And also: don’t be afraid to lose your good material in order to save your great material. Nobody wants to read six pages about something only you find amazing.
Interesting interview – I read an excerpt from her book in last weekends WSJ and blogged about it (Cheers? on runningawayfrom49.wordpress.com) as my suburban neighborhood underscores much of what she says.
Goodness. Starting out with Johnny Apple is a great place to start!
I suppose it became easier for women to drink alcohol once certain social barriers were lifted. As women began to travel on business, they were more inclined to go down to the hotel restaurant for dinner and order a drink.The Betty Drapers of the world didn’t have to dip into the liquor cabinets stocked with whatever their husbands brought home. As fewer women married, they ventured into the liquor stores on their own.
Nothing wrong with any of this if it’s done in moderation.
Interesting point about AA being designed for men, though. I hadn’t considered that/
I went to some Al-Anon meetings and it was very much NOT for me. The larger issue she also talks about is that drinkers are sometimes ordered into AA when it may not be the their best choice…I am not sure what is.
Pretty much everything. The whole structure is VERY American — spilling your guts to a roomful of strangers (?!), the religiosity, the depressing fact that I’d walk out feeling worse listening to everyone’s misery. And no compassion. The hell with it. Friends or therapy have been more useful.
It is, indeed. I also went for the requisite six sessions they tell you to hang in for. I even tried two different groups. It was just not at all helpful for me. And the effects of my family’s alcoholism have been very corrosive for me.
Thanks. Everything is material — and tuning out the ^%@@*()+ drunk people say to you is actually probably very useful training to be a freelance writer, where rejection is normal. Or just being ignored. 🙂
Very interesting post. Thanks for this perspective on women’s culture change.
What I found fascinating is this section, “I had lunch .. and all around us, women were drinking… We started talking about women’s drinking habits, (and our own), and the cultural shift we’d seen around us.”
A similar shift occurred (with smoking first, then drinking) overseas in Muslim Azerbaijan while I was living there. Local women weren’t required to wear headscarves, but there was a cultural “code” that said no sleeveless tops or low necklines- and certainly no cigarettes; modesty and propriety were understood as given. .
Sometime before 9/11, however, I began to notice in cafes and restaurants, I was literally the only female not smoking. And this was happening regularly. How did modest women become emboldened to defy parents and brothers and adopt the habits of “western women”? What precipitated and fueled the shift? Advertising, free markets, religious decay?
It would be interesting to see if (how) the same story is playing out across cultures around the world.
Great interview. I’m going to keep my eye out for this book. I’m in a weird situation as someone who would be categorized as a “heavy drinker” (I drink a glass of wine or two every night) who is married to a recovered alcoholic/an addictions counselor, and so this book feels like it would be super relevant to my life in many ways.
I was drinking a glass or two every night but am so fed up being overweight that I am trying to only drink (3 drinks mx. becs of my mother’s many cancers) on weekends. It’s easier to simply NOT open a beer or wine bottle than try to moderate. I love beer, and really enjoy cocktails and wine…now at my age with a slower metabolism, I’m screwed. So annoying!
|
{
"pile_set_name": "Pile-CC"
}
|
Aspects of this disclosure relate generally to telecommunications, and more particularly to techniques for sounding sequence protection in multi-user multiple-input-multiple-output (MU-MIMO) communications for wireless local area networks (WLANs).
The deployment of WLANs in the home, the office, and various public facilities is commonplace today. Such networks typically employ a wireless access point (AP) that connects a number of wireless stations (STAs) in a specific locality (e.g., home, office, public facility, etc.) to another network, such as the Internet or the like. A set of STAs can communicate with each other through a common AP in what is referred to as a basic service set (BSS). Nearby BSSs may have overlapping coverage areas and such BSSs may be referred to as overlapping BSSs or OBSSs. In some scenarios, communications that occur in nearby BSSs can result in collisions and failure in the transmission of information.
In dense enterprise deployments of WLANs, such as in stadiums, airports, or other large venues, for example, there may be multiple APs deployed, and the coverage of several of those APs can overlap creating OBSS scenarios. For example, in these dense deployments, multiple STAs can be in the common coverage of multiple BSSs. Moreover, when these dense deployments are unplanned, some of the APs may be automatically configured to work on the same channel, which may cause transmission collisions between OBSSs. The collisions that occur may result in sounding sequence failures and, upon detection of a sounding sequence failure, an AP may terminate a transmission opportunity (TxOP) and would need to contend for the medium again. System throughput can be severely impacted if this happens frequently.
For MU-MIMO transmissions, however, the WLAN standards (e.g., IEEE 802.11-based standards) have not defined a specific mechanism that may be used for MU-MIMO sounding sequence protection. One option for MU PLCP Protocol Data Unit (PPDU) protection is to send multiple RTSs one by one to all of the STAs that will be part of the subsequent MU PPDU transmission and expect a CTS from each of those STAs. However, this solution may not be practical for MU-MIMO sounding sequence protection because it incurs a large overhead that may not be needed in non-OBSS scenarios.
Accordingly, for scenarios that create OBSSs between nearby BSSs and that can result in sounding sequence collisions and failures, it may be desirable to have a mechanism that protects the sounding sequence while providing low overhead.
|
{
"pile_set_name": "USPTO Backgrounds"
}
|
---
abstract: 'Compression is a key step to deploy large neural networks on resource-constrained platforms. As a popular compression technique, quantization constrains the number of distinct weight values and thus reducing the number of bits required to represent and store each weight. In this paper, we study the representation power of quantized neural networks. First, we prove the universal approximability of quantized ReLU networks on a wide class of functions. Then we provide upper bounds on the number of weights and the memory size for a given approximation error bound and the bit-width of weights for function-independent and function-dependent structures. Our results reveal that, to attain an approximation error bound of $\epsilon$, the number of weights needed by a quantized network is no more than $\mathcal{O}\left(\log^5(1/\epsilon)\right)$ times that of an unquantized network. This overhead is of much lower order than the lower bound of the number of weights needed for the error bound, supporting the empirical success of various quantization techniques. To the best of our knowledge, this is the first in-depth study on the complexity bounds of quantized neural networks.'
author:
- |
Yukun Ding$^1$, Jinglan Liu$^1$, Jinjun Xiong$^2$, Yiyu Shi$^1$\
$^1$ University of Notre Dame\
$^2$ IBM Thomas J. Watson Research Center\
`{yding5,jliu16,yshi4}@nd.edu, jinjun@us.ibm.com`\
bibliography:
- 'iclr2019\_conference.bib'
title: |
On the Universal Approximability and\
Complexity Bounds of Quantized ReLU\
Neural Networks
---
Introduction {#sec:intro}
============
Various deep neural networks deliver state-of-the-art performance on many tasks such as object recognition and natural language processing using new learning strategies and architectures [@chen2017learning; @he2016identity; @kumar2016ask; @ioffe2015batch; @vaswani2017attention]. Their prevalence has extended to embedded or mobile devices for edge intelligence, where security, reliability or latency constraints refrain the networks from running on servers or in clouds. However, large network sizes with the associated expensive computation and memory consumption make edge intelligence even more challenging [@cheng2018recent; @sandler2018inverted].
In response, as will be more detailed in Section \[sec:related\], substantial effort has been made to reduce the memory consumption of neural networks while minimizing the accuracy loss. The memory consumption of neural networks can be reduced by either directly reducing the number of weights or decreasing the number of bits (bit-width) needed to represent and store each weight, which can be employed on top of each other [@choi2016towards]. The number of weights can be reduced by pruning [@han2015learning], weight sparsifying [@liu2015sparse], structured sparsity learning [@wen2016learning] and low rank approximation [@denton2014exploiting]. The bit-width is reduced by quantization that maps data to a smaller set of distinct levels [@sze2017efficient]. Note that while quantization may stand for linear quantization only [@li2017training; @gysel2016hardware] or nonlinear quantization only [@han2015deep; @choi2016towards] in different works, our discussion will cover both cases.
However, as of today quantization is still only empirically shown to be robust and effective to compress various neural network architectures [@hubara2016quantized; @zhou2017adaptive; @zhuang2017towards]. Its theoretical foundation still remains mostly missing. Specifically, many important questions remain unanswered. For example:
- Why even binarized networks, those most extremely quantized with bit-width down to one, still work well in some cases?
- To what extent will quantization decrease the expressive power of a network? Alternatively, what is the overhead induced by weight quantization in order to maintain the same accuracy?
In this paper, we provide some insights into these questions from a theoretical perspective. We focus on ReLU networks, which is among the most widely used in deep neural networks [@xu2015empirical]. We follow the idea from [@yarotsky2017error] to prove the complexity bound by constructing a network, but with new and additional construction components essential for quantized networks. Specifically, given the number of distinct weight values $\lambda$ and a target function $f$, we construct a network that can approximate $f$ with an arbitrarily small error bound $\epsilon$ to prove the universal approximability. The memory size of this network then naturally serves as an upper bound for the minimal network size.
The high-level idea of our approach is to replace basic units in an unquantized network with quantized sub-networks [^1] that approximate these basic units. For example, we can approximate a connection with any weight in an unquantized network by a quantized sub-network that only uses a finite number of given weight values. Even though the approximation of a single unit can be made arbitrarily accurate in principle with unlimited resources (such as increased network depth), in practice, there exists some inevitable residual error at every approximation, all of which could propagate throughout the entire network. The challenge becomes, however, how to mathematically prove that we can still achieve the end-to-end arbitrary small error bound even if these unavoidable residual errors caused by quantization can be propagated throughout the entire network. This paper finds a solution to solve the above challenge. In doing so, we have to propose a number of new ideas to solve related challenges, including judiciously choosing the proper finite weight values, constructing the approximation sub-networks as efficient as possible (to have a tight upper bound), and striking a good balance among the complexities of different approximation steps.
Based on the bounds derived, we compare them with the available results on unquantized neural networks and discuss its implications. In particular, the main contributions of this paper include:
- We prove that even the most extremely quantized ReLU networks using two distinct weight values are capable of representing a wide class of functions with arbitrary accuracy.
- Given the number of distinct weights and the desired approximation error bound, we provide upper bounds on the number of weights and the memory size. We further show that our upper bounds have good tightness by comparing them with the lower bound of unquantized ReLU networks established in the literature.
- We show that, to attain the same approximation error bound $\epsilon$, the number of weights needed by a quantized network is no more than $\mathcal{O}\left(\log^5(1/\epsilon)\right)$ times that of an unquantized network. This overhead is of much lower order compared with even the lower bound of the number of weights needed for the error bound. This partially explains why many state-of-the-art quantization schemes work well in practice.
- We demonstrate how a theoretical complexity bound can be used to estimate an optimal bit-width, which in turn enables the best cost-effectiveness for a given task.
The remainder of the paper is organized as follows. Section \[sec:related\] reviews related works. Section \[sec:models\] lays down the models and assumptions of our analysis. We prove the universal approximability and the upper bounds with function-independent structure in Section \[sec:independent\] and extend it to function-dependent structure in Section \[sec:dependent\]. We analyze the bound-based optimal bit-width in Section \[sec:bitwidth\]. Finally, Section \[sec:comparison\] discusses the results and gets back to the questions raised above.
Related Works {#sec:related}
=============
**Quantized Neural Networks:** There are rich literatures on how to obtain quantized networks, either by linear quantization or nonlinear quantization [@zhou2017incremental; @leng2017extremely; @shayar2017learning]. Linear quantization does mapping with a same distance between contiguous quantization levels and is usually implemented by storing weights as fixed-point numbers with reduced bit-width [@li2017training; @gysel2016hardware]. Nonlinear quantization maps the data to quantization levels that are not uniformly distributed and can be either preselected or learned from training. Then the weights are stored using lossless binary coding (the index to a lookup table) instead of the actual values [@han2015deep; @choi2016towards]. It is reported that a pruned AlexNet can be quantized to eight bits and five bits in convolutional layers and fully connected layers, respectively, without any loss of accuracy. Similar results are also observed in LENET-300-100, LENET-5, and VGG-16 [@han2015deep]. One may argue that some of these benchmark networks are known to have redundancy. However, recent works show that quantization works well even on networks that are designed to be extremely small and compact. SqueezeNet, which is a state-of-the-art compact network, can be quantized to 8-bit while preserving the original accuracy [@gysel2016hardware; @iandola2016squeezenet]. There are some representative works that can achieve little accuracy loss on ImageNet classification even using binary or ternary weights [@courbariaux2015binaryconnect; @rastegari2016xnor; @li2016ternary; @zhu2016trained]. More aggressively, some works also reduce the precision of activations, e.g. [@hubara2016quantized; @rastegari2016xnor; @faraone2018syq]. Although the classification accuracy loss can be minimized, the universal approximation property is apparently lost, as with limited output precision the network cannot achieve arbitrary accuracy. Accordingly, we do not include them in the discussion of this paper. The limit of quantization is still unknown while the state-of-the-art keeps getting updated. For example, VGG-16 is quantized to 3-bit while maintaining the original accuracy [@leng2017extremely]. Motivated by the great empirical success, the training of quantized neural networks has been analyzed theoretically, but not the network capacity [@li2017training; @choi2016towards].
**Universal Approximability and Complexity Bounds:** The universal approximability of ReLU networks is proved in [@mhaskar1992approximation] and revisited in [@sonoda2017neural]. Recently, [@hanin2017universal] discusses the expressive power of ReLU networks with bounded width and proves that a ReLU network with width $d+1$ can approximate any continuous convex function of $d$ variables arbitrarily well. [@shaham2016provable] construct a sparsely-connected depth-4 ReLU network and prove its error bound. [@liang2016deep] prove that, for a large class of piecewise smooth functions, a network with ReLU and binary step units can provide an error bound $\epsilon$ with $\mathcal{O}(1/\epsilon)$ layers and $\mathcal{O}(\text{poly}\log(1/\epsilon))$ neurons. The universal approximation property of low displacement rank (LDR) neural networks has been proved by [@zhao2017theoretical] under a mild condition on the displacement operator, which is the result of another effective technique of neural network compression.
Models and Assumptions {#sec:models}
======================
Throughout this paper, we define ReLU networks as feedforward neural networks with the ReLU activation function $\sigma(x)=\text{max}(0,x)$. The ReLU network considered includes multiple input units, a number of hidden units, and one output unit. Without loss of generality, each unit can only connect to units in the next layer. Our conclusions on ReLU networks can be extended to any other networks that use piecewise linear activation functions with finite breakpoints such as leaky ReLU and ReLU-6 immediately, as one can replace a ReLU network by an equivalent one using these activation functions while only increasing the number of units and weights by constant factors [@yarotsky2017error].
We denote the finite number of distinct weight values as $\lambda$ ($ \lambda \in \mathbb{Z}^+$ and $\lambda \geq2$), for both linear quantization and nonlinear quantization. For linear quantization, without loss of generality, we assume the finite number of distinct weight values are given as $ \{-1, \frac{1}{\lambda},\frac{2}{\lambda},\dots,\frac{\lambda-1}{\lambda}\}$, where $\{\frac{1}{\lambda},\frac{2}{\lambda},\dots,\frac{\lambda-1}{\lambda}\}$ are uniformly spaced (hence called “linear”) in $(0,1)$ and $-1$ is used to obtain the negative weight values. For nonlinear quantization, we assume the finite number of distinct weight values are not constrained to any specific values, i.e., they can take any values as needed. To store each weight, we only need $\log (\lambda)$ [^2] bits to encode the index, i.e. the bit-width is $\log (\lambda)$. The overhead to store sparse structures can be ignored because it varies depending on the implementation and can be easily reduced to the same order as the weight storage using techniques such as compressed sparse row (CSR) for nonlinear quantization. The number of bits needed to store the codebook can also be ignored because it has lower order of complexity.
We consider any function $f$ in the Sobolev space: $f\in\mathscr{W}^{n,\infty}([0,1]^d)$ and $$\max_{\textbf{n}:|\textbf{n}|\leq n}\operatorname*{ess\,sup}_{x\in[0,1]^d}|D^{\textbf{n}}f(\textbf{x})|\leq1.$$ The space $\mathscr{W}^{n,\infty}$ consists of all locally integrable function $f:\Omega\to\mathbb{R}$ such that $D^{\textbf{n}}f\in L^{\infty}(\Omega)$, where $|\textbf{n}|\leq n$ and $\Omega$ is an open set in $\mathbb{R}^d$. We denote this function space as $\mathcal{F}_{d,n}$ in this paper.
Note that we only assume weak derivatives up to order $n$ exist where $n$ can be as small as 1 where the function is non-differentiable. We also only assume the Lipschitz constant to be no greater than 1 for the simplicity of the derivation. When the Lipschitz constant is bigger than 1, as long as it is bounded, the whole flow of the proof remains the same though the bound expression will scale accordingly.
When constructing the network to approximate any target function $f$, we consider two scenarios for deriving the bounds. The first scenario is called function-dependent structure, where the constructed network topology and their associated weights are all affected by the choice of the target function. In contrast, the second scenario is called function-independent structure, where the constructed network topology is independent of the choice of the target function in $ f\in\mathcal{F}_{d,n}$ with a given $\epsilon$. The principle behind these design choices (the network topology constructions and the choice of weights) is to achieve a tight upper bound as much as possible.
One might consider that we can transform an unquantized network within the error bound to a quantized one in a straightforward way by approximating every continuous-value weight with a combination of discrete weights with arbitrary accuracy. However, the complexity of such approximation (number of discrete weights needed) depends on the distribution of those continuous-value weights (e.g., their min and max), which may vary depending on the training data and network structure and a closed-form expression for the upper bounds is not possible. As such, a more elegant approach is needed. Below we will establish a constructive approach which allows us to bound the approximation analytically.
Function-independent Structure {#sec:independent}
==============================
We start our analysis with function-independent structure, where the network topology is fixed for any $f\in \mathcal{F}_{d,n}$ and a given $\epsilon$. We first present the approximation of some basic functions by sub-networks in Section \[sqaure\]. We then present the sub-network that approximates any weight in Section \[weights\], and finally the approximation of general functions and our main results are in Section \[general\].
Approximation of squaring/multiplication {#sqaure}
----------------------------------------
\[p1\] Denote the design parameter that determines the approximation error bound as $r$. Let $f_s^r$ be a ReLU sub-network with only two weight values $\frac{1}{2}$ and $-\frac{1}{2}$. The function $f_s(x)=x^2$ on the segment $[0,1]$ can be approximated by $f_s^r$, such that (1) if $x=0$, $f_s^r(x) = 0$; (2) the approximation error $\epsilon_s\leq 2^{-2(r+1)}$; (3) the depth is $\mathcal{O}\left(r\right)$; (4) the width is a constant; (5) the number of weight is $\mathcal{O}\left(r\right)$.
The proof and the details of the sub-network constructed are included in Appendix \[PP1\]. Once the approximation to squaring function is obtained, we get Proposition \[p2\] by the fact that $2xy=(x+y)^2-x^2-y^2$.
\[p2\] Denote the design parameter that determines the approximation error bound as $r$. Given $x\in[-1,1]$, $y\in[-1,1]$, and only two weight values $\frac{1}{2}$ and $-\frac{1}{2}$, there is a ReLU sub-network with two input units that implements a function $\times'$: $\mathbb{R}^2 \mapsto \mathbb{R}$, such that (1) if $x=0$ or $y=0$, then $\times'(x,y)=0$; (2) for any $x$, $y$, the error $\epsilon_{\times'}=|\times'(x,y)-xy| \leq 6\cdot2^{-2(r+1)}$; (3) the depth is $\mathcal{O}\left(r\right)$; (4) the width is a constant; (5) the number of weights is $\mathcal{O}\left(r\right)$.
Build three sub-networks $f_s^r$ as described in Proposition \[p1\] and let $$\label{constructX}
\times'(x,y)=2\left(f_{s}^r\left(|x+y|/2\right)-f_{s}^r\left(|x|/2\right)-f_{s}^r\left(|y|/2\right)\right).$$ Then the statement (1) is followed by property (1) of Proposition \[p1\]. Using the error bound in Proposition \[p1\] and Equation (\[constructX\]), we get the error bound of $\times'$: $$\label{Xerror}
\epsilon_{\times'}\leq6\cdot2^{-2(r+1)}.$$ Since a sub-network $B_{abs}$ that computes $\sigma(x)+\sigma(-x)$ can be constructed to get the absolute value of $x$ trivially, we can construct $\times'(x,y)$ as a linear combination of three parallel $f_s^r$ and feed them with $\frac{|x|}{2},\frac{|y|}{2}$, and $\frac{|x+y|}{2}$. Then claims of statement (3), (4), and (5) are also obtained.
Approximation of weights {#weights}
-------------------------
\[w\] Denote the design parameter that determines the approximation error bound as $t$. A connection with any weight $w\in[-1,1]$ can be approximated by a ReLU sub-network that has only $\lambda \geq 2$ distinct weights, such that (1) the sub-network is equivalent to a connection with weight $w'$ while the approximation error is bounded by $2^{-t}$ i.e., $|w'-w|<2^{-t}$; (2) the depth is $\mathcal{O}\left(\lambda t^{\frac{1}{\lambda-1}}\right)$; (3) the width is $\mathcal{O}(t)$; (4) the number of weights is $\mathcal{O}\left(\lambda t^{\frac{1}{\lambda-1}+1}\right)$.
Consider that we need a weight $w$ to feed the input $x$ to a unit in the next layer as $wx$. With a limited number of distinct weight values, we can construct the weight we need by cascade and combination.
For clarity, we first consider $w\geq0$ and $x\geq0$, and relax these assumptions later. The connections with $w=0$ can be seen as an empty sub-network while $w=1$ can be easily implemented by 4 units with weight $\frac{1}{2}$. Now we show how to represent all integral multiples of $2^{-t}$ from $2^{-t}$ to $ 1-2^{-t}$, which will lead to the statement (1) by choosing the nearest one from $w$ as $w'$. Without loss of generality, we assume $t^{\frac{1}{\lambda-1}}$ is an integer. We use $\lambda$ weights that include $-\frac{1}{2}$ and $W$: $$W\triangleq\{2^{-1},2^{-t^{\frac{1}{\lambda-1}}},2^{-t^{\frac{2}{\lambda-1}}},\cdots,2^{-t^{\frac{\lambda-2}{\lambda-1}}}\}.$$ We first construct all $w$ from $W_c$ which is defined as $$W_c\triangleq\{2^{-1},2^{-2},\cdots,2^{-(t-1)}\}.$$ Similar to a numeral system with radix equal to $t^{\frac{1}{\lambda-1}}$, any $w_i\in W_c$ can be obtained by concatenating weights from $W$ while every weights in $W$ is used no greater than $t^{\frac{1}{\lambda-1}}-1$ times.
After that, all integral multiples of $2^{-t}$ from $2^{-t}$ to $ 1-2^{-t}$ can be represented by a binary expansion on $W_c$. Note that connections in the last layer for binary expansion use weight $\frac{1}{2}$, thus additional $2^{-1}$ is multiplied to scale the resolution from $2^{-(t-1)}$ to $2^{-t}$. Since for any weight in $W_c$ we need to concatenate no more than $\lambda\left(t^{\frac{1}{\lambda-1}}-1\right)$ weights in a straight line, the sub-network has no greater than $\lambda\left(t^{\frac{1}{\lambda-1}}-1\right)+1$ layers, and no greater than $4t\lambda\left(t^{\frac{1}{\lambda-1}}-1\right)+8t+4$ weights.
We now relax the assumption $w\geq0$. When $w<0$, the sub-network can be constructed as $w=|w|$, while we use $-\frac{1}{2}$ instead of $\frac{1}{2}$ in the last layer. To relax the assumption $x\geq0$, we can make a duplication of the sub-network. Let all the weights in the first layer of the sub-network be $\frac{1}{2}$ for one and $-\frac{1}{2}$ for the other. Here we are utilizing the gate property of ReLU. In this way, one sub-network is activated only when $x>0$ and the other is activated only when $x<0$. The sign of the output can be adjusted by flipping the sign of weights in the last layer. Note that the configuration of the sub-network is solely determined by $w$ and works for any input $x$.
The efficiency of the weight approximation is critical to the overall complexity. Compared with the weight selection as $\{2^{-1},2^{{-t\frac{1}{\lambda-1}}},2^{-t{\frac{2}{\lambda-1}}},\dots,2^{-t{\frac{(\lambda-2)}{\lambda-1}}}\}$, our approximation reduces the number of weights by a factor of $t^{\frac{\lambda-2}{\lambda-1}}$.
Approximation of general functions {#general}
----------------------------------
With the help of Proposition \[p2\] and Proposition \[w\], we are able to prove the upper bound for general functions.
\[T1\] For any $f\in \mathcal{F}_{d,n}$ , given $\lambda$ distinct weights, there is a ReLU network with fixed structure that can approximate $f$ with any error $\epsilon\in(0,1)$, such that (1) the depth is $\mathcal{O}\left(\lambda\log^{\frac{1}{\lambda-1}}\left(1/\epsilon\right)+\log\left(1/\epsilon\right)\right)$; (2) the number of weights is $\mathcal{O}\left(\lambda \log^{\frac{1}{\lambda-1}+1}\left(1/\epsilon\right)\left(1/\epsilon\right)^{\frac{d}{n}}\right)$; (3) the number of bits needed to store the network is $\mathcal{O}\left(\lambda\log\left(\lambda\right) \log^{\frac{1}{\lambda-1}+1}\left(1/\epsilon\right)\left(1/\epsilon\right)^{\frac{d}{n}}\right)$.
The complete proof and the network constructed can be found in Appendix \[PT1\]. We first approximate $f$ by $f_2$ using the Taylor polynomial of order $n-1$ and prove the approximation error bound. Note that even when $f$ is non-differentiable (only first order weak derivative exists), the Taylor polynomial of order 0 at $\textbf{x}=\frac{\textbf{m}}{N}$ can still be used, which takes the form of $P_{\textbf{m}}=f(\frac{\textbf{m}}{N})$. Then we approximate $f_2$ by a ReLU network that is denoted as $f'$ with bounded error. After that, we present the quantized ReLU network that implements $f'$ and the complexity.
The discussion above focuses on nonlinear quantization which is a more general case compared to linear quantization. For linear quantization, which strictly determines the available weight values once $\lambda$ is given, we can use the same proof for nonlinear quantization except for a different sub-network for weight approximation with width $t$ and depth $\frac{t}{\log \lambda}$+1. Here we give the theorem and the proof is included in Appendix \[PT2\].
\[T1linear\] For any $f\in \mathcal{F}_{d,n}$ , given weight maximum precision $\frac{1}{\lambda}$, there is a ReLU network with fixed structure that can approximate $f$ with any error $\epsilon\in(0,1)$, such that (1) the depth is $\mathcal{O}\left(\log \left(1/\epsilon\right)\right)$; (2) the number of weights is $\mathcal{O}\left(\left(\log\left(1/\epsilon\right)+\frac{\log^2\left(1/\epsilon\right)}{\log \lambda}\right)\left(1/\epsilon\right)^{\frac{d}{n}}\right)$; (3) the number of bits needed to store the network is $\mathcal{O}\left(\left(\log (\lambda)\log\left(1/\epsilon\right)+\log^2\left(1/\epsilon\right)\right)\left(1/\epsilon\right)^{\frac{d}{n}}\right)$.
Function-dependent Structure {#sec:dependent}
============================
The network complexity can be reduced if the network topology can be set according to a specific target function, i.e. function-dependent structure. In this section, we provide an upper bound for function-dependent structure when $d =1$ and $n=1$, which is asymptotically better than that of a fixed structure. Specifically, we first define an approximation to $f(x)$ as $\widetilde{f}(x)$ that has special properties to match the peculiarity of quantized networks. Then we use piecewise linear interpolation and “cached” functions [@yarotsky2017error] to approximate $\widetilde{f}(x)$ by a ReLU network.
Function Transformation
-----------------------
While simply using piecewise linear interpolation at the scale of $\epsilon$ can satisfy the error bound with $\mathcal{O}\left(1/\epsilon\right)$ weights, the complexity can be reduced by first doing interpolation at a coarser scale and then fill the details in the intervals to make the error go down to $\epsilon$. By assigning a “cached” function to every interval depending on specific function and proper scaling, the number of weights is reduced to $\mathcal{O}\left(\left(\log^{-1}\left(1/\epsilon\right)\right)1/\epsilon\right)$ when there is no constraint on weight values [@yarotsky2017error].
The key difficulty in applying this approach to quantized ReLU networks is that the required linear interpolation at $\frac{i}{T}$ exactly where $i = 1,2,\cdots,T$ is not feasible because of the constraint on weight selection. To this end, we transform $f(x)$ to $\widetilde{f}(x)$ such that the approximation error is bounded; the Lipschitz constant is preserved; $\widetilde{f}\left(\frac{i}{T}\right)$ are reachable for the network under the constraints of weight selection without increasing the requirement on weight precision. Then we can apply the interpolation and cached function method on $\widetilde{f}(x)$ and finally approximate $f(x)$ with a quantized ReLU network. Formally, we get the following proposition and the proof can be found in Appendix \[PP4\].
\[ftp\] For any $f\in \mathcal{F}_{1,1}$, $t\in \mathbb{Z^+}$, and $T\in \mathbb{Z^+}$, there exists a function $\widetilde{f}(x)$ such that (1) $\widetilde{f}(x)$ is a continuous function with Lipschitz constant 1; (2) $\widetilde{f}(\frac{i}{T})$ = $\left\lceil T f\left(\frac{i}{T}\right) /2^{-t}\right\rceil\frac{2^{-t}}{T}$; (3) $|\widetilde{f}(x) - f(x)| < \frac{2^{-t}}{T} $.
Approximation by ReLU Networks
------------------------------
With the help of Proposition \[ftp\] and the weight construction method described in Section \[weights\], we are able to apply the interpolation and cached function approach. Denoting the output of the network as $f''(x)$, we have $|f(x)-f''(x)| = |f(x)-\widetilde{f}(x)|+|\widetilde{f}(x)-f''(x)|\leq\epsilon$ by choosing appropriate hyper-parameters which are detailed in Appendix \[PT3\] and the network complexity is obtained accordingly.
\[T3\] For any $f\in \mathcal{F}_{1,1}$ , given $\lambda$ distinct weights, there is a ReLU network with function-dependent structure that can approximate $f$ with any error $\epsilon\in(0,1)$, such that (1) the depth is $\mathcal{O}\left(\lambda\left(\log\log\left(1/\epsilon\right)\right)^{\frac{1}{\lambda-1}}+\log\left(1/\epsilon\right)\right)$; (2) the number of weights is $\mathcal{O}\left(\lambda\left(\log\log\left(1/\epsilon\right)\right)^{\frac{1}{\lambda-1}+1}+(1/\epsilon)\right)$ (3) the number of bits needed to store the network is $\mathcal{O}\left(\log \lambda\left(\lambda\left(\log\log\left(1/\epsilon\right)\right)^{\frac{1}{\lambda-1}+1}+(1/\epsilon)\right)\right)$.
Using the different weight construction approach as in the case of function-independent structure, we have the result for linear quantization:
\[T4\] For any $f\in \mathcal{F}_{1,1}$ , given weight maximum precision $\frac{1}{\lambda}$, there is a ReLU network with function-dependent structure that can approximate $f$ with any error $\epsilon\in(0,1)$, such that (1) the depth is $\mathcal{O}\left(\log\left(1/\epsilon\right)\right)$; (2) the number of weights is $\mathcal{O}\left(1/\epsilon\right)$; (3) the number of bits needed to store the network is $\mathcal{O}\left(\log (\lambda)/\epsilon\right)$.
Bound-based Optimal Bit-width {#sec:bitwidth}
=============================
In this section, we first introduce the optimal bit-width problem and then show how a theoretical bound could potentially be used to estimate the optimal bit-width of a neural network.
Because of the natural need and desire of comparison with competitive approaches, most quantization techniques are evaluated on some popular reference networks, without modification of the network topology. On the one hand, the advancement of lossless quantization almost stalls at a bit-width between two and six [@han2015deep; @choi2016towards; @sze2017efficient; @blott2017scaling; @su2018accuracy; @faraone2018syq]. A specific bit-width depends on the compactness of the reference network and the difficulty of the task. On the other hand, the design space, especially the different combinations of topology and bit-width, is largely underexplored because of the complexity, resulting in sub-optimal results. A recent work by [@su2018accuracy] empirically validates the benefit of exploring flexible network topology during quantization. That work adds a simple variable of network expanding ratio, and shows that a bit-width of four achieves the best cost-accuracy trade-off among limited options in $\{1,2,4,8,16,32\}$. Some recent effort on using reinforcement learning to optimize the network hyper-parameters [@he2018amc] could potentially be used to address this issue. But the current design space is still limited to a single variable per layer (such as the pruning ratio based on a reference network). How to estimate an optimal bit-width for a target task without training could be an interesting research direction in the future.
The memory bound expression as derived in this paper helps us to determine whether there is an optimal $\lambda$ that would lead to the lowest bound and most compact network (which can be translated to computation cost in a fully connected structure) for a given target function. For example, by dropping the lower-order term and ignoring the rounding operator, our memory bound can be simplified as $$M(\lambda)=\theta_1 \lambda
\log(\lambda)\log^{\frac{1}{\lambda-1}+1}(3n2^{d}/\epsilon)$$ where $\theta_1$ is a constant determined by $\epsilon,n,$ and $d$. We can find an optimal $\lambda$ that minimizes $M(\lambda)$: $$\lambda_{opt}=\operatorname*{argmin}_\lambda M(\lambda)$$ As is detailed in Appendix \[proofBitwidth\], we prove that there exists one and only one local minimum (hence global minimum) in the range of $[2,\infty)$ whenever $\epsilon<\frac{1}{2}$. We also show that $\lambda_{opt}$ is determined by $\log( 3n2^{d}/\epsilon)$, which can be easily dominated by $d$. Based on such results, we quantitatively evaluate the derivative of $M(\lambda)$, and based on which the optimal bit-width $\log(\lambda_{opt})$ under various settings in Figure \[fig:derivative\] and Figure \[fig:bitwidth\], respectively. In Figure \[fig:bitwidth\], we also mark the input dimension of a few image data sets. It is apparent to see that the optimal bit width derived from $M(\lambda)$ is dominated by $d$ and lies between one and four for a wide range of input size. This observation is consistent with most existing empirical research results, hence showing the potential power of our theoretical bound derivation.
[0.5]{} {width="\linewidth"}
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Since the bounds are derived for fully connected networks and depend on the construction approach, the interesting proximity between $\log(\lambda_{opt})$ and the empirical results cannot be viewed as a strict theoretical explanation. Regardless, we show that the complexity bound may be a viable approach to understand the optimal bit-width problem, thus potentially accelerating the hyper-parameter optimization of deep neural networks. We defer such a thorough investigation of the optimal bit-width or optimal hybrid bit-width configuration across the network to our future work.
Discussion {#sec:comparison}
==========
In this section, we further discuss the bound of nonlinear quantization with a function-independent structure as the generality of nonlinear quantization. The availability of unquantized function-independent structures in literature also makes it an excellent reference for comparison.
**Comparison with the Upper Bound:** The quality of an upper bound lies on its tightness. Compared with the most recent work on unquantized ReLU networks [@yarotsky2017error], where the upper bound on the number of weights to attain an approximation error $\epsilon$ is given by $\mathcal{O}\left(\log(1/\epsilon)\left(1/\epsilon\right)^{\frac{d}{n}}\right)$, our result for a quantized ReLU network is given by $\mathcal{O}\left(\lambda \left(\log^{\frac{1}{\lambda-1}+1}(1/\epsilon)\right)\left(1/\epsilon\right)^{\frac{d}{n}}\right)$, which translates to an increase by a factor of $\lambda \left(\log^{\frac{1}{\lambda-1}}(1/\epsilon)\right)$. Loosely speaking, this term reflects the loss of expressive power because of weight quantization, which decreases quickly as $\lambda$ increases.
**Comparison with the Lower Bound:** We also compare our bound with the lower bound of the number of weights needed to attain an error bound of $\epsilon$ to have a better understanding on the tightness of the bound. We use the lower bound for unquantized ReLU networks from [@yarotsky2017error], as it is also a natural lower bound for quantized ReLU networks. Under the same growth rate of depth, the lower bound is given by $\Omega(\log^{-3}(1/\epsilon)\left(1/\epsilon\right)^{d/n})$, while our upper bound is, within a polylog factor when $\lambda$ is a constant, $\mathcal{O}(\lambda\log^{\frac{1}{\lambda-1}+1}(1/\epsilon)(1/\epsilon)^{d/n})$. The comparison validates the good tightness of our upper bound.
**The Upper Bound of Overhead:** More importantly, the above comparison yields an upper bound on the possible overhead induced by quantization. By comparing the expressions of two bounds while treating $\lambda$ as a constant, we can show that, to attain the same approximation error bound $\epsilon$, the number of weights needed by a quantized ReLU network is no more than $\mathcal{O}(\log^5(1/\epsilon))$ times that needed by an unquantized ReLU network. Note that this factor is of much lower order than the lower bound $\Omega(\log^{-3}(1/\epsilon)\left(1/\epsilon\right)^{d/n})$. This little overhead introduced by weight quantization explains in part the empirical success on network compression and acceleration by quantization and also answers in part the questions as raised in Section \[sec:intro\]. Given the significant benefits of quantization in term of memory and computation efficiency, we anticipate that the use of quantization networks will continue to grow, especially on resource-limited platforms.
**Future Work:** There remain many other avenues for future investigation. For example, although we derived the first upper bound of quantized neural networks, the lower bound is still missing. If a tight lower bound of the network size is established, it could be combined with the upper bound to give a much better estimation of required resources and the optimal bit-width. We believe the trends associated with the bounds can also be useful and deserve some further investigation. For example, the trend may help hardware designers in their early stage of design exploration without the need of lengthy training. While we assume a uniform bit-width across all layers, another area of research is to allow different bit-widths in different layers, which could achieve better efficiency and potentially provide theoretical justifications on the emerging trend of hybrid quantization [@zhang2017high; @wang2018design].
Proofs {#sec:A}
======
The proof of Proposition 1 {#PP1}
--------------------------
Denote the design parameter that determines the approximation error bound as $r$. Let $f_s^r$ be a ReLU sub-network with only two weight values $\frac{1}{2}$ and $-\frac{1}{2}$. The function $f_s(x)=x^2$ on the segment $[0,1]$ can be approximated by $f_s^r$, such that (1) if $x=0$, $f_s^r(x) = 0$; (2) the approximation error $\epsilon_s\leq 2^{-2(r+1)}$; (3) the depth is $\mathcal{O}\left(r\right)$; (4) the width is a constant; (5) the number of weight is $\mathcal{O}\left(r\right)$.
For $f_s(x)=x^2$, let $f_s^r$ be the piecewise linear interpolation of $f$ with $2^r+1$ uniformly distributed breakpoints $\frac{k}{2^r},k=0,\dots,2^r$. We have $f_s^r\left(\frac{k}{2^r}\right)=\left(\frac{k}{2^r}\right)^2, k=0,\dots,2^r$ and the approximation error $\epsilon_{s}=||f_s^r(x)-f_s(x)||_{\infty}\leq2^{-2(r+1)}$. We can use the function $g:[0,1]\mapsto[0,1]$ to obtain $f_s^r$: $$g(x) =
\begin{cases}
2x & x<\frac{1}{2} \\
2(1-x) & x\geq\frac{1}{2}, \\
\end{cases}$$ $$f_s^{r}(x)=x-\sum_{i=1}^{r}2^{-2i}g^{\circ i}(x)$$ where $g^{\circ i}(x)$ is the $i$-th iterate of $g(x)$. Since $g(x)$ can be implemented by a ReLU sub-network as $g(x)=2\sigma(x)-4\sigma(x-\frac{1}{2})$, $g^{\circ r}(x)$ can be obtained by concatenating such implementation of $g(x)$ for $r$ times. Now, to implement $f^r_s(x)$ based on $g^{\circ r}(x)$, all we need are weights $\{2^{-2},2^{-4},\cdots,2^{-2(r-1)},2^{-2r}\} $, which can be easily constructed with additional $2r$ layers and the weight $\frac{1}{2}$.
Note that a straightforward implementation will have to scale $g^{\circ i}(x)$ separately (multiply by different numbers of $\frac{1}{2}$) before subtracting them from $x$ because each $g^{\circ i}(x)$ have a different coefficient. Then the width of the network will be $\Theta(r)$. Here we use a “pre-scale” method to reduce the network width from $\Theta(r)$ to a constant. The network constructed is shown in Figure \[frx\]. The one-layer sub-network that implements $g(x)$ and the one-layer sub-network that scales the input by $4$ are denoted as $B_g$ and $B_m$ respectively. Some units are copied to compensate the scaling caused by $\frac{1}{2}$. The intermediate results $g^{\circ i}(x)$ are computed by the concatenation of $B_g$ at the $(i+1)$-th layer. The first $B_m$ takes $x$ as input and multiply it by $4$. The output of $i$-th $B_m$ is subtracted by $g^{\circ i}(x)$ and then fed to the next $B_m$ to be multiplied by $4$ again. There are $r$ layers of $B_m$ and all $g^{\circ i}(x)$ are scaled by $2^{2(r-i)}$ respectively. As a result, we obtain $2^{2r}x-\sum_{i=1}^{r}2^{2(r-i)}g^{\circ i}(x)$ after the last $B_m$. Then it is scaled by $2^{-2r}$ in the later $2r$ layers to get $f^r_s(x)$. In this way, we make all $g^{\circ i}(x)$ sharing the same scaling link and a constant width can be achieved.
![A qunatized ReLU network that implements $f^r_s(x)$. In the interest of clarity, we depict the sub-networks with different functions as different colored blocks. A connection from or to a block indicates connections from or to all units in the block. Details of block $B_m$ and block $B_g$ are depicted on the left. $b$ and $w$ denote bias and weight respectively. []{data-label="frx"}](frxICLR2.pdf){width="4.0in"}
The proof of Theorem 1 {#PT1}
----------------------
For any $f\in \mathcal{F}_{d,n}$ , given $\lambda$ distinct weights, there is a ReLU network with fixed structure that can approximate $f$ with any error $\epsilon\in(0,1)$, such that (1) the depth is $\mathcal{O}\left(\lambda\log^{\frac{1}{\lambda-1}}\left(1/\epsilon\right)+\log\left(1/\epsilon\right)\right)$; (2) the number of weights is $\mathcal{O}\left(\lambda \log^{\frac{1}{\lambda-1}+1}\left(1/\epsilon\right)\left(1/\epsilon\right)^{\frac{d}{n}}\right)$; (3) the number of bits needed to store the network is $\mathcal{O}\left(\lambda\log\left(\lambda\right) \log^{\frac{1}{\lambda-1}+1}\left(1/\epsilon\right)\left(1/\epsilon\right)^{\frac{d}{n}}\right)$.
The proof is composed of four steps. We first approximate $f$ by $f_2$ using the Taylor polynomial of order $n-1$ and prove the approximation error bound. Note that even when $f$ is non-differentiable (only first order weak derivative exist), the Taylor polynomial of order 0 at $\textbf{x}=\frac{\textbf{m}}{N}$ can still be used, which takes the form of $P_{\textbf{m}}=f(\frac{\textbf{m}}{N})$. Then we approximate $f_2$ by a ReLU network that is denoted as $f'$ with bounded error. After that, we present the quantized ReLU network that implements the network $f'$ and the complexity of the network.
We use a partition of unity on $[0,1]^d$: $\sum_{\textbf{m}}\psi_{\textbf{m}}(\textbf{x})\equiv1, \textbf{x}\in [0,1]^d$ where $\textbf{m}=(m_1,\cdots,m_d)\in\{0,1,\cdots,N\}^d$, and $h(x)$ is defined as follows: $$\psi_{\textbf{m}}(\textbf{x})=\prod_{k=1}^{d}h(3Nx_k-3m_k),$$ where $N$ is a constant and $$h(x) =
\begin{cases}
1 & |x|\leq1 \\
2-|x| & 1<|x|<2 \\ 0 & |x|\geq2 \\
\end{cases}.$$ Note that $\text{supp } \psi_{\textbf{m}}\subset \{\textbf{x}:\left|x_k-\frac{m_k}{N}\right|<\frac{1}{N} \forall k\}$. For all $\textbf{m}$, we have the order $n-1$ Taylor polynomial for the function $f$ at $x=\frac{\textbf{m}}{N}$ as $$P_{\textbf{m}}(\textbf{x})=\sum_{\textbf{n}:|\textbf{n}|<n}\frac{D^{\textbf{n}}f}{\textbf{n}!}\Bigr|_{\textbf{x}=\frac{\textbf{m}}{N}}\left(\textbf{x}-\frac{\textbf{m}}{N}\right)^\textbf{n}.$$ To get a more realizable approximation for quantized networks, we define $P'_{\textbf{m}}(\textbf{x})=\sum_{\textbf{n}:|\textbf{n}|<n}\beta_{\textbf{m},\textbf{n}}\left(\textbf{x}-\frac{\textbf{m}}{N}\right)^\textbf{n}$ where $\beta_{\textbf{m},\textbf{n}}$ is $\frac{D^{\textbf{n}}f}{\textbf{n}!}\Bigr|_{\textbf{x}=\frac{\textbf{m}}{N}}$ rounded to the nearest integral multiple of $\frac{1}{n}\left(\frac{d}{N}\right)^{n-|\textbf{n}|}$. Then we get an approximation to $f$ using $P'_{\textbf{m}}$ and $\psi_{\textbf{m}}$ as $f_2 \triangleq \sum_{\textbf{m}\in\{0,\cdots,N\}^d}\psi_{\textbf{m}} P'_{\textbf{m}}$.
Then the approximation error of $f_2$ is bounded by Equation (\[Taylor\]). $$\label{Taylor}
\begin{aligned}
|f(\textbf{x})-f_2(\textbf{x})|&=|\sum_{\textbf{m}}\psi_{\textbf{m}}(\textbf{x})(f(\textbf{x})-P'_{\textbf{m}}(\textbf{x}))|\\
&\leq\sum_{\textbf{m}:|x_k-\frac{m_k}{N}|<\frac{1}{N}\forall k}|f(\textbf{x})-P'_{\textbf{m}}(\textbf{x})|\\
&\leq 2^d \max_{\textbf{m}:|x_k-\frac{m_k}{N}|<\frac{1}{N}\forall k}|f(\textbf{x})-P_{\textbf{m}}(\textbf{x})|+ 2^d\max_{\textbf{m}:|x_k-\frac{m_k}{N}|<\frac{1}{N}\forall k}|P_{\textbf{m}}(\textbf{x})-P'_{\textbf{m}}(\textbf{x})|\\
&\leq\frac{2^dd^n}{n!}\left(\frac{1}{N}\right)^n \max_{\textbf{n}:|\textbf{n}|=n}\operatorname*{ess\,sup}_{\textbf{x}\in[0,1]^d}|D^{\textbf{n}}f(\textbf{x})|+2^d\sum_{\textbf{n}:|\textbf{n}|<n}\max \left(|\beta_{\textbf{m},\textbf{n}}-\frac{D^{\textbf{n}}f}{\textbf{n}!}|\right)(x-\frac{\textbf{m}}{N})^\textbf{n}\\
&\leq\frac{2^dd^n}{n!}\left(\frac{1}{N}\right)^n+\frac{2^d}{n}\left(\left(\frac{d}{N}\right)^n+\cdots +\left(\frac{d}{N}\right)^{1}\left(\frac{d}{N}\right)^{n-1}\right)\\
&\leq2^d\left(\frac{d}{N}\right)^n\left(1+\frac{1}{n!}\right)
\end{aligned}$$ The second step follows $\psi_{\textbf{m}} (\textbf{x})=0$ when $ \textbf{x}\notin \text{supp} \psi_{\textbf{m}}$. In the third step we turn the sum to multiplication, because for any $\textbf{x}$ there are up to $2^d$ terms $\psi_{\textbf{m}}(\textbf{x})$ that are not equal to zero. The fourth step uses a Lagrange’s form of the Taylor remainder. The fifth step follows different round precision of $\beta_{\textbf{m},\textbf{n}}$ in different order and the fact that the number of terms with order $i$ is not greater than $d^i$.
We rewrite $f_2$ as $$f_2(\textbf{x})=\sum_{\textbf{m}\in\{0,\cdots,N\}^d}\sum_{\textbf{n}:|\textbf{n}|<n} \beta_{\textbf{m},\textbf{n}}f_{\textbf{m},\textbf{n}}(\textbf{x}),$$ where $$f_{\textbf{m},\textbf{n}}(\textbf{x})=\psi_{\textbf{m}} \left(\textbf{x}-\frac{\textbf{m}}{N}\right)^\textbf{n}.$$ Note that $\beta_{\textbf{m},\textbf{n}}$ is a constant and thus $f_2$ is a linear combination of at most $d^n(N+1)^d$ terms of $f_{\textbf{m},\textbf{n}}(\textbf{x})$. Note that when $d=1$, the number of terms should be $n(N+1)^d$ instead; but for simplicity of presentation we loosely use the same expression as they are on the same order.
We define an approximation to $f_{\textbf{m},\textbf{n}}(\textbf{x})$ as $f'_{\textbf{m},\textbf{n}}(\textbf{x})$. The only difference between $f_{\textbf{m},\textbf{n}}(\textbf{x})$ and $f'_{\textbf{m},\textbf{n}}(\textbf{x})$ is that all multiplication operations are approximated by $\times'$ as discussed in Proposition 2. Consider that if we construct our function $\times'$ with $|\times'(x,y)-xy|<\epsilon_{\times'}=2^{-2(r+1)}$, then $$\label{xyz}
|\times'(x,y)-xz|\leq|x(y-z)|+\epsilon_{\times'}.$$ Applying Equation (\[xyz\]) to $|f'_{\textbf{m},\textbf{n}}(\textbf{x})-f_{\textbf{m},\textbf{n}}(\textbf{x})|$ repeatedly, we bound it to Equation (\[fmn\]).
$$\label{fmn}
\begin{aligned}
&\bigl|f'_{\textbf{m},\textbf{n}}(\textbf{x})-f_{\textbf{m},\textbf{n}}(\textbf{x})\bigr|=\\&\bigg|\times'\left(h(3Nx_1-3m_1),\cdots,\times'\left(h(3Nx_d-3m_d),\times'\left(\left(x_{i_1}-\frac{m_1}{N} \right),\times'\left(\cdots,\left(x_{i_{|\textbf{n}|}}-\frac{m_{|\textbf{n}|}}{N}\right)\right)\right)\right)\right)\\
&-\left(h(3Nx_1-3m_1)\left(h(3Nx_2-3m_2)\cdots\left(h(3Nx_d-3m_d)\left(\left(x_{i_1}-\frac{m_{i_1}}{N}\right)\cdots\left(x_{i_{|\textbf{n}|}}-\frac{m_{i_{|\textbf{n}|}}}{N}\right)\right)\right)\right)\right)\bigg|\\
&\leq (d+|\textbf{n}|)\epsilon_{\times'} \qquad i_1,\cdots,i_{|\textbf{n}|}\in\{1,2,\cdots,d\}
\end{aligned}$$
Finally, we define our approximation to $f(\textbf{x})$ as $f'(\textbf{x})$: $$\label{f'x}
f'(\textbf{x}) \triangleq \sum_{\textbf{m}\in\{0,\cdots,N\}^d}\sum_{\textbf{n}:0<|\textbf{n}|<n}\beta_{\textbf{m},\textbf{n}}f'_{\textbf{m},\textbf{n}}(\textbf{x}).$$ Using Equation (\[fmn\]), we get the error bound of the approximation to $f_2(x)$ as in Equation (\[imlementerror\]). $$\label{imlementerror}
\begin{aligned}
|f'(\textbf{x})-f_2(\textbf{x})|&=|\sum_{\textbf{m}\in\{0,\cdots,N\}^d}\sum_{\textbf{n}:|\textbf{n}|<n}\beta_{\textbf{m},\textbf{n}}\left(f'_{\textbf{m},\textbf{n}}(\textbf{x})-f_{\textbf{m},\textbf{n}}(\textbf{x})\right)|\\
&=|\sum_{\textbf{m}:\textbf{x}\in\text{supp}\psi_{\textbf{m}}}\sum_{\textbf{n}:|\textbf{n}|<n}\beta_{\textbf{m},\textbf{n}}\left(f'_{\textbf{m},\textbf{n}}(\textbf{x})-f_{\textbf{m},\textbf{n}}(\textbf{x})\right)|\\
&\leq2^d\max_{\textbf{m}:x\in\text{supp}\psi_{\textbf{m}}}\sum_{\textbf{n}:|\textbf{n}|<n}|f'_{\textbf{m},\textbf{n}}(\textbf{x})-f_{\textbf{m},\textbf{n}}(\textbf{x})|\\
&\leq2^d d^n\left(d+n-1 \right)\epsilon_{\times'}.
\end{aligned}$$ The second line follows again the support property and statement (1) of Proposition 2. The third line uses the bound $|\beta_{\textbf{m},\textbf{n}}|\leq1$. The fourth line is obtained by inserting Equation (\[fmn\]).
Then the final approximation error bound is as follows: $$\label{finalerrorbound}
\begin{aligned}
|f'(\textbf{x})-f(\textbf{x})|&\leq|f'(\textbf{x})-f_2(\textbf{x})|+|f(\textbf{x})-f_2(\textbf{x})|\\
&\leq2^dd^{n}\left(d+n-1 \right)\epsilon_{\times'}+2^{d+1}\left(\frac{d}{N}\right)^n.\\
\end{aligned}$$ Using statement (2) of Proposition 2 and choosing $r$ as $r=\frac{ \log\left(6N^n(d+n-1)\right)}{2}-1$, the approximation error turns to $$\label{finalerrorbound_r}
\begin{aligned}
|f'(\textbf{x})-f(\textbf{x})|&
\leq3\cdot2^d\left(\frac{d}{N}\right)^n.\\
\end{aligned}$$ Therefore, for any $f\in \mathcal{F}_{d,n}$ and $\epsilon\in(0,1)$, there is a ReLU network $f'$ that approximate $f$ with error bound $\epsilon$ if we choose $N\geq\left(3\cdot2^dd^n\right/\epsilon)^{\frac{1}{n}}$.
We now present the construction of the network for $f'(\textbf{x})$. If every $f'_{\textbf{m},\textbf{n}}(\textbf{x})$ can be computed by a sub-network, then $f'(\textbf{x})$ is simply a weighted sum of all outputs of $f'_{\textbf{m},\textbf{n}}(\textbf{x})$. By Proposition 3, we can implement the needed weights $\beta_{\textbf{m},\textbf{n}}$ by choosing $t=\log\frac{nN^n}{d^n}$. Then we simplify the task to constructing $f'_{\textbf{m},\textbf{n}}(\textbf{x})$.
$\times'$ can be implemented as discussed in Proposition 2. For $h(\left(3N\left(x_i-\frac{m_i}{N}\right)\right)$, noticing that $h(x)=h(-x)$, we can first compute $|x_i-\frac{m_i}{N}|$ as $\sigma(x_i-\frac{m_i}{N})+\sigma(\frac{m_i}{N}-x_i)$ and then scale it to $3N\left(|x_i-\frac{m_i}{N}|\right)$. The implementation of $h(x)$ can thus be simplified as $1-\sigma(x-1)+\sigma(x-2)$ since the input is nonnegative. Furthermore, by choosing $N$ as $cd^2$ where $c\in \mathbb{N}$ and $c>1$, $\frac{1}{N}$ is an integral multiple of $\frac{1}{n}\left(\frac{d}{N}\right)^{n}$ if $n>1$. When $n=1$, $\frac{1}{N}$ is an integral multiple of $\left(\frac{1}{n}\left(\frac{d}{N}\right)^{n}\right)^2$. As discussed in Proposition 3, we build a weight construction network $B_w$ in the way that all integral multiples of the minimal precision can be obtained. Therefore, all $\frac{m_{i}}{N}$ can be obtained in the same way as $\beta_{\textbf{m},\textbf{n}}$, except that we need to concatenate two weight construction sub-networks.
Now we analyze the complexity of the network. The implementation of $f'(x)$ is shown in Figure \[whole\]. The function and size of blocks are listed in Table \[tab:block\]. Then we are able to obtain the complexity of the network. While we can write the complexity of the network in an explicit expression, here we use the $\mathcal{O}$ notation for clarity. Let $N_{d},N_{w},N_{b}$ be the depth, the number of weights, and the number of bits required respectively. The weight construction blocks $B_w$ have the highest order of number of weights and we have $N_w=\mathcal{O}\left(\lambda t^{\frac{1}{\lambda-1}+1}
N^d\right)$. Meanwhile, we get $N_{d}=\mathcal{O}\left(\lambda t^{\frac{1}{\lambda-1}}+\log N\right)$. Inserting $t=\log\frac{nN^n}{d^n}$ and $N=\mathcal{O}\left(\left(1/\epsilon\right)^{\frac{1}{n}}\right)$, we get $N_{d}=\mathcal{O}\left(\lambda\log^{\frac{1}{\lambda-1}}\left(1/\epsilon\right)+\log\left(1/\epsilon\right)\right)$ and $N_{w}=\mathcal{O}\left(\lambda \log^{\frac{1}{\lambda-1}+1}\left(1/\epsilon\right)\left(1/\epsilon\right)^{\frac{d}{n}}\right)$. Multiplying $N_w$ by $\log \lambda$, $N_b$ is obtained. This concludes the proof of Theorem 1.
![A qunatized ReLU network that implements $f'(x)$. The connections of all $B_{f_{mn}}$ are the same. Every connection from $B_N$ to other blocks has no greater than two weights.[]{data-label="whole"}](whole.pdf){width="3.0in"}
block function width depth
--------------- ---------------------------------------------- ------- ----------------------------------------------------
$B_w$ construct weights $t$ $\lambda\left( t^{\frac{1}{\lambda-1}}-1\right)+1$
$B_N$ construct $\frac{1}{N},\cdots,\frac{N-1}{N}$ $2N$ 1
$B_{abs}$ get absolute values 4 1
$B_{s}$ scale by $3N$ 4 $\log \frac{3N}{2}$
$B_{h}$ implement $h(x)$ 12 1
$B_{\times'}$ implement $\times'(x,y)$ 60 $3r+1$
: Block configuration for function-independent structure[]{data-label="tab:block"}
The proof of Theorem 2 {#PT2}
----------------------
For any $f\in \mathcal{F}_{d,n}$ , given weight maximum precision $\frac{1}{\lambda}$, there is a ReLU network with fixed structure that can approximate $f$ with any error $\epsilon\in(0,1)$, such that (1) the depth is $\mathcal{O}\left(\log \left(1/\epsilon\right)\right)$; (2) the number of weights is $\mathcal{O}\left(\left(\log\left(1/\epsilon\right)+\frac{\log^2\left(1/\epsilon\right)}{\log \lambda}\right)\left(1/\epsilon\right)^{\frac{d}{n}}\right)$; (3) the number of bits needed to store the network is $\mathcal{O}\left(\left(\log (\lambda)\log\left(1/\epsilon\right)+\log^2\left(1/\epsilon\right)\right)\left(1/\epsilon\right)^{\frac{d}{n}}\right)$.
With $\lambda$ distinct values, a linearly quantized network has a minimal resolution of $\frac{1}{\lambda}$. The proof for the approximability of linear quantization can be done in the same way as Theorem \[T1\] except for a different sub-network for weight approximation. We still construct $W_c$ in Proposition 3 first and any weight value from $W_c$ can be obtained by multiply at most $\frac{t}{\log\lambda}$ weights. Thus the width and depth of the weight approximation network will be $t$ and $\frac{t}{\log \lambda}+1$ respectively. Updating the $B_w$ in Table 1, we obtain the complexity accordingly.
The proof of Proposition 4 {#PP4}
--------------------------
For any $f\in \mathcal{F}_{1,1}$, $t\in \mathbb{Z^+}$, and $T\in \mathbb{Z^+}$, there exists a function $\widetilde{f}(x)$ such that (1) $\widetilde{f}(x)$ is a continuous function with Lipschitz constant 1; (2) $\widetilde{f}(\frac{i}{T})$ = $\left\lceil T f\left(\frac{i}{T}\right) /2^{-t}\right\rceil\frac{2^{-t}}{T}$; (3) $|\widetilde{f}(x) - f(x)| < \frac{2^{-t}}{T} $.
We first divide $[0,1]$ into $T$ intervals uniformly and define $f^{+}(x)$ as $$\label{fplus}
f^{+}(x) \triangleq f(x) + \left(\left\lceil T f\left(\frac{\lceil Tx\rceil}{T}\right)/2^{-t} \right\rceil\frac{2^{-t}}{T} - f\left(\frac{\lceil Tx\rceil}{T}\right)\right).$$ Note that $f^{+}(\frac{i}{T}) = \left\lceil T f\left(\frac{i}{T}\right) /2^{-t}\right\rceil\frac{2^{-t}}{T}$ and $\dv{f^{+}(x)}{x} = \dv{f(x)}{x}$ on$(\frac{i}{T},\frac{i+1}{T})$ where $, i= 1,2,\cdots,T$. Then, we define $\widetilde{f}(x)$: $$\label{ft}
\widetilde{f}(0) \triangleq \left\lceil{\frac{T f\left(0\right) }{2^{-t}}}\right\rceil\frac{2^{-t}}{T},$$ $$\label{dft}
\dv{\widetilde{f}(x)}{x} \triangleq
\begin{cases}
\text{sgn}
(f^{+}(x) - \widetilde{f}(x)) & \widetilde{f}(x) \neq f^{+}(x)\\
\dv{f(x)}{x} & \widetilde{f}(x) = f^{+}(x). \\
\end{cases}$$ $f^{+}(x)$ is parallel with $f(x)$ on any given interval $(\frac{i}{T},\frac{i+1}{T}]$ and is shifted to let $f^{+}(\frac{i}{T})$ be an integral multiple of $\frac{2^{-t}}{T}$. $\widetilde{f}(\frac{i}{T})$ is $f(\frac{i}{T})$ rounded up to an integral multiple of $\frac{2^{-t}}{T}$. Meanwhile, $\widetilde{f}(x)$ approaches $f(x)$ with fixed slope whenever they are not equal. An example is shown in Figure \[f\].
![An example to illustrate the relationship between $f(x)$, $f^{+}$ and $\widetilde{f}(x)$. []{data-label="f"}](f5.pdf){width="2.5in"}
Statement (1) follows the definition of $\widetilde{f}(x)$ directly. We give a proof for statement (2) by contradiction and induction. If $\widetilde{f}(\frac{i}{T})=f^{+}(\frac{i}{T})$, then $\widetilde{f}(x)=f^{+}(x)$ on $(\frac{i}{T},\frac{i+1}{T}]$. The proof idea for $\widetilde{f}(\frac{i}{T})>f^{+}(\frac{i}{T})$ and $\widetilde{f}(\frac{i}{T})<f^{+}(\frac{i}{T})$ are basically the same thus we present the proof of the latter for brevity. We first assume $\widetilde{f}(\frac{i}{T}) = \left\lceil T f\left(\frac{i}{T}\right) /2^{-t}\right\rceil\frac{2^{-t}}{T}$, which is satisfied by Equation (\[ft\]) when $i = 0$. Since $\widetilde{f}(x) = f^{+}(x)$ after the first intersection on $(\frac{i}{T},\frac{i+1}{T}]$, if $\widetilde{f}(x)$ and $f^{+}(x)$ have no intersection on $(\frac{i}{T},\frac{i+1}{T}]$, then $\widetilde{f}(\frac{i+1}{T})<f^{+}(\frac{i+1}{T})$ because $\widetilde{f}(\frac{i}{T})<f^{+}(\frac{i}{T})$. Meanwhile, we have $\dv{\widetilde{f}(x)}{x} = 1$, and $$\begin{aligned}
\widetilde{f}\left(\frac{i+1}{T}\right) &= \widetilde{f}\left(\frac{i}{T}\right)+\int_{\frac{i}{T}}^{\frac{i+1}{T}} \dv{\widetilde{f}(x)}{x} dx\\
&=\left\lceil T f\left(\frac{i}{T}\right) /2^{-t}\right\rceil\frac{2^{-t}}{T}+\frac{1}{T}\\
&=\left\lceil T\left( f\left(\frac{i}{T}\right)+\frac{1}{T}\right) /2^{-t}\right\rceil\frac{2^{-t}}{T}\\
&\geq \left\lceil T f\left(\frac{i+1}{T}\right) /2^{-t}\right\rceil\frac{2^{-t}}{T}\\
&\geq f^{+}\left(\frac{i+1}{T}\right).
\end{aligned}$$ This contradicts the fact that $\widetilde{f}(\frac{i+1}{T})<f^{+}(\frac{i+1}{T})$. Thus $\widetilde{f}(x)$ and $f^{+}(x)$ intersect on $(0,\frac{i}{T}]$ and in turn guarantee that $\widetilde{f}(\frac{i+1}{T}) = \left\lceil T f\left(\frac{i+1}{T}\right) /2^{-t}\right\rceil\frac{2^{-t}}{T}$. By induction, we prove that $\widetilde{f}(x)$ and $f^{+}(x)$ intersect on every interval $(\frac{i}{T},\frac{i+1}{T}]$. This implies statement (2).
Now we prove the statement (3). Note that we have $0\leq \widetilde{f}(\frac{i}{T})-f(\frac{i}{T})\leq \frac{2^{-t}}{T}$ by statement (2). In every interval $(\frac{i}{T},\frac{i+1}{T})$, $\widetilde{f}(x)=f^{+}(x)$ after the their intersection. Therefore we have $0\leq|f^{+}(x)-f(x)|\leq \frac{2^{-t}}{T}$ by Equation (\[fplus\]). Before the intersection, if $\widetilde{f}(0)<f^{+}(0)$, $\dv{(\widetilde{f}(x)-f^{+}(x))}{x}\geq0$. Since $\dv{f^{+}(x)}{x} = \dv{f(x)}{x}$ on $(\frac{i}{T},\frac{i+1}{T})$, we have $\dv{(\widetilde{f}(x)-f(x))}{x}\geq0$, thus $0\leq \widetilde{f}(\frac{i}{T})-f(\frac{i}{T})\leq \widetilde{f}(x)-f(x)\leq f^{+}(x)-f(x)\leq \frac{2^{-t}}{T}$. If $\widetilde{f}(\frac{i}{T})\geq f^{+}(\frac{i}{T})$, apply the same logic and we obtain $0\leq f^{+}(x)-f(x)\leq \widetilde{f}(x)-f(x)\leq \widetilde{f}(\frac{i}{T})-f(\frac{i}{T}) \leq \frac{2^{-t}}{T}$. This implies statement (3) and concludes the proof.
The proof of Theorem 3 {#PT3}
----------------------
For any $f\in \mathcal{F}_{1,1}$ , given $\lambda$ distinct weights, there is a ReLU network with function-dependent structure that can approximate $f$ with any error $\epsilon\in(0,1)$, such that (1) the depth is $\mathcal{O}\left(\lambda\left(\log\log\left(1/\epsilon\right)\right)^{\frac{1}{\lambda-1}}+\log\left(1/\epsilon\right)\right)$; (2) the number of weights is $\mathcal{O}\left(\lambda\left(\log\log\left(1/\epsilon\right)\right)^{\frac{1}{\lambda-1}+1}+(1/\epsilon)\right)$ (3) the number of bits needed to store the network is $\mathcal{O}\left(\log \lambda\left(\lambda\left(\log\log\left(1/\epsilon\right)\right)^{\frac{1}{\lambda-1}+1}+(1/\epsilon)\right)\right)$.
We first transform $f$ to $f''$ with Proposition 4. Then we apply the interpolation and cached function method from \[35\] while using the weight construction method described in Proposition 3. Denoting the output of the network as $f''(x)$, we have $|f(x)-f''(x)| = |f(x)-\widetilde{f}(x)|+|\widetilde{f}(x)-f''(x)|\leq\epsilon$ by choosing the hyper-parameters as $m=\lceil\frac{1}{2}\log\left(1/\epsilon\right)\rceil $, $t=\lceil\log m\rceil$, $\delta = \frac{1}{8m}$, $T=\lceil\frac{8}{\epsilon\log\left(1/\epsilon\right)}\rceil$.
The approximation network is shown in Figure \[adaptivef\]. The sizes of blocks are given in Table \[tab:block2\] where $f^{T}$ is the uniform linear interpolation function of $f$ with $T-1$ breakpoints, $f^{*}$ is the sum of the selected cached functions, $\Phi(x)$ is a filtering function. The inputs connections to $B_{f^{*}_1}$ and the connections inside $B_m$ have higher order to the number of weights than others. Then the complexity can be obtained accordingly.
![A qunatized ReLU network that implements $f''(x)$. Illustration only, details are omitted. For example, arrows between blocks can represent more than one connection in the network and there are short-cut connections that allow scaling only part of the inputs. []{data-label="adaptivef"}](a3.pdf){width="3.0in"}
block function width depth
--------------- ---------------------------------------------- ---------- ------------------------------------
$B_T$ construct $1,2,\cdots,T$ $\log T$ $\log T$
$B_{\delta}$ construct $\delta$ $1$ $\lambda(t^{\frac{1}{\lambda-1}})$
$B_m$ construct $\frac{1}{m},\cdots,\frac{m-1}{m}$ $t$ $\lambda(t^{\frac{1}{\lambda-1}})$
$B_{f^T}$ implement $f^T(x)$ $T$ $1$
$B_{\Phi}$ implement $\Phi(x)$ 4$T$ $1$
$B_{s1}$ scale by $T$ 4 $\log T$
$B_{s2}$ scale by $\frac{1}{T}$ 1 $\log T$
$B_{s3}$ scale by $\frac{1}{\delta}$ 4 $\log m$
$B_{f^{*}_1}$ first layer of $f^{*}$ $T$ $1$
$B_{f^{*}_2}$ second layer of $f^{*}$ $3^m$ $1$
$B_{f^{*}_3}$ third layer of $f^{*}$ $m3^m$ $1$
$B_{f''}$ implement $f''(x)$ $4$ $1$
: Block configuration for function-dependent structure. Terms with lower order are omitted.[]{data-label="tab:block2"}
The proof of Theorem 4 {#PT4}
----------------------
For any $f\in \mathcal{F}_{1,1}$ , given weight maximum precision $\frac{1}{\lambda}$, there is a ReLU network with function-dependent structure that can approximate $f$ with any error $\epsilon\in(0,1)$, such that (1) the depth is $\mathcal{O}\left(\log\left(1/\epsilon\right)\right)$; (2) the number of weights is $\mathcal{O}\left(1/\epsilon\right)$; (3) the number of bits needed to store the network is $\mathcal{O}\left(\log (\lambda)/\epsilon\right)$.
The proof for the approximability of linear quantization can be done in the same way as Theorem \[T3\] except for a different sub-network for weight approximation. We still construct $W_c$ in Proposition 3 first and any weight value from $W_c$ can be obtained by multiply at most $\frac{t}{\log\lambda}$ weights. Thus the width and depth of the weight approximation network will be $t$ and $\frac{t}{\log \lambda}+1$ respectively. Updating the $B_{\delta}$ and $B_m$ in Table \[tab:block2\], we obtain the complexity accordingly.
The existence of an optimal bit-width {#proofBitwidth}
=====================================
In this section, we prove the statement in Section \[sec:bitwidth\] that there exists one and only one local minimum (hence global minimum) for $M(\lambda)$ in the range of $[2,\infty)$ whenever $\epsilon<\frac{1}{2}$. Denote $\log( 3n2^{d}/\epsilon)$ as $\theta_2$ and we get the derivative of $M(\lambda)$ as: $$\displaystyle\frac{d M} {d \lambda}=\theta^{\frac{\lambda}{\lambda-1}}_2\left(\log(\lambda)+\frac{1}{\ln2}-\ln(\theta_2)\frac{\lambda\log(\lambda)}{(\lambda-1)^2}\right)$$
Let $M_s(\lambda)=\log(\lambda)+\frac{1}{\ln2}-\ln(\theta_2)\frac{\lambda\log(\lambda)}{(\lambda-1)^2}$. Since $\theta^{\frac{\lambda}{\lambda-1}}_2>0$, we have ${\operatorname{sgn}}(M_s)={\operatorname{sgn}}\left(\displaystyle\frac{d M} {d \lambda}\right)$. We have $$\displaystyle\frac{d M_s} {d \lambda}=\frac{1}{\lambda}+\frac{1-\lambda+\log(\lambda)+\lambda\log(\lambda)}{(\lambda-1)^3}>0, \qquad \forall \lambda\geq2$$ $M_s(2)=1+\frac{1}{\ln2}-2\ln(\theta_2)<0$ given $\epsilon<\frac{1}{2}$, and $\lim_{\lambda\to\infty} \displaystyle M_s(\lambda)=\infty$. It is clear that there exist a $\lambda_{opt}$ determined by $\theta_2$ such that ${\operatorname{sgn}}(M_s(\lambda))=-1$ on $[2,\lambda_{opt})$ and ${\operatorname{sgn}}(M_s(\lambda))=1$ on $(\lambda_{opt},\infty)$. Remember that ${\operatorname{sgn}}(M_s)={\operatorname{sgn}}\left(\displaystyle\frac{d M} {d \lambda}\right)$, then $\lambda = \lambda_{opt}$ is the one and only one local minimum of $M(\lambda)$ on $[2,\infty)$.
[^1]: Throughout this paper, we use “sub-network" to denote a network that is used as a part of the final network that approximates a target function.
[^2]: Throughout this paper, we omit base 2 for clarity of presentation
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{
"pile_set_name": "ArXiv"
}
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Ginger polyphenols attenuate cyclosporine-induced disturbances in kidney function: Potential application in adjuvant transplant therapy.
Cyclosporine (CYA), a common immuno-suppressant drug that is used in organ transplants, is associated with nephrotoxic effects. Scientific exploration of natural products of plant origin should be considered; especially, in a world with increasing prevalence of kidney diseases. Effects of ginger polyphenols (GP) in Wistar rats with CYA-induced perturbations in electrolyte balance and kidney function was determined. Fifty Wistar rats were recruited for this study such that graded doses of GP were administered following CYA-induced kidney injury and comparisons were made against control and toxic groups at p < 0.05. Distilled water, CYA (50 mg/kg p.o. for 10 days) and GP (100, 200 and 400 mg/kg p.o. for 21 days) were administered to the rats at 0.2 ml/100 g. CYA administration induced kidney injury as characterized by significant deleterious alterations in plasma and urine levels of creatinine, urea, Na+ and K+ electrolyte balance as well as creatinine clearance. Also, there was a significant derangement in feeding pattern and relative kidney weight. Using GSH and SOD as antioxidant indicators, there was significant disturbance of the anti-oxidant system while histopathological results showed evidence of interstitial vacuolations with atrophic glomeruli. These conditions were significantly attenuated (p < 0.05) following administration of graded doses of GP. It was, therefore, concluded that GP could potentially be a therapeutic choice for patients with CYA-induced kidney injury.
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{
"pile_set_name": "PubMed Abstracts"
}
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Read the original text at 112.ua.
Do we, citizens of Ukraine, have a reason to be happy from the economic successes of the Cabinet of Groysman? Only according to official statistics, by the end of 2017, Ukraine's GDP will grow only to 1.8%, and inflation will reach 12.8%! In this case, the national debt to GDP in 2017 will reach 86.2%.
I do not learn about this from TV news or television talk shows, but directly from interviews with entrepreneurs. Maybe Groisman is just joking about some kind of investment growth and the real sector of the economy? But who will finally tell the truth in the government? For the sake of justice, I note that it is not the ministers, but the experts have already started talking frankly about the sore point. For example, recently Svitlana Kovalyvska, deputy director of the Institute for Social and Economic Research, bitterly noted in her article that the volume of direct foreign investment in Ukraine in the first half of 2017, compared to the same period last year, was reduced 4-fold and amounted to only 711.2 million dollars (in the equivalent of 18.9 billion UAH at the rate of 26.5 UAH / USD).
And this is because the national investment structure preserves the investment prospects of enterprises and indicates an ineffective state policy. In turn, investors and other players in the financial market do not have real incentives and tools to accumulate and invest in the fixed assets of Ukrainian joint-stock companies. Moreover, a number of other experts began to characterize our economy as a pole of trouble. Why? Because Ukrainians called inflation, declining incomes and self-restraint the main manifestations of this economic crisis.
Unfortunately, today Ukraine among the poorest countries. Modestly. But with a national identity. And all who receive foreign grants, experiment with the Ukrainian economy. One of them hopes for the European Union, and someone for the actions of Donald Trump to tighten sanctions against Russia. Well, where are our political and economic leaders with at least one really feasible national economic strategy?!
By the way, then the American president confidently bet on the intellect, rightly believing that it is time to listen not to the rich, but to the smart ones. Most likely, Roosevelt's example is now being followed in Armenia. Judge for yourself. During the V summit of the Eastern Partnership in Brussels, the Armenian delegation managed to achieve its goal, and as a result, Armenia signed the Association Agreement with the European Union. At the same time, Armenia remained a member of the Eurasian (Customs) Union, a member of the CSTO and is a military and political ally of the Russian Federation in the Caucasus.
Armenians have shown that the EU and Russia can pursue a single and non-confrontational policy towards the countries of the "Eastern Partnership". And what did our delegation achieve at this summit? For example, the European Commissioner for European Neighborhood Policy and Extension Johannes Khan again dismissed the idea of an investment assistance program for Kyiv "The European Plan for Ukraine," advising his Ukrainian counterparts to spend more money on reforms.
Although there is still a hope that our top officials and people's deputies will take into account the hard-hitting remarks of EU colleagues, they will draw the appropriate conclusions, and, perhaps, in 2018 a new program of macro-financial assistance of the European Union, the volume of which can reach 1.8 billion euros, would be launched. In this regard, Poroshenko stressed that this new program will include a list of certain conditions that Ukraine must necessarily fulfill, but did not list these conditions.
I do not expect that any economic leaders will soon appear from the "bottom". I think that there should still be people in the country's leadership who will have a sense of self-preservation, and they will correct the strategy for the development of the Ukrainian economy in the correct direction and finally formulate the national idea of a comprehensive reform of Ukrainian markets.
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{
"pile_set_name": "OpenWebText2"
}
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Q:
What does 'ignore reason: pending' in cucumber tests means?
I am using wdio v4.12.0 and wdio-cucumber-framework which is using cucumber v1.3.3 One of tests is ignored and only information in cmd output is that ignore reason: pending. All previous and later steps are executed without error.
[field with default name is visible] Test ignored: field with default name is visible, ignore reason: pending
Feature file:
Scenario: User is able to add field
Given user is on fields page
When user creates new field with default name
Then field with default name is visible
What can be cause of skipping this step? What does pending means (is it just unresolved promise or what)?
A:
I believe scenarios are marked as pending when Cucumber cannot find the underlying definition for one or more steps. In this case, it probably cannot find the step definition for "Then field with default name is visible" so check if you have implemented this definition.
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{
"pile_set_name": "StackExchange"
}
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Preoperative prognostic factors in diabetic pars plana vitrectomy.
The postoperative, six-month visual acuities of 1056 diabetic vitrectomy cases were compared to the following preoperative findings: duration of decreased vision associated with detachments, pupillary responses, iris rubeosis, intraocular tensions, extent of neovascularization, macular status, the ability to recognize entoptic phenomena, bright-flash ERG, and ultrasonography. By comparing these findings to the postoperative visual results, several factors were detected that could be helpful in determining the preoperative prognosis for improved vision. However, major operative complications reduced the incidence of successful visual results from 53% to 22%.
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{
"pile_set_name": "PubMed Abstracts"
}
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SHORT HISTORY OF THE CYRILLIC ALPHABET
IVAN G. ILIEV*
Summary
This work describes the history of the Cyrillic alphabet, which is one of the oldest, and one of the most widespread alphabets in the world nowadays, from its creation at the end of the 9th century AD to present-day times. At the beginning, the author discusses the name of the alphabet, its probable creators, and the period it was created in during the First Bulgarian Kingdom, as well as the model for the alphabet. Then he traces the spread of the Cyrillic letters to other countries and regions: Russia, Serbia, Croatia, Romania, the Caucasus, Siberia, Alaska, etc. Particular attention is dedicated to tsar Peter's orthographic reform in Russia in 1708, its influence over other Slavic and Orthodox peoples, and, at the end, to the withdrawal from the Cyrillic alphabet at the end of the 20th century. In the article there are also notes on Cyrillic hand-writing styles (uncial, semi-uncial, quickscript) and typography. Maps and a list of the languages which have used the alphabet are included, too.
Key Words: Cyrillic alphabet, Bulgaria, Russia, Slavic countries, Cyrillic typography.
The Cyrillic alphabet is one of the oldest, and one of the most widespread alphabets in the world nowadays, alongside with the Latin (or Roman) alphabet, the Chinese characters, the Arabic alphabet, and the Devanagari script. It originated during the 10th century in Bulgaria, on whose present-day territory several other alphabets were born even before this one: the Gothic alphabet of Wulfila (4th century AD), the alphabet of the Thracian tribe Bessi, invented by St. Nicetas of Remesiana (4th century AD), and the Slavic Glagolitic alphabet, invented by St. Cyril (9th century AD). Later, the Cyrillic letters spread to Serbia, Croatia, and Russia. Through Russian influence this script was accepted also by many Asian peoples, and even by some native peoples in Alaska (North America). With the accession of Bulgaria to the European Union on January 1st 2007, Cyrillic became the third official script of the European Union, following the Latin and Greek scripts.
I. TERRITORIAL SPREAD AND CHANGES IN THE ORTHOGRAPHIES OF THE CYRILLIC ALPHABETS
1. CREATION AND USE OF THE CYRILLIC ALPHABET DURING THE FIRST BULGARIAN KINGDOM (10-11th C.)
А. THE MEDIEVAL SLAVS – FROM THE STROKES AND NOTCHES TO EUROPEAN ALPHABETS
In the beginning, the Slavs made attempts to write ‘with strokes and notches’, and later they tried to use Greek and Latin letters for this purpose, as we know from the Slavic writer Chernorizets Hrabar. On the Balkan peninsula, between the 7-9th C AD, the Slavs lived together with the (Proto)Bulgarians (and under their rule) till the former assimilated the latter. The Bulgarians came from Asia, and at that time used to speak a non-Slavic language (most probably Turkic), and used to write their official documents in Greek, with Greek letters (using at the same time undeciphered runic signs as well). The Bulgarians also faced difficulties in writing some sounds with Greek letters, for instance, the sounds [tʃ] and [ʒ] were written by the Greek τζ and ζ. The Arab Ibn-Fadlan wrote in the 10th century AD that the Slavs who lived in present-day Russia used to put on the grave poles, bearing inscriptions with the names of the dead people. However, it is not clear what letters were used for that purpose. If it is true, as D. Cheshmedzhiev supposes, that the passage in Life of Saint Cyrill, in which the so-called р№шка писмена ’Rush letters’ were mentioned (which Constantine-Cyrill was said to have seen in Kherson, in Crimea, during his mission trip to the Khazar Khaganate, in the year 860, and which were considered by some Russian scientists to be an original script of the Russian Slavs), was inserted in that literary work not earlier than the 12th century (when the Russians already knew the Cyrillic letters), there will be no point in arguing what the national character of these letters was. At the end of the 9th century AD, the Slavs in Moravia, Panonia, and Bulgaria began writing in the newly created by St. Cyrill original Glagolitic script. However, the Glagolitic alphabet was replaced little by little by other alphabets, and only the Croats used it for several more centuries, alongside with the Latin and the Cyrillic scripts.
The so called Cyrillic alphabet (а misleading name), which originated in the First Bulgarian Kingdom at the beginning of the 10th century, and replaced the official Bulgarian Glagolitic script, was created by Constantine the Philosopher (Saint Cyril), and accepted by the Bulgarian ruler Boris I, at the end of the 9th century. The change took place in the reign of Boris’s son, Tsar Simeon I, who was strongly influenced by Greek culture. After a period of parallel use of the Glagolitic and the Cyrillic scripts during the 10-11th centuries in the first Bulgarian kingdom (sometimes even in mixed texts), since the 11th century, the latter has been an official Bulgarian, Russian, and Ukrainian alphabet (while the other Slavic peoples have used the Latin script during certain periods or unceasingly).
B. THE NAME OF THE ALPHABET
There was a supposition by Pavel Šafárik (Shafarik) that first the Glagolitic alphabet was called Cyrillic, and then, when it wasn’t in use anymore, this name was transferred to the invented later alphabet, currently called Cyrillic. This supposition was based on a note by the Russian scrivener Upir Lihyi, from the year 1047, who wrote that he had transcribed a book ис кУрилоцэ [is kurilotsya]. However, as Ivan Dobrev explains, the meaning of this phrase is ’from the original’, and not ’from Cyrillic’. Although the interpretation was wrong, it was supported by many Russian scholars. As a consequence, even modern Western authors (such as Schenker) cite this passage wrongly (ис к¹риловицэ). On the other hand, the modern term Glagolitic (designating the original Slavic alphabet) originated in Croatia where the word for a scrivener was glagolash (from глаголати ’to speak’, глаголъ ’word’), but the alphabet itself was called there bukvitsa (from the word for ‘letter’).
During the Bulgarian Renaissance, the Medieval Cyrillic alphabet was called slavenski pravopis ‘Slavic writing’, and later, from Russian was accepted the term Cyrillic alphabet, alongside with the simple but true balgarska azbuka ‘Bulgarian alphabet’. In the same way, in Ukraine the alphabet is called ukrainska abetka ‘Ukrainian alphabet’, although in different periods, it was called after the names of several orthography reformers (see further). The Cyrillic variant, used in Bosnia and Croatia, was called bosanchitsa ‘Bosnian alphabet’ or arvatitsa ‘Croatian alphabet’. In some other Slavic countries, the name of the alphabet is also given after a certain person: vukovitsa in Serbia, after Vuk Karadžić (Karadzich), tarashkevitsa in Belorusia (after B. Tarashkevich).
C. THE CREATOR OF THE CYRILLIC ALPHABET AND THE TIME WHEN IT WAS CREATED
There are no certain data about who and when has created the Cyrillic alphabet, although some scholars say that it was created by Constantine-Cyril himself (who presumably created both alphabets) or his disciples Clement of Ochrid and Konstantine of Preslav. However, there is no proof of that. The first accretion is not serious, and the other two are not supported by the facts, even the opposite is more likely (see the wonderful article by Ivan Dobrev in The Cyrillo-Methodian Encyclopedia).
In Life of of St. Clement of Ochrid or The Legend of Ohrid (in which, according to K. Mirchev, one can find a number of distorted facts), it was mentioned that the latter made some amendments to the alphabet, which his teacher (Constantine-Cyril) had created. That is why, it is more likely that the changes related to the Glagolitic alphabet; according to Chernorizets Hrabar, at the end of the 9th century or at the beginning of the 10th century, the latter was still being amended. Besides, it is a fact that in South-Western Bulgaria (Macedonia) the Glagolitic script prevailed over the Cyrillic. Nevertheless, Šafárik (Shafarik) thought that the second Slavic alphabet, which is now called Cyrillic, was created by St. Clement. According to Dobrev, it is hardly probable that Constantine of Preslav could possibly be the creator of the Cyrillic script since, in his Alphabetic Prayer (893), the acrostic was built after the order of the Glagolitic letters, and not of the Cyrillic ones. This shows also that the latter were created after that year. That is why, although some scholars (Emil Georgiev) consider the Cyrillic alphabet to have been invented even before the Glagolitic one, there are no preserved written data about that. Moreover, in Life of Cyril it was written that when the Byzantine emperor asked Constantine the Philosopher (St. Cyril) to create an alphabet for the Slavs (the Glagolitic one), the former complained to Constantine that the previous two emperors had not been able to cope with that task.
D. NUMBER, NAMES AND ORDER OF THE FIRST CYRILLIC LETTERS
The Cyrillic letters have names (the same as the Glagolitic), and both alphabets differ in some cases because the Cyrillic letters resemble the number values of the Greek alphabet). Unfortunately, the question of the choice of names for the Slavic letters is still open. The first letter is called азъ [azə] and literally means ‘I’ (but there may be another motivation for that naming – see below). Other letters literally mean ‘people’ (люди¬), ‘good’ (добро), ‘how’ (како), ‘word’ (слово), and so on. The modern names of the Cyrillic letters are simplified. For instance, the letters in the Russian alphabet are pronounced like this: [a], [be], [ve], [ge], [de] ...
The Cyrillic alphabet first consisted of 43 letters (according to К. Мirchev). 24 of them were the letters of the Greek alphabet, and the other letters were for the rest of the Slavic sounds: б, ж, щ, ц, ч, ш, ъ, ь, э, ю, , ©, ¤, etc. Six of the characters were used only in Greek words (for example, θ in θеодора ‘a female name’).
A table with the most of the Medieval Cyrillic letters (Kyrillisch). In the first three columns are the Greek model letters. Columns 5-6 contain the letters of the Cyrillic civil script of Peter the Great, called Grazhdanka (see further). In the last column are the original names of the Medieval Cyrillic letters (Source: Trunte 2001).
Some of the letters had variants: for the nasal [ę] were used the letters , ®, ¯, and even in one manuscript, written by several persons, different variants of one letter were sometimes used. Not all of the letters (for example, in the Enina Apostle, there is only ъ [ə], and not ь [’ə]) were used in other manuscripts. The sound [о] was written with different letter (о, w) acсording to its position in the word. Some letters could be written backwards (е - э, ¤ - ¤, etc.). Generally speaking, the orthography was more fixed in East Bulgaria.
Several tables, called abecedaria, containing the letters of the alphabet, have been preserved. In them, as well as in the acrostic works, the order of the letters is shown (there are some discrepancies, too). Constantine of Kostenets, who lived in the 14-15th centuries, placed the letter б and the rest of the non-Greek letters at the end of the alphabet in order to show his respect to the Greek original.
E. THE MODEL FOR THE ALPHABET
The alphabet itself is not a completely new invention. Like the Gothic ( / / / / …) and Coptic ( / / / / …) alphabets (source for the fonts – Wikipedia.org), the Cyrillic alphabet, invented after the year 893, is an expended Greek uncial writing system, and not an original alphabet like the Glagolitic one. In it, there are some supposed borrowings from other alphabets for the letters that are missing in the Greek alphabet.
The Munich abecedarium, containing the Cyrillic (above) and Glagolitic alphabets (below) (Source: Hamm 1974).
A text written in mixed Glagollitic and Cyrillic letters from South-East Bulgaria (Source: Илиев 2005).
Comparison between the Greek letters in column 1,2; the Cyrillic letters in column 3; and the Glagolitic letters in column 5 (Source: 강 [Kang] 2005).
Borrowings from and through the Glagolitic alphabet:
ш à ш (the letter was first borrowed from the Samaritan alphabet);
ù à щ;
φ à ц (less probably).
Borrowings from the Latin alphabet:
х à ж;
i à ь (?).
Ivan Dobrev thought that the letter ж was also borrowed from the Glagolitic script (from ć) but later he suggested that it could have also been influenced by the Latin x because, in Dalmatia, it was used like ж [ʒ] in Latin inscriptions: xeна (= жена) ’woman’, xivot (= животъ) ’life’. In the Freising folia (a Slavic text from the 10-11th centuries, written in Latin letters), ь is designated by i. Besides, Dobrev supposes that the Merovingian letter for the capital A (u) is the model for ©, which stands for the nasal o.
Borrowings from the Gothic alphabet (?):
à ч.
There is also an opinion (by Rossen Milev) that the Cyrillic alphabet was also influenced by the Gothic one, created by bishop Wulfila (311-383 AD) in the 4th century, also on the territory of present-day Bulgaria (the Gothic alphabet like the Coptic, is based on the Greek alphabet, with some extra letters from the Latin and Runic alphabets, that is why there is a visual resemblance between them). Both Gothic and Old Bulgarian ч [tʃ] correspond in numerical value to the digit 90 (as it was mentioned, in old alphabets the numbers were designated by letters). Similar are also the names of some letters – the Slavic азъ [azə] resembles the Gothic aza ’God’, while in Greek, there is Alpha from older Phoenician Aleph.
Other opinions look for connection between the Cyrillic letters (ж, ш) and the Chinese characters: mi (米) ‘rice’, shan (山) ‘mountain’, transferred to the Balkan Peninsula by the Bulgarians (Slavi Donchev); or with old Thracian-Balkanic writing traditions (Sv. Popov).
CHANGES IN THE BULGARIAN CYRILLIC ORTHOGRAPHY AND SPREAD OF THE CYRILLIC LETTERS TO RUSSIA, SERBIA, BOSNIA, CROATIA, DALMATIA, AND ROMANIA (WALLACHIA AND MOLDOVA)
From Bulgaria, the Old Bulgarian literary language and the Cyrillic alphabet were transferred to Russia (the Glagolitic alphabet was also transferred there and used as cryptography) and the Serbian principalities, where during the 11-12th centuries Old Russian and Old Serbian literatures were born. The Cyrillic alphabet was also used in the lands of present-day Romania, which were under Bulgarian rule. After the Romanian principality of Wallachia became independent in the 12-13 centuries, the Cyrillic alphabet was still in use there, as in the principality of Moldova for several centuries more. А Bulgarian tombstone inscription from the 11th century (Here lies prince Presian …) was found even in the town of Michalovce, Slovakia.
An inscription on a tombstone from Preslav, Bulgaria (Source: Хаджиев, Карадимитрова, Меламед 2010).
А coin of the Bulgarian Tsar Ivan-Assen II (Source: Хаджиев, Карадимитрова, Меламед 2010).
А. KIEVAN RUSSIA, THE RUSSIAN PRINCIPALITIES, LITHUANIA, AND THE URALIC PEOPLES
At the end of the 10th century, the Kievan ruler Vladimir baptized Kievan Rus’ and the Bulgarian books came to Kiev – see Iv. Dobrev, Insights into the Bulgarian Past. Literature flourished. In Novgorod, besides books, birch bark documents were written in Cyrillic, too.
А Novgorod birch-bark document (Source: Trunte 2001).
A birch- bark abecedarium from Novgorod (Source: Wikipedia).
After Vladimir’s death, several independent Russian principalities appeared (Kiev, Pereyaslavl, Smolensk, Polotsk, Galicia, Volinia, Vladimir, etc., as well as the Republic of Novgorod), and little by little separate East-Slavic peoples began to develop: the Ukrainian (with centre in Kiev, and later, in the 12-th century – in Galicia and Volyn), the Russian (with centre in Moscow), and the Belorusian (with centre in Polotsk). In neighboring Lithuania, which later conquered the Ukrainian and Belorusian lands (the Latvian people were under the rule of the Livonian Order), and then unified with Poland, the Ruthenian (Western-Russian, Ukrainian-Belorusian) language was used as official, as well as the Cyrillic alphabet, in the period of the 14-17th centuries (in 1696, it was replaced by Polish).
However, not only the Slavic and some of the Baltic peoples used the Cyrillic alphabet at that time. So did some of the neighbouring Uralic peoples: the Karelians and the Komi. A Karelian document numbered 292 from the Novgorod excavations, which was written in Cyrillic, is the oldest known document in any Finnic language, written on birch bark. It is dated to the beginning of the 13th century.
In the 14th century the Old Permic script appeared, sometimes called Abur or Anbur (derived from the names of the first two characters). It is an original ancient Permic writing system for the Komi people, derived from Cyrillic and Greek, and Komi tribal runes. The alphabet was introduced by a Russian missionary, Stepan Khrap (apparently of a Komi mother), also known as Saint Stephen of Perm, in 1372, in Veliky Ustyug. The alphabet was in use until the 16th century, when it was superseded by the Cyrillic script with certain modifications for affricates. Abur was also used as cryptographic writing for the Russian language, alongside with the Glagolitic script.
The Karelian birch-bark document N: 292 (Source: Wikipedia).
It is possible that the Khazars have also used a modification of the Cyrillic alphabet. The Arab Fakhr ad-Din wrote in 1206 that they also had a writing system (writing from left to right), which derived from the Russian one.
After the 14th century, the Grand Duchy of Moscow gradually emancipated from Mongol-Tatarian rule, and became the centre of the Russian lands. The German Schweipolt Fiol (Sebald Vehl) published, in 1491 in Cracow, the first book ever printed in Cyrillic script, in Church Slavonic (a literary language which originated in Russia on the basis of Old Bulgarian literary language) The Oktoikh or Octoechos (however, in the Wikipedia article about Božidar Vuković (Bozhidar Vukovich) at http://en.wikipedia.org it is written: The oldest printed book in Serbian-Slavonic was first issued in 1483, from the printing-press of Andreas Torresanus de Asula in Venice – if this were true, then Fiol’s book wasn’t the first one). The Russians began printing books in their own country, too – the first one, in 1564, was The Apostle, printed by Ivan Fyodorov.
Fiol’s Book (Source: Йончев 1964).
B. SERBIA AND MONTENEGRO
At the end of the 12th century, Stefan (Stephen) Nemanja created a unified Serbian state (Rascia), which also included the Principality of Zeta (present-day Montenegro), and other smaller principalities which were under Bulgarian rule during the 10-11th centuries (which meant they knew both the Glagolitic and Cyrillic scripts), and later under Byzantine rule. After a period of glory under Tsar Stefan Dušan (Stephen Dushan), in the 14th century, Serbia was once more divided into several feudal principalities, and later conquered by the Turks. An important role for the development of the Serbian culture played the Bulgarian, Constantine of Kostenets, who settled in Stefan Lazarević's Serbia, probably around 1402. He was warmly welcomed and was given the position of educator at the palace in Belgrade and the Manasija monastery, where he helped establish the Serbian Resava School of Literature. During that time, the historical memory changed, and he himself thought that the first Slavic books had appeared in Russia (not in Moravia and Bulgaria), and considered the Russian language to be the finest Slavic language.
Several decades later, The Serbian nobleman Božidar Vuković (Bozhidar Vikovich) bought a printing-press in Venice and established it at Obod in Montenegro, from which he issued in 1493 the Octoechos in Church Slavonic.
С. BOSNIA, CROATIA, AND DALMATIA
In the 9th century, Trpimir created unified Croatia, which reached its apogee at the beginning of the 10th century under Tomislav. Although the Glagolitic alphabet survived in Croatia, and even books were printed in it up to the 20th century, the Cyrillic script penetrated into that country, as well as into Bosnia, which became independent in the 14th century (after a period of Croatian and Hungarian dominance). For several centuries, the Cyrillic alphabet was widely used in Bosnia and Croatia (including Dubrovnik – the Republic of Ragusa, where Serbo-Croatian was spoken along with the Romance Dalmatian language; and the Poljica principality near Split). Its name in Bosnian and Croatian is bosančica or bosanica, which can literally be translated as Bosnian script. Croats also call it Croatian script - arvatica or Western Cyrillic. Рaleographers consider that the Humac tablet is the first document of this type of script and dates back supposedly to the 10th-11th century. Bosnian Cyrillic lasted continuously until the 18th century, with sporadic uses even in the 20th century. Today it is preserved in a Franciscan monastery of Humac near Ljubuški in Herzegovina.
D. THE CYRILLIC SCRIPT DURING THE TIME OF THE SECOND BULGARIAN KINGDOM, AND THE TIME OF THE OTTOMAN RULE OVER BULGARIA (12-19th CENTURIES)
From 1018 till 1187, Bulgaria was under Byzantine rule but the Cyrillic tradition wasn’t interrupted. It even flourished again in the years of the Second Bulgarian Kingdom. However, there were some changes. Besides the backwards letters (е – э, ¤ - ¤) the accent and aspiration marks, which were in use even in printed Cyrillic books, were introduced from Greek.
The Bosnian/Croatian Cyrillic alphabet – columns 1 and 3 (Source: Wikipedia).
A computer text in Bosnian Cyrillic (Source: Trunte 2001).
During the Middle-Bulgarian period, because of the language changes, there were several unnecessary letters which were used after artificial rules (for instance, always ь at the end of the word: градь ’town’ instead of градъ). An important literary Slavic centre during the 14th century was Mount Athos in Greece. Later, Euthymius of Turnovo founds and heads the Turnovo literary school. He is said to have conducted a language reform, although, these days, its opponents are more than its supporters. After the fall of the Bulgarian kingdoms and principalities (Momchil’s Despotate of Xanthi, Kingdom of Turnovo, Principality of Karvuna, Kingdom of Vidin) under the Turkish rule (the last one - in 1396), many Bulgarian writers (Gregory Tsamblak, Konstantine of Kostenets, etc.) went to Serbia, Walachia or the Russian principalities, and played an important role in cultural life there.
The overloaded Middle Bulgarian orthography was used and in the period of the 16-18th centuries, when Bulgaria was ruled by the Ottoman Turks, and the damaskin literature flourished. Between 1566-1570, Jacob Krajkov printed several books in Venice (Book of Hours, Psalter, Prayer Book), without abbreviated words (previously, instead of богъ ’God’ was used бгЌъ, for instance), and using elements of the colloquial Bulgarian language. The traditional orthography was also used in the printed books during the Bulgarian Renaissance (after 1762 – when Paisii of Hilandar wrote also in Church Slavonic mixed with Bulgarian colloquial elements his Slavonic-Bulgarian History) – for example, in Peter Beron’s Рrimer from the year 1824. During the 17-18th centuries, the literature of the Bulgarian Catholics, which was developed on the basis of the so-called Illyrian literary language (an artificial South-Slavic language on Croatian basis, with Serbian and Bulgarian elements, used by the Catholic priests as common South-Slavic language - not to be taken for Ancient Illyrian) flourished also. In Illyrian, on the basis of the Bosnian Cyrillic script, Filip (Philip) Stanislavov wrote the miscellany Аbagar, and had it printed in Rome in 1651. The period of the 17-19th centuries was characterized by chaotic use of different letters (old and new) by different authors. Yoakim Karchovski in Different Instructive Directions (1819) and Beron in his Рrimer use the letter џ for the sound [dʒ]. Instead of ъ, at that time was written ă. In 1825, in Holy History by V. Nenovich was restored © for [ъ]. In this way that sound was written in three ways: ъ, ©, ă. N. Gerov distinguished between ъ and © on etymological basis in 1849.
Е. WALLACHIA MOLDOVA, AND TRANSYLVANIA
The independent Romanian principalities of Wallachia and Moldova appeared in the 12th century. For about five centuries, the Cyrillic script was the liturgical and administrative script in these two states – first in Slavic, and later in Romanian language, and the Wallach and Moldavian rulers used the Cyrillic alphabet for writing their official documents. Several Bulgarian books, printed in the Wallachian city of Targovishte, are particularly precious, among them, a Gospel printed by Macarius, in 1512, by order of the ruler John Basarab. This Macarius printed earlier Liturgy (1508) and Octoechos (1510). In Szeben (Cibinium, Sibiu), Transylvania, the printing of liturgical books for the orthodox church began in 1544. They were also printed with Cyrillic script, and their language was either Slavic or native Romanian. The Cyrillic books printed in Transylvania were transported and sold in the Romanian Principalities of Moldavia and Wallachia. A printer working in Szeben with Cyrillic types was Philip deacon who followed the tradition of early liturgical books.
A page from the book Abagar (Source: Радев, Кабакчиев 2006).
The earliest known text in Romanian dates from 1521 and is a letter from Neacşu of Câmpulung to the Mayor of Braşov (Brashov). Neacşu wrote in a version of the old Cyrillic alphabet similar to the one for Old Bulgarian, and which was used in Walachia and Moldova until 1859. From the late 16th century a version of the Latin alphabet using Hungarian spelling conventions was used to write Romanian in Translyvania. Then in the late 18th century a spelling system based on Italian was adopted. In 1860–1862, the Cyrillic was officially replaced by a Latin-based Romanian alphabet. Cyrillic remained in occasional use until circa 1920 (mostly in Bessarabia). It was not the same as the Russian-based Moldovan Cyrillic alphabet. Between its discarding and the full adoption of the Latin alphabet, a so-called transitional alphabet was in place for a few years (it combined Cyrillic and Latin letters, and included some of the Latin letters with diacritics which came to be used in Romanian spelling).
TSAR PETER’S ORTHOGRAPHIC REFORM IN RUSSIA, AND ITS INFLUENCE OVER OTHER SLAVIC AND ORTHODOX PEOPLES
А. RUSSIA
In 1708, the Russian Tsar Peter I the Great conducted an orthographic reform, introducing a new type of Cyrillic letters, called civil script, modelled in a Dutch work shop. It was helped by the spread of the Latin script among the educated people in Russia in the period between 1680–1690. The reform was a compromise between the supporters of the old Cyrillic tradition and the supporters of West-European culture. Many of the old Cyrillic letters were replaced by newer ones, similar to them, and accentuation marks and abbreviations as well as the different letters for designating one sound in a different position in the word were no longer used,. The letter was replaced by я. The use of the backwards э instead of е (which was borrowed from Bulgarian books) began to designate the hard [е] in borrowed words: мэр ‘mayor’, from French maire.
The Lord’s Prayer in Romanian Cyrillic (Source: Wikipedia).
A text in Romanian transitional alphabet (Source: Wikipedia)
The letters ѕ, θ, ξ, ψ, v were thrown out. The civil script is the basis of all modern Cyrillic alphabets. The first book, printed with the new script was ГЕОМЕТРIА ‘geometry’.
The first book printed in civil script (Source: Wikipedia).
Beron’s Bulgarian Primer (Source: Wikipedia).
B. BELORUSSIA
The Russian principalities on the territory of present-day Belorussia were not affected by the Mongol invasion. However, they were included in the Grand Duchy of Lithuania, and later, in the Polish-Lithuanian Commonwealth, and in these lands the Orthodoxy and the Cyrillic alphabet were losing ground till the 18th century when they became part of the Russian Empire. The Belorussian typography had a long tradition even before Peter I the Great. The Belorussian F. Skaryna was one of the first to publish in the Cyrillic script. In 1517, he established a printing press in Prague, where he printed his first book, The Psalter, in the same year, in a mixture of Church Slavonic and Belarusian. Since 1560s the Nesvizh Cyrillic Typography, established by Symon Budny, began to work. The Kutein Typography, established by Spiridon Sobol (who probably was Ukrainian) in 1630, near Orsha, became a centre of the Belorussian book printing.
The modern Belorussian Cyrillic alphabet was made up at the end of the 19th century, and several slightly different versions were used informally. During its evolution, fifteen letters were dropped, the last four of them going after the introduction of the first official Belorussian grammar in 1918.
C. UKRAINE
In the period of the 12-17th centuries, Ukraine was under the rule of the Mongols, then of the Polish-Lithuanian kingdom, and finally – of Bohdan Khmelnytsky’s Cossacks, till it became part of the Russian kingdom in the 17th century. Several scholars worked in the 16-17th centuries. Lavrentiy Zyzaniy, a Ukrainian and Belorussian scholar, published a Church Slavonic Grammar in 1596 in Vilnius, Lithuania. So did Meletius Smotrytsky in 1619, another Ruthenian (Ukrainian and Belorussian) linguist. His Slavonic Grammar, published in 1619, was very influential on the use of Church Slavonic, and codified the use of the letters Я (ja), Е (e), and Ґ (g).
One of Skaryna ’s printed books (Source: Йончев 1964).
Zyzaniy’s Grammar (Source: Wikipedia).
Another great name was the Kievan and All-Rus’ Metropolitan Peter (secular name Petro Mohyla) who was born in a Moldavian boyar family. In the 1620s, Mohyla traveled to Ukraine, and settled in Kyevo-Pechers’ka Lavra in Kiev – the political and cultural centre of Ukraine. In 1632, Mohyla became the bishop of Kiev and abbot of Pecherska Lavra. There he founded a school for young monks where the tutoring was conducted in Latin. Later this school was merged with the Kiev Brotherhood school and turned into the Mohyla collegiums or the Kyiv Mohyla Academy. Mohyla significantly improved the print shop at Lavra where Orthodox books were published in Latin, and for over 20 years, he played a leading role in Ukraine’s book printing, being one of the first to print in the Ukrainian language. Mohyla wanted to preserve the Ukrainian nation’s identity that had been experiencing enormous pressure from the Polish and Russian regimes. He initiated the publication of sermons for the laity in Ukrainian, Biblical texts in Church Slavonic, and scientific books in Ukrainian, Polish, Greek, and Latin. One of his most important publications was Catechesis (1640). Another notable works included Trebnyk or Euchologion (1646). There are data that he first used the civil script letters, which later Peter I of Russia introduced in 1708.
Various alphabet reforms were influential in Ukraine, besides Peter the Great's civil script of 1708 (the Grazhdanka), which influenced Mykhaylo Maksymovych's nineteenth-century Galician Maksymovychivka script, and its descendent, the Pankevychivka, which is still in use, in a slightly modified form, for the Rusyn language in Carpathia Ruthenia. Several other reforms attempted to introduce a phonemic Ukrainian orthography during the nineteenth century, based on the example of Vuk Karadzhich's Serbian Cyrillic. These included Oleksiy Pavlovskiy's Grammar, Panteleimon Kulish's Kulishivka, the Drahomanivka, promoted by Mykhailo Drahomanov. In Galicia, the Polish-dominated local government tried to introduce a Latin alphabet for Ukrainian, which backfired by prompting a heated War of the Alphabets, bringing the issue of orthography into the public eye. The Cyrillic script was favoured, but conservative Ukrainian cultural factions (the Old Ruthenians and Russophiles) opposed publications which promoted a pure Ukrainian orthography. In 1876, the Ems Ukaz (decree) banned the Kulishivka and imposed a Russian orthography until 1905, called the Yaryzhka, after the Russian letter ы (yery). The Yevhen Zhelekhivsky's Zhelekhivka, which standardized the letters ї (ji) and ґ (g) became official in Galicia in Austro-Hungary in 1893, and was adopted by many eastern Ukrainian publications after 1917.
D. POLAND AND LITHUANIA
The Kingdom of Poland, informally known as Congress Poland or Russian Poland, was created in 1815 by the Congress of Vienna. It was a personal union of the Russian part of Poland with the Russian Empire. It was gradually politically integrated into Russia over the course of the 19th century, made an official part of the Russian Empire in 1867, and finally replaced during the Great War by the Central Powers in 1915 with the theoretically existing Regency Kingdom of Poland. Though officially the Kingdom of Poland was a state with considerable political autonomy guaranteed by a liberal constitution, its rulers, the Russian Emperors, generally disregarded any restrictions on their power. Thus effectively it was little more than a puppet state of the Russian Empire. The Cyrillic script was used for short period during the Congress Poland era because required by Russian law. In the middle of the 19th century, the Russian Tsar Nicholas I tried to replace the Polish Latin alphabet with the Cyrillic one but the effort was not successful. Here is a sample text of that time:
Пóйдзьце о дзятки, пóйдзьце вшистке разэм
За място, подъ слупъ на взгóрэкъ,
Тамъ прĕдъ цудовнымъ клęкнийце образэмъ,
Побожне змóвце пацёрэкъ… (Поврóтъ Таты, пр̌езъ А. Мицкевича).
Another variant of the same text:
Пуйдьте о дятки, пуйдьте вшистке разэм
За място, под слуп на взгурэк,
Там пред цудовным клЄкнийте образэм,
Побожне змувте патëрэк.
The idea of introducing the Cyrillic alphabet for the Polish language has supporters even now – see the site Ортографя цырылицка для Єзыка польскего in the bibliography.
After the Uprising of 1863-1864 in the North-West part of the Russian Empire, the general-governor M. Muravyov forbade printing in Latin letters for the Lithuanians, and everything had to be printed in Cyrillic up to 1904.
E. THE URALIC PEOPLES
Besides being in use among the Russians, the Ukrainians, the Belorussians, the Polish, and the Lithuanians, the Cyrillic script kept on spreading through the Uralic people during the 18-19th centuries: the Mordvins (Erzya and Moksha), the Mari in the 18th century, the Karelians in the 19th century, and the Nenetsр at the same time. However, it was used mainly for religious purposes – for creation of orthodox texts and dictionaries. Works of national literatures were not created. The first Erzya religious texts appeared in 1803. In 1884, a Primer was printed, too. A Gospel of John in the Moksha language was published in 1901 (the modern alphabet was created in the second half of the 18th century). In the 19th century, a few books were published in Karelian using the Cyrillic script, too, notably A Translation of some Prayers and a Shortened Catechism into North Karelian and Olonets (Aunus) dialects in 1804, and the Gospel of St. Matthew in South Karelian Tver dialect, in 1820.
F. SERBIA, MONTENEGRO, AND ALBANIA
While the people in Croatia used the Latin (and to some extent the Glagolitic) alphabet, and in Bosnia even books in the Arabic script appeared during the 18-19th centuries, in Serbia the literary language was the Church Slavonic (and its variant, the Serbian-Slavonic). At the beginning of the 19th century, Sava Mrkal simplified significantly the Serbian Cyrillic script (the Russian Civil script was accepted first in that country).
In the middle of the 19th century, Vuk Stefanović Karadžić (Karadzhich) conducted an orthographic reform: the unnecessary letters ъ and ь were discarded and the letters љ, њ, џ, j were introduced. After that reform, the Serbian Cyrillic script was called after Karadzhich: vukovitsa. In 1850, the so-called Vienna Literary Agreement was signed. It was the first step to the creation of a standardized Serbo-Croatian language on the basis of Vuk’s reform (representatives from Serbia and Croatia took part in signing the Agreement).
Although the oldest surviving Albanian document of the 15th century was written in the Latin script, and early Albanian writers also used a Latin-based script, adding Greek characters to represent extra sounds, Christophoridēs published a book in Cyrillic, in 1872.
A Lithuanian Cyrillic text from 1866 (Source: Wikipedia).
A modern Mongolian banknote (Source: Wikipedia).
A Serbian-Slavonic magazine (Source: Wikipedia).
The Serbian grammar written by Karadzhich (Source: Wikipedia).
G. BULGARIA
After Serbia, the civil script was accepted in Bulgaria as well in about 1830, and it was called просветително писмо ‘instructive script’. Printed books from Russia and Serbia came to that country, spreading the Russian and Serbian influence. In this way, © began designating [ъ] instead of nasal о, and designated soft [’а] instead of nasal e. In 1806, Sophronius of Vratsa published in Church Slavonic (written in the old Cyrillic script) the first printed Bulgarian book, called A Sunday Book. The first Bulgarian book printed in the civil script in 1821 (in Chisinau, Moldova), was Instructions for the Duties of the Rural Institutions (in Bulgarian and Russian). Then, Аrithmetics by Hristaki Pavlovich appeared in 1833 in Belgrade. After 1850, the Civil script dominated the laic literature, and later, even the religious, although in his memoirs, the great Bulgarian poet and writer, Ivan Vazov, wrote that his father had used the old ‘church’ letters in his commercial book long after that time. At that period, Neofit Rilski and Ivan Momchilov completed several grammar works.
4. THE MISSIONARY WORK OF THE RUSSIAN ORTHODOX CHURCH IN SIBERIA, THE NORTH PACIFIC REGION, AND NORTH AMERICA (ALASKA), AND THE FURTHER SPREAD OF THE CYRILLIC ALPHABET
In 1582, the Cossack ataman Yermak Timofeyevich conquered the capital of the Siberian Tatar Khanate, and thus began the Siberian conquest. It took a long time; for example, the Chukchi people fought about 150 years against the Russian invasion but finally surrendered (by the end of the 19th century the conquest of Middle Asia – Kazakhstan, Uzbekistan, etc., was completed.). The Russian explorers even reached Alaska, which became a Russian territory, governed from 1799 to 1867 by the Russian-American Company, based in Irkutsk (Siberia). It had colonies along the whole West Coast of North America, as far as California. In 1816, a Russian fortress was even built on the Hawaii islands but the idea of making that archipelago a Russian territory was given up. Otherwise, even the people there could have used the Cyrillic alphabet.
In the 16-18th centuries, the Russian missionaries established several Orthodox missions in Siberia and even in Middle Asia (where the population originally followed Islam), and tried to teach God’s word to the native Siberian peoples in Russian. Later, attempts were made to publish books for the Siberian Tatars and the Buryats not only in Arabic and Old Mongol scripts but in Cyrillic letters, too. However, the native Siberian peoples did not like Christianity, and the printed materials were scarce – usually only the missionary had a single book, and the local people themselves could never see it. In 1897, the census showed less than 5 % literacy among the native Siberian population, and it was literacy in Russian, not in native languages. Only the situation among Buryats was a little better. At the end ot the 19th century, and at the beginning of the 20th, a Russian missionary, St. Nicholas of Japan, spread Orthodox Christianity in the Land of the Rising Sun, and translated the Bible into Japanese. Unfortunately, there is no proof of attempts having been made to introduce the Cyrillic alphabet in that country. However, a system for Cyrillic transcription for the Japanese language, called Rosiadzi or Kiridzi, was created in 1917 by E. Polivanov (Such systems were created for other languages, too, even for Hungarian: the Hungarian Cyrillic alphabet, or маЃар цирилл, was invented by Samuel P. Bateman, who wanted to make it easier for Hungarians to learn Russian as a second language).
The Russians sold Alaska to the Americans in 1867. However their culture, religion, and alphabet stayed there, among the native peoples (the Aleut, the Inuit or Eskimos, and the Tlingit), and even were better accepted than in Siberia where the influence of Islam and Buddhism was strong. In the Yupik Eskimo dialect, the word for a white person is still Kass'aq, a derivative of Cossack.
At the end of the 19th and at the beginning of the 20th century, religious Cyrillic books were published in Aleut, Yupik, and Tlingit (first, in the old medieval script). Today, in Alaska, there is still an Orthodox Church – All Saints of North America Orthodox Church. The native Cyrillic texts can be found in its website (http://www.asna.ca/alaska). An example of the Cyrillic Tlingit alphabet can be found in the text Indication of the Pathway into the Kingdom of Heaven (in Russian – Указаніе пути въ Царствіе Небесное, in Tlingit-Cyrillic – Ка-вак-шіи ев-у-ту-ци-ни-и дте Тики Ан-ка-у хан-те), written by the priest John Veniaminov in 1901.
5. REFORMS AND SPREAD OF THE CYRILLIC ALPHABET AFTER 1917
A. RUSSIA
After Lenin came to power in Russia in 1917, an orthographic reform discarded some letters (э, Ї) from the Russian Cyrillic alphabet, which was imposed on many European, Siberian and Middle-Asian peoples that lived in the state. Some of them did not have writing systems before (see further); others used the Mongolian (the Buryats), the Arabic (the Tatars, the Avars, the Kazakh), the Georgian (the Abkhaz, part of the Ossetians) or the Greek scripts (the Alans or Ossetians, the Gagauz).
A Kazakh text in Arabic and Cyrillic scripts (Source: Wikipedia).
An Aleut Gospel with a parallel Russian text (Source: www.asna.ca).
A Tlingit Orthodox text with explanation in Russian (Source: www.asna.ca).
Yupik Eskimo religious brochures in Latin and Cyrillic scripts (Source: Jacobson 2001).
Many languages in Russia changed their alphabets several times in the 20th century. For example, in the 1920s, the Komi language was written with the Molodtsov alphabet, derived from Cyrillic. It was replaced by the Latin alphabet in 1931 (which was accepted for a short period by many other peoples), and later by the Cyrillic alphabet in the Komi Autonomous Soviet Socialist Republic. For Karelian, a number of Cyrillic-based spelling systems were developed during the Soviet period, though none of them took off due to Stalin's suppression and outlawing of Karelian. Some of the languages are already extinct. Ter Sami (which used the Cyrillic alphabet after the Second World War), in the northeast of the Kola Peninsula in Russia in 2010 was spoken only by two people. The rapid decline in the number of speakers was caused by Soviet collectivization, during which use of the language was prohibited in schools in the 1930s.
B. UKRAINE
Ukraine enjoyed a brief period of independence from 1918 to 1919 (when an official Ukrainian orthography was accepted), then it was taken over by the USSR and declared a Soviet Republic. In 1925, the Ukrainian SSR created a Commission for the Regulation of Orthography. A standardized Ukrainian orthography and method for transliterating foreign words were established, a compromise between Galician and Soviet proposals, called the Kharkiv Orthography, or Skrypnykivka, after Ukrainian Commissar of Education Mykola Skrypnyk. It was the first universally-adopted native Ukrainian orthography. However, in 1933, the orthographic reforms were abolished, decrees were passed to bring the orthography steadily closer to Russian. An official orthography was published in Kiev in 1936, with revisions in 1945 and 1960. This orthography is sometimes called Postyshivka, after Pavel Postyshev, Stalin's Russian official who oversaw the dismantling of Ukrainization. In the meantime, the Skrypnykivka continued to be used by Ukrainians in Galicia and the diaspora worldwide. During the period of Perestroika in the USSR, a new Ukrainian Orthographic Commission was created in 1987. A revised orthography was published in 1990. Ukraine declared independence in 1991.
There is a form of the Ukrainian language, called Rusyn, also known in English as (Modern) Ruthenian. Some linguists treat it as a distinct language; others treat it as a dialect of Ukrainian. The Rusyn alphabet has several variants, used in Voivodina (in Serbia), Slovakia, Poland, and Ukraine. In Crimea and Bessarabia, several Turkic peoples accepted the Cyrillic alphabet (the Tatars, the Karaims, the Gagauz, etc.).
C. BELORUSSIA
During the early 20th century, many Belarusian publications were printed in both the Latin and Cyrillic alphabets. After the Soviet invasion of eastern Belorussia in 1919-1920, the Cyrillic alphabet became the only alphabet used in official writings. Meanwhile, in western Belorusssia, the Latin and Cyrillic alphabets continued to coexist, though after 1943 the majority of publications were printed in the Cyrillic alphabet. Belorussian Classical Orthography or Tarashkievitsa is a variant of the orthography of the Belorussian language, based on the literary norm of the modern Belorusian language, the first normalization of which was made by B. Taraškievič in 1918, and was in official use in Belorussia until the Belorussian orthography reform of 1933, which brought the Belorussian language closer to Russian – Narkomovka.
Since 1933, Tarashkievica has been used only informally in Belorussia and by Belorussian diaspora abroad since the legitimacy of the reform of grammar in 1933 was adopted neither by certain political groups in West Belorussia, nor by the emigrants, who left thecountry after 1944. During the Perestroika period of the late 1980s, the movement for the return of Tarashkievica in Belorussia was initiated. Belorussia gained independence in 1991. In 2005, with the publishing of the Belorussian Classical Orthography, the modern normalization of Tarashkievica was made. This proposal was adopted by some media, including the Belorussian Wikipedia. In fact, two Belorussian orthographies are used today.
In the 1980s, attempts were made for standardizing the West Polesian micro language – a transitional form between Belorussian and Ukrainian.
D. MOLDOVA AND TRANSNISTRIA
The historical Romanian Cyrillic alphabet was used in Moldova until 1918. A version of the Cyrillic alphabet was used in the Soviet Republic of Moldova from 1924-32, and from 1940 until 1989 (except 1941-44). The standard alphabet now is Latin. However, the Cyrillic alphabet is still used [update]in Transnistria. The official languages there are Russian, Ukrainian, and Moldavian (with Cyrillic alphabet).
E. THE CAUCASUS
In the 10th century, the Arabs called the Caucasus The mountain of the languages due to the numerous languages spoken there (in some cases, it is difficult to differentiate between a language and a dialect). Some of the peoples in the region, such as the Avars, used the Arabic letters as early as the 11th century AD; others, such as the Abkhaz, made attempts to write with Georgian letters. Excluding Georgian and Armenian, most languages in the Caucasus use or have used the Cyrillic alphabet in the 20th century. On the whole, many languages in the Soviet Union have changed their alphabets several times: Arabic à Latin à Cyrillic à Latin/Arabic. For instance, until 1928, Kumyk also was written with the Arabic alphabet. Between 1928 and 1938, it was written with the Latin alphabet, and with the Cyrillic alphabet since then. The Ossetians (or Alans) have been using a standardized Cyrillic alphabet since 1844 (created by Andreas Sjögren). However, a Cyrillic Catechism was printed in Ossetic much earlier – in 1798. In 1923-38 this Indo-Iranian people used the Latin script. Later, since 1938, the Northern Ossetians have been using the Cyrillic, and the South Ossetians used the Georgian script up to 1954, and then changed to Cyrillic, too.
Alongside with major languages, like Azeri, and to less extent, Chechen or Ossetic, there are languages spoken in only one village. For example, Archi is a Northeast Caucasian language with about 1000 speakers in the village of Archi in the Dagestan. Some of the languages even have no standard written form – the Dagestanian Akhvakh. It is used mainly in homes, while Avar and Russian are used elsewhere. Since the 1940s a number of linguistics studies of Akhvakh have been undertaken, and a few texts in Akhvakh have been published including a collection of stories in 1949. In the 20th century, the Caucasian Ubykh language and the Indo-European Kilit became extinct, the latter being similar to Talysh, which is still spoken by a small population.
Although the creation of Cyryllic based alphabets for the native Caucasian and Asian peoples was a great achievement for Russian linguists, these alphabets are not quite successful, and in many cases the creators deliberately designated one sound by different signs in different variants of the same language (Kabardian and Adyghe, for instance).
F. SIBERIA
Almost all native languages in Siberia use the Cyrillic alphabet although for some of them it was invented after the 1990s, and most of them are close to extinction (excluding widespread languages like Yakut or Even). Ket is the last surviving member of the Yenisei family of languages, and is spoken by about 550 people along the Yenisei River and its tributaries in Central Siberia. Its Cyrillic-based system was developed in the 1980s by G. K. Verner and G. H. Nikolayeva. Northern Yukaghir is spoken by about 150 people, while Southern Yukaghir has fewer than 50 speakers. The Yukaghir languages were first written in the 1970s using a spelling system using the Cyrillic alphabet devised by Gavril Kurilov, a native speaker of Tundra Yukaghir. Both Yukaghir languages have been taught to some extent in schools since the 1980s.
Itelmen is a Chukotko-Kamchatkan language with fewer than 100 speakers in the Kamchatka Peninsula in Siberia. There is no Aleut primer even now, the only Cyrillic book in Aleut, a school dictionary, was published in the 1990s. In Outer Manchuria (the region of the Amur river), there are several small peoples, like the Orok and the Orochi peoples (both less than 100 persons in number), and several more. The Cyrillic alphabet first has been used for descriptions of their languages, and later, in the period 2008-2010, materials for learning these languages were published. One of the newest Cyrillic alphabets is the Negidal – its alphabet was created in 2009, and in the next year, a manual for the primary school grades was published.
A very interesting case is that of the Soyot people. Originally they spoke a Uralic language. Then they were assimilated by the Turkic population of Siberia, and later - by the Buryats. For the revitalization of the Soyot language, in 2001, a Cyrillic script was designed. Two years later, a Soyot-Buryat-Russian dictionary appeared. In 2005, the Soyot language was introduced in the primary school grades.
G. MIDDLE ASIA
The region is inhabited by a number of peoples, some of them quite numerous, like the Uzbek or the Kazakh. In 1927, the Arabic script was banned and the Latin alphabet was imposed for writing Kazakh. The Latin alphabet was in turn replaced by the Cyrillic alphabet in 1940.
Uyghur is another Turkic language, with about 10 million speakers mainly in the Xinjiang Uyghur Autonomous Region of China, and also in Afghanistan. The Uyghur Cyrillic alphabet was devised around 1937 in the Soviet Union, because they wanted an alternative to the Latin-derived alphabet they had devised some eleven years earlier, in 1926, as they feared a romanization of the Uyghur language would strengthen the relationship of the Uyghurs to Turkey. After the proclamation of the Communist People's Republic of China in 1949, Russian linguists began helping the Chinese with codifying the various minority languages of China and promoting Cyrillic-derived alphabets, and thus the Uyghurs of China also came to use the Uyghur Siril Yëziqi. As the tensions between the Soviet Union and China grew stronger, in 1959, the Chinese devised Uyghur Pinyin Yëziqi for Uyghurs, and eventually restored the Arabic script to write Uyghur to the present day. The Cyrillic script continued to be used in the Soviet Union, however, and is currently used in Kazakhstan.
Dungan is a variety of Chinese spoken in Kyrgyzstan, Kazakhstan and Uzbekistan, and written in Cyrillic letters. There are approximately 50 000 speakers. A Cyrillic alphabet for the Daur people in China was invented and used for two years: from 1956 to 1958, when it was abandoned, like the Uyghur one.
In Pamir, there are a number of small peoples of Indo-Iranian origin, too. Some of them still don’t have writing systems despite the attemps to introduce Latin or Cyrillic alphabet among them (Yazgulyam, for instance), among others (Shughni), there is a limited use of Cyrillic letters, and for others, translation of the Gospel of Luke have been made both in Latin and Cyrillic alphabets – for Rusahni, Wakhi. More such translations could be expected, because the Institute for Bible Translation (http://www.ibt.org.ru) keeps on working in that field.
Apart from Russian Middle Asia and North-West China, the Cyrillic writing system has also been used in Mongolia by the Khalkha Mongols and the Oirats (close relatives to the Kalmyk people who live in European Russia, near the Volga River) since 1941,.
Of course, various letters characteristic only of the local alphabets, are used in all Caucasian and Asian Cyrillic alphabets .
H. BULGARIA
In Bulgaria, after the Liberation from Ottoman rule, in 1878, the first Bulgarian official orthography was imposed in 1899, called Ivanchov’s orthography (after T. Ivanchov). It was replaced for a short time (1921-1923) by the Omarchev’s orthography of the government of Bulgarian Agrarian National Union, and then enacted again, slightly changed, till the Comunist orthographic reform in 1945, which resembled Omarchev’s spelling. In 1945, the letters э and © were removed from the alphabet, and the letters ъ, ь at the end of the words were no longer used.
The Cyrillic script is used also by the Gagauz and in some dialects of the Romani (Gipsy) language (in Bulgaria, as well as in Serbia and Russia). In the past, even the Ladino (Judaeo-Spanish) speakers in Bulgarian used it.
Ivan Momchilov’s Grammar from 1847 (Source: http://www.libsu.uni-sofia.bg/slavica/rarafontes.html).
Yashar Malikov’s Romani-Bulgarian dictionary. The back cover with the phrase Be happy! in capital letters in Romani (Photo: Ivan Iliev).
I. YUGOSLAVIA AND THE POST-YUGOSLAVIAN STATES
In 1918, the Serbo-Croat-Slovene Kingdom was created, and in 1929, its name was changed to Yugoslavia. In 1954, linguists and scholars signed the Novi Sad Literary Agreement, which made the Latin and the Cyrillic scripts equally acceptable in the country. However, only the Serbs used both alphabets in fact, while the Croats and the Bosnians preferred the Latin one. Albanians in Yugoslavia who were educated in Serbian schools used Cyrillic letters to communicate in Albanian during the 20th century. However, this was restricted to vulgar usage only. Yugoslavia finally fell apart in 2003, and several Slavic states replaced it: Serbia, Montenegro, Croatia, Bosnia and Herzegovina, Slovenia, Macedonia. Nowadays, the Cyrillic alphabet is used in the following of these countries: Macedonia, Serbia (alongside with the Latin alphabet), Bosnia and Herzegovina (informally), Montenegro (alongside with the Latin alphabet).
The standard Macedonian orthography appeared in 1945 on the pages of New Macedonia newspaper. The modern Macedonian alphabet was created by Krum Toshev, Krume Kepeski, and Blazhe Koneski. It has 31 letters (unlike the Bulgarian, which has 30), and mostly resembles the Serbian alphabet (typical for the Macedonian alphabet are the letters Ѕ, Ќ, and Ѓ).
The first Montenegrin Cyrillic alphabet appeared in 2009, designed by Milenko Perovich, Lyudmila Vasileva, and Yosip Silich. With the two new letters, ć and з, added to it in 2011, it contains totally 32 letters.
6. THE WITHDRAWAL FROM THE CYRILLIC ALPHABET AT THE END OF THE 20th CENTURY
Many rulers have tried to forbid the Cyrillic alphabet, in different times and in different states. The Austro-Hungarian goverrnment did not allow the Serbs to write Cyrillic during World War I. Ante Pavelich did the same in Croatia, in 1941. In 1991, the Soviet Union fell apart, and many people from the Caucasus and Middle Asia replaced the Cyrillic letters with Latin or some other alphabets: the Azeri (1991), the Chechen (1992), the Uzbek (1992), the Turkmens (1996). The Assirian Cyrillic alphabet, introduced in the 1920s, was replaced with the Latin one only ten years later (one of the few such examples). Since Belorussia gained independence in 1991, efforts have been made to revive writing in the Latin alphabet. One major problem is that nobody can agree on a spelling system. Recently as part of a modernization program, the government of Kazakhstan has stated plans to replace the Cyrillic alphabet with the Latin script. Currently the costs and consequences of such a move are being investigated. Today, although Mongolian is still written using the Cyrillic alphabet, an official reintroduction of the old script was planned for 1994, but has not yet taken place as older generations encountered practical difficulties. However, the traditional alphabet is being slowly reintroduced through schools. Several years ago, even in Bulgaria the idea (given by the Austrian Otto Kronsteiner) of replacing the traditional Cyrillic alphabet was suggested.
There are several small peoples in Russia, who could acquire neither the Latin, nor the Cyrillic script, although for some of them, there are grammar descriptions in Cyrillic: Yazgulyam, Bats, Budukh, Khwarshi, Enets (by the way, in some sources, like Omniglot, some of them are also considered to be languages, using the Cyrillic alphabet).
Most of the Western scientists use the Latin alphabet for transcribing Cyrillic sources in the bibliography of their works, and this is not professional. Imagine what would happen, if a scientist from Bulgaria or Russia cited in the same way the titles he or she has used. Then, instead of Jacobson, S. A Practical Grammar of Yupik…, for instance, there would be Джейкъбсън, С. Ъ пректикъл гремъ ъф юпик ... Isn’t it funny?
7. TRADITIONS AND NEW INVENTIONS
It is difficult to say if some day the Cyrillic alphabet will be totally out of use. Nowadays, alongside with the use of the civil script in everyday life, and the use of the Medieval Cyrillic script in the Orthodox typography, we can see how the latter even penetrates the internet. A special mixture of civil-script letters and medieval letters can be seen in Wikipedia (http://cu.wikipedia.org). If you visit Wikipedia’s main page, you will see the inscription ДОБРэ ПРИТИ ВЪ ВИКИПЄД·« ’Welcome to Wikipedia’. The Cyrillic letters are also used for writing the so-called Рadonkaffsky jargon (падонкаффский or олбанский йезыг or йазык падонкафф) – a cant language developed by padonki of Runet. It started as an Internet slang language. The language is based on phonetic spelling of the Russian language and sometimes transliteration of Ukrainian language, and often uses profanity. It combines complex orthography with creative use of idioms and literary expression. It is often used to express disagreement, amusement, or to create political satire. A similar jargon existed among young people in Russia even in the 19th century. In one of his novels, Y. Tynyanov narrates about the young idle prince Obolenskiy, who wrote in such a manner: Дарагой сасед завут меня княсь Сергей Абаленской я штап-ротмистр гусарскаво полка сижу черт один знает за што бутто за картеж и рулетку а главнейшее што побил командира а начальнику дивизии барону будбергу написал афицияльное письмо што он холуй царской, сидел в Свияборги уже год целой, сколько продержат в этой яме бох знает.
Another experimental innovation is the creation of artificial Slavic and non-Slavic languages, in the way Esperanto was created (the Esperanto alphabet officially has only Latin version but, in Soviet times, it was even printed in Cyrillic letters, because it was difficult to find type-writers with Latin letters). Slovianski (Словянски or Словјански) is a Slavic interlanguage, created in 2006 by a group of language creators from different countries: Ondrej Rečnik, Gabriel Svoboda, Jan van Steenbergen, Igor Polyakov. Its purpose is to facilitate communication between representatives of different Slavic nations, as well as to allow people who don't know any Slavic language to communicate with Slavs. For the latter, it can fulfill an educational role as well. Slovianski can be classified as a semi-artificial language with several hundred speakers. Sample text (the Lord’s prayer): Отче наш, кторы jеси в небах, да свечено jе твоjе имено, да приjде твоjе кролевство, да буде твоjа вольа, как в небах так и на земjе. Хлеб наш всекоденны даj нам тутдень, и извиниj нам наше грехи, так как мы извиньамо наших грешников. И не ведиj нас в покушенjе, але спасиj нас од злого.
Another artificial Slavic language is Slovio (from the Slavic slovo ‘word’). It is a constructed language launched in 1999 by Mark Hučko. Hučko claims that the language should be relatively easy for non-Slavs to learn as well, as an alternative to tongues such as Esperanto which are based more on Latin root words. The vocabulary is based on the shared lexical foundation of the Slavic languages. As of October 2007, Slovio had over 44,000 words. Sample text in Slovio (Cyrillic alphabet): Гворийт муж: Мои удрагйу золотйу жен, мои прекрасйу млодица, целойу ноч и целойу ден мислим толк о те. Целойу ноч имам сонис о те, и целойу ден имам видениес о твои прекрасйу очис, рукис и тело. Or: Словио ес новю межународю язика ктор разумиют чтирсто милион лудис на целою земла. Учийте Словио тпер!
Lingua Franca Nova (abbreviated LFN) is an auxiliary constructed language created by C. George Boeree of Shippensburg University, Pennsylvania. Its vocabulary is based on the Romance languages French, Italian, Portuguese, Spanish, and Catalan. The grammar is highly reduced and similar to the Romance creoles. The language has phonemic spelling, using 22 letters of either the Latin or Cyrillic scripts. Sample (the Lord’s prayer): Нос Падре, ке ес ен сиело, санте ес ту номе, ту рениа ва вени, ту воле ва ес фада, ен теро комо ен сиело…
II. NOTES ON CYRILLIC HAND-WRITTEN STYLES AND TYPOGRAPHY
1. HAND-WRITTEN CYRILLIC STYLES
There were four types of medieval hand-written Cyrillic script: uncial, semi-uncial, quickscript, and vjaz (embroidery style), between which were transitional stages. These scripts could use either only capital letters (majuscules), or only small letters (minuscules), besides the calligraphic letters (like the letter K in the picture below). The oldest script was the uncial - a majuscule script, written entirely in capital letters, commonly used from the 3rd to 8th centuries AD by Latin and Greek scribes. The Slavic uncial derived from the Greek majuscule of the 9th century AD. In the 12th century popular uncial scripts appeared, and the majuscule Italic script was invented for writing notes, signatures, etc.
The Slavic uncial script developed into another majuscule script - the semi-uncial, which later became the basis for the typographical pre-civil Cyrillic script. For example, the Dubrovnik Charter of the Bulgarian Tsar Ivan-Assen II (from 1230) was written in semi-uncial. In the 15th century, it totally replaced the uncial.
Middle Bulgarian liturgical uncial script (with a calligraphic letter K, and embroidery style in the title) from the Middle Bulgarian Tsar Ivan-Alexander’s 4 Gospels (Source: Джурова 1981).
А Middle Bulgarian semi-uncial script (Source: Йончев 1964).
The quickscript (sometimes called italic or cursive, and more precisely, semi-cursive) developed from the semi-uncial in the 14th century, and first, it was used as administrative writing. Calligraphy developed out of it and later (19th century), the modern hand-written script, which is taught at schools, when no intervals were left between the letters. This hand-written style is the most diverse, and the least researched of the scripts. For example, in the 19th century, in Bulgaria, there were three types of quickscript: a Church Slavonic type, a Greek type, and a Russian semi-cursive type.
The vjaz or embroidery style is a kind of writing, in which the letters stay close to each other, and get connected into a continuous ornament. These models were known among the Greeks and the South Slavs but they were mostly practiced in Russia, after the 14-15th centuries, even in Ivan Fyodorov’s printed books.
Croatian Cyrillic quickscript (Source: http: // www.croatianhistory.net/etf/et04.html).
Russian Cyrillic quickscript (Source: Карский 1928).
Ukrainian Cyrillic quickscript: Bohdan Khmelnytsky’s signature (Source: Wikipedia).
, , , , , , , , , …
Hand-written forms of the Modern Russian Cyrillic letters (Source: Wikipedia).
2. TYPOGRAPHIC AND COMPUTER CYRILLIC STYLES
Although Gutenberg (1394 -1468) had as model only hand-written scripts, his first typographic scripts looked different from the old hand-written letters. During the Renaissance period (the second half of the 15th century), attempts began to design scripts with pair of compasses and a ruler. Since then, a lot of scripts have been created, not only typographic, but also cartographic, placard, decorative, etc. One of the first typographs, who made new printing scripts, in the 15th century, were Aldus Manutius, Claude Garamond, etc. The first typographic Russian scripts resembled the old semi-uncial script, for example, Ivan Fyodorov’s printed books (the script of Statute of Lithuania was a rare example of a Slavic typographic quickscript; besides, in Russia, some scientific books were printed in typographic uncial). The Russian semi-uncial was used in religious and secular literature till 1708, when the civil script was invented for the laic books, and the typographic semi-uncial was identified for the religious works only. In designing the civil script, Peter I was helped by Ilya Kopievsky (or Kopievich). Between 1699-1700, he worked with the Dutch Yan Tessing in publishing Slavic books, and in 1700, he opened his own typography in Amsterdam.
The Cyrillic typography passed directly from the medieval stage to the late Baroque, without a Renaissance phase as in Western Europe: New Roman cursive, also called minuscule cursive or later Roman cursive, developed from old Roman cursive, and later evolved into the medieval script known as Carolingian minuscule, which was used in 9th century France and Germany in the imperial chancery, and whose revival in the Renaissance (by Petrarca and other writers) forms the basis of the modern Latin lowercase letters, which Peter I the Great took as a model for the civil script. However, the first models for Peter’s civil script appeared even before him. With the purpose of stylization, original scripts were created and used in Ukrainian engravings from the 17th century and, later, in Petro Mohyla’s books. Peter I the Great only legalized this practice. The westernized letter forms which he mandated to be used in the early 18th century, were largely adopted in the other languages that use the script. Thus, unlike the majority of Modern Greek fonts modern Cyrillic fonts are much the same as modern Latin fonts of the same font family.
Carolingian minuscule (Source: Йончев 1964).
A title written in Russian calligraphic Vjaz’ script (Source: Wikipedia).
The modern typographic cursive originated from the hand-written minuscule cursive. Since it was very typical for Italy during the Renaissance, in France and England it was called italic (script), unlike the upright roman (script). The cursive variant of the typographic civil script has been used since 1734 (for the first time – in the newspaper Sankt Petersburg News). The form of the typographic cursive first was similar to the hand-written cursive but with time it changed under the influence of the roman script.
Tessing’s Cyrillic font (Source: Wikipedia).
Gothic Style Cyrillic script (Source: Wikipedia).
Russian and Serbian/Macedonian Roman and Italic letters (Source: http:// jankojs.tripod.com).
Statute of Lithuania of 1588 in Ruthenian (Source: Wikipedia).
Similarly to Latin fonts, italic and cursive types of many Cyrillic letters are very different from their upright roman types: а/а, б/б,в/в, г/г, д/д, е/е, etc. In certain cases, the correspondence between uppercase and lowercase glyphs does not coincide in Latin and Cyrillic fonts: for example, italic Cyrillic т is the lowercase counterpart of Т not of М. In Serbian, as well as in Macedonian, some italic and cursive letters are different from those used in other languages.
Nowadays, the design of new Cyrillic scripts is going on. In Russia, several famous font designers, such as Vladimir Efimov, Artemiy Lebedev, Olga Florenskaya, Sergey Serov, and Yuri Gordon work in this field. Throughout the world, there are competitions on designing scripts. One of them, the Granshan competition, was initiated by the Ministry of Culture of Armenia in 2008 and received woldwide popularity. The Ministry of Culture of the Republic of Armenia and the Typographic Society Munich (Typographische Gesellschaft Munchen) intended to enhance the importance of other script systems, beginning with Armenian, Cyrillic and Greek. Later, Indic and Arabic text typeface categories were included in the competition. In addition, an international triennial of stage poster was held in Sofia, Bulgaria, in 2011.
Various Cyrillic scripts can be found on the internet – for example, at http://www.fontyukle.net/en/1,cyrillic or at http://fonts.ru/help/language/ (in the latter, they are arranged in alphabetical order according to the language). Typographic Church Slavonic fonts are available at http://irmologion.ru/fonts.html. At http://graphics-video.ru/photoshop/fonts?page=1, funny Cyrillic scripts, more Church Slavonic, and Eastern-style Cyrillic scripts can be seen.
A book on Bulgarian Cyrillic epigraphy (Photo: Ivan Iliev).
Posters from the International triennial of stage poster The Letters of Bulgaria with the Cyrillic letters У and Ф (Photo: Ivan Iliev).
Eastern-Style Russian Cyrillic Scripts (Source: http://graphics-video.ru).
Bulgarian Cyrillic scripts (Source: Йончев 1964).
The development of some Cyrillic computer typefaces from Latin ones has also contributed to the visual Latinization of Cyrillic type. Modern Cyrillic fonts, as well as Latin ones, have roman (upright type) and italic or cursive type.
Funny Russian scripts for children (Source: http://graphics-video.ru).
A special system, called Unicode is used for facilitating computer writing in Cyrillic (and other scripts, as well). It is a computing industry standard for the consistent encoding, representation and handling of text, expressed in most of the world's writing systems. Developed in conjunction with the Universal Character Set standard, and published in book form as The Unicode Standard, the latest version of Unicode consists of a repertoire of more than 110 000 characters covering 100 scripts.
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A computer text, written in one of the modern Old Bulgarian fonts (Source: Тончева 2006).
APPENDIX 1 - INDEX OF SLAVIC LANGUAGES WHICH USE OR HAVE USED CYRILLIC ALPHABETS (SEE THE MAPS IN APPENDIX 3 ON P. 148)
A. MODERN SPOKEN SLAVIC LANGUAGES:
1 – Bulgarian with 1b – Macedonian (български език/македонски јазик) – two
literary variants of one language with differences in the graphic systems – the latter must not be confused with Ancient Macedonian;
2 – Russian (русский язык);
3 – Serbo-Croatian (3a – српски/3b – црногорски/3c – босански or бошњачки/3d –хрватски језик);
4 – Ukrainian with 4b – Rusyn or Ruthenian (українська мова/русинська бесіда or русиньскый язык);
5 – Belorussian with 5b West Polesian (беларуская мова/заходышнополіська лытырацька волода or jiтвјежа);
6 – Polish (ªзык польски).
B. CLASSICAL AND ARTIFICIAL SLAVIC LANGUAGES
7 – Old (Church) Slavonic or Old Bulgarian (cловэньскъ Єзъ¶къ) and 7b – New Church Slavonic variants: Russian, Ukrainian, Serbian (црькъвьнословэ ньскъ Єзъ¶къ, славено-сербскiи);
8 – Illyirian (илирски jeзик);
9 – Slovianski (cловянски or cловјански);
10 – Slovio (словио).
APPENDIX 2 - INDEX OF NON-SLAVIC LANGUAGES WHICH USE OR HAVE USED CYRILLIC ALPHABETS
11 – Abaza (абаза бызшва);
12 – Abkhaz (aҧсуа бызшәа);
13 – Adyghe (адыгэбзэ or адыгaбзэ) with 13b – Kabardian (къэбэрдеибзэ);
14 – Aghul (aгъул чIал);
15 – Akhvakh (aшwалlи мицlи);
16 – Albanian (in Latin letters: gjuha shqipe);
17 – Aleut (унан,ам тунуу or унаyн,ам умсуу);
18 – Altai (алтай тили) with 18b - Kumandin (къуманды, or къубанды or къуўанды or къувандыг), and 18 c – Teleut (тадар тил);
19 – Archi (аршаттен чӀат);
20 – Assyrian Neo-Aramaic or Aisor (лишана д-атурайе or лишана хата);
21 – Avar (магIарул мацI);
22 – Azerbaijani or Azeri (азәрбајҹан дили);
23 – Balkar – with 23b – Karachay (къарачай-малкъар тил or таулу тил);
24 – Balochi (балучи or балочи);
25 – Bashkir (башҡорт теле);
26 – Budukh (будад мез);
27 – Buryat (буряад хэлэн);
28 – Chechen (нохчийн мотт);
29 – Chukchi (ԓыгъоравэтԓьэн йиԓыйиԓ);
30 –Chulym (шұлымша or июс тили);
31 – Chuvash (чӑваш чӗлхи);
32 – Dargwa (дарган мез);
33 – Daur (in Latin letters: Dáwòěr Zú);
34 – Dungan (хуэйзў йүян or чжунъюань хуа);
35 – Enets (oнай базаан);
36 – Even (эвэды торэн or оратты торэн) with 36b – Evenki or Evenk (эвэды̄ турэ̄н);
37 – Gagauz (гагауз дили or гагаузча);
38 – Godoberi (гъибдилӀи мицци);
39 – Hunzib (гьонкьос мыц);
40 – Ingush (гӀалгӀай мотт);
41 – Itelmen (итэнмэн);
42 – Kalmyk with 42b Oirat (хальмг келн/in Latin letters: Oyirad kelen);
43 – Karaim (къарай тили);
44 – Karakalpak (қарақалпақ тили);
45 – Karelian (карялан киели);
46 – Kazakh (қазақ тілі);
47 – Ket (остыганна ӄа');
48 – Khakas (хакас тілі);
49 – Khanty (in Latin letters: ханты ясян);
50 – Khinalug (каьтш мицӀ);
51 – Khwarshi (акьилхъо);
52 – Kilit (?);
53 – Komi-Zyrian (коми кыв) with 53b – Komi-Permyak (перем коми кыв);
54 – Koryak (нымылг'ын or чав"чывав");
55 – Kubachi (гӀугъбуган);
56 – Kumyk (къумукъ тил);
57 – Kurdish (кöрди or курманджи or сорани);
58 – Kyrgyz (кыргыз тили);
59 – Ladino or Judaeo-Spanish or Sephardic (ладино);
60 – Lak (лакку маз);
61 – Lezgi (лезги чӀал);
62 – Lingua Franca Nova (лингва франка нова);
63 – Lithuanian (ли́етувю калба);
64 – Mansi (маньси or моаньсь; in Latin letters: maan's'i latyng);
65 – Mari Western or Hill with 65b – Mari Eastern or Medow (кырык мары йӹлмӹ/олык марий йылме);
66 – Meskhetian Turkish (aҳыска тÿркчäси);
67 – Mongolian or Khalkha Mongolian (монгол хэл);
68 – Mordvin: Erzya with 68b – Moksha (эрзянь кель/мокшень кяль);
69 – Nanai (нанай);
70 – Negidal (неғида);
71 – Nenets (ненэця’ вада and нешаӈ вата);
72 – Nganasan (ня'');
73 – Nivkh (нивхгу диф or ньиғвӈгун);
74 – Nogai (ногай тили);
75 – Oroch (орочи);
76 – Orok (уйльта);
77 – Ossetic or Ossetian (ирон ӕвзаг or дигорон ӕвзаг);
78 – Romani (pомани чшиб);
79 – Romanian with 79b Moldovan or Moldavian (in Latin letters: limba română /лимба молдовеняскэ);
80 – Rushani (in Latin letters: Rihūn ziv);
81 – Rutul (мыхIабишды чIел or мыхӀабыж);
82 – Sami: Kildin Sami with 82b – Ter Sami (кӣллт са̄мь кӣлл/са̄мь кӣлл);
83 – Selkup (шӧльӄумыт әты or чумыль ӄумыт әты or сӱccӱ ӄумыт әты or шӧш ӄумыт әты or тӱй ӄумыт әты);
84 – Shor (шор тили);
85 – Shughni (хугни - ?, in Latin letters: xuãnūn ziv);
86 – Slovio;
87 – Soyot (сойыт тыл or тyъha тыл);
88 – Tabassaran (табасаран чIал);
89 – Tajik (забо́ни тоҷикӣ́ or форси́и тоҷикӣ́);
90 – Talysh (толышə зывон);
91 – Tat (зуун тати or зуун
парси);
92 – Tatar: Kazan Tatar with 92b – Kreshen Tatar (tatarça or татар теле); with 92c – Crimean Tatar (къырымтатар тили), with 92d – Krymchak (кърымчах тыльы) and 92e Urum (урум тыль); with 92f – Astrakhan Tatar; with 92g – Alabugat Tatar, 92h – Tobol Tatar (себертатар тел or себер тел), and 92i – Baraba Tatar (себертатар тел or себер тел);
93 – Tlingit (in Latin letters: Lingít);
94 – Tsakhur (цIаIхна миз);
95 – Tsez (цез мец);
96 –Turkmen (түркмен дили);
97 – Tuvan (тыва дыл);
98 – Tofalar or Tofa (тоъфа дыл);
99 – Ubykh (твaҳəбзa);
100 – Udi (удин муз);
101 – Udihe or Udekhe or Udege (орочи - ?);
102 – Udmurt (удмурт кыл);
103 – Ulch (?);
104 – Uyghur (уйғурчә or уйғур тили);
105 – Uzbek (Ўзбек тили);
106 – Veps (in Latin letters: vepsän kel');
107 – Votic (in Latin letters: vaďďaa ceeli);
108 – Wakhi (хик зик);
109 – Yaghnobi (яғнобӣ зивок);
110 – Yakut or Saka or Aka (саха тыла) with 110b – Dolgan (дулҕан);
111 – Siberian Yupik or Yuit (ун,азиг,мит and нывук,аг,мит) with 111b – Alaskan Yupik (in Latin letters: Yugtun), and 111c – Kodiak Yupik (in Latin letters: Alutiiq);
112 – Yukaghir: Northern and Southern (вадун аруу/одун ажуу).
Below: A teacher and activist from Bulgaria (Svetla Ilieva) introduces the Bulgarian alphabet to Korean pupils in 2007-2008, as member of UNESCO’s Cross-Cultural Awareness Programme. In the background – the Bulgarian national flag, the Bulgarian letters and their Korean counterparts: А/ㅏ, Б/ ㅂ, Н/ ㄴ, O/ ㅓ(Photo: Ivan Iliev).
APPENDIX 3 (MAPS)
MAP N: 1 – EAST EUROPE
MAP N: 2 – THE CAUCASUS
MAP N: 3 – EUROPEAN RUSSIA, MIDDLE ASIA, SIBERIA, MONGOLIA, CHINA
MAP N: 4 – CHUKOTKA AND ALASKA
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© 2010, IJORS - INTERNATIONAL JOURNAL OF RUSSIAN STUDIES
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---
abstract: 'We study the chiral expansion of the baryon octet and decuplet masses in the isospin limit. It is illustrated that a chiral expansion of the one-loop contributions is rapidly converging up to quark masses that generously encompasses the mass of the physical strange quark. We express the successive orders in terms of physical meson and baryon masses. In addition, owing to specific correlations amongst the chiral moments, we suggest a reordering of terms that make the convergence properties more manifest. Explicit expressions up to chiral order five are derived for all baryon masses at the one-loop level. The baryon masses obtained do not depend on the renormalization scale. Our scheme is tested against QCD lattice data, where the low-energy parameters are systematically correlated by large-$N_c$ sum rules. A reproduction of the baryon masses from PACS-CS, LHPC, HSC, NPLQCD, QCDSF-UKQCD and ETMC is achieved for ensembles with pion and kaon masses smaller than 600 MeV. Predictions for baryon masses on ensembles from CLS as well as all low-energy constants that enter the baryon masses at N$^3$LO are made.'
address:
- |
GSI Helmholtzzentrum für Schwerionenforschung GmbH,\
Planck Str. 1, 64291 Darmstadt, Germany
- 'Technische Universität Darmstadt, D-64289 Darmstadt, Germany'
author:
- 'M.F.M. Lutz'
- Yonggoo Heo
- 'and Xiao-Yu Guo'
bibliography:
- 'literature.bib'
title: 'On the convergence of the chiral expansion for the baryon ground-state masses'
---
Introduction
============
By now there is large set of QCD lattice data on the lowest baryon masses composed of up, down and strange quarks and with $J^P = \frac{1}{2}^+$ and $\frac{3}{2}^+$ [@MILC2004; @LHPC2008; @PACS-CS2008; @HSC2008; @BMW2008; @Alexandrou:2009qu; @Durr:2011mp; @WalkerLoud:2011ab; @NPLQCD:2011; @Andersen:2017una]. The recent and unexpected success of a quantitative description of this data set based on the chiral three-flavour Lagrangian [@Semke:2012gs; @Lutz:2013kq; @Lutz:2014oxa; @Ren:2013dzt; @Ren:2013oaa] makes it paramount to unravel further the chiral convergence domain of this sector of QCD. It is an important question how small the quark masses have to be chosen as to render a chiral expansion framework meaningful in the flavour $SU(3)$ case. Based on two flavour studies of the nucleon mass the power-counting domain (PCD) was estimated in various studies to be as low at $m_\pi < $ 200 MeV$-$300 MeV [@Young:2002ib; @Leinweber:2003dg; @Beane:2004ks; @Leinweber:2005xz; @McGovern:2006fm; @Djukanovic:2006xc; @Schindler:2007dr; @Hall:2010ai]. Due to the important role played by the baryon decuplet fields it is not quite straight forward to conduct such studies in the three flavour case. In the two-flavour case there are different power counting schemes as to incorporate the spin three half field in a consistent manner [@Banerjee:1994bk; @Banerjee:1995wz; @Fettes:2001cr; @Pascalutsa:2002pi; @Long:2009wq]. It is an open challenge how to adapt such schemes to the flavour $SU(3)$ case.
A strict chiral expansion for the baryon masses following the rules of heavy-baryon $\chi$-PT appears futile. Applications to current QCD lattice data do not seem promising [@MILC2004; @LHPC2008; @PACS-CS2008; @HSC2008; @BMW2008; @Alexandrou:2009qu; @Durr:2011mp; @WalkerLoud:2011ab]. In oder to make progress we have to leave the safe haven of conventional $\chi$PT. State of the art chiral extrapolations of the lattice data set are based on the relativistic chiral Lagrangian with baryon octet and decuplet fields [@Semke:2011ez; @Semke:2012gs; @Lutz:2012mq; @Ren:2012aj; @Ren:2013oaa; @Geng:2013xn; @Lutz:2014oxa]. A quantitative reproduction of the lattice data requires a summation scheme and the consideration of counter terms that turn relevant at next-to-next-to-next-to-leading order (N$^3$LO). Any summation scheme, be it a phenomenological form factor, relativistic kinematics or the use of physical masses in the loop functions, is set up in a manner that the results of a strict chiral expansion are recovered to some given order upon the neglect of formally higher order terms. One may rightfully argue that possibly some model dependence is encountered once the quark masses reach their physical values. While in [@Semke:2011ez; @Semke:2012gs; @Lutz:2012mq] the $\chi-$MS scheme of [@Semke2005; @Semke:2006hd] was used, the EOMS of [@Gegelia:1999gf] was used in [@Ren:2013dzt; @Ren:2013oaa]. Both schemes protect the analytic structure of the one-loop contributions in the baryon self energies as requested by micro causality. In contrast, the IR scheme of [@Becher:1999he] was applied in [@Bruns:2012eh].
The target of our present study is to scrutinize and further improve the most comprehensive analysis of the QCD lattice data set in the isospin limit [@Lutz:2014oxa]. A quantitative description of more than 220 lattice data points for the baryon octet and decuplet states of five different lattice groups, PACS-CS, LHPC, HSC, NPLQCD and QCDSF-UKQCD [@PACS-CS2008; @LHPC2008; @HSC2008; @NPLQCD:2011; @Bietenholz:2011qq], was achieved in terms of a 12 parameter fit. The number of parameters was reduced significantly by large-$N_c$ sum rules [@Lutz:2010se; @Lutz:2011fe; @Lutz:2014jja]. More recent lattice simulation data from the ETM collaboration [@Alexandrou:2014sha] for the baryon decuplet and octet masses were predicted by this approach. The analysis was based on the relativistic chiral Lagrangian and the use of physical meson and baryon masses in the one-loop expressions that include effects up to N$^3$LO. A conventional counting, where $M_\Delta - M_N \sim m_K $ was taken as the guide for the construction of the chiral extrapolation formulae. While such a counting is justified for larger meson masses, in the limit of very small meson masses like $m_\pi \ll M_\Delta - M_N$ some chiral constraints are realized only in an approximate manner. It is the purpose of the present work to establish an approximation strategy that is efficient uniformly well from the small up and down quark masses up to a large strange quark mass.
The work is organized as follows. In the second chapter we review all large-$N_c$ sum rules that are relevant for the chiral extrapolation of the baryon masses. So far unknown subleading terms in the $1/N_c$ expansion will be derived for the first time. It follows Chapter 3 in which the previous approach [@Lutz:2014oxa] is further developed to restore chiral constraints close to the chiral limit at $m_\pi \ll M_\Delta - M_N$. A novel chiral expansion scheme, in which the various moments are expressed in terms of the physical meson and baryon masses is presented in Chapter 4. The convergence properties of such an expansion are examined.
In Chapter 5 we report on a global fit to the baryon masses from PACS-CS, LHPC, HSC, NPLQCD, QCDSF and ETMC [@PACS-CS2008; @LHPC2008; @HSC2008; @NPLQCD:2011; @Bietenholz:2011qq; @Alexandrou:2013joa]. Based on parameter sets obtained predictions for the baryon sigma terms at physical quark masses and baryon masses for the ensembles of the CLS collaboration are made [@Bruno:2014jqa; @Bruno:2016plf]. Since we do not consider yet lattice discretization effects a systematic error analysis of our results is outside the scope of this work.
Primer on large-$N_c$ sum rules
===============================
Before we turn to the chiral extrapolation of the baryon masses we recall and further develop the large-$N_c$ sum rules previously applied in the studies [@Semke:2011ez; @Semke:2012gs; @Lutz:2014oxa]. They are of crucial importance in a chiral extrapolation study of the baryon masses since they provide a significant parameter reduction at N$^3$LO. The sum rules are a consequence of a large-$N_c$ analysis of baryon matrix elements of axial-vector, vector and pseudo-scalar, scalar quark currents of QCD, which are $$\begin{aligned}
&& A_\mu^{(a)}(x)= \bar q(x) \,\gamma_\mu \,\gamma_5 \,\frac{\lambda^{(a)}}{2} \,q(x)\,, \qquad V_\mu^{(a)}(x)= \bar q(x) \,\gamma_\mu \,\frac{\lambda^{(a)}}{2} \,q(x)\,,
\nonumber\\
&& P^{(a)}(x)= \bar q(x) \, \gamma_5\,\frac{\lambda^{(a)}}{2} \,q(x)\,,\qquad \quad \, S^{(a)}(x)= \bar q(x) \, \frac{\lambda^{(a)}}{2} \,q(x)\,.\end{aligned}$$ On the one hand one may compute such matrix elements from a given truncated chiral Lagrangian. On the other hand they may be analyzed systematically in a $1/N_c$ expansion. A matching of the two results leads to a correlation of the low-energy parameters of the chiral Lagrangian formulated with the baryon octet and decuplet fields. We use here the conventions for the various low-energy parameters as introduced previously in [@Semke:2011ez].
For the reader’s convenience all terms relevant for our study are recalled explicitly in this chapter. The applied conventions are illustrated at the hand of the kinetic terms $$\begin{aligned}
&& \mathcal{L}^{(1)} =
\mathrm{tr}\, \Big\{ \bar B\, (i\, \Dslash\, - M_{[8]})\, B \Big\} +
\mathrm{tr}\, \Big\{ \bar B_\mu \cdot \big((i\,\Dslash\, - M_{[10]})\,g^{\mu\nu}
\nonumber\\
&& \qquad \qquad \qquad -\,i\,(\gamma^\mu D^\nu + \gamma^\nu D^\mu) + \gamma^\mu(i\,\Dslash + M_{[10]})\gamma^\nu \big)\, B_\nu \Big\}\,,
\nonumber\\
&&\Gamma_\mu ={\textstyle{1\over 2}}\,u^\dagger \,\big[\partial_\mu -i\,(v_\mu + a_\mu) \big] \,u
+{\textstyle{1\over 2}}\, u \,
\big[\partial_\mu -i\,(v_\mu - a_\mu)\big] \,u^\dagger\,,
\nonumber\\
&& D_\mu \, B \;\,= \partial_\mu B + \Gamma_{\mu}\, B -
B\,\Gamma_{\mu} \,, \qquad \qquad \qquad
u = e^{i\,\frac{\Phi}{2\,f}} \,,
\label{def-L1}\end{aligned}$$ for the baryon spin 1/2 and 3/2 fields $B$ and $B_\mu$. Here we encounter the covariant derivative $D_\mu$ which involves the vector and axial vector source fields $v_\mu$ and $a_\mu$. The SU(3) matrix field of the Goldstone bosons is $\Phi$. Throughout this chapter we apply the convenient flavour ’$\cdot $’ product notation for terms involving the symmetric baryon fields $B_\mu$ and $\bar B_\mu$ (see [@Lutz:2001yb; @Semke:2011ez]). For instance the product of the two flavour decuplet fields $\bar B_\mu \cdot B_\nu $ is constructed to transform as a flavour octet.
Matrix elements of an axial-vector current
-------------------------------------------
0.3cm
We recall the well known operator analysis for the axial-vector current, which correlate the axial-vector coupling constants, $F,D,C,H$ of the baryon octet and decuplet states [@Dashen1994; @Dashen1995]. The matrix elements at zero momentum transfer, $$\begin{aligned}
&&{\langle \bar p\,,\,\bar\chi\,|}\,A^{(a)}_i(0)\,
{|\,p\,,\chi \rangle} = {(\bar\chi\,|}\, \hat g_1\,G^{a}_i + \hat g_2\,\big\{ J_i\,,\,T^a\big\}\,
{|\chi )} + {\mathcal O}\left(\frac{1}{N_c} \right)\,,
\label{1-axial-opt}\end{aligned}$$ are parameterized in terms of $\hat g_1$ and $\hat g_2$ and the spin, $J_i$, flavour, $T^a$ and spin-flavour, $G_i^a$ operators [@LutzSemke2010]. It suffices to compute matrix elements at $N_c=3$ only for which the effective spin-flavour states ${|\,p\,,\chi \rangle}$ are introduced. As emphasized in [@Lutz:2001yb; @Semke:2011ez; @Semke:2012gs] the hierarchy of the large-$N_c$ sum rules can efficiently be derived once a complete compilation of the action of the three operators $J_i$, $T^a$ and $G_i^a$ on the spin-flavour states ${|\,p\,,\chi \rangle}$ is available. Such a compilation is provided in [@Lutz:2001yb; @Semke:2011ez] for the first time. The $1/N_c$ expansion is implied by a proper selection of spin-flavour operators in the truncation (\[1-axial-opt\]) (see [@tHooft74; @Witten1979; @Luty1994; @Dai1995] for more technical details). We recall the relevant terms in the chiral Lagrangian $$\begin{aligned}
&& \mathcal{L}^{(1)}= F\, \mathrm{tr} \Big\{ \bar{B}\, \gamma^\mu \gamma_5\, [i\,U_\mu,B]\, \Big\} + D\, \mathrm{tr}\Big\{ \bar{B}\, \gamma^\mu \gamma_5\, \{i\,U_\mu,\,B\}\, \Big\}
\nonumber \\
&& \qquad +\, C\left( \mathrm{tr} \Big\{ (\bar{B}_\mu \cdot i\, U^\mu)\, B\Big\} + \mathrm{h.c.} \right)
+ H\, \mathrm{tr} \Big\{ (\bar{B}^\mu\cdot \gamma_5\,\gamma_\nu B_\mu)\, i\,U^\nu \Big\}\,,
\nonumber\\
&& U_\mu = {\textstyle{1\over 2}}\,u^\dagger \, \big(
\partial_\mu \,e^{i\,\frac{\Phi}{f}} \big)\, u^\dagger
-{\textstyle{i\over 2}}\,u^\dagger \,(v_\mu+ a_\mu)\, u
+{\textstyle{i\over 2}}\,u \,(v_\mu-a_\mu)\, u^\dagger\;,
\label{def-FDCH}\end{aligned}$$ where the object $(\bar B_\mu \cdot U^\mu)$ transforms as a flavour octet by construction. For the particular case (\[1-axial-opt\]) the well known hierarchy of sum rules $$\begin{aligned}
&& F= \frac{2}{3}\, D \,,\qquad C=2\,D \,,\qquad H = 3\,D\,, \qquad {\rm for } \qquad \hat g_2 =0 \,,
\nonumber\\
&& C=2\,D\,,\qquad H= 9\,F-3\,D \,,\qquad\qquad \qquad \! {\rm for } \qquad \hat g_2 \neq 0 \,,
\label{res-FDCHs}\end{aligned}$$ is recovered. At leading order $( N_c)$ there are three sum rules and at subleading order $(N_c^0)$ there remain two sum rules only.
Matrix elements of a scalar current
------------------------------------
0.3cm
Less well studied are matrix elements of the scalar current $$\begin{aligned}
&&{\langle \bar p\,,\,\bar\chi\,|}\,S^{(a)}(0)\,
{|\,p\,,\chi \rangle} = {(\bar\chi\,|}\, \delta_{a0}\,\big(\hat b_1\,{\mathbbm 1} + \hat b_2\,J^2 \big)
\nonumber\\
&& \qquad \qquad +\, \hat b_3\,T^{a} + \hat b_4\,\big\{ J_i\,,\,G_i^a\big\}\,
{|\chi )} + {\mathcal O}\left(\frac{1}{N^2_c} \right)\,,
\label{1-scal-opt}\end{aligned}$$ where the spin-flavour operators are supplemented by their flavour singlet counter parts $$\begin{aligned}
T^0 = \sqrt{ \frac 1 6}\, {\mathbbm 1} \,, \qquad G_i^0 =\sqrt{ \frac 1 6}\,J_i \,.\end{aligned}$$ We recall the relevant terms in the chiral Lagrangian $$\begin{aligned}
&& \mathcal{L}^{(2)}_\chi = 2\, b_0 \,\mathrm{tr} \left(\bar B \,B\right) \mathrm{tr}\left(\chi_+\right) + 2 \,b_D\,\mathrm{tr}\left(\bar{B}\,\{\chi_+,\,B\}\right) + 2\, b_F\,\mathrm{tr}\left(\bar{B}\,[\chi_+,B]\right) \nonumber \\
&& \qquad -\, 2\, d_0\, \mathrm{tr}\left(\bar B_\mu \cdot B^\mu\right) \mathrm{tr}(\chi_+) - 2\, d_D\, \mathrm{tr} \left( \left(\bar{B}_\mu \cdot B^\mu\right) \chi_+\right)\,,
\nonumber\\
&& \chi_+ = {\textstyle{1\over 2}}\, \big( u \,\chi_0 \,u + u^\dagger \,\chi_0 \,u^\dagger \big) = 2\,B_0\, s + \cdots \,,
\label{def-b-d}\end{aligned}$$ where we encounter the scalar source field $s$. For the particular case (\[1-scal-opt\]) the hierarchy of sum rules $$\begin{aligned}
&& b_D = 0\,,\qquad d_0 - b_0 = - \frac13\,d_D\,,\qquad d_D = 3 \,b_F\, \qquad {\rm for} \qquad \hat b_{2,4} = 0 \,,
\nonumber\\
&& b_F + b_D = \frac13\,d_D\,, \qquad d_0+ \frac13\,d_D- b_0 = 2\,b_D\,, \; \qquad {\rm for} \qquad \hat b_{2} = 0 \,,
\nonumber\\
&& b_F + b_D = \frac13\,d_D\,, \qquad \qquad \qquad \qquad \qquad \qquad \qquad \;{\rm for} \qquad \hat b_{2,4} \neq 0 \,,
\label{res-bds}\end{aligned}$$ is predicted. The relations (\[res-bds\]) are a straight forward consequence of the technical results of [@Dashen1994; @Dashen1995; @LutzSemke2010]. At leading order $( N_c)$ there are three sum rules, at subleading order $(N_c^0)$ there are two sum rules and at the accuracy level $(1/N_c)$ there remains one sum rule only. The leading order symmetry breaking parameters of the chiral Lagrangian $b_0,b_F, b_D$ and $d_0, d_D$ as used in [@Semke:2011ez; @Semke:2012gs; @Lutz:2014oxa] are correlated.
Such relations (\[res-bds\]) were obtained before in [@Jenkins1995], however, with a method slightly distinct to our approach. In [@Jenkins1995] the contribution of the counter terms to the baryon masses was analyzed and expanded in powers of the flavour breaking parameter $$\begin{aligned}
\varepsilon \sim m_s- \frac{1}{2}\,(m_u +m_d)\,,\end{aligned}$$ with the current quark masses $m_{u,d,s}$ of QCD. Accordingly the large-$N_c$ operator expansion was sorted according to powers of the $T_8$ and $G_8^i$ operators. At subleading order in $\varepsilon$, the following operators were considered $$\begin{aligned}
\label{lbl:Nc_baryonmass_epsilon2}
&& M_B = {(\bar \chi|}\, c_1^{(0,1)}\mathbbm 1 + c_2^{(0,1)} J_i\, J_i + \varepsilon\, c_1^{(0,8)} T^8
\nonumber\\
&& \qquad \qquad +\, \varepsilon\,c_2^{(0,8)} \{J_i, G^{8}_i\} + \varepsilon^2\, c_2^{(0,27)} \{T^8, T^8\}\, {|\chi)}\,,
\quad
\label{old-ces}\end{aligned}$$ where for the matching of the symmetry breaking parameters $b_0,b_F, b_D$ and $d_0, d_D$ the first four operators are relevant only. Keeping the first four operators in (\[old-ces\]) the last sum rule in (\[res-bds\]) is obtained.
Product of a scalar and a vector current
----------------------------------------
0.3cm
A further set of symmetry breaking low-energy constants of the chiral Lagrangian can be large-$N_c$ correlated upon a study of the current-current correlation with one scalar and one vector current $$\begin{aligned}
&& O^{ab}_\mu (q) = i\,\int d^4 x \,e^{-i\,q\cdot x} \,{\mathcal T}\,S^{(a)} (x)\,V^{(b)}_\mu(0) \,,
\label{def:scalar-scalar}\end{aligned}$$ in the baryon states. Terms in the chiral Lagrangian that involve a covariant derivative and a scalar source term will contribute to this correlation function. In [@Semke:2012gs] such terms were constructed systematically in terms of the five parameters $\zeta_0,\zeta_D, \zeta_F$ and $\xi_0, \xi_D$, where the flavour structure resembles the one of the $Q^2$ parameters $b_0,b_D, b_F$ and $d_0, d_D$ studied in the previous section. The wave-function renormalization terms of the chiral Lagrangian are recalled with $$\begin{aligned}
&& \mathcal{L}^{(3)}_\chi = \zeta_0\, \mathrm{tr} \big(\bar{B}\, (i\,\Dslash -M_{[8]})\, B\big)\, \mathrm{tr}(\chi_+) + \zeta_D\, \mathrm{tr} \big(\bar{B}\, (i\,\Dslash -M_{[8]})\, [B, \chi_+]\big) \nonumber\\
&& \qquad + \,\zeta_F\, \mathrm{tr} \big(\bar{B}\, (i\,\Dslash -M_{[8]})\, \{B, \chi_+\} \big)
- \xi^{}_0\, \mathrm{tr} \big(\bar B_\mu\,\cdot (i\,\Dslash -M_{[10]})\, B^\mu \big)\, \mathrm{tr}(\chi_+)
\nonumber \\
&& \qquad -\, \xi^{}_D\, \mathrm{tr} \big( \big(\bar B_\mu\,\cdot (i\,\Dslash -M_{[10]})\,B^\mu \big)\, \chi_+ \big) \,.
\label{def-zeta-xi}\end{aligned}$$ We introduce the leading orders operator ansatz for the correlator as $$\begin{aligned}
&&{\langle \bar p, \, \bar \chi |}\, O^{ab}_i\, {|p,\, \chi\rangle} = (\bar p+p)_i\,{(\bar \chi|}\,
+ \delta_{a0}\,\hat \zeta_1\, T^{b}
\nonumber\\
&& \qquad \qquad+\, \hat \zeta_2\,\{T^{a} ,\,T^{b}\} + \hat \zeta_3\,\{J_i,\,\{T^b,\, G^a_i\}\} \,{|\chi)} + \cdots \,,
\label{def-SV-expansion}\end{aligned}$$ which leads to the following two sum rules $$\begin{aligned}
&& 3\,\zeta_F + 3\,\zeta_D= \xi_D \,,\qquad \qquad
\xi_0+ \frac{1}{3}\,\xi_D=\zeta_0+ 2\,\zeta_D\,.
\label{def-combinations}\end{aligned}$$ If the subleading operator with $\hat \zeta_3$ in (\[def-SV-expansion\]) would be dropped the additional relation $\zeta_D=0$ arises. Such results are in full analogy to the relations obtained for the symmetry breaking $Q^2$ parameters in (\[res-bds\]).
Product of two scalar currents
------------------------------
0.3cm
We turn to matrix elements of the product of two scalar currents. They probe the symmetry breaking counter terms $c_i$ and $e_i$ of the chiral Lagrangian that are proportional to the square of the current quark masses. We recall their particular form $$\begin{aligned}
\mathcal{L}^{(4)}_\chi &=& c_0\, \mathrm{tr}\left(\bar B\, B\right) \mathrm{tr} \left(\chi_+^2\right) + c_1\, \mathrm{tr} \left(\bar B \,\chi_+\right) \mathrm{tr}\left(\chi_+ B\right) \nonumber \\
&+& c_2\, \mathrm{tr} \left( \bar B\, \{\chi_+^2,\, B\} \right) + c_3\,\mathrm{tr} \left( \bar B\, [\chi_+^2, \,B] \right)
\nonumber \\
&+& c_4\, \mathrm{tr} \left(\bar B\, \{\chi_+,\,B\} \right) \mathrm{tr} (\chi_+) + c_5\, \mathrm{tr}\left(\bar B\, [\chi_+,\,B]\right) \mathrm{tr} (\chi_+) \nonumber \\
&+& c_6\, \mathrm{tr} \left(\bar B \,B\right) \left(\mathrm{tr}(\chi_+)\right)^2
\nonumber \\
&-& e_0\, \mathrm{tr}\left(\bar B_\mu \cdot B^\mu \right) \mathrm{tr}\left(\chi_+^2\right) - e_1\, \mathrm{tr}\left( \left(\bar{B}_\mu \cdot \chi_+\right) \left(\chi_+ \cdot B^\mu\right) \right)
\nonumber \\
&-& e_2\, \mathrm{tr}\left( \left(\bar B_\mu \cdot B^\mu\right)\cdot \chi_+^2\right) - e_3\, \mathrm{tr}\left( \left(\bar B_\mu \cdot B^\mu\right)\cdot \chi_+\right) \mathrm{tr}(\chi_+) \nonumber \\
&-& e_4\, \mathrm{tr}\left(\bar B_\mu \cdot B^\mu\right) \left(\mathrm{tr}(\chi_+)\right)^2\,.
\label{def-c-e}\end{aligned}$$ Sum rules are derived by a study of the following matrix elements $$\begin{aligned}
&&i\, \int d^4 x \,e^{-i\,q\cdot x} \,{\langle \bar p\,,\,\bar\chi\,|}\, {\mathcal T}\,S^{(a)} (x)\,S^{(b)}(0) {|\,p\,,\chi \rangle}
= {(\bar\chi\,|}\,\hat c_1\,\delta_{a0}\,\delta_{b0}\,{\mathbbm 1}
\nonumber\\
&& \quad \!+ \,\hat c_2\,\delta_{ab}\,{\mathbbm 1}
+ \hat c_3\,\big( T^a\,\delta_{b0} + \delta_{a0}\,T^b \big)
+ \hat c_4\,d_{abc}\,T^c +\hat c_5\,\{ T^a,T^b\}
\nonumber\\
&& \quad \!+\, \hat c_6\,d_{abc}\,\{ J_i,G_i^c\}
+ \hat c_7\,\Big( \big\{ J_i\,,\,G_i^a \big\}\,\delta_{b0}
+ \delta_{a0}\,\big\{ J_i\,,\,G_i^b \big\}\Big)
\nonumber\\
&& \quad \!+\, \hat c_8 \,\Big( \big\{ J_i\,,\big\{T^a,\,\,G_i^b \big\}\big\} +\big\{ J_i\,,\big\{T^b,\,\,G_i^a \big\}\big\} \Big)
{|\chi )}
+ \cdots\,,
\label{SS-expanded}\end{aligned}$$ where we consider leading and subleading order operators only. Note that the two sums over $c$ in (\[SS-expanded\]) are from $c=0$ to $c=8$. At leading order with $\hat c_6 =\hat c_7 =\hat c_8 =0$ a matching with the tree-level expression derived from the chiral Lagrangian leads to the following 7 sum rules $$\begin{aligned}
&& 2\,c_2=-3\,c_1\,,\qquad 2\,c_0 = c_1 +2\,(c_3+e_0)\,, \qquad 3\,c_1 =e_1\,,\qquad c_4=c_1\,,
\nonumber\\
&& 3\,e_1+2\,e_2 =6\,c_3 \,, \qquad e_3=3\,(c_4+c_5)\,, \qquad c_6 = c_5+e_4 \,.
\label{res-ces}\end{aligned}$$ At subleading order there remain 4 sum rules only $$\begin{aligned}
&& c_0 = 2\,c_3 + e_0 - {\textstyle{ 1\over 6}}\,e_1 - {\textstyle{ 1\over 3}}\,e_2 - {\textstyle{ 1\over 2}}\,c_1\,, \qquad
c_1 = {\textstyle{ 1\over 3}}\,(e_1 + e_2) - c_2 - c_3\,,
\nonumber\\
&& e_3 = 3\,(c_4 + c_5)\,, \qquad
e_4 = c_0 + c_2 + c_4 + c_6 - c_3 - c_5 - e_0\,.
\label{ces-subleading}\end{aligned}$$
It is interesting to observe that sum rules (\[res-ces\]) differ from the sum rules applied previously in [@Semke:2011ez; @Semke:2012gs; @Lutz:2014oxa] $$\begin{aligned}
&&c_1 = 2\,c_0, \qquad c_2=-3\,c_0,\qquad c_3=0 \,, \quad
\nonumber\\
&& e_0 = 0\,, \quad e_1 = 6\, c_0, \qquad e_2 = -9\, c_0\,, \qquad e_3 = 3\, ( c_4 + c_5)\,.
\label{result:large-Nc-chi}\end{aligned}$$ The latter were derived in application of the $\varepsilon$ expansion (\[old-ces\]), where the contribution of the counter terms to the baryon masses was considered. Here the fifths term proportional to $\varepsilon^2$ turns relevant. The 12 symmetry breaking counter terms are expressed in terms of the five coefficients in (\[old-ces\]). This leads to the 7 sum rules in (\[result:large-Nc-chi\]).
Product of two axial-vector currents
------------------------------------
0.3cm
There remain the sum rules derived from the product of two axial-vector currents, studied previously in [@LutzSemke2010]. They correlate two-body meson-baryon counter terms. A complete list of chiral symmetry conserving $Q^2$ counter terms was given in [@Lutz2002a; @LutzSemke2010]. Here we recall all terms relevant for the calculation of the N$^3$LO baryon masses. The terms are grouped according to their Dirac structure $ \mathcal{L}^{(2)}=\mathcal{L}^{(S)} + \mathcal{L}^{(V)} $ with $$\begin{aligned}
&& \mathcal{L}^{(S)} =- \frac{1}{2}\,g_0^{(S)}\,\mathrm{tr} \,\Big\{\bar{B}\,B \Big\}\, \mathrm{tr}\Big\{ U_\mu\, U^\mu \Big\} - \frac{1}{2}\,g_1^{(S)}\,\mathrm{tr} \,\Big\{ \bar{B}\, U^\mu \Big\}\, \mathrm{tr}\,\Big\{U_\mu\, B \Big\}
\nonumber \\
&&\qquad -\,\frac{1}{4}\,g_D^{(S)} \mathrm{tr}\,\Big\{\bar{B}\left\{\left\{U_\mu, U^\mu\right\}, B\right\}\Big\}
-\frac{1}{4}\,g_F^{(S)}\mathrm{tr}\,\Big\{ \bar{B}\left[\left\{U_\mu, U^\mu\right\}, B\right]\Big\}
\nonumber\\
&&\qquad + \,\frac{1}{2}\,h_1^{(S)}\,\mathrm{tr}\,\Big\{ \bar{B}_\mu \cdot B^\mu \Big\}\, \mathrm{tr}\,\Big\{U_\nu\; U^\nu\Big\} +
\frac{1}{2}\,h_2^{(S)}\,\mathrm{tr}\,\Big\{\bar{B}_\mu \cdot B^\nu \Big\}\, \mathrm{tr}\,\Big\{U^\mu\, U_\nu\Big\}
\nonumber \\
&& \qquad + \,h_3^{(S)}\,\mathrm{tr}\,\Big\{\Big(\bar{B}_\mu \cdot B^\mu\Big)\, \Big(U^\nu\, U_\nu\Big) \Big\} + \frac{1}{2}\,h_4^{(S)}\,\mathrm{tr}\,\Big\{ \Big(\bar{B}_\mu \cdot B^\nu\Big)\, \{U^\mu,\, U_\nu \} \Big\}
\nonumber \\
&&\qquad +\, h_5^{(S)}\, \mathrm{tr}\, \Big\{ \Big( \bar{B}_\mu \cdot U_\nu\Big)\, \Big(U^\nu\cdot B^\mu \Big) \Big\}
\nonumber \\
&& \qquad +\, \frac{1}{2}\,h_6^{(S)}\, \mathrm{tr} \Big\{ \Big( \bar{B}_\mu \cdot U^\mu\Big)\, \Big(U^\nu\cdot B_\nu \Big)
+\Big( \bar{B}_\mu \cdot U^\nu\Big)\, \Big(U^\mu\cdot B_\nu \Big) \Big\} \, ,
\nonumber\\
&&\mathcal{L}^{(V)} = -\frac{1}{4}\,g_0^{(V)}\, \Big( \mathrm{tr}\,\Big\{\bar{B}\, i\,\gamma^\mu\, D^\nu B\Big\} \,
\mathrm{tr}\,\Big\{ U_\nu\, U_\mu \Big\}\Big)
\nonumber \\
&& \qquad -\, \frac{1}{8}\,g_1^{(V)} \,\Big( \mathrm{tr}\,\Big\{\bar{B}\,U_\mu \Big\} \,i\,\gamma^\mu \, \mathrm{tr}\,\Big\{U_\nu\, D^\nu B\Big\}
+ \mathrm{tr}\,\Big\{\bar{B}\,U_\nu \Big\} \,i\,\gamma^\mu \, \mathrm{tr}\,\Big\{U_\mu\, D^\nu B\Big\} \Big)
\nonumber \\
&& \qquad -\, \frac{1}{8}\,g_D^{(V)}\, \Big(\mathrm{tr}\,\Big\{\bar{B}\, i\,\gamma^\mu \left\{\left\{U_\mu,\, U_\nu\right\}, D^\nu B\right\}\Big\} \Big)
\nonumber\\
&& \qquad -\, \frac{1}{8}\,g_F^{(V)}\,\Big( \mathrm{tr}\,\Big\{ \bar{B}\, i\,\gamma^\mu\, \left[\left\{U_\mu,\, U_\nu\right\},\, D^\nu B \right]\Big\} \Big)
\nonumber \\
&& \qquad +\, \frac{1}{4}\,h_1^{(V)}\,\Big(\mathrm{tr}\,\Big\{ \bar{B}_\lambda \cdot i\,\gamma^\mu\, D^\nu B^\lambda\Big\} \,\mathrm{tr}\,\Big\{U_\mu\, U_\nu\Big\}\Big)
\nonumber \\
&& \qquad +\, \frac{1}{4}\,h_2^{(V)}\,\Big(\mathrm{tr}\,\Big\{ \left(\bar{B}_\lambda \cdot i\,\gamma^\mu\, D^\nu B^\lambda \right) \{U_\mu,\, U_\nu\}\Big\} \Big)
\nonumber \\
&& \qquad +\, \frac{1}{4}\,h_3^{(V)}\, \Big( \mathrm{tr}\, \Big\{ \left( \bar{B}_\lambda \cdot U_\mu\right) i\,\gamma^\mu \left(U_\nu\cdot D^\nu B^\lambda \right)
\nonumber\\
&& \qquad \qquad \qquad \qquad +\, \left( \bar{B}_\lambda \cdot U_\nu\right) i\,\gamma^\mu \left(U_\mu\cdot D^\nu B^\lambda \right) \Big\} \Big)
+ \mathrm{h.c.} \, .
\label{def-Q2-terms}\end{aligned}$$ We extend the previous large-$N_c$ analysis [@LutzSemke2010] and construct the subleading contributions. Altogether we find the relevance of the following operators $$\begin{aligned}
&&i\,\int d^4 x \,e^{-i\,q\cdot x} \,{\langle \bar p\,,\,\bar\chi\,|}\, {\mathcal T}\,A^{(a)}_i (x)\,A^{(b)}_j(0) {|\,p\,,\chi \rangle}
\nonumber\\
& & = ( \bar \chi | - \delta_{ij}\,\Big[
\, \hat g_1\,\delta_{ab}\,\quarknumberoperator+\hat g_2\,
d_{abc}\,T^c + \hat g_3\,\{T^a,\,T^b\} + \hat g_4\,d_{abc}\, \{J_k,\,G_k^c\}
\nonumber\\
& & \quad + \,\hat g_5\,\Big( \{ J_k,\, \{T^{a},\,G^{b}_k\} \} + \{ J_k,\,\{G^{a}_k,\,T^{b} \} \Big) \Big]
+ \hat g_6\,\Big( \{G^{a}_i,\,G^{b}_j\} +\{G^{a}_j,\,G^{b}_i \} \Big)
\nonumber\\
& & + \,(\bar p+p)_i \,(\bar p+p)_j \,\Big[
\,\hat g_7\,\delta_{ab}\,\quarknumberoperator+ \hat g_8\,
d_{abc}\,T^c + \hat g_9\,\{T^a,\,T^b \} + \hat g_{10}\,d_{abc}\, \{J_k,\,G_k^c\}
\nonumber\\
& & \quad
+ \,\hat g_{11}\,\Big( \{ J_k,\, \{T^{a},\,G^{b}_k\} \} + \{ J_k,\,\{G^{a}_k,\,T^{b} \} \Big) \Big]
\, | \chi ) + \cdots \,.
\label{QCD-identity-AA}\end{aligned}$$ A matching with the terms form (\[def-Q2-terms\]) leads to the following six sum rules $$\begin{aligned}
&& \bar g^{(S)}_F = \bar g^{(S)}_0 + \frac{3}{2}\, \bar g^{(S)}_1 + \bar g^{(S)}_D - \bar h^{(S)}_1 - \frac{1}{3}\, \bar h^{(S)}_5 + \frac{2}{9}\, \bar h^{(S)}_6\,,
\nonumber\\
&& \bar h^{(S)}_2 = 0\,, \qquad \bar h^{(S)}_4 = - \bar h^{(S)}_6\,,
\nonumber\\
&& \bar h^{(S)}_3 = \frac{3}{2}\,\bar g^{(S)}_0 + \frac{15}{4}\, \bar g^{(S)}_1 + 3\, \bar g^{(S)}_D - \frac{3}{2}\, \bar h^{(S)}_1
- \frac{3}{2}\, \bar h^{(S)}_5 + \frac{1}{3}\, \bar h^{(S)}_6\,, \qquad
\nonumber\\ \nonumber\\
&& \bar g^{(V)}_F = \bar g^{(V)}_0 + \frac{3}{2}\, \bar g^{(V)}_1 + \bar g^{(V)}_D - \bar h^{(V)}_1 - \frac{1}{3}\, \bar h^{(V)}_3\,, \qquad
\nonumber\\
&& \bar h^{(V)}_2 = \frac{3}{2}\, \bar g^{(V)}_0 + \frac{15}{4}\, \bar g^{(V)}_1 + 3\, \bar g^{(V)}_D - \frac{3}{2}\, \bar h^{(V)}_1 - \frac{3}{2}\, \bar h^{(V)}_3\,,
\label{Q4-subleading}\end{aligned}$$ with $\bar g = g$ and $\bar h = h$. The leading order operators of [@LutzSemke2010] are recovered with $3\,\hat g_1 = \hat g_2$, $3\,\hat g_7 = \hat g_8$ and $\hat g_4 = \hat g_5 = 0 =
\hat g_{10} = \hat g_{11} =0 $. This leads to an additional six leading order sum rules $$\begin{aligned}
&& \bar h^{(S)}_1 = 0\,,\qquad
\bar h^{(S)}_5 = \bar g^{(S)}_D + 3\, \bar g^{(S)}_1\,\qquad \bar h^{(S)}_6 = -3\,\Big( \bar g^{(S)}_D + \frac{3}{2}\,\bar g^{(S)}_1 \Big)\,,
\nonumber\\
&& \bar h^{(V)}_1= 0 \,, \qquad \bar g^{(V)}_D = -\frac{3}{2}\,\bar g^{(V)}_1\,,\qquad \quad \bar h^{(V)}_3 = \frac{3}{2}\, \bar g^{(V)}_1\,.
\label{Q4-leading}\end{aligned}$$ Combining the sum rules of (\[Q4-subleading\], \[Q4-leading\]) confirms the leading order sum rules derived first in [@LutzSemke2010] [^1].
As a further cross check we computed the contributions from the s- and u-channel baryon exchange diagrams. They may modify the sum rules obtained previously and lead to a renormalization of the low-energy constants with $g \to \bar g$ and $h \to \bar h$.
Here we need to be more specific about the kinematics of the correlation function. We assume on-shell baryons with $p_0= \sqrt{M^2+\vec p\,^2} = \bar p_0$. The energy of the current $A^{(a)}_i$ in (\[QCD-identity-AA\]) is $q_0 $. For simplicity we assume the frame where $\vec p+\vec q= 0$, i.e. we have only the two three vectors of $ p$ and $\bar p$ around. In an analysis of the correlation function there are additional terms that are singular in $q_0$, which are a consequence of the s- and u-channel exchange diagrams. The sum rules (\[Q4-subleading\], \[Q4-leading\]) with $\bar g = g$ and $ \bar h = h$ follow from the analysis of the contributions that are regular in the limits $q_0 \to 0$ and $q_0 \to \pm\, 2\,M$. However, significant results can only be expected if in addition the poles at $q_0 \to \pm \,2\,M$ are expanded for small $q_0$. This leads to a renormalization of the sum rules. The result of such an analysis is $$\begin{aligned}
&& \bar g_0^{(S)} = g_0^{(S)} - \frac{4}{3}\, g^{(S)}_C \,, \qquad \quad
\bar g_1^{(S)} = g_1^{(S)} +\frac{1}{3}\,g^{(S)}_C \,,
\nonumber\\
&& \bar g_D^{(S)} = g_D^{(S)} + g^{(S)}_C\,, \qquad \qquad
\bar g_F^{(S)} =g_F^{(S)} - g^{(S)}_C \,,\qquad g^{(S)}_C = \frac{2\,C^2}{3\,M}\,\alpha_5 \,,
\nonumber\\
&& \bar g_0^{(V)} = g_0^{(V)} - \frac{4}{3}\, g^{(V)}_C \,, \qquad
\bar g_1^{(V)} = g_1^{(V)} + \frac{1}{3}\,g^{(V)}_C\,,
\nonumber\\
&& \bar g_D^{(V)} = g_D^{(V)} + g^{(V)}_C\,,\qquad \quad
\bar g_F^{(V)} = g_F^{(V)} - g^{(V)}_C\,,\qquad g^{(V)}_C = \frac{C^2}{3\,M^2}\,\alpha_{6} \,,
\nonumber\\
&&\bar h_1^{(V)} = h_1^{(V)} \,, \qquad \qquad \qquad
\bar h_2^{(V)} = h_2^{(V)} - \frac{2}{9}\,\frac{H^2}{(M+ \Delta)^2}\,,
\nonumber \\
&& \bar h_3^{(V)} = h_3^{(V)} + \frac{4}{27}\,\frac{H^2}{(M+ \Delta)^2} - \frac{1}{6}\,\frac{\beta_{6}\,C^2}{M\,(M+\Delta)}\,,
\nonumber\\ \nonumber\\
&& \bar h_n^{(S)} = h_n^{(S)} \quad {\rm for} \qquad n \neq 5 \qquad {\rm and }\qquad \bar h_5^{(S)} = h_5^{(S)} + \frac{C^2}{3\,M}\,\beta_5\,,
\label{Q4-renormalization}\end{aligned}$$ where the coefficients $\alpha_{5,6}$ and $\beta_{5,6}$ depend on the ratio $\Delta/M$ only and approach $ 1$ in the limit with $\Delta \to 0$ (see Appendix A and B).
An analysis of the singular terms may be used to correlate the axial-vector coupling constants, $F,D,C, H$ of the baryon octet and decuplet states. It is more convenient, however, to derive such sum rules in terms of matrix elements of a single axial-vector current (\[1-axial-opt\]).
Chiral extrapolation of baryon masses
=====================================
We consider the chiral extrapolation of the baryon masses to unphysical quark masses. Assuming exact isospin symmetry, the hadron masses are functions of $m_u=m_d\equiv m$ and $m_s$. The ultimate goal is to establish a decomposition of the baryon masses into their power-counting moments $$\begin{aligned}
M_B = \sum_{n=0}^\infty M^{(n)}_B \,,\end{aligned}$$ where there is a significant controversy in the community [@Bernard:1993nj; @Banerjee:1994bk; @Banerjee:1995wz; @Lehnhart2004; @Semke2005] as to whether any significant results can be obtained in the flavour SU(3) case.
At leading order the octet and decuplet masses are determined by the tree-level mass parameters of the chiral Lagrangian. At next-to-leading order the chiral symmetry breaking counter terms $b_0,b_D, b_F$ and $d_0, d_D$ in (\[res-bds\]) turn relevant $$\begin{aligned}
&& M^{(2)}_{N}= -2\,{m^{\!\!\!\!\!^o\;\,2}_{\pi}}\,(b_0+2\,b_F) - 4\,{m^{\!\!\!\!\!^o\;\,2}_{K}}\, (b_0+b_D-b_F)\,,
\nonumber\\
&& M^{(2)}_{\Sigma} - M^{(2)}_{\Lambda}={\textstyle{16\over 3}}\, b_D\, ({m^{\!\!\!\!\!^o\;\,2}_{K}}-{m^{\!\!\!\!\!^o\;\,2}_{\pi}})\,, \quad
M^{(2)}_{\Xi} - M^{(2)}_{N}=- 8\, b_F \,({m^{\!\!\!\!\!^o\;\,2}_{K}}-{m^{\!\!\!\!\!^o\;\,2}_{\pi}})\,,
\nonumber\\
&& M^{(2)}_\Xi- M^{(2)}_\Sigma = - 4\,(b_D+b_F)\,({m^{\!\!\!\!\!^o\;\,2}_{K}}-{m^{\!\!\!\!\!^o\;\,2}_{\pi}})
\,,
\nonumber\\ \nonumber\\
&& M^{(2)}_{\Delta}
= - 2\,(d_0+d_D)\,{m^{\!\!\!\!\!^o\;\,2}_{\pi}}-4\, d_0\,{m^{\!\!\!\!\!^o\;\,2}_{K}}\,,
\nonumber\\
&& M^{(2)}_\Sigma- M^{(2)}_\Delta
= - {\textstyle{4\over 3}}\,d_D \,({m^{\!\!\!\!\!^o\;\,2}_{K}}-{m^{\!\!\!\!\!^o\;\,2}_{\pi}}) \,, \quad
M^{(2)}_{\Xi}- M^{(2)}_\Sigma
= - {\textstyle{4\over 3}}\,d_D\,({m^{\!\!\!\!\!^o\;\,2}_{K}}-{m^{\!\!\!\!\!^o\;\,2}_{\pi}}) \,,
\nonumber \\
&& M^{(2)}_{\Omega}- M^{(2)}_\Xi
= - {\textstyle{4\over 3}}\,d_D\,({m^{\!\!\!\!\!^o\;\,2}_{K}}-{m^{\!\!\!\!\!^o\;\,2}_{\pi}}) \,,
\label{res-Q2}\end{aligned}$$ where the meson masses are to be taken at leading order with e.g. ${m^{\!\!\!\!\!^o\;\,2}_{\pi}} = 2\,B_0\,m$. Based on (\[res-Q2\]) the parameters $b_D, b_F$ and $d_D$ may be adjusted to the mass differences of the physical baryon states: $$\begin{aligned}
&& b_D \simeq 0.07 \,{\rm GeV}^{-1} \,, \quad
b_F \simeq - 0.21 \,{\rm GeV}^{-1} \,, \quad
d_D \simeq - 0.49 \,{\rm GeV}^{-1} \,,
\label{parameters-Q2A} \end{aligned}$$ where the uncertainties as implied by the use of distinct mass differences is rather small. The estimate of the parameter $b_0$ and $d_0 $ requires additional input. If we insist on the leading chiral moments of the baryon masses as deduced recently from a comprehensive analysis of the available lattice data [@Lutz:2014oxa] we obtain the estimates $$\begin{aligned}
&& \qquad M= M^{(0)}_N \simeq 800 \,{\rm MeV} \qquad \qquad M+ \Delta = M^{(0)}_\Delta \simeq 1100 \,{\rm MeV} \,,
\nonumber\\
\rightarrow &&\qquad b_0 \simeq -0.39\,{\rm GeV}^{-1} \,, \qquad \qquad \quad d_0 \simeq -0.11\,{\rm GeV}^{-1} \,.
\label{parameters-Q2B} \end{aligned}$$ All together at this order the physical baryon masses can be reproduced with an uncertainty of 3.1 MeV and 3.5 MeV for the octet and decuplet states respectively.
Yet, it is well known that the loop contributions to the baryon masses that arise in a strict chiral expansion are very large - much too large as to suggest a convincing expansion pattern convergent at physical quark masses [@Bernard:1993nj; @Banerjee:1994bk; @Banerjee:1995wz; @Lehnhart2004; @Semke2005]. Thus the above parameter estimate, despite its deceiving success, may not to be very reliable. Nevertheless, such parameters play an important role in low-energy QCD. In principle they can be extracted from 3-flavour QCD lattice data at sufficiently small up, down and strange quark masses. While at present such simulations are not available one may explore that chiral power counting domain of QCD by analyzing extrapolation studies of the current lattice data set.
The bubble-loop contributions to the baryon masses
---------------------------------------------------
0.3cm
We take the most comprehensive analysis [@Lutz:2014oxa] that is based on relativistic kinematics and the use of physical masses in the loop expressions. This will serve as our starting point to reconsider the convergence properties of the chiral expansion for the baryon octet and decuplet masses with three light flavours. We will scrutinize further the particular summation scheme that is implied by the use of physical baryon and meson masses inside the one-loop expressions. In a more conventional scheme for such masses approximate values are assumed. For a rapidly converging system either of the two approaches is fine. In contrast, for a slowly converging system a summation scheme can be of advantage even though this may imply some model dependence. The target of this and the following sections is to decompose the one-loop expressions for the baryon self energies into chiral moments, which may depend on physical meson and baryon masses.
The one-loop self energy of a baryon of type $B$, can be written as a sum of contributions characterized by $Q$ and $R$, where $Q$ and $R$ indicate the presence of an intermediate meson or baryon state of mass, $m_Q$ or $M_R$, respectively. The previous computations [@Semke2005; @Semke:2011ez; @Semke:2012gs; @Lutz:2012mq; @Lutz:2014oxa] are based on the Passarino-Veltman reduction scheme. Results that are consistent with the expected chiral power as deduced by conventional dimensional counting rules are obtained by a minimal subtraction of the scalar loop diagrams that define the Passarino-Veltman reduction [@Semke2005]. At the one-loop level expressions can always be cast into a form where the scale dependence of a given diagram is exclusively determined by the coefficient in front of the scalar tadpole term $\bar I_Q$, a structure already encountered here in (\[def-tadpole-integral\]). It was argued in [@Semke2005] that tadpole terms involving a ’heavy’ particle mass, i.e. $M_R$ in our case, can be dropped consistently without violating chiral Ward identities. Scale independent results are obtained once suitable counter terms of chiral order $Q^4$ and higher are activated. The leading chiral order of the one-loop diagrams starts at chiral order $Q^3$, where one does not expect a scale dependence. Thus at this order all terms proportional to $m_Q^{2\,n}\,\bar I_Q$ with $n \geq 1$ should be dropped at least. This is an immediate consequence of the chiral counting rule $$\begin{aligned}
\frac{m_Q^2}{M_R^2} \sim \frac{m_Q^2}{M_B^2} \sim Q^2\,.
\label{def-counting}\end{aligned}$$ Using the previous results derived in [@Semke2005; @Semke:2011ez; @Semke:2012gs; @Lutz:2012mq; @Lutz:2014oxa] it is straight forward to verify the according expressions for the baryon octet and decuplet states with $$\begin{aligned}
&&\Sigma^{\rm bubble}_{B \in [8]} = \sum_{Q\in [8], R\in [8]}
\left(\frac{G_{QR}^{(B)}}{2\,f} \right)^2 \Bigg\{ \frac{M^2_R-M^2_B}{2\,M_B}\, \bar I_Q
\nonumber\\
&& \qquad \qquad \qquad
- \,\frac{(M_B+M_R)^2}{E_R+M_R}\, p^2_{QR}\,\bar I_{QR}
\Bigg\}
\nonumber \\
&& \qquad \;\,\,\,+\sum_{Q\in [8], R\in [10]}
\left(\frac{G_{QR}^{(B)}}{2\,f} \right)^2 \, \Bigg\{
\frac{(M_R+M_B)^2}{12\,M_B\,M^2_R}\,\Big(M^2_R-M^2_B\Big)\,\bar I_Q
\nonumber\\
&& \qquad \qquad \qquad
-\, \frac{2}{3}\,\frac{M_B^2}{M_R^2}\,\big(E_R+M_R\big)\,p_{QR}^{\,2}\,
\bar I_{QR} + \frac{4}{3}\,\alpha^{(B)}_{QR}
\Bigg\}\,,
\label{result-loop-8} \\ \nonumber\\
&& p_{Q R}^2 =
\frac{M_B^2}{4}-\frac{M_R^2+m_Q^2}{2}+\frac{(M_R^2-m_Q^2)^2}{4\,M_B^2} \,,\qquad \qquad
E_R^2=M_R^2+p_{QR}^2 \,,
\nonumber\\ \nonumber\\
&&\Sigma^{\rm bubble}_{B\in [10]} = \sum_{Q\in [8], R\in [8]}
\left(\frac{G_{QR}^{(B)}}{2\,f} \right)^2 \Bigg\{
\frac{(M_R+M_B)^2}{24\,M^3_B}\,\Big(M^2_R-M^2_B\Big)\,\bar I_Q
\nonumber\\
&& \qquad \qquad \qquad
-\,\frac{1}{3}\,\big( E_R +M_R\big)\,p_{QR}^{\,2}\,
\bar I_{QR}+ \frac{2}{3}\,\alpha^{(B)}_{QR}
\Bigg\}
\nonumber\\
&& \qquad \;\,\,\,+\sum_{Q\in [8], R\in [10]}
\left(\frac{G_{QR}^{(B)}}{2\,f} \right)^2 \, \Bigg\{
- \frac{ M_B^2 + M_R^2}{18\,M^2_B\,M_R}\,\Big(M^2_R-M^2_B\Big)\,\bar I_Q
\nonumber\\
&& \qquad \qquad \qquad
+\,\frac{M_R^4+M_B^4 + 12\,M_R^2\,M_B^2 }{36\,M^3_B\,M_R^2}\,\Big(M^2_R-M^2_B\Big)\,\bar I_Q
\nonumber\\
&& \qquad \qquad \qquad
-\,\frac{(M_B+M_R)^2}{9\,M_R^2}\,\frac{2\,E_R\,(E_R-M_R)+5\,M_R^2}{E_R+M_R}\,
p_{QR}^{\,2}\,\bar I_{QR}
\Bigg\}\,,
\label{result-loop-10}\end{aligned}$$ where the sums in (\[result-loop-8\], \[result-loop-10\]) extend over the intermediate Goldstone bosons and the baryon octet and decuplet states. The notations of [@Semke2005; @Semke:2011ez] are applied throughout this work. All Clebsch coefficients are listed therein. The coupling constants $G_{QR}^{(B)}$ are determined by the axial-vector coupling constants $F,D,C,H$ of the baryon states in (\[def-FDCH\]). The renormalized scalar bubble loop integral $\bar I_{Q R}$ and the additional subtraction terms $\alpha^{(B)}_{QR}$ will be discussed in more detail below. It is emphasized that with (\[result-loop-8\], \[result-loop-10\]) we have yet an intermediate result only. A further decomposition into chiral moments, in particular of the scalar bubble loop $\bar I_{Q R}$ is required. Such a decomposition will rely crucially on how to power count the mass differences $M_B-M_R$, a central issue of the following development.
There is a subtle issue owing to the manner the scalar tadpole integral $\bar I_Q$ appears in (\[result-loop-8\], \[result-loop-10\]). The renormalized tadpole integral $$\begin{aligned}
&& \bar I_Q =\frac{m_Q^2}{(4\,\pi)^2}\,
\log \left( \frac{m_Q^2}{\mu^2}\right)\,,
\label{def-tadpole-integral}\end{aligned}$$ depends on the renormalization scale $\mu$. Unlike a term proportional to $m_Q^2\,\bar I_Q$, which causes a renormalization of the symmetry preserving $g$ and $h$ coupling constants in (\[def-Q2-terms\]), a term proportional to $(M_R -M_B)\,\bar I_Q$ cannot be dropped without jeopardizing the chiral Ward identities. Moreover such a term implied a particular renormalization scale dependence of the low-energy parameters $c_i$ and $e_i$ in (\[def-c-e\]). From the results of Appendix A and B we extract the leading behavior in the $1/N_c$ expansion $$\begin{aligned}
\mu\, \frac{d}{d\,\mu} \,c^{\rm ano}_i \sim \left(\frac{\hat g_1}{4\,\pi f} \right)^2 \,\hat b_{1,3} \sim N^2_c\,,\quad \quad
\mu\, \frac{d}{d\,\mu} \,e^{\rm ano}_i \sim \left(\frac{\hat g_1}{4\,\pi f} \right)^2 \,\hat b_{1,3} \sim N^2_c\,,
\label{def-c-e-ano}\end{aligned}$$ which is determined by the axial coupling constant $\hat g_1 \sim N_c$ of (\[1-axial-opt\]) and the scalar coupling constants $\hat b_1 \sim N_c $ and $\hat b_3 \sim N_c$ of (\[1-scal-opt\]). We conclude the leading scaling behavior $\sim N_c^2$ is in conflict with the maximal scaling behavior $\sim N_c$ set by QCD. This signals further terms not considered here that are expected to mend this anomalous behavior. A power-counting respecting remedy to this problem is provided by the following simple rewrite $$\begin{aligned}
\big(M_R -M_B\big)\,\bar I_Q = \underbrace{\frac{M_R-M_B}{(4\pi)^2}\,m_Q^2 \,\log \frac{m_Q^2}{M_R^2}}_{\equiv \,(M_R-M_B)\,I_Q^R} + \underbrace{\frac{M_R-M_B}{M_R^2}\,m_Q^2\,\bar I_R}_{\to \;{\rm counter \;terms}}\,,
\label{eliminate-mu}\end{aligned}$$ which suggests the scale dependent part to be systematically absorbed into counter terms of chiral order $Q^2, Q^4$ and higher. Owing to our renormalization prescription that drops all baryon tadpole contributions like $\bar I_R$ the second term in (\[eliminate-mu\]) should be moved into counter terms in any case. Since we are not in the position to follow up all possible terms proportional to a baryonic tadpole $\bar I_R$ this offers an easy way to get rid of the anomalous $ N_c^2$-terms. After dropping the $\bar I_R$ terms all scale dependent terms relevant for the running of the $c_i$ and $e_i$ parameters scale with at most $\sim N_c $. In view of this prescription the results (\[result-loop-8\], \[result-loop-10\]) can be considered scale invariant and therefore used to study the convergence properties of the chiral decomposition we are after. This is what we will do in the following. The corresponding baryon self energy we denote with $\bar \Sigma_B^{\rm bubble}$.
We turn to the subtracted scalar bubble loop integral $\bar I_{Q R}= \bar I_{QR}(p^2\!=\!M_B^2)$ which a priori is a function of the 4-momentum $p$ of the considered baryon of type $B$. It is finite and does not depend on the renormalization scale. A dispersion-integral representation of the following form holds for the unsubtracted bubble function $$\begin{aligned}
&& I_{Q R}(p^2) = \frac{\bar I_Q-\bar I_R}{M_R^2-m_Q^2} + \int_{(m_Q+M_R)^2}^\infty \frac{d s}{8\,\pi^2}
\,\frac{p^2}{s^{3/2}}\,\frac{p_{Q R}(s)}{s-p^2}\,,
\nonumber\\
&& p_{Q R}^2(s) = \frac{s}{4}-\frac{M_R^2+m_Q^2}{2}+\frac{(M_R^2-m_Q^2)^2}{4\,s} \,.
\label{disp-integral}\end{aligned}$$ In the previous works [@Semke2005; @Semke:2011ez; @Semke:2012gs; @Lutz:2012mq; @Lutz:2014oxa] the scalar bubble was subtracted such that upon a conventional chiral expansion the leading moment is of chiral order $Q$ as expected from dimensional counting rules. In more detail it was argued that the scale invariant combination $$\begin{aligned}
\bar I_{QR}(p^2 ) = I_{QR}(p^2) - \frac{\bar I_Q-\bar I_R}{M_R^2-m_Q^2} -\frac{1}{16\,\pi^2}\,,
\label{def-previous}\end{aligned}$$ is of chiral order $Q$ once the baryon tadpole contribution $\bar I_R $ is dropped. While this procedure can be implemented unambiguously at the one-loop level it introduces an artificial pole at $m_Q = M_R$ once the renormalization prescription $\bar I_R \to 0$ is applied. Since the singularity occurs at outrageously large masses $m_Q$ there is a priori no conceptual problem with it. However, if possible one should remedy this issue. In this work we further improve the renormalization scheme by the following prescription. We insist on a rewrite analogously to (\[eliminate-mu\]) introducing an updated scale invariant bubble function $$\begin{aligned}
&& \bar I_{QR}(p^2) = I_{QR}(p^2) + \frac{\bar I_R}{M_R^2} -\frac{1 - \gamma^R_{B}}{16\,\pi^2}\,,
\nonumber\\
{\rm with } \qquad && \gamma^R_{B} = - \lim_{m, m_s\to 0}\,\frac{M_R^2-M_B^2}{M_B^2}\,\log \left|\frac{M_R^2-M_B^2}{M_R^2}\right| \,,
\label{def-IQR-new}\end{aligned}$$ where again the renormalization prescription $\bar I_R \to 0$ is applied in the following. Altogether at $p^2=M_B^2$ our subtracted bubble loop takes the form $$\begin{aligned}
&& \bar I_{Q R}=\frac{1}{16\,\pi^2}
\left\{ \gamma^R_{B} - \left(\frac{1}{2} +\frac{m_Q^2-M_R^2}{2\,M_B^2}
\right)
\,\log \left( \frac{m_Q^2}{M_R^2}\right)
\right.
\nonumber\\
&& +\left.
\frac{p_{Q R}}{M_B}\,
\left( \log \left(1-\frac{M_B^2-2\,p_{Q R}\,M_B}{m_Q^2+M_R^2} \right)
-\log \left(1-\frac{M_B^2+2\,p_{Q R}\,M_B}{m_Q^2+M_R^2} \right)\right)
\right\}\;,
\nonumber\\
&& p_{Q R}^2 =
\frac{M_B^2}{4}-\frac{M_R^2+m_Q^2}{2}+\frac{(M_R^2-m_Q^2)^2}{4\,M_B^2} \,,\qquad
E_R^2=M_R^2+p_{QR}^2 \,.
\label{def-master-loop}\end{aligned}$$ According to the Passarino-Veltman reduction scheme all one-loop integrals can be unambiguously decomposed into the updated renormalized bubble $\bar I_{QR}(p^2= M_B^2)$, the tadpole terms $\bar I_Q$ or $\bar I_R$ and an infinite hierarchy of finite, scale invariant and power-counting respecting set of scalar loop integrals [@Semke2005]. Like the prescription (\[def-previous\]) the new function $\bar I_{QR}(p^2)$ introduced in (\[def-IQR-new\]) is consistent with the chiral power expected for the bubble function from dimensional counting rules.
In contrast to the previous works [@Semke2005; @Semke:2011ez; @Semke:2012gs; @Lutz:2012mq; @Lutz:2014oxa] the finite subtraction term $\gamma^R_{B}$ in (\[def-master-loop\]), discriminates the case $R\in [8]$ from $R\in [10]$. Note that the dimension less $\gamma^R_{B}\neq 0 $ is active only for the off-diagonal cases with neither $B,R \in[8]$ nor $B,R \in [10]$. It depends on the chiral limit values, $M$ and $M+ \Delta$ of the baryon octet and decuplet masses only. Such subtractions are useful in a study of the chiral regime where $m_Q \ll \Delta$, which we will recapitulate briefly in the following.
In the chiral regime all meson and baryon masses are expanded strictly in powers of the quark masses with $m_Q \ll \Delta$. While the loop expressions (\[result-loop-8\], \[result-loop-10\]) can be consistently expanded according to the counting rule $\Delta \sim m_Q$, a further renormalization may be required in the chiral regime. Such a need is nicely illustrated by terms proportional to $m_Q^3\,\Delta^2 $ that arise from an expansion valid for $m_Q \ll \Delta$. Within the counting world $\Delta \sim m_Q$ such terms are of order $Q^5$, which are beyond the accuracy of the one-loop level. Two loop effects are expected to modify such terms and therefore such terms are not fully controlled. They would be part of a summation scheme. If they are numerically small they do not cause a problem for physical meson masses. However, in the strict chiral limit at unphysically small quark masses a conceptual issue arises. This is so since all terms proportional to $m_Q^3$ are protected by a chiral theorem that has to be recovered in the chiral regime. Rather than computing explicitly such contributions from two-loop integral it suffices to construct a suitable subtraction scheme. This is achieved by the terms $\gamma^R_{B}$ and $\alpha^{(B)}_{QR}$.
Our $\gamma^R_{B}$ and $\alpha^{(B)}_{QR}$ subtractions are effective in contributions to the baryon self energies only that are proportional to $C^2$. In particular the scalar bubble-loop function $ \bar I_{Q R}$ vanishes in the chiral limit with $ \bar I_{Q R} \sim m_Q^2/\Delta$ irrespective of the particular behavior of $M_R \neq M_B $ in that limit. This is convenient since this allows for an efficient integrating-out of the decuplet degrees of freedom in the chiral limit region where $m_Q \ll \Delta$. We will return to this issue below. Here we detail the specific form of the further subtraction constant $\alpha^{(B)}_{QR}$ with $$\begin{aligned}
&& \alpha^{(B\in\,[8])}_{QR}\, = \frac{\alpha_1\,\Delta^2}{(4\,\pi)^2} \Bigg\{
- \Big( M_B - M \Big)\, \Big( \frac{\Delta\,\partial}{\partial\,\Delta} -\frac{\Delta\,\partial}{\partial\,M}
+ \frac{M+ \Delta}{M} \Big)
\nonumber\\
&& \qquad +\, \Big( M_R - M -\Delta \Big)\, \Big( \frac{\Delta\,\partial}{\partial\,\Delta}
+ 1 \Big) \, \Bigg\}\,\gamma_1
+ \frac{\Delta\, m_Q^2}{(4\,\pi)^2}\,\alpha_1\,\gamma_2 \,,
\nonumber\\
&& \alpha^{(B\in[10])}_{QR} = \frac{\beta_1\,\Delta^2}{(4\,\pi)^2} \Bigg\{
+\Big( M_B - M - \Delta\Big)\, \Big( \frac{\Delta\,\partial}{\partial\,\Delta} + 1\Big)
\nonumber\\
&& \qquad -\,\Big( M_R - M \Big)\, \Big( \frac{\Delta\,\partial}{\partial\,\Delta} - \frac{\Delta\,\partial}{\partial\,M}
+ \frac{M+ \Delta}{M}\Big)
\Bigg\}\,\delta_1
+ \frac{\Delta\,m_Q^2}{(4\,\pi)^2}\,\beta_1\,\delta_2 \,,
\label{def-alphaBR}\end{aligned}$$ where the dimension less parameters $\alpha_n, \beta_n$ and $\gamma_n, \delta_n$ depend on the ratio $\Delta/M$ only. They are detailed in Appendix A and Appendix B. We note that while the $\alpha_n$ and $\beta_n$ characterize the chiral expansion of the coefficients in front of $\bar I_{QR}$ and $\bar I_Q$ in (\[result-loop-8\], \[result-loop-10\]), the $\gamma_n$ and $\delta_n$ follow from a chiral expansion of $\bar I_{QR}$ at $m_Q < \Delta$. In the limit $\Delta \to 0 $ it holds $\alpha_n \to 1$ and $\beta_n \to 1$. In contrast the coefficients $\gamma_i$ and $\delta_i$ show a log divergence in this limit. For instance we find $\gamma_1 \to + 2\, \log (2\,\Delta/M) $ and $\delta_1 \to - 2\, \log (2\,\Delta/M) $.
As a consequence of the subtraction term $\gamma^R_{B}$ in (\[def-master-loop\]) the loop functions (\[result-loop-8\], \[result-loop-10\]) do not affect the baryon masses in the chiral limit. The additional subtraction term $\alpha^{(B)}_{QR}$ has various effects. The combination of all terms in (\[def-alphaBR\]) prevent a renormalization of the counter terms $b_0, b_D, b_F $ and $d_0, d_D$ in (\[res-bds\]). This is in contrast to the previous works [@Semke2005; @Semke:2011ez; @Semke:2012gs; @Lutz:2012mq; @Lutz:2014oxa] where the chiral limit masses as well as the parameters $b_0, b_D, b_F $ and $d_0, d_D$ are renormalized by loop effects.
Renormalization scale invariance: meson masses
-----------------------------------------------
0.3cm
The main target of our work is an attempt to reformulate conventional $\chi$PT, which is constructed in terms of bare masses rather than the physical meson and baryon masses. An immediate concern arises as to whether this can be done keeping the renormalization scale independence of the effective field theory. We discuss this issue at hand of the meson masses first and then turn to the more complicated baryon masses in the next section.
Within a conventional $\chi$PT approach loop correction terms to the meson masses would impact the baryon masses at N$^4$LO, which is beyond the target of our work. However, since we wish to formulate our chiral expansion scheme in terms of physical meson masses a reliable and quantitative approximation of the meson masses should be used, particularly in any chiral extrapolation attempt of QCD lattice data. This requires the consideration of chiral correction terms to the meson masses. Let us consider the NLO expressions for the pion, kaon and eta masses of [@Gasser:1984gg] where we keep the physical meson masses wherever they occur in the evaluation of the relevant diagrams. The expressions $$\begin{aligned}
&& m_\pi^2 \,=2\,B_0\,m - \frac{1}{3\,f^2}\,\Big\{ \underbrace{5\,B_0 \, m - 4\,m_\pi^2}_{\to \,\frac{1}{6}\,(-10\, m_\pi^2 + \,4\,m_K^2- 3\,m_\eta^2) }\Big\}\,\bar I_\pi
\nonumber\\
&& \quad \; \;\; -\,\frac{1}{3\,f^2}\,\Big\{\underbrace{B_0 \, (3\,m+m_s) - m_\pi^2-m_K^2}_{\to\, 0}\Big\}\,\bar I_K - \frac{1}{6\,f^2}\,\underbrace{2\,B_0 \, m}_{\to \,m_\pi^2}\,\bar I_\eta
\nonumber\\
&& \quad \; \;\; +\,\frac{1}{f^2}\,\underbrace{32\,B^2_0\,m\, (2\, m+m_s)}_{\to \,8\,m_\pi^2\,(m_\pi^2 + \,2\,m_K^2)}\,(2\,L_6-L_4)
\nonumber\\
&& \quad \;\; \;+\,\frac{1}{f^2}\, \underbrace{32\,B^2_0\,m^2}_{\to \,8\,m_\pi^4}\, (2\,L_8-L_5)\,,
\nonumber\\
&& m_K^2 = B_0\,(m+m_s) -\frac{1}{4\,f^2}\,\Big\{ \underbrace{B_0 \,(3\,m +m_s) - m_\pi^2 -m_K^2}_{\to \,0} \Big\}\,\bar I_\pi
\nonumber\\
&& \quad \; \;\; -\,\frac{1}{f^2}\,\Big\{ \underbrace{B_0 \, (m +m_s) -m_K^2}_{\to \,\frac{1}{6}\,( m_\pi^2 -\,4\, m_K^2 +\,3\,m_\eta^2 )}\Big\}\,\bar I_K
\nonumber\\
&& \quad \; \;\;-\,\frac{1}{12\,f^2}\,\Big\{ \underbrace{B_0 \, (m+3\,m_s) -3\,m_K^2-3\,m_\eta^2}_{\to\,-4\,m_K^2}\Big\}\,\bar I_\eta
\nonumber\\
&& \quad \;\; \;+\,\frac{1}{f^2}\,\underbrace{16 \,B^2_0\,(m+ m_s)\,(2\,m+m_s)}_{\to \,12\,m_K^2\,(m_\pi^2+\,m_\eta^2)}\,(2\,L_6-L_4)
\nonumber\\
&& \quad \;\; \;+\,\frac{1}{f^2}\, \underbrace{8\,B^2_0\,( m+m_s)^2}_{\to\, 8\,m_K^4}\,(2\,L_8-L_5)\,,
\nonumber\\
&& m_\eta^2 \,= \frac{2}{3}\,B_0\,(m+2\,m_s)- \frac{1}{2\,f^2}\,\Big\{ \underbrace{2\,B_0\,m}_{\to\,m_\pi^2} \Big\} \,\bar I_\pi
- \frac{1}{9\,f^2}\,\Big\{\underbrace{B_0\,(m+8\,m_s)}_{\to \,\frac{3}{2}\,(7\,m_\eta^2-\,4\,m_K^2)} \Big\} \bar I_\eta
\nonumber\\
&& \quad \;\; \;-\,\frac{1}{3\,f^2}\,\Big\{ \underbrace{B_0\,(m+ 3\,m_s)-3\,m_K^2-3\,m_\eta^2}_{\to \, -4\,m_K^2} \Big\} \,\bar I_K
\nonumber\\
&& \quad \;\;\; +\, \frac{8}{3\,f^2}\,\underbrace{4\,B^2_0\,(m + 2\,m_s)\,(2\, m+m_s)}_{\to \,9\,m_\eta^2\,( 2\,m_K^2-\,m_\eta^2)}\,(2\,L_6-L_4)
\nonumber\\
&& \quad \;\; \;+\,\frac{8}{9\,f^2}\,\underbrace{4\, B^2_0\,(m + 2\,m_s)^2}_{\to \,9\,m_\eta^4}\, (2\,L_8-L_5)
\nonumber\\
&& \quad \;\; \;+\,\frac{128}{9\,f^2}\,\underbrace{B_0\,( m_s-m )^2}_{\to\, \frac{9}{40}\,(3\,m_\pi^4-\,8\,m_K^4-\,8\,m_\eta^2\,m_K^2+\,13\,m_\eta^4)} \,(3\,L_7+L_8) \,,
\label{meson-masses-q4}\end{aligned}$$ involve a set of low-energy parameters $L_i$ and the renormalized mesonic tadpole integral $\bar I_Q$ already recalled in (\[def-tadpole-integral\]).
The parameter $f$ labels the pion-decay constant in the flavour $SU(3)$ limit with $m=m_s =0$. We recall that the tadpole contributions in (\[meson-masses-q4\]) have two distinct sources. The terms proportional to the quark masses are a consequence of the symmetry breaking counter terms that give rise to the leading order Gell-Mann-Oakes-Renner relations. The remaining terms are implied by the symmetry conserving Weinberg-Tomozawa interaction terms.
The renormalization scale $\mu$ can be absorbed into the low-energy constants $L_i$ if all meson masses on the r.h.s. of (\[meson-masses-q4\]), particularly in the tadpole terms $\bar I_Q$, are used at leading chiral order as given by the Gell-Mann-Oakes-Renner relations. We assure, that alternatively, scale invariant results are implied also if the replacement rules as indicated in (\[meson-masses-q4\]) are applied. In this case the physical meson masses can be used in the tadpole contributions. Such rules can be viewed as a solution to a suitable renormalization group equation that generates specific higher order terms that are needed to arrive at renormalization scale independent results. In this work we will use the latter procedure. For a given set of quark masses this requires the numerical solution of a set of three coupled and non-linear equations. By construction this set of non-linear equations recovers the conventional NLO result of $\chi$PT if expanded in powers of the quark masses.
Renormalization scale invariance: baryon masses
-----------------------------------------------
0.3cm
We turn to the N$^3$LO effects in the baryon masses. In a conventional $\chi$PT approach this is the minimal oder at which renormalization scale dependent counter terms turn relevant. There are three types of contributions to a fourth order approximation: terms from symmetry breaking and conserving counter terms and the fourth order moment of the one-loop expressions (\[result-loop-8\], \[result-loop-10\]).
Let us begin with a discussion of the contributions from the symmetry breaking and conserving counter terms. Using the notations of [@Semke:2011ez] we recall such terms $$\begin{aligned}
&& \Sigma^{(4-\rm ct )}_{B} = \frac{1}{(2\,f)^2}\sum_{Q\in [8]} \Big( G^{(\chi )}_{BQ}
- m_Q^2\,G^{(S)}_{BQ} - \frac 14 \, m_Q^2\,M^{(0)}_B \,G^{(V)}_{BQ}\Big)\, \bar I_Q
\nonumber\\
&& \qquad \quad \,+\,\Sigma^{(4-\chi)}_B \,.
\label{def-tadpole} \end{aligned}$$ While the coefficients $G_{QR}^{(\chi)}$ probe the symmetry breaking parameters $b_0,b_D, b_F$ and $d_0,d_D$ already encountered in (\[def-b-d\], \[res-Q2\]), the scalar and vector coupling constants $G^{(S)}_{BQ}$ and $G^{(V)}_{BQ}$ encode the symmetry conserving set of parameters $ g^{(S)}_{\dots}, h^{(S)}_{\dots}$ and $g^{(V)}_{\dots}, h^{(V)}_{\dots}$ respectively (see (\[def-Q2-terms\])).
Here it is important to remember that the parts of the one-loop contribution that are proportional to $m_Q^2\,\bar I_Q $ were excluded in (\[result-loop-8\], \[result-loop-10\]) and therefore renormalized values have to be taken in (\[def-tadpole\]). The bare coupling constants $g, h$ are to be replaced by renormalized ones $\bar g, \bar h$. In application of the previous results [@Semke2005; @Semke:2011ez; @Semke:2012gs; @Lutz:2012mq; @Lutz:2014oxa] we derive their specific form for the octet and decuplet baryons. It should not be surprsing that we recover identically the expressions (\[Q4-renormalization\]) of Section 2.5 obtained in an analysis of the s- and u-channel baryon exchange contributions to the correlation function of two axial-vector currents in the baryon gound states. Note that our large-$N_c$ sum rules (\[Q4-subleading\]) and (\[Q4-leading\]) hold for such renormalized low-energy constants (\[Q4-renormalization\]).
We recall from [@Lutz:2014oxa] that the scalar and vector terms can be discriminated by their distinct behavior in the finite box variant of our approach. In this case two different types of tadpole integrals occur. While the scalar terms $g^{(S)}_ {\cdots }$ come with $\bar I_Q$, the vector terms $g^{(V)}_{\cdots}$ come with $\bar I^{(2)}_Q$. The two structures are redundant only in the infinite volume limit with $
4\,\bar I^{(2)}_Q \to m_Q^2\,\bar I_Q\,.
$ Here we wish to correct an error in [@Lutz:2014oxa] where the scalar coupling constants $h_n^{(S)}$ were not treated properly in the finite volume case. It was overlooked that the latter contribute to $G^{(S)}_{BQ}$ [*and*]{} $G^{(V)}_{BQ}$. Our remedy is readily implemented by using $\tilde h^{(S)}_n$ [*and* ]{} $\tilde h^{(V)}_n$ parameters with $$\begin{aligned}
&& \tilde h_1^{(S)} = \bar h_1^{(S)} + \frac{1}{3}\, \bar h_2^{(S)}\,, \qquad \qquad \tilde h_1^{(V)} = \bar h_1^{(V)} - \frac{\bar h_2^{(S)}\,}{3\,(M + \Delta)} \,
\nonumber\\
&& \tilde h_2^{(S)} = \bar h_3^{(S)} + \frac{1}{3}\,\bar h_4^{(S)} \,, \qquad \qquad\tilde h_2^{(V)} = \bar h_2^{(V)} - \frac{\bar h_4^{(S)}\,}{3\,(M + \Delta)}\,,\quad
\nonumber\\
&& \tilde h_3^{(S)} =\bar h_5^{(S)} +\frac{1}{3}\, \bar h_6^{(S)} \, ,\qquad \qquad \tilde h_3^{(V)} = \bar h_3^{(V)} - \frac{\bar h_6^{(S)}\,}{3\,(M + \Delta)} \,,
\label{def-tildeh}\end{aligned}$$ in (\[def-tadpole\]) where the Clebsch are to be taken from Tab. I of [@Semke:2011ez]. Note that the factors $1/4$ rather than the $1/3 $ in (\[def-tildeh\]) were claimed in the identification of $\tilde h_n^{(S)}$ coupling constants.
[c|cc]{}$\Sigma_B^{(4-\chi)}$ & $B=N$ & $B=\Lambda$\
$m_\pi^4$ & $ 63 \,\tilde c_1 + 9 \,\tilde c_2 + 9 \,\tilde c_3 - 3 \,\tilde c_6$ & $42 \,\tilde c_1 + 6 \,\tilde c_3 - 3 \,\tilde c_6 $\
$m_K^4$ & $ 80 \,\tilde c_1 - 6 \,\tilde c_2 + 18 \,\tilde c_3 - 4 \,\tilde c_6$ & $ 4\,(35 \,\tilde c_1 + 5 \,\tilde c_3 - \,\tilde c_6)$\
$m_\eta^4$ & $35 \,\tilde c_1 - 3 \,\tilde c_2 + 5 \,\tilde c_3 - \,\tilde c_6 $ & $ -4 \,\tilde c_1 + 6 \,\tilde c_3 - \,\tilde c_6$\
$B_0\,m\,m_\pi^2$ & $27 \,\tilde c_4 - 9 \,\tilde c_5 $ & $ 18 \,\tilde c_4$\
$B_0\,(m+m_s)\,m_K^2$ & $3 \,(9 \,\tilde c_4 + \,\tilde c_5) $ & $30 \,\tilde c_4 $\
$B_0\,m\,m_\eta^2$ & $3 \,\tilde c_4 - \,\tilde c_5 $ & $2 \,\tilde c_4 $\
$B_0\,m_s\,m_\eta^2$ & $ 4 \,(3 \,\tilde c_4 + \,\tilde c_5)$ & $ 16 \,\tilde c_4$\
$B_0^2\,\tilde c_0\,m\,m_s$ & $-943/r - 946 - 829 \,r $ & $ -6 \,(71/r + 198 + 184\,r)$\
\
$\Sigma_B^{(4-\chi)}$ & $B=\Sigma$ & $B=\Xi$\
$m_\pi^4$ & $80 \,\tilde c_1 + 18 \,\tilde c_3 - 3 \,\tilde c_6 $ & $63 \,\tilde c_1 - 9 \,\tilde c_2 + 9 \,\tilde c_3 - 3 \,\tilde c_6 $\
$m_K^4$ & $84 \,\tilde c_1 + 12 \,\tilde c_3 - 4 \,\tilde c_6 $ & $80 \,\tilde c_1 + 6 \,\tilde c_2 + 18 \,\tilde c_3 - 4 \,\tilde c_6 $\
$m_\eta^4$ & $14 \,\tilde c_1 + 2 \,\tilde c_3 - \,\tilde c_6 $ & $35 \,\tilde c_1 + 3 \,\tilde c_2 + 5 \,\tilde c_3 - \,\tilde c_6 $\
$B_0\,m\,m_\pi^2$ & $54 \,\tilde c_4 $ & $ 9 \,(3 \,\tilde c_4 + \,\tilde c_5)$\
$B_0\,(m+m_s)\,m_K^2$ & $18 \,\tilde c_4 $ & $ 27 \,\tilde c_4 - 3 \,\tilde c_5$\
$B_0\,m\,m_\eta^2$ & $ 6 \,\tilde c_4$ & $ 3 \,\tilde c_4 + \,\tilde c_5$\
$B_0\,m_s\,m_\eta^2$ & $0 $ & $12 \,\tilde c_4 - 4 \,\tilde c_5 $\
$B_0^2\,\tilde c_0\,m\,m_s$ & $-2 \,(1247/r + 110 + 2 \,r) $ & $- 943/r - 946 - 829 \,r $\
[c|cc]{}$\Sigma_B^{(4-\chi)}$ & $B=\Delta$ & $B=\Sigma^*$\
$m_\pi^4$ & $ 51 \,\tilde e_1 + 9 \,(\tilde e_2 - 6 \,\tilde e_4) $ & $ 11 \,\tilde e_1 + 6 \,(\tilde e_2 - 9 \,\tilde e_4) $\
$m_K^4$ & $ 6 \,(-2 \,\tilde e_1 + \tilde e_2 - 12 \,\tilde e_4) $ & $ 76 \,\tilde e_1 + 8 \,(\tilde e_2 - 9 \,\tilde e_4) $\
$m_\eta^4$ & $ 21 \,\tilde e_1 + \,\tilde e_2 - 18 \,\tilde e_4 $ & $ -27 \,\tilde e_1 + 2 \,(\tilde e_2 - 9 \,\tilde e_4) $\
$B_0\,m\,m_\pi^2$ & $ -27 \,\tilde e_3 $ & $-18 \,\tilde e_3 $\
$B_0\,(m+m_s)\,m_K^2$ & $ -9 \,\tilde e_3 $ & $ -12 \,\tilde e_3 $\
$B_0\,m\,m_\eta^2$ & $ -3 \,\tilde e_3 $ & $ -2 \,\tilde e_3 $\
$B_0\,m_s\,m_\eta^2$ & $ 0 $ & $ -4 \,\tilde e_3 $\
$B_0^2\,\tilde e_0\,m\,m_s$ & $ 11/r + 14 + 2\,r $ & $11/r + 14 + 2\,r $\
\
$\Sigma_B^{(4-\chi)}$ & $ B=\Xi^*$ & $ B=\Omega $\
$m_\pi^4$ & $ -6 \,\tilde e_1 + 3 \,\tilde e_2 - 54 \,\tilde e_4 $ & $ -54 \,\tilde e_4 $\
$m_K^4$ & $ 72 \,\tilde e_1 + 10 \,\tilde e_2 - 72 \,\tilde e_4 $ & $ -12 \,(2 \,\tilde e_1 - \,\tilde e_2 + 6 \,\tilde e_4) $\
$m_\eta^4$ & $ 3 \,(-2 \,\tilde e_1 + \,\tilde e_2 - 6 \,\tilde e_4) $ & $ 84 \,\tilde e_1 + 4 \,\tilde e_2 - 18 \,\tilde e_4 $\
$B_0\,m\,m_\pi^2$ & $ -9 \,\tilde e_3 $ & $ 0 $\
$B_0\,(m+m_s)\,m_K^2$ & $ -15 \,\tilde e_3 $ & $ -18 \,\tilde e_3 $\
$B_0\,m\,m_\eta^2$ & $ -\,\tilde e_3 $ & $ 0 $\
$B_0\,m_s\,m_\eta^2$ & $ -8 \,\tilde e_3 $ & $ -12 \,\tilde e_3 $\
$B_0^2\,\tilde e_0\,m\,m_s$ & $ 11/r + 14 + 2\,r $ & $11/r + 14 + 2\,r $\
We continue with the symmetry breaking counter terms, $\Sigma^{(4-\chi)}_B$. The specific form of their contributions to the baryon octet and decuplet self energies is recalled in Appendix A and B, where also more details on the effect of the renormalization as implied by (\[eliminate-mu\]) is provided. There are two classes of contributions. There are terms that contribute to the baryon wave function renormalization and terms that are proportional to the product of two quark masses (see (\[def-c-e\])). The latter contributions are driven by the parameters $c_i$ and $e_i$, for which in Chapter 2 we derived their large-$N_c$ sum rules in (\[res-ces\], \[ces-subleading\]). They are the only renormalization scale dependent low-energy parameters relevant in our work. Altogether the term $\Sigma^{(4-\rm ct )}_B$ should not depend on the renormalization scale $\mu$. This can indeed be achieved by either expanding the meson masses in $\bar I_Q$ and $m_Q^2\,\bar I_Q$ to leading order in the quark masses or similarly to (\[meson-masses-q4\]), by reinterpreting the contributions proportional to $c_i$ and $e_i$ in terms of physical meson masses. In Tab. \[tab:zz1\] and Tab. \[tab:zz2\] the details of such a rewrite are provided for the baryon octet and baryon decuplet terms respectively. For that purpose it is convenient to identify linear combinations that go together with specific combinations of quark and meson masses. In the octet sector $$\begin{aligned}
&& \tilde c_0 = \frac{2}{2277}\,\Big(33\,c_0 + 6\,c_1 + 22\,c_2 - 30\,c_4 - 45\,c_6 \Big) \,,\qquad \tilde c_1 = \frac{3}{23}\,c_1\,,\qquad
\nonumber\\
&& \tilde c_2 = \frac{1}{46}\,\Big( 22\,c_3 - 3\,c_5\Big) \,,\qquad
\tilde c_3 = \frac{1}{46}\,\Big( 22\,c_2 - 3\,c_4\Big) \,,\qquad
\nonumber\\
&& \tilde c_4 = \frac{1}{23}\,\Big(22\,c_0 + 6\,c_2 - 23\,c_4 - 30\,c_6 \Big) \,,\qquad
\tilde c_5 = \frac{1}{23}\,\Big( 26\,c_3 + 9\,c_5\Big) \,,\qquad
\nonumber\\
&& \tilde c_6 = \frac{1}{253}\,\Big( 924\,c_0 + 621\,c_1 + 528\,c_2 - 828\,c_4 - 846\,c_6\Big) \,,\qquad
\label{def-tilde-c}
\end{aligned}$$ we identify the parameter combinations $\tilde c_1, \tilde c_2, \tilde c_3$ and $\tilde c_6$ that probe the fourth power of some meson mass. As can be seen from Tab. \[tab:zz1\] only the particular term $\tilde c_0$ keeps the original structure being a product of two quark masses. The remaining parameters $\tilde c_4$ and $\tilde c_5$ select the terms involving the product of a quark mass with the square of some meson mass. Analogous combinations in the decuplet sector are: $$\begin{aligned}
&& \tilde e_0 = \frac{4}{207}\,\Big(33\,e_0 + 12\,e_1 + 11\,e_2 - 15\,e_3 - 45\,e_4 \Big)\,,\qquad
\tilde e_1 = \frac{1}{23}\,e_1\,,\qquad
\nonumber\\
&& \tilde e_2 = \frac{1}{46}\,\Big(22\,e_2 - 3\,e_3 \Big)\,,\qquad
\tilde e_3 = \frac{1}{69}\,\Big(12\,e_1 + 26\,e_2 + 9\,e_3 \Big)\,,\qquad
\nonumber\\
&& \tilde e_4 = \frac{1}{138}\,\Big(7\,e_0 +\,e_2 - 3\,e_3 + 3\,e_4 \Big)\,.\qquad
\label{def-tilde-e}\end{aligned}$$ The expressions in Tab. \[tab:zz1\] and (\[result-counter-terms-octet\]) and also Tab. \[tab:zz2\] and (\[result-counter-terms-decuplet\]) agree identically if the Gell-Mann-Oakes Renner relations for the meson masses are used. We recall that the merit of Tab. \[tab:zz1\] and Tab. \[tab:zz2\] lie in their property of making the fourth order contribution (\[def-tadpole\]) independent on the renormalization scale $\mu$ even if the physical masses for the pion, kaon and eta meson are used. We note a particularity: at leading order the effects of $b_0$ and $ d_0$ in $G^{(\chi )}_{BQ}$ cannot be discriminated from $g_0^{(S)}$ and $h_1^{(S)}$ in $G^{(S)}_{BQ}$. Scale invariance requires to consider the particular combinations $$\begin{aligned}
g_0^{(S)} - 8\,b_0\,,\qquad \qquad \qquad h_1^{(S)} - 8\,d_0\,,
\label{scale-particular}\end{aligned}$$ in $G^{(S)}_{BQ}$ and in turn use $b_0 = 0 = d_0$ in $G^{(\chi)}_{BQ}$. In the following we will continue with such scale invariant representation of the term $\Sigma^{(4-\rm ct )}_B$.
Effects from the wave-function renormalization
----------------------------------------------
0.3cm
The bubble-loop contributions to the baryon self energy implies a renormalization of the baryon wave-function $Z_B$ of the form $$\begin{aligned}
Z_B - 1= \frac{\partial }{\partial M_B}\,\bar \Sigma^{\rm bubble}_B\,,
\label{def-ZB}\end{aligned}$$ where we insist on (\[result-loop-8\]) and (\[result-loop-10\]) to be renormalized expressions already. In the meson-baryon coupling constant $G_{QR}^{(B)}$ the wave-function factor $\sqrt{Z_R\,Z_B}$ is already incorporated. The renormalized coupling constants $G_{QR}^{(B)}$ are approximated by the renormalized leading order parameters $F,D,C,H$ as introduced in (\[def-FDCH\]) at tree-level.
We emphasize that as a consequence of $\alpha^{(B)}_{QR}$ in (\[result-loop-8\], \[result-loop-10\]) the wave-function factors are identical to one in the chiral limit. This is implied by the terms proportional to $M_B -M$ in (\[def-alphaBR\]). Recall that the terms involving $M_B -M$ [*and*]{} $M_R -M$ are indispensable to cancel terms proportional to $m_Q^3\,\Delta^2$. The need of such a cancellation was discussed below (\[def-master-loop\]).
The Dyson equation for the baryon propagator determines the physical baryon masses $M_B$. A set of coupled equations is obtained since the renormalized loop functions depend themselves on the physical masses of the baryons. We find $$\begin{aligned}
M_B - M^{(0)}_B - M_B^{(2)} - \bar \Sigma^{\rm bubble}_B / Z_B = 0\,,
\label{gap-equation-A}\end{aligned}$$ where $ M^{(0)}_B =M$ and $ M^{(0)}_B = M + \Delta$ for the octet and decuplet cases respectively. The second order terms $ M_B^{(2)}$ are the tree-level second order contributions (\[res-Q2\]) written in terms of the parameters $b_0, b_D, b_F $ and $d_0, d_D$. It should be stressed that the wave-function renormalization $Z_B$ has a quark-mass dependence which cannot be fully moved into the counter terms of the chiral Lagrangian. Therefore it is best to work with the bare parameters first and derive any possible renormalization effect explicitly.
$B$ $Z_B$ $\bar \Sigma^{\rm bubble }_B$ $B$ $Z_B$ $ \bar \Sigma^{\rm bubble }_B$
----------- ------- ------------------------------- ------------ ------- --------------------------------
$N$ 1.118 -303.9 $\Delta$ 1.570 -313.7
$\Lambda$ 2.064 -458.9 $\Sigma^*$ 1.915 -324.9
$\Sigma$ 2.507 -653.6 $\Xi^*$ 2.438 -340.2
$\Xi$ 3.423 -764.8 $\Omega$ 3.064 -371.4
: The axial coupling constants are $F=0.45$ and $D =0.80$ together with $C=2\,D$ and $H= 9\,F-3\,D$. The self energies $\Sigma^{\rm bubble }_B$ \[MeV\] are evaluated with physical meson and baryon masses properly averaged over isospin states. []{data-label="tab:1"}
We compute the numerical values of the wave-function terms assuming that all masses can take their physical values. The results for the size of the loop and wave-function contributions are collected in Tab. \[tab:1\]. The presence of the subtraction terms $\gamma^R_B$ and $\alpha^{(B)}_{QR}$ changes the size of the wave-function factor and the loop function significantly, in particular for the octet states. For instance at $\gamma^R_{B} = 0 = \alpha^{(B)}_{QR}$ we would obtain $Z_\Xi \simeq 1.60$ and $\Sigma^{\rm bubble}_{\Xi}\simeq -1291$ MeV as compared to $Z_\Xi \simeq 3.42$ and $\Sigma^{\rm bubble}_{\Xi}\simeq -765$ MeV for $\gamma^R_{B} \neq 0 \neq \alpha^{(B)}_{QR}$. Moreover, with $\gamma^R_B =0$ and $\alpha^{(B)}_{QR}= 0$ it followed $Z_{[8]} \simeq -0.19$ in the chiral limit. This is striking since $$\begin{aligned}
Z_{[8]} - 1= \underbrace{\frac{10}{3}\,\left(\frac{C\,\Delta}{4\,\pi\,f} \right)^2
\Bigg( 1+ 3\,\log \frac{2\,\Delta}{M}\Bigg)}_{\simeq \,0.09 } + \,{\mathcal O} \left( \Delta^3\right)\,,
\label{def-Z8-expanded}\end{aligned}$$ the change of the wave-function factor is suppressed formally by a factor $Q^2 \sim (\Delta/M)^2$ in the conventional counting [@Banerjee:1994bk; @Banerjee:1995wz]. The leading order result $Z_{[8]} - 1 \simeq 0.09$ of (\[def-Z8-expanded\]) is to be compared with the exact unexpanded value $Z_{[8]} - 1 \simeq -1.19$. This indicates that any expansion in powers of $\Delta/M \sim Q$ is converging rather slowly.
The source of such a slow convergence is readily uncovered. Factors like $(M+ \Delta)^{-n}$ with $n> 1$ arise typically from relativistic kinematics (see Appendix A and B). A formal expansion that is truncated at low orders is not able to provide a reliable estimate always. Consider the expansion $$\begin{aligned}
&& \frac{1}{(M+ \Delta)^n} = \frac{1}{M^n} \,\Big( 1- n\,\frac{\Delta}{M}
+ \frac{1}{2}\,n\,(n+1)\,\frac{\Delta^2}{M^2}
\nonumber\\
&& \qquad \qquad \qquad \qquad -\,\frac{1}{6}\,n\,(2+3\,n +n^2)\,\frac{\Delta^3}{M^3} + \cdots \Big)\,,
\label{example-inefficient}\end{aligned}$$ which is convergent for $\Delta < M$ but requires more and more terms in the alternating expansion as $n$ gets larger. In particular the first two terms in the expansion have opposite signs and may be of almost equal size. This may cause trouble making the conventional expansion ineffective. Thus the counting should be modified towards $\Delta/M \sim Q^{1/2}$ or even more extremely $\Delta/M \sim Q^{0}$. Since we are primarily interested in the quark mass dependence of the baryon masses we may easily avoid this issue by expanding the baryon self energy in the quark masses only, where the ratio $\Delta/M$ is kept fixed. This is what we do in the following.
$Z_B\neq 1$ $Z_B=1$ tree-level
-------------------------------------- ------------- --------- ------------
$ b_0\, \hfill \mathrm{[GeV^{-1}]}$ -0.617 -0.994 -0.370
$ b_D\, \hfill \mathrm{[GeV^{-1}]}$ 0.087 0.206 0.063
$ b_F\, \hfill \mathrm{[GeV^{-1}]}$ -0.172 -0.438 -0.198
$ d_0\, \hfill \mathrm{[GeV^{-1}]}$ -0.297 -0.396 -0.110
$ d_D\, \hfill \mathrm{[GeV^{-1}]}$ -0.377 -0.519 -0.460
: In application of (\[gap-equation-A\]) the parameters at N$^2$LO (1-loop level) and NLO (tree-level) are adjusted to the physical baryon masses with $M =800$ MeV and $\Delta = 300$ MeV. The large-$N_c$ sum rules $C= 2\,D$ and $H = 9\,F-3\,D$ together with $f= 92.4$ MeV, $F = 0.45$, $D=0.80$ are used. []{data-label="tab:FitParameters:N2LO"}
In order to illustrate the resumed N$^2$LO approximation we adjust the values of the low-energy parameters $M, \Delta$ and $ b_0, b_D, b_F $ and $ d_0, d_D$ to the physical baryon masses. We use $ {m^{\!\!\!\!\!^o\;\,2}_{\pi}} = m_\pi^2$, ${m^{\!\!\!\!\!^o\;\,2}_{K}} = m_K^2$ and ${m^{\!\!\!\!\!^o\;\,2}_{\eta}} = m_\eta^2$ in (\[res-Q2\]) and take the chiral limit values of the octet and decuplet masses as assumed at NLO in (\[parameters-Q2A\], \[parameters-Q2B\]). The remaining parameters are fitted to the empirical baryon masses. We perform two types of fits. First we assume the wave-function factors, $Z_B$, of Tab. \[tab:1\] and second we insist on $Z_B=1$. The resulting parameters are shown in Tab. \[tab:FitParameters:N2LO\]. In both cases the isospin averaged baryon masses are recovered quite accurately. The averaged error in the octet and decuplet masses is 4.3 MeV and 0.8 MeV only for the case with $Z_B \neq 1$. Assuming $Z_B=1$ a slightly worse description with an error of 9.5 MeV and 1.8 MeV is obtained instead. In both cases the size of the error is similarly good as the description at NLO, which is characterized by a typical error 3 MeV. Note, that the typical isospin splittings in the baryon masses, which is not considered in this work, is about 3 MeV also.
At sufficiently small quark masses a linear dependence of the baryon masses is expected as recalled in (\[res-Q2\]). The associated slope parameters $b_0, b_D, b_F$ and $d_0,d_D$ are scale independent. We find remarkable that the values of the parameters in the first column in Tab. \[tab:FitParameters:N2LO\] determined at the one-loop level are quite compatible with the tree-level estimate (\[parameters-Q2A\], \[parameters-Q2B\]).
We close this section with a discussion of how to generalize the third order ansatz (\[gap-equation-A\]) to the fourth order case where the effect of $\Sigma^{(4-{\rm ct})}_{B } $ should be considered. Here the low-energy parameter $\zeta_{0,D,F}$ and $\xi_0, \xi_D$ have an additional impact on the wave-function renormalization of the baryons (see (\[def-zeta-xi\])). The set of Dyson equations that determine the physical baryon masses should take the form $$\begin{aligned}
&& M_B - M^{(0)}_B - M_B^{(2)} - \Sigma^{(4-{\rm ct})}_{B } - \bar \Sigma^{{\rm bubble} }_B / Z_B = 0\,,
\nonumber\\
&& Z_B = \Big(1 + \frac{\partial }{\partial M_B}\,\bar \Sigma^{\rm bubble}_B \Big)/ \Big( 1- \frac{\partial }{\partial M_B}\,\Sigma^{(4-{\rm ct})}_B\Big)\,,
\label{gap-equation-B}\end{aligned}$$ with the updated wave-function renormalization $Z_B$. We emphasize the importance of the wave function factor $Z_B$ in (\[gap-equation-B\]). Only in the presence of this factor it is justified to take tree-level estimates for the coupling constants $F, D , C$ and $H$ from the empirical axial-vector coupling constants of the baryon octet and decuplet states.
Large-$N_c$ sum rules and loop effects
--------------------------------------
0.3cm
We close this chapter with a discussion of the role of possible loop corrections to the large-$N_c$ sum rules. One may expect that loop contributions are suppressed as compared to tree-level contributions in the $1/N_c$ expansion. Thus leading-order sum rules should not be renormalized. On the other hand sum rules that are derived at subleading orders in the $1/N_c$ expansion may have to be renormalized to sustain the claimed higher accuracy level. In the target application of this work, the chiral extrapolation of baryon masses at N$^3$LO, the axial-coupling constants are not considered at the accuracy level where loop corrections would contribute. Thus it is justified to use the subleading sum rules (\[res-FDCHs\]) without a further renormalization. A similar argument holds for the sum rules (\[Q4-subleading\]).
In contrast, the sum rules (\[res-bds\]) for the symmetry breaking parameters $b_0,b_D, b_F$ and $d_0,d_D$ are affected by the one-loop diagrams considered in this work. There is a correction to the matrix elements of the scalar currents proportional to $$\begin{aligned}
\frac{C^2\,\Delta}{(4\,\pi f)^2} \sim N_c^0 \quad \qquad {\rm with} \quad \qquad
\Delta = \lim_{m_u,m_d,m_s\to 0} (M_\Delta - M_N) \,,\end{aligned}$$ that needed to be considered to keep the accuracy of the relations in the second and third lines of (\[res-bds\]). In our work this effect are taken care of by the suitable subtraction scheme that avoids a renormalization of the parameters $b$ and $d$ such that the predictions (\[res-bds\]) can be scrutinized in our work directly.
How about the sum rules derived from the study of the product of two scalar currents? Here the low-energy parameters develop a renormalization-scale dependence $$\begin{aligned}
\mu\, \frac{d}{d\,\mu} \,c_i = - \frac{1}{2}\,\frac{\Gamma_{c_i}}{(4\,\pi f)^2} \,,\qquad \qquad
\mu\, \frac{d}{d\,\mu} \,e_i = - \frac{1}{2}\,\frac{\Gamma_{e_i}}{(4\,\pi f)^2} \,,
\label{c-e-running}\end{aligned}$$ which specific form is worked out in (\[res-Gamma-ci\]) and (\[res-Gamma-ei\]) of Appendix A and B. The coefficients $\Gamma_{c_n}$ and $\Gamma_{e_n}$ depend on the symmetry breaking parameters $b, d$ and symmetry preserving parameters $\bar g, \bar h$. Insisting on the leading order identities (\[res-ces\]) the corresponding seven relations $$\begin{aligned}
&& 2\,\Gamma_{c_2}=-3\,\Gamma_{c_1}\,,\qquad 2\,\Gamma_{c_0} = \Gamma_{c_1} +2\,(\Gamma_{c_3}+\Gamma_{e_0})\,, \qquad 3\,\Gamma_{c_1} =\Gamma_{e_1}\,,
\nonumber\\
&& 3\,\Gamma_{e_1}+2\,\Gamma_{e_2} =6\,\Gamma_{c_3} \,, \qquad \Gamma_{e_3}=3\,(\Gamma_{c_4}+\Gamma_{c_5})\,, \qquad \Gamma_{c_4}=\Gamma_{c_1}\,,\qquad
\nonumber\\
&& \Gamma_{c_6} = \Gamma_{c_5}+\Gamma_{e_4}\,,
\label{res-ces-B}\end{aligned}$$ control the scale invariance of the correlation function (\[SS-expanded\]). It is interesting to analyze the impact of (\[res-ces-B\]) on the low-energy parameters $b, d$ and $\bar g, \bar h$. This can readily be done in application of the detailed expressions provided in Appendix A and B. Initially, the set of equations is examined insisting on the leading order large-$N_c$ sum rules for the $b, d$ and $\bar g, \bar h$ parameters. Using the first line of (\[res-bds\]) together with (\[Q4-subleading\], \[Q4-leading\]) scale invariance of (\[SS-expanded\]) is observed if and only if $$\begin{aligned}
M\,\bar g_1^{(V)} = -4\,\bar g_1^{(S)}\,, \qquad \qquad \bar g_1^{(S)} = -\frac{2}{3}\,\bar g_D^{(S)} = \frac{2}{9}\,\Big( 3\,\bar h_5^{(S)} + \bar h_6^{(S)}\Big)\,,
\label{res-large-Nc-mu-A}\end{aligned}$$ holds. This is a remarkable result: the seven scale equations (\[res-ces-B\]) are largely compatible with the leading order large-$N_c$ sum rules. Only two additional scale-invariance relations arise[^2].
What is the true nature of the two additional constraint equations (\[res-large-Nc-mu-A\]) discovered by the requirement of a renormalization scale invariant correlation function? We argue, that in fact they are a direct consequence of large-$N_c$ QCD. This can be seen by a study of the large-$N_c$ scaling behavior of (\[c-e-running\]). At leading order the coefficients $ \Gamma_{c_n},\Gamma_{e_n}\sim N_c$ scale linear in $N_c$. Therefore, from a large-$N_c$ point of view the set of equations (\[c-e-running\]) can be significant only, if the sum rules for the $c_n$ and $e_n$ are imposed to subleading order. This implies a set of four equations (\[ces-subleading\]) only. From the requirement of scale independence of the correlation function (\[SS-expanded\]) the following set of corresponding large-$N_c$ sum rules is obtained $$\begin{aligned}
&& \Gamma_{c_0} = 2\,\Gamma_{c_3} + \Gamma_{e_0} - {\textstyle{ 1\over 6}}\,\Gamma_{e_1} - {\textstyle{ 1\over 3}}\,\Gamma_{e_2} - {\textstyle{ 1\over 2}}\,\Gamma_{c_1}\,, \qquad
\nonumber\\
&& \Gamma_{c_1} = {\textstyle{ 1\over 3}}\,(\Gamma_{e_1} + \Gamma_{e_2}) - \Gamma_{c_2} - \Gamma_{c_3}\,, \qquad \qquad \Gamma_{e_3} = 3\,(\Gamma_{c_4} + \Gamma_{c_5})\,, \qquad
\nonumber\\
&& \Gamma_{e_4} = \Gamma_{c_0} + \Gamma_{c_2} + \Gamma_{c_4} + \Gamma_{c_6} - \Gamma_{c_3} - \Gamma_{c_5} - \Gamma_{e_0}\,,
\label{ces-subleading-Gamma}\end{aligned}$$ valid for the leading large-$N_c$ moments of the $\Gamma_{c_n}$ and $\Gamma_{e_n}$. This is an interesting result because (\[ces-subleading-Gamma\]) provides additional leading order large-$N_c$ constraints on the symmetry preserving parameters $\bar g , \bar h$ in (\[Q4-subleading\], \[Q4-leading\]). With this we rediscover the two scale relations (\[res-large-Nc-mu-A\]), i.e. $$\begin{aligned}
M\,\bar g_1^{(V)} = -4\,\bar g_1^{(S)}\,, \qquad \qquad \bar g_1^{(S)} = -\frac{2}{3}\,\bar g_D^{(S)} = \frac{2}{9}\,\Big( 3\,\bar h_5^{(S)} + \bar h_6^{(S)}\Big)\,,
\label{res-large-Nc-mu}\end{aligned}$$ which now are shown to be valid at leading order in the $1/N_c$ expansion. In the derivation of (\[res-large-Nc-mu\]) we used the leading order relations, i.e. the first line of (\[res-bds\]) together with the two set of equations (\[Q4-subleading\], \[Q4-leading\]). We find remarkable that the result (\[res-large-Nc-mu\]) does not depend on any of the symmetry breaking parameters $\hat b_{1,3}$ and also that the four equations in (\[ces-subleading-Gamma\]) provide only two additional constraints as given in (\[res-large-Nc-mu\]).
We may analyze the type of relations (\[ces-subleading-Gamma\]) at the next order in the $1/N_c$ expansion for the $\Gamma_{c_n}$ and $\Gamma_{e_n}$. Note, however, that including into (\[SS-expanded\]) all operators relevant at order $1/N_c$ reduces the number of sum rules further, in fact there would be no obvious sum rule constraint left at this accuracy level. However, it should be recalled that given our framework we cannot exclude the existence of some residual relations valid at this accuracy level. This phenomenon is illustrated by the newly discovered leading order large-$N_c$ sum rules (\[res-large-Nc-mu\]). Therefore we feel that it is reasonable to extend our initial analysis to the subleading order level.
In the following we will insist on (\[ces-subleading\]) together with (\[Q4-subleading\], \[ces-subleading-Gamma\]) as parametric relations. The symmetry conserving parameters $\bar g$ and $\bar h$ relevant at subleading order in the $1/N_c$ expansion are invoked. With the second line of (\[res-bds\]) and (\[Q4-subleading\]) it follows from (\[ces-subleading-Gamma\]) the four relations: $$\begin{aligned}
&& M\, \bar g_1^{(V)} = - 4\, \bar g_1^{(S)} + \frac{8}{3}\, \bar h_5^{(S)} + \frac{2}{3}\, \bar h_6^{(S)} -\frac{2}{3}\, (M +\Delta )\, \bar h_2^{(V)}\, ,\qquad \bar h_3^{(V) } = - \bar h_2^{(V)} \,,
\nonumber\\
&& \bar h_3^{(S)} = \frac{3}{2}\,\bar g_0^{(S)} + \frac{183}{652}\, \bar g_1^{(S)} - h_5^{(S)} + \frac{3}{8}\,M\, \bar g_0^{(V)} +
\frac{183}{2608 }\,M\, \bar g_1^{(V)}
\nonumber\\
&& \qquad \qquad -\, \frac{3}{8}\,( M+\Delta)\, \bar h_1^{(V)}-\frac{3}{2}\, \bar h_1^{(S)}
+24\,b_D\,\frac{111}{ 163}\,,
\label{res-large-Nc-mu-B}\\
&& \bar h_2^{(V)} = \frac{1467 \,\Delta \,\bar h_1^{(V)} + 3780\, \bar h_5^{(S)} + 2738\, \bar h_6^{(S)}}{945\,M +1434\, \Delta }
- 24\, b_D\,\frac{96 }{315\, M + 478 \,\Delta }\,.
\nonumber\end{aligned}$$ Our result (\[res-large-Nc-mu-B\]) is surprising to the extent that it suggests the existence of large-$N_c$ sum rules that correlate the low-energy parameters $b, d$ and $\bar g, \bar h$. We are not in a position to add any more to this at this stage, but can only repeat that the relations (\[res-large-Nc-mu-B\]) are mandatory identities to protect the renormalization scale invariance of the correlation function (\[SS-expanded\]) in a scenario where its loop corrections are evaluated with large-$N_c$ sum rules for the $b, d$ and $\bar g, \bar h$ low-energy parameters accurate to subleading order.
We summarize the two scenarios I) and II) scrutinized so far. Both cases will lead to renormalization scale invariant results for the baryon masses.
- We insist of the leading order sum rules uniformly. That leaves the parameters $b_0,b_F$ together with $e_0, e_1, e_2, e_3, c_6$ and $g_0^{(S)}, h_5^{(S)}, g_0^{(V)}$. Altogether with $M, \Delta$ we count 12 independent parameters.
- We insist on subleading order sum rules uniformly. That leaves the parameters $b_0,b_D,b_F$ together with $e_0, e_1, e_2, e_3, c_2, c_3, c_4 ,c_6$ and $g_0^{(S)},h_1^{ (S)},\- h_5^{(S)}, h_6^{(S) }, g_0^{(V)}, g_1^{(V)}, h_1^{ (V)}$. Altogether with $M, \Delta$ we count 20 independent parameters.
Our parameter count reveals the relevance of 12 and 20 parameters for the two scenarios considered. Those values are reasonably small for an attempt to interpolate the quite large set of QCD lattice simulation data on the baryon masses at various choices of the quark masses and lattice volumes of about 300 points altogether. Using the isospin averages of the empirical baryon masses as further strict constraints reduces the number of fit parameters down to 4 and 12 respectively.
There is a subtle issue to be discussed that is related to the symmetry breaking parameters $b$ and $d$. They enter the computation of the baryon self energy at different chiral orders. On the one hand they determine the strength of the contributions linear in the quark masses, but there are also one-loop tadpole contributions that are proportional to those parameters. Clearly, only the latter have impact on the $\Gamma_{c_n}$ and $\Gamma_{e_n}$. While we worked out a strategy how to deal with the tadpole terms, what to do with the chirally more important tree-level terms? We see two distinct strategies how to proceed. First we may simply use slightly different values for the $b$ and $d$ parameters depending on the chiral accuracy level they enter. For instance the tree-level parameters may be left unconstrained by large-$N_c$ sum rules or only related by the subsubleading order sum rules in (\[res-bds\]). The price to pay is a breaking of chiral constraints, which however, should be suppressed in a large-$N_c$ world. The second path is to insist on universal $b$ and $d$ parameters but simply update the scale relations (\[res-large-Nc-mu-B\]) accordingly. This is readily achieved. Giving up on the leading order relations (\[res-bds\]) our result (\[res-large-Nc-mu-B\]) receives further terms proportional to the $b$ and $d$ parameters. In this case it holds for instance $$\begin{aligned}
&& M\, \bar g_1^{(V)} = - 4\, \bar g_1^{(S)} + \frac{8}{3}\, \bar h_5^{(S)} + \frac{2}{3}\, \bar h_6^{(S)} -\frac{2}{3}\, (M +\Delta )\, \bar h_2^{(V)}\,
\nonumber\\
&& \qquad \qquad +\, \frac{416}{21}\,\Big(M - \frac{10}{13}\,\Delta\Big)\,\frac{d_D- 3\,(b_D+b_F)}{\Delta}\,,
\nonumber\\
&& \bar h_3^{(V) } = - \bar h_2^{(V)} + \frac{208}{7}\,\frac{d_D- 3\,(b_D+b_F)}{\Delta}\,,
\label{res-large-Nc-mu-C}\end{aligned}$$ where the corresponding expressions for $\bar h_3^{(S)}$ and $\bar h_2^{(V)}$ are considerably more complicated and involve the singlet parameters $b_0$ and $d_0$ in addition. We have two options here: either insist on the subsubleading order relation $d_D = 3\,(b_D+b_F)$ (scenario III) or keep the parameters $b$ and $d$ fully unconstrained (scenario IV). The two cases lead to a total number of fit parameters of 13 and 14 respectively, a minor increase for the number of 12 fit parameters in our second scenario.
A power-counting decomposition of the bubble loop
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In the previous chapter we presented the contributions of the set of counter terms together with the tadpole and bubble-loop contributions as they are implied by the chiral Lagrangian as recalled in Chapter 2. While one may well justify the use of the expressions of Chapter 3 at a phenomenological level, it can a priori not be linked to a systematic power-counting expansion as it is requested in any effective field theory approach. In particular, given the counting rules of strict $\chi$PT the bubble-loop contribution must be truncated if one claims to work at the level N$^3$LO. As we will illustrate in the following and as it is well known from many previous studies, any conventional chiral expansion attempt of the bubble loop function does not appear to converge sufficiently fast as to arrive at any significant result. How could one justify its application to the flavour SU(3) case nevertheless? We would argue that the only way out of this misery is to modify the power-counting rules as to make them more effective. Could this be the case once the counting rules are formulated in terms of physical meson and baryon masses?
The purpose of the following sections is to decompose the loop function $\bar \Sigma_B^{\rm bubble}$ into power counting moments $$\begin{aligned}
\bar \Sigma_B^{\rm bubble} = \bar \Sigma_B^{{\rm bubble}-3} + \bar \Sigma_B^{{\rm bubble}-4}+ \bar \Sigma_B^{{\rm bubble}-5} + \cdots \,,\end{aligned}$$ where we will derive explicit expressions for the first three moments. A useful decomposition will rely on a novel counting scheme formulated in terms of physical masses. In particular it avoids an expansion in powers of $\Delta/M$.
Convergence studies for the scalar bubble-loop function
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In this section we will try to shed further light on the convergence properties of a chiral expansion for the baryon masses. Is it possible to further extend the convergence domain beyond the chiral regime with $$\begin{aligned}
m_Q \ll \Delta = M_\Delta^{(0)}-M_N^{(0)} \,?
\label{def-chiral-regime}\end{aligned}$$ This may be the case upon the summation of terms of the form $(m_Q/\Delta)^n$. Since the physical kaon mass is significantly larger than $\Delta$ a successful chiral expansion in a flavour SU(3) context must rest necessarily on some summation scheme. Is it possible to identify the convergence domain of any such approach? To what extent is it required to impose the use of physical baryon masses inside the multi-loop contributions as suggested repeatedly by the first author?
Based on the general one-loop expressions (\[result-loop-8\]) and (\[result-loop-10\]) expressed in terms of the physical meson and baryon masses the chiral expansion of the baryon masses can be scrutinized [@Young:2002ib; @Hall:2012iw; @Geng:2013xn]. At the center of any convergence study for the baryon masses are the properties of the scalar bubble integral $\bar I_{QR} = \bar I_{QR}(M_B,m_Q,M_R)$ as recalled in (\[def-master-loop\]). How to reliably expand this integral into its chiral moments?
![The loop function $(4\pi)^2\,\bar I_{QR}$ is plotted as a function of $x=m_Q/M_B$ at $M_B=M_R$ (solid line). The different broken lines correspond to the correlated truncation of the three functions $f_n(x)$ in (\[IQR-x\], \[fn-exp\]), where 1, 2, 3, or 4 terms in (\[fn-exp\]) are kept. []{data-label="fig:IQRa"}](IQRa.pdf){width="14cm"}
Let us first recapitulate some properties of the scalar bubble at $M_R=M_B$ with either $R,B\in[8]$ or $R,B\in[10]$. In this case it is a function of $x = m_Q/M_B$ only, which we may want to expand in powers of $x$ following the conventional power counting rule $x\sim m_Q \sim Q$. The function in (\[IQR-x\]) is analytic in $x$ with branch points at $x = 0$ and $x =\pm\, 2$ only. Thus an expansion around $x=0$ involves necessarily some terms that are non-analytic at $x=0$. The function may be decomposed as follows $$\begin{aligned}
(4\pi)^2\,\bar I_{QR} = - \pi\,\sqrt{x^2}\,f_1(x^2) + x^2\,f_2(x^2) - \frac{1}{2}\,x^2\,f_3 (x^2)\,\log x^2 \,,
\label{IQR-x}\end{aligned}$$ where the functions $f_n(x^2)$ are analytic in the complex plane with the exception of a branch point at $x^2 = 4$. Therefore the functions $f_n(x^2)$ with $f_n(0) =1 $ may be Taylor expanded around $x^2 =0$ with the convergence domain of $|x|< 2$. We observe a significant cancellation amongst the three terms in (\[fn-exp\]) at small values of $x$ already. It is emphasized that such a cancellation is not a consequence of fine-tuned low-energy parameters, rather a general consequence of the analytic structure of the bubble loop. In turn it is justified and efficient to expand the three functions $f_n(x^2)$ uniformly, i.e. the first order term is defined by $f_n(x^2) = 1 $, the second order terms are implied by $f_n(x^2) = 1 + x^2\,f_n'(0)$ etc. This leads to the following approximation hierarchy $$\begin{aligned}
&& (4\pi)^2\,\bar I_{QR} = -\Big\{ 1 - \frac{1}{8}\,x^2 - \frac{1}{128}\, x^4 - \frac{1}{1024} \,x^6
+ {\mathcal O} (x^8)\Big\} \,\pi \,\sqrt{x^2}
\nonumber\\
&& \qquad \qquad \;\;\;\;\, +\, \Big\{ 1 - \frac{1}{12}\,x^2 -\frac{1}{120}\, x^4 - \frac{1}{840}\,x^6 + {\mathcal O} (x^8) \Big\} \,x^2
\nonumber\\
&& \qquad \qquad \;\;\;\;\,
- \,\frac{1}{2}\,x^2\,\log x^2 \,,
\label{fn-exp}\end{aligned}$$ where in fact it holds $f_3(x^2) = 1$. In Fig. \[fig:IQRa\] it is illustrated that indeed such an expansion converges rapidly up to the convergence limit $|x| < 2$. This would imply a surprisingly large convergence radius for a chiral expansion bounded by $m_Q < 2\,M_B$.
We continue with a study of the bubble loop $ \bar I_{QR}$ this time evaluated at $M_R \neq M_B $ with $B\in [8]$ and $R\in[10]$ for instance. It is a function of two variables $$\begin{aligned}
x = \frac{m_Q}{M_B} \,,\qquad \qquad d = \frac{M_R}{M_B} - 1\,,
\label{def-x-d}\end{aligned}$$ only, which we may want to expand in $x$ at fixed value of $d$. For $x \ll d$ an expansion in powers of $x$ with $$\begin{aligned}
&& (4\pi)^2\,\bar I_{QR} = \gamma_B^R + d\,\gamma_1(d)
\nonumber\\
&& \qquad \qquad \;+\, d\,\sum_{n=1}^\infty \Big[ \gamma_{2\,n}(d) + 2\,\gamma_{2\,n+1}(d)\, \log \frac{x}{1+d}\Big]\left(\frac{x}{d}\right)^{2\,n}\,,
\label{def-gammas}\end{aligned}$$ can be justified in terms of specific functions, $\gamma_n(d)$, that are regular and nonzero in the limit $d \to 0$. For values $x \sim d$ a reorganization of the expansion (\[def-gammas\]) is required. The function in (\[IQR-x-delta\]) is analytic in $x$ with branch points at $x = 0$, $x = -d$ and $x =\pm\, (2 + d)$. Thus an expansion around $x=0$ involves necessarily some terms that are non-analytic at $x=0$ and at $x = -d$, if the expansion is expected to be effective at $x^2 > d^2$. The function may be decomposed into four terms $$\begin{aligned}
&& (4\pi)^2\,\bar I_{QR} = \gamma_B^R + \underbrace{x_d\,\Big( \log (d+ x_d) - \log (d- x_d)}_{\equiv f^{(d)}_0 (x^2)}\Big)\,f^{(d)}_1(x^2)
\nonumber\\
&& \qquad \qquad \;+\, \Big[x^2-d^2\Big]\,f^{(d)}_2(x^2) - \frac{1}{2}\,\Big[x^2-d\,(2+d) \Big]\,\log\frac{x^2}{(1+d)^2} \,,
\nonumber\\
&& x_d = \big( d^2-x^2 \big)^{1/2} \,,
\label{IQR-x-delta}\end{aligned}$$ where the functions $f^{(d)}_{n\neq 0}(x^2)$ are analytic in the complex plane with the exception of a branch point at $x^2 = (2+d)^2$. Therefore the functions $f^{(d)}_{n\neq 0}(x^2)$ may be Taylor expanded around $x^2 =0$ with the convergence domain of $|x|< 2+d$.
![The loop function $(4\pi)^2\,\bar I_{QR}$ is plotted as a function of $x=m_Q/M_B$ at fixed value of $d =M_R/M_B -1$ (solid lines). The different broken lines correspond to the correlated truncations of the three functions $f^{(d)}_n(x)$ in (\[IQR-x-delta\], \[fndelta-exp\]).[]{data-label="fig:IQRb"}](IQRb.pdf){width="14cm"}
We chose a normalization with $f^{(d)}_{n\neq 0}(0) =1 $ at $d=0$ that matches the convention used already in (\[IQR-x\]). The leading order coefficients are derived $$\begin{aligned}
&& f^{(d)}_1(x^2 ) = 1+ {\textstyle{1 \over 2}}\,d - \textstyle{ \frac{1}{4}\, \frac{x^2}{(2+d)} }
- \textstyle{ \frac{1}{16}\, \frac{x^4}{(2+d)^3} }
- \textstyle{ \frac{1}{32}\, \frac{x^6}{(2+d)^5} } + {\mathcal O} (x^8) \,,
\label{fndelta-exp} \\ \nonumber\\
&& f^{(d)}_2(x^2 ) = \textstyle{\frac{2+d}{d}\,\log\frac{2\,(1+d)}{2+d} }
-\,\Big( \textstyle{ \frac{4+d}{4\,d^2\,(2+d)} - \frac{2\,(1+d)}{d^3\,(2+d)}\,\log\frac{2\,(1+d)}{2+d} }\Big)\,x^2
\nonumber\\
&& \qquad \quad \;\; -\,\Big(\textstyle{ \frac{(4 + 3 \,d)\, (24 + d \,(12 + d))}{32\,d^4\,(2+d)^3}
- \frac{2\,(1+d)\,(3+ d\,(3+d))}{d^5\,(2+d)^3}\,\log\frac{2\,(1+d)}{2+d} } \Big)\,x^4
\nonumber\\
&& \qquad \quad \;\;-\,\Big(\textstyle{ \frac{ (960 + d \,(2160 + d\, (1856 + d \,(750 + d \,(126 + 5\, d))))) }{96\,d^6\,(2+d)^5} }
\nonumber\\
&& \qquad \qquad \qquad \quad\;\; -\,\textstyle{\frac{2\,(1+d)\,(10 + d\, (20 + d\, (16 + d\, (6 + d ))))}{d^7\,(2+d)^5}\,
\log \frac{2\,(1+d)}{2+d} } \Big)\,x^6
+ {\mathcal O} (x^8) \,,
\nonumber\end{aligned}$$ where it is emphasized that all coefficients in front of the $(x^{2})^{n} $ terms are analytic at $d=0$ and therefore can be expanded in a Taylor series around that point. This is not immediate from (\[fndelta-exp\]), but follows from the general property $$\begin{aligned}
f^{(d=0)}_{n\neq 0}(x^2 ) = f_n(x^2 ) \,,\end{aligned}$$ where we remind the reader of the functions $f_n(x^2 )$ Taylor expanded already in (\[fn-exp\]) around $x=0$. While the convergence domain of an expansion around $d=0$ is readily identified with $|d| <1$, we observe a rather slow and inefficient convergence behavior. This again reflects our previous observation (\[example-inefficient\]).
There are two ways how to use the expansion (\[IQR-x-delta\], \[fndelta-exp\]). Within a chiral expansion one would identify $M_B = M, M_R = M+\Delta$ or $M_R = M, M_B = M+\Delta$. This implies $$\begin{aligned}
&& d= \frac{M+ \Delta}{M} -1 = \frac{\Delta}{M}\,\qquad {\rm or} \qquad d= \frac{M}{M+\Delta} -1 = -\frac{\Delta}{M+\Delta}\,,
\nonumber\\
&& \qquad {\rm with }\qquad \gamma_B^R = - d\,(2+d)\,\log \Bigg|\frac{d\,(2+d)}{(1+d)^2}\Bigg|\,,\end{aligned}$$ and that the function $\bar I_{QR} =\bar I_{QR}(x,d)$ vanishes at $x=0$ for any choice of $d$. This is the case illustrated in Fig. \[fig:IQRb\]. While on the l.h.p. of the figure the two cases with $d=+0.2$ and $d=+0.4$, on the r.h.p. of the figure the two cases with $d=-0.2$ and $d=-0.4$ are shown. Like for the limiting case $d=0$ in Fig. \[fig:IQRa\] a simultaneous truncation of the three functions $f^{(d)}_n(x^2)$ with increasing and correlated order in $x^2$ leads to a rapidly converging approximation to the bubble function $\bar I_{QR}(x,d)$. The figure illustrates that such an expansion converges uniformly and rapidly within the convergence domain $|x/(2+d)| < 1$.
Yet there is a potential source for a small convergence radius of the chiral expansion. This is linked to the case where one keeps the quark-mass dependence of $M_B$ and $M_R$ in (\[def-x-d\]). That asks for a further expansion of the system (\[IQR-x-delta\], \[fndelta-exp\]). In any conventional counting $$\begin{aligned}
d = d(x)= d_0 + \# \,x^2 + \cdots\end{aligned}$$ the term proportional to $x^2$ is at least one power down as compared to the first term $d_0$ with $d_0=\Delta/M$ or $d_0 = -\Delta/(M+\Delta)$. Thus to further scrutinize the convergence properties of the chiral expansion requires a study of the analytic properties of $\bar I_{QR}= \bar I_{QR}(x,d)$ in the variable $d$.
For the two functions $f_{n\neq 0}^{(d)}(x^2)$ in (\[IQR-x-delta\]) the convergence domain in this variable $d$ is readily identified with $$\begin{aligned}
|d-d_0 | < 1 + d_0 \,,
\label{d-condition-A}\end{aligned}$$ which is implied by the presence of the structure $\log (1+d)$ in the expansion coefficients (\[fndelta-exp\]). For the baryon octet and decuplet the conditions $$\begin{aligned}
&& \Bigg| \frac{M_R}{M_B} - \frac{M+ \Delta}{M}\Bigg| < \frac{M+ \Delta}{M} \qquad {\rm for}\qquad B\in[8] \;\,\,\quad \&\quad R\in [10] \,,
\nonumber\\
&& \Bigg|\frac{M_R}{M_B} - \frac{M}{M+ \Delta} \Bigg| < \frac{M}{M+ \Delta} \qquad {\rm for}\qquad B\in[10] \, \quad \& \quad R\in [8] \,,
\label{def-ineq-1}\end{aligned}$$ arise. For physical quark masses we are far from violating these conditions. Any accessible pair of physical masses $M_B, M_R$ satisfies the inequalities in (\[def-ineq-1\]) comfortably for reasonable choices of $M$ and $\Delta$. For $\Delta =0.3$ GeV and $M= 0.8$ GeV the ratio of left-hand to right-hand sides in (\[def-ineq-1\]) is always smaller than $\simeq 0.25$ and $\simeq 0.35$ for the octet and decuplet baryons.
How about the remaining so far not considered structure in (\[IQR-x-delta\])? It is readily expanded $$\begin{aligned}
&& f^{(d)}_0(x^2)= x_d\,\Big( \log (d+ x_d) - \log (d- x_d)\Big)\,,\end{aligned}$$ with $$\begin{aligned}
&& f^{(d)}_0(x^2) =\, f_0 + \Big( 2+ \frac{d_0}{x_0^2}\, f_0\Big)\,(d-d_0)
+ \Big( \frac{d_0}{x_0^2} - \frac{x^2}{2\,x_0^4}\, f_0\Big)\, (d-d_0) ^2
\nonumber\\
&& \qquad \quad \;\;-\,\Big( \frac{d^2_0 +2\,x^2}{3\,x_0^4} - \frac{d_0\,x^2}{2\,x_0^6}\, f_0\Big)\, (d-d_0)^3
\nonumber\\
&& \qquad \quad \;\;+\,\Big( \frac{(2\,d^2_0 +13\,x^2)\,d_0}{12\,x_0^6} - \frac{(4\,d^2_0 +x^2)\,x^2}{8\,x_0^8}\, f_0\Big)\, (d-d_0)^4
+ {\mathcal O}\left( d-d_0\right)^5\!,
\nonumber\\ \nonumber\\
&& f_0 = x_0\,\Big( \log (d_0+ x_0) - \log (d_0- x_0)\Big) \,,\qquad x_0 = \sqrt{d_0^2-x^2}\,,
\label{f0-exp}\end{aligned}$$ around $d=d_0$, where we note that all expansion coefficients in (\[f0-exp\]) are regular at $x_0 =0$. The determination of the analytic structure of $f^{(d)}_0(x^2)$ considered as a function of $d$ at fixed value of $x$ may not be obvious. We identify one branch point at $d =-\sqrt{x^2}$ rather than two branch points at $d = \pm \,\sqrt{x^2}$ as one may naively but erroneously expect. Our claim is readily confirmed by plotting the function $f^{(d)}_0(x^2)$ in the complex plane. As a consequence we obtain the convergence condition $$\begin{aligned}
\big|d - d_0 \big| < |x+d_0 |\,.
\label{d-condition-B}\end{aligned}$$ Though the result (\[d-condition-B\]) does not directly determine the convergence domain, it does provide a necessary condition that should hold if there is convergence. We need to discriminate two cases with either $d_0> 0$ or $d_0< 0$.
First we assume $d_0 >0$ as implied by the baryon octet states. We illustrate the convergence behavior in Fig. \[fig:IQRc\] where the function $f^{(d)}_0(x^2)$ is plotted in the variable $d$ at various choices of $x$. Note that only the ratios $d/x$ and $d_0/x$ are relevant for our convergence study. Therefore it suffice to set $d_0=1$ for convenience and select a few representative values for x with $x \in\{0.5,1.0,1.5,2.0\}$. According to the convergence condition (\[d-condition-B\]) we expect the expansion in (\[f0-exp\]) to be faithful for $1-(1+x) <d< 1+(1+x)$. This is indeed confirmed by the figure, which verifies the approximation hierarchy within the expected convergence domain.
Similar results are obtained for $d_0 <0$ as implied by the baryon decuplet states. It is emphasized however, that in this case convergence is expected only in the significantly smaller interval $-1-|1-x| <d< -1+|1-x|$. The convergence domain is quite unfavorable, which ultimately is a consequence of open decay channels in the decuplet states.
![The multi-valued function $f_0^{(d)}(x^2)$ is plotted in the variable $(d-d_0)/|d_0 +x|$ at fixed values of $x$ and $d_0=1$. The different broken lines correspond to the first few truncations in (\[f0-exp\]). The range in $d$ is shown where the expansion (\[f0-exp\]) is expected to convergence.[]{data-label="fig:IQRc"}](IQRc.pdf){width="14cm"}
Let us scrutinize the condition (\[d-condition-B\]) for physical quark masses, for which all meson and baryon masses are known accurately: $$\begin{aligned}
&&\Bigg| \frac{M_R}{M_B} - \frac{M+ \Delta}{M}\Bigg| \,\theta^{(B)}_{QR}\,< \Bigg|\frac{m_Q }{M_B} +\frac{\Delta}{M} \Bigg|
\qquad \quad \quad {\rm for}\quad B\in[8] \;\,\,\& \;R\in [10] \,,
\nonumber\\
&& \Bigg|\frac{M_R}{M_B} - \frac{M}{M+ \Delta} \Bigg|\,\theta^{(B)}_{QR}\, < \Bigg|\frac{m_Q }{M_B} - \frac{\Delta}{M+\Delta} \Bigg|
\qquad {\rm for}\quad B\in[10] \;\& \;R\in [8] \,,
\nonumber\\
&& \qquad \,{\rm with} \qquad \theta^{(B)}_{QR} = \left\{
\begin{array}{ll}
1 \qquad & {\rm if } \qquad G^{(B)}_{QR} \neq 0 \\
0 \qquad & {\rm else}
\end{array}
\right. \,.
\label{res-ratios} \end{aligned}$$ Taking the ratio of the left-hand sides over the right-hand side in (\[res-ratios\]) provides a convenient measure for the convergence property of the expansion in (\[f0-exp\]). The ratios depend somewhat on the choice of $\Delta$ and $M$. For the particular choice $\Delta =0.3$ GeV and $0.8$ GeV $ < M< 0.9$ GeV we find the range $0.30-0.44 $ for the maximum of all ratios for the baryon octet. Note that for the nucleon this value is significantly smaller with $ 0.12-0.16$. We conclude that for the baryon octet states the function $f_0^{(d)}(x^2)$ may be expanded around $d=d_0$ successfully. This is distinct for the baryon decuplet states for which the maximum of all ratios is larger than one with the range $1.9-2.6$ at $\Delta =0.3$ GeV and $0.8$ GeV $ < M< 0.9$ GeV. For a given species the ratios depend here quite significantly on $\Delta$ and $M$ and can even reach values below one in some cases. Whenever a ratio larger than one arises one must not expand the function $f_0^{(d)}(x^2)$ around $d=d_0$.
In conclusion it is advantageous not to further expand the function $f^{(d)}_0(x^2)$ around $d= d_0$. Otherwise an asymmetric treatment of the baryon octet and decuplet would arise necessarily. In the following we keep the function $f_0^{(d)}(x^2)$ as it is but expand the coefficient function in $f^{(d)}_{n>0}(x^2)$ in powers of $d- d_0$. More specifically we note the decomposition $$\begin{aligned}
&&(x^2-d^2)\,f_2^{(d)}(x^2) = d\,\tilde \gamma_1+ \sum_{n =1 }^\infty \frac{\tilde \gamma_{2\,n}}{d^{2\,n-1}}\,x^{2\,n}\,, \qquad \tilde \gamma_3 = -2\,d\,,
\label{def-tilde-gamma}\end{aligned}$$ characterized by suitable coefficients $\tilde \gamma_n$ that depend on $d$ only. Given such a strategy we do not see any stringent reason to expect a non-converging chiral expansion of the baryon masses already at the physical quark masses. However, from our analysis it also follows that a conventional chiral expansion of the baryon masses that is not formulated in terms of physical meson and baryon masses can not be convergent at physical quark masses.
Chiral expansion of the bubble-loop: third order
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We derive the N$^2$LO and N$^3$LO chiral correction term of the baryon masses applying the correlated expansion strategy of the previous section. For the baryon octet and decuplet states we expand the loop functions (\[result-loop-8\]) and (\[result-loop-10\]) in powers of the meson masses at fixed ratios $m_Q/\Delta$ and $\Delta/M$.
Consider first the contributions with either $B,R\in[8]$ or $B,R\in[10]$ in (\[result-loop-8\], \[result-loop-10\]). At third order $Q^3$ there are terms only from the scalar bubble-loop function $\bar I_{QR}$ that are relevant. If expanded according to (\[IQR-x\], \[fn-exp\]) we obtain $$\begin{aligned}
&& \Sigma^{(3-\chi)}_{B \in [8]} \,= \sum_{Q\in [8], R\in [8]} \left(\frac{1}{4\,\pi\,f}\,G_{QR}^{(B)} \right)^2 \Big\{
\frac{m_Q^2}{2\,M_B}\,\Big( 1-\log\frac{m_Q}{M_R} \Big)
\nonumber\\
&& \qquad \qquad \qquad -\,\frac{\pi}{2}\,m_Q \Big\}\,\Big( m_Q^2- (M_R-M_B)^2\Big) \,,
\nonumber\\
&& \Sigma^{(3-\chi)}_{B \in [10]} \!= \sum_{Q\in [8], R\in [10]} \left(\frac{1}{4\,\pi\,f}\,G_{QR}^{(B)} \right)^2 \frac{5}{9}\,
\Big\{
\frac{m_Q^2}{2\,M_B}\,\Big( 1-\log\frac{m_Q}{M_R} \Big)
\nonumber\\
&& \qquad \qquad \qquad -\,\frac{\pi}{2}\,m_Q\Big\}\,\Big( m_Q^2- (M_R-M_B)^2\Big) \,,
\label{res-Q3}\end{aligned}$$ where all terms are implied by (\[IQR-x\]) with all $f_{n} (x^2)$ truncated at leading order. In addition we kept the $\log (1+d)$ structure in (\[IQR-x-delta\]) unexpanded and protected the property of the phase-space factor in front of $\bar I_{QR}$ that it vanishes at the threshold and pseudo-threshold conditions with $x=\pm\, d$.
We recall the significant cancellation amongst the $m^3_Q$ and $m_Q^4$ terms in (\[res-Q3\]). As worked out in the previous section this cancellation does not determine the convergence domain of the chiral expansion. Therefore it is justified to slightly reorganize the chiral expansion insisting on a specific correlation as suggested by the general decompositions (\[IQR-x\]) and (\[IQR-x-delta\]) of the bubble loop.
There are further terms of third chiral order that arise from the loop contributions involving terms with either $B\in[8], R\in[10]$ or $B\in[10], R\in [8]$. The corresponding scalar bubble-loop function was analyzed in (\[IQR-x-delta\], \[fndelta-exp\]). An appropriate correlated expansion of the one-loop expressions (\[result-loop-8\], \[result-loop-10\]) leads to the following expressions $$\begin{aligned}
&&\bar \Sigma^{{\rm bubble}-3}_{B \in [8]} =\Sigma^{(3-\chi)}_{B \in [8]} +\!\!\!\sum_{Q\in [8], R\in [10]}
\left(\frac{1}{4\,\pi\,f}\,G_{QR}^{(B)} \right)^2 \,\frac{\alpha_1}{3}\, \Bigg\{ \hat \gamma_2\, \Delta\,m_Q^2
\nonumber\\
&& \qquad \quad + \, \Big[\gamma_1\, \Delta_B -\tilde \gamma_1\,\big( M_R-M_B\big)\Big]\,\Delta_Q^2 + \hat \gamma_1 \,\Delta^2\,\Big( M_R-M_B -\Delta_B \Big)
\nonumber\\
&& \qquad\quad - \,\frac{2\,M+ \Delta}{2\,M}
\Bigg[ \Big( \Delta_Q^2\,- \frac{1}{2}\,m_Q^2\Big)\,\big( M_R-M_B\big)\, \log \frac{m_Q^2}{M_R^2}
\nonumber\\
&& \qquad \qquad \quad +\, \Delta_Q^3\,\Big( \log \big( M_R-M_B + \Delta_Q \big) - \log \big( M_R-M_B - \Delta_Q\big)\Big) \Bigg]
\nonumber\\
&&\qquad \quad +\, \frac{m_Q^2}{\Delta_B}\, \Big[ -\tilde \gamma_2 \,\Delta_Q^2+ \tilde \gamma_3\,m_Q^2\,\log \frac{m_Q^2}{M_R^2} \Big]\Bigg\}\,,
\nonumber\\ \nonumber\\
&& \Delta_Q = \Big[ (M_B -M_R)^2- m_Q^2\Big]^{1/2} \,, \qquad \qquad \Delta_B = \Delta \,M_B \,\lim_{m_{u,d,s}\to \,0}\frac{1}{M_B}\,,
\nonumber\\
&& \hat \gamma_1 =\frac{2\,M+\Delta}{2\,M} \frac{\partial }{\partial \Delta}\,\frac{2\,\Delta\,M}{2\,M+\Delta}\,\big(\gamma_1-\tilde \gamma_1\big) + \tilde \gamma_1\,, \quad \quad
\nonumber\\
&& \hat \gamma_2 = \gamma_2 + \frac{1}{2}\,(\gamma_1 - \tilde \gamma_1)\,\frac{\Delta^2}{(2\,M+\Delta)^2} \,,
\label{loop-HB-3}\end{aligned}$$ where the coefficients $\alpha_n$ and $\gamma_n, \tilde \gamma_n$ are detailed at the beginning of Appendix A. All such coefficients are dimension less and depend on the ratio $\Delta/M$ only. The various terms in (\[loop-HB-3\]) are a consequence of the expansion strategy illustrated in (\[IQR-x-delta\], \[fndelta-exp\]). At the given order we use in particular $d=d_0$ in the truncated functions $f^{(d)}_{n\neq 0 }(x^2)$ with $$\begin{aligned}
d_0=\frac{\Delta}{M} \,,\qquad \qquad \qquad \frac{x}{d_0} = \frac{m_Q}{\Delta_B}\,.\end{aligned}$$
We recall that $\alpha_n$ characterize the chiral expansion of the coefficients in front of $\bar I_{QR}$ and $\bar I_Q$ in (\[result-loop-8\]). In the limit $d_0=\Delta/M \to 0 $ it holds $\alpha_n \to 1$. The coefficients $\gamma_n$ follow from a chiral expansion of $\bar I_{QR}$ at $m_Q < \Delta$ (see (\[def-gammas\])). They are supplemented by $\tilde \gamma_n$ which encode the chiral moments of the functions $f^{(d)}_n(x^2)$ considered in (\[IQR-x-delta\], \[def-tilde-gamma\]). This implies in particular that all coefficients $\tilde \gamma_n$ are analytic functions at $d_0 =0$. In contrast the coefficients $\gamma_{1,2,4}$ have a branch point of the type $\log d_0$.
All contributions in (\[loop-HB-3\]) originate from an expansion of terms proportional to the scalar bubble integral $\bar I_{QR}$, an anomalous contribution proportional to $\Delta \,\alpha_4\,\bar I_Q $ and the subtraction terms introduced in (\[result-loop-8\],\[eliminate-mu\], \[def-alphaBR\]). Like in (\[res-Q3\]) we keep the $\log (1+d)$ structure in (\[IQR-x-delta\]) unexpanded and the kinematical constraint that the phase-space factor in front of $\bar I_{QR}$ vanishes at the thresholds $x=\pm\, d$. The result (\[loop-HB-3\]) generalizes (\[res-Q3\]) which follows from the leading order expansion of $\bar I_{QR}$ only, with $\Delta \to 0$ in this case (see (\[IQR-x\], \[fn-exp\])).
A few more comments on (\[loop-HB-3\]) may be useful for the reader. We recall that the $m_Q^2\,\log \mu^2$ dependence in $ (M_R-M_B)\,\bar I_Q \to (M_R-M_B)\,I^R_Q$ is eaten up by subtraction terms discussed at (\[eliminate-mu\]). The troublesome $(M_R-M_B)\,I_Q^R$ term is canceled identically by a corresponding contribution from the scalar bubble $\bar I_{QR}$. This is reflected in a particular relation, $ \alpha_4= 2\,\alpha_1\,\gamma_3$, amongst various coefficients we introduced. Owing to the coefficients $\gamma^R_{B}$ and $\alpha_{QR}$ in (\[result-loop-8\]) the loop contributions neither renormalize the chiral limit mass of the octet states nor any of the counter terms $b_0, b_D, b_F$. These conditions are indeed respected by our result (\[loop-HB-3\]), where we point at the specific role played by the terms proportional to $\gamma_1-\tilde\gamma_1$ and $\hat \gamma_2$. Moreover, the baryon wave function derived from (\[loop-HB-3\]) turns one in the chiral limit. This is a consequence of (\[def-alphaBR\]) also and at the given order of the term proportional to $\hat \gamma_1$ in (\[loop-HB-3\]).
We return to the loop contributions for the decuplet masses. Like in the octet case at the given order we use $d=d_0$ in the truncated functions $f^{(d)}_{1,2}(x^2)$ with $$\begin{aligned}
d_0=-\frac{\Delta}{M+ \Delta} \,,\qquad \qquad \frac{x}{d_0} = -\frac{m_Q}{\Delta_B}\,,
$$ In contrast to the octet states, for which the expansion (\[f0-exp\]) can be justified, here it is crucial not to expand the function $f^{(d)}_0(x^2)$ around $d=d_0$. Following this strategy we obtain $$\begin{aligned}
&&\bar \Sigma^{{\rm bubble}-3}_{B \in [10]} =\Sigma^{(3-\chi)}_{B \in [10]} +\!\!\! \sum_{Q\in [8], R\in [8]}
\left(\frac{1}{4\,\pi\,f}\,G_{QR}^{(B)} \right)^2 \, \frac{\beta_1}{6}\,\Bigg\{ \hat \delta_2\,\Delta\,m_Q^2
\nonumber\\
&& \qquad \;\quad + \,\Big[\delta_1\,\Delta_B - \tilde \delta_1\,\big( M_B-M_R\big) \Big]\,\Delta_Q^2 - \hat \delta_1\,\Delta^2\, \Big( M_R-M_B + \Delta_B \Big)
\nonumber\\
&& \qquad \;\quad + \, \frac{(2\,M+ \Delta)\,M}{2\,(M+ \Delta)^2} \,
\Bigg[ \Big( \Delta_Q^2\,- \frac{1}{2}\,m_Q^2\Big)\, \big(M_B-M_R \big)\, \log \frac{m_Q^2}{M_R^2}
\nonumber\\
&& \qquad \; \qquad \quad +\, \Delta_Q^3\,\Big( \log \big( M_R-M_B - \Delta_Q \big) - \log \big( M_R-M_B + \Delta_Q\big)\Big)
\Bigg]\,
\nonumber\\
&& \qquad \;\quad +\, \frac{m_Q^2}{\Delta_B}\, \Big( - \tilde \delta_2\,\Delta_Q^2 +\tilde \delta_3\,m_Q^2\, \log \frac{m_Q^2}{M_R^2} \Big)
\Bigg\} \,,
\nonumber\\ \nonumber\\
&& \hat \delta_1 = \frac{(2\,M+ \Delta)}{2\,M} \,\frac{\partial }{\partial \Delta }\,\frac{2\,(M+ \Delta)}{2\,M+ \Delta}\,\Delta \,( \delta_1 - \tilde \delta_1)
+\tilde \delta_1\,, \qquad \quad
\nonumber\\
&& \hat \delta_2 = \delta_2 + \frac{1}{2}\,(\delta_1 - \tilde \delta_1)\,\frac{\Delta^2}{(2\,M+\Delta)^2} \,,
\label{loop-HB-3-B}\end{aligned}$$ where the decuplet coefficients $\beta_n$ and $ \delta_n ,\tilde \delta_n$ play the role of the octet coefficients $\alpha_n$ and $\gamma_n, \tilde \gamma_n$ respectively. The latter are documented at the beginning of Appendix B.
We claim the functional form of $\bar \Sigma^{{\rm bubble}-3}_B$ on $M_B, M_R$ and $\Delta/M$ to be model independent. They are a consequence of relativistic kinematics for the meson-baryon vertex and can not be altered by higher order terms in the chiral expansion. Clearly, a further expansion of the terms (\[loop-HB-3\], \[loop-HB-3-B\]) in powers of $m_Q$ has a convergence domain strictly bounded by $m_Q <\Delta$.
The leading order results of the heavy-baryon formulation [@Bernard:1993nj; @Banerjee:1994bk; @Banerjee:1995wz; @Lehnhart2004; @Semke2005] are recovered from (\[res-Q3\], \[loop-HB-3\]) by an additional formal expansion: the baryon masses $M_B$ and $M_R$ in (\[res-Q3\], \[loop-HB-3\]) have to be replaced by their chiral limit values and an expansion in powers of $\Delta/M $ is to be applied.
Chiral expansion of the bubble-loop: fourth order
-------------------------------------------------
0.3cm
Finally there are the 4th order contributions from the one-loop expressions (\[result-loop-8\], \[result-loop-10\]), following the expansion scheme illustrated with (\[IQR-x-delta\], \[fndelta-exp\], \[f0-exp\]). While it is straight forward to extract the fourth order terms from the loop contributions with $B,R\in [8]$ or $B,R\in [10]$ this may not be so immediate for some of the remaining terms. All contributions from $\bar I_{QR}$ can be deduced by an appropriate expansion of the functions $f^{(d)}_n(x^2)$ in (\[IQR-x-delta\]). The latter functions characterize the scalar bubble loop at $M_B \neq M_R$ with $d = M_R/M_B -1$ and $x = m_Q/M_B$. We recall that the third order terms in (\[loop-HB-3\]) are implied by a leading order truncation of $$\begin{aligned}
f^{(d)}_0(x^2) \to f^{(d)}_0(x^2) \,,\qquad \qquad
f^{(d)}_1(x^2) \to f^{(d=d_0)}_1(x^2=0)\,,\end{aligned}$$ in (\[fndelta-exp\]). The next term in $f^{(d)}_1(x^2)$ proportional to $x^2\sim Q^2$ is two orders suppressed as compared to the leading term and therefore does not contribute to our fourth order terms. In contrast, the expansion $f^{(d)}_{n\neq 0}(x^2)$ around $d=d_0$ does lead to terms of chiral order four. Note that the diagonal cases with $B,R\in [8]$ or $B,R\in [10]$ is covered with $d_0 =0$ in the latter expansion. An expansion of $f^{(d)}_{2}(x^2)$ around $d=d_0$ generates powers of $$\begin{aligned}
\Bigg(\frac{M_R-M_B }{M_B} \Bigg)^n \sim Q^{2\,n} \qquad {\rm or} \qquad \Bigg(\frac{M_R-M_B \pm \Delta_B}{M_B} \Bigg)^n \sim Q^{2\,n}
\label{def-mass-differences:A}\end{aligned}$$ depending on the species $B$ and $R$. While we convinced ourselves that such an expansion is rapidly convergent, this may not necessarily be the case once mass differences $M_R-M_B$ are decomposed further into chiral moments. Recall that despite the convergence of the chiral expansion there are significant cancellations amongst various chiral terms. Therefore we avoid the approximate treatment of the mass differences in (\[def-mass-differences:A\]) and work out the correlated expansion of the baryon self energies in powers of $x$ and $d-d_0$.
We collect the contributions from (\[result-loop-8\], \[result-loop-10\]) as implied by our chiral decomposition. While this is straight forward for the diagonal cases with $B,R\in[8]$ or $B,R\in[10]$ the results for the off-diagonal cases are most efficiently derived from the third order result $\bar \Sigma^{{\rm bubble}-3}_{B \in [8]}$ in (\[loop-HB-3\]) by taking an appropriate derivative of it with respect to $d_0$. After some algebra the following expressions are obtained $$\begin{aligned}
&&\bar \Sigma^{{\rm bubble}-4}_{B \in [8]} = \!\! \sum_{Q\in [8], R\in [8]}
\left(\frac{1}{4\,\pi\,f}\,G_{QR}^{(B)} \right)^2 \Big( M_R-M_B\Big) \,\Bigg\{ \Big( 1+ \log \frac{m_Q}{M_R }
\nonumber\\
&& \qquad \qquad -\, \frac{3\,\pi}{4} \,\frac{m_Q}{M_B} \Big)\,\Big(m_Q^2 - (M_R-M_B)^2 \Big) + \frac{1}{4}\,m_Q^2\,\log \frac{m_Q^2}{M_R^2} \Bigg\}
\nonumber\\
&& \quad +\sum_{Q\in [8], R\in [10]}
\left(\frac{1}{4\,\pi\,f}\,G_{QR}^{(B)} \right)^2 \,\Bigg\{ \frac{\alpha_1}{3}\,\Delta^2\,\Big( \frac{\partial}{\partial \Delta}\,\Delta\, \gamma_1
- \hat \gamma_1 \Big) +\frac{\tilde \alpha_4}{3}\,\Delta_Q^2
\nonumber\\
&& \quad \quad -\, \frac{\tilde \alpha_5}{3}\,\frac{ M_R-M_B}{\Delta_B}\,\Delta_Q^2
- \frac{\tilde \alpha_1}{3\,\Delta_B}\, \Bigg[ \Big( \Delta^2_Q- \frac{1}{2}\,m_Q^2\Big) \, \big( M_R-M_B\big)\,\log \frac{m_Q^2}{M_R^2}
\nonumber\\
&& \qquad \qquad + \, \Delta_Q^3\,\Big(\log ( M_R-M_B + \Delta_Q ) -\log (M_R-M_B - \Delta_Q )\Big)
\Bigg]
\nonumber\\
&& \quad \quad +\,\frac{1}{3}\,\frac{m_Q^2}{\Delta^2_B}\,\Big( -\tilde \alpha_2\,\Delta_Q^2+ \tilde \alpha_3\,m_Q^2\,\log \frac{m_Q^2}{M_R^2}\Big)
\Bigg\} \,\Big( M_R - M_B - \Delta_B\Big)\,,
\label{loop-HB-4}\end{aligned}$$ with $\Delta_Q$ and $\Delta_B$ already introduced in (\[loop-HB-3\]). Our fourth order term (\[loop-HB-4\]) considers contributions that are formally one power suppressed. The extra structures are either proportional to $\pi\,m_Q/M_B$ or to $\tilde \alpha_{1,2,3} $. Such a rearrangement is required since there are significant cancellations in (\[loop-HB-4\]). For instance the $1 +\log (m_Q/M_R) $ term in (\[loop-HB-4\]) may be largely canceled by the associated $\pi\,m_Q/M_B$ term. This resembles the cancellation mechanism within our third order terms (\[loop-HB-3\]). We emphasize that our reordering of terms is not caused by a poor convergence of the chiral expansion, rather it is suggested by specific correlation properties of the chiral moments.
We turn to the decuplet sector. The derivation of our results is analogous to the octet sector. Again the role of $\alpha_n, \tilde \alpha_n$ and $\gamma_n,\tilde \gamma_n$ is taken over by $\beta_n, \tilde \beta_n$ and $\delta_n, \tilde \delta_n$. Altogether we find: $$\begin{aligned}
&& \bar \Sigma^{{\rm bubble}-4}_{B \in [10]} = \!
\sum_{Q\in [8], R\in [10]}\!
\left(\frac{1}{4\,\pi\,f}\,G_{QR}^{(B)} \right)^2 \!\frac{5}{9}\,\Big( M_R-M_B\Big) \, \Bigg\{\Big( 1 +\log \frac{m_Q}{M_R }
\nonumber\\
&& \qquad \qquad - \, \frac{3\,\pi}{4} \,\frac{m_Q}{M_B}\Big)\,\Big(m_Q^2 - (M_R-M_B)^2 \Big) + \frac{1}{4}\,m_Q^2\,\log \frac{m_Q^2}{M_R^2} \Bigg\}
\nonumber\\
&& \quad + \sum_{Q\in [8], R\in [8]}\!
\left(\frac{1}{4\,\pi\,f}\,G_{QR}^{(B)} \right)^2 \Bigg\{
\frac{\beta_1}{6}\,\Delta^2\,\Big( \hat \delta_1 -\frac{M+ \Delta}{M}\,\frac{\partial}{\partial \Delta}\,\Delta \, \delta_1\Big) -\frac{\tilde \beta_4}{6}\,\Delta_Q^2
\nonumber\\
&& \quad \quad -\,\frac{\tilde \beta_5}{6}\, \frac{ M_R-M_B}{\Delta_B}\,\Delta_Q^2
- \frac{\tilde \beta_1}{6\,\Delta_B}\,\Bigg[
\Big( \Delta_Q^2\,-\frac{1}{2}\,m_Q^2\Big) \,\big( M_B-M_R\big)\, \log \frac{m_Q^2}{M_R^2}
\nonumber\\
&& \qquad \qquad + \,
\Delta_Q^3\,
\Big( \log ( M_R-M_B - \Delta_Q ) -\log ( M_R-M_B + \Delta_Q ) \Big)
\Bigg]
\nonumber\\
&& \quad \quad -\, \frac{1}{6} \,\frac{m_Q^2}{\Delta^2_B}\,\Big(- \tilde \beta_2\,\Delta_Q^2 + \tilde \beta_3\,m_Q^2\,\log \frac{m_Q^2}{M_R^2}\Big)
\Bigg\} \,\Big( M_R - M_B + \Delta_B\Big)\,.
\label{loop-HB-4-B}\end{aligned}$$ Like our third order terms (\[loop-HB-3\], \[loop-HB-3-B\]) the fourth order loop contributions (\[loop-HB-4\], \[loop-HB-4-B\]) neither renormalize the chiral limit mass of the baryon states nor any of the counter terms $b_0, b_D, b_F$ and $ d_0, d_D$. Moreover, the baryon wave functions derived from (\[loop-HB-4\], \[loop-HB-4-B\]) remain one in the chiral limit.
Convergence at physical quark masses
------------------------------------
0.3cm
In this section we scrutinize the chiral decomposition of the one-loop contribution into its chiral moments as developed in the previous section by providing numerical values. Since in our approach the use of physical meson and baryon masses inside the loop functions is a crucial element such a convergence test requires the solution of a set of coupled and nonlinear equations at each given order of the truncation.
At this stage we can perform such studies meaningfully at $c=e=0$ and $\bar g = \bar h =0$ only. The size of the set of those low-energy parameters is not well established yet. Ultimately they have to be extracted from QCD lattice simulation data, which will be the target of the next chapter. Any ad-hoc choice thereof may disguise the expected convergence pattern. We will return to this issue after a determination of such parameters from lattice data. In this section we identify the nth moment of the baryon self energy $$\begin{aligned}
\Sigma^{(n)}_B = \bar \Sigma_B^{{\rm bubble}-n}\,.\end{aligned}$$ with the nth moment of the one-loop expressions.
$B$ $\Sigma_B$ $\Sigma^{(3+4+5)}_B$ $\Sigma^{(3)}_B$ $\Sigma^{(4)}_B$ $\Sigma^{(5)}_B$
------------ ------------ ---------------------- ------------------ ------------------ ------------------
$N$ -247.3 -250.4 -185.2 -87.4 22.2
$\Lambda$ -340.6 -319.1 -434.7 75.3 40.3
$\Sigma$ -513.4 -515.3 -453.6 -87.9 26.1
$\Xi$ -571.6 -554.1 -714.8 126.9 33.8
$\Delta$ -198.3 -198.7 -174.5 -39.1 15.0
$\Sigma^*$ -262.3 -256.4 -270.2 -10.3 24.1
$\Xi^*$ -335.4 -327.6 -383.4 28.8 27.1
$\Omega$ -425.6 -418.4 -511.6 67.8 25.3
: The self energies $\Sigma^{}_B$ in units of MeV are evaluated at the physical isospin averaged meson and baryon masses. The axial coupling constants are $F=0.45$ and $D =0.80$ together with $H = 9\,F-3\,D$ and $C=0$. []{data-label="tab:3"}
A first result, that avoids an explicit solution of the set of coupled and nonlinear Dyson equations, can be obtained at the physical quark masses. This is so since typically the mass splittings of the physical baryon masses can be reproduced quite accurately in terms of the three parameters $b_D,b_F, d_D$ only (see e.g. Tab. \[tab:FitParameters:N2LO\]). Given such a parameter set it is justified to analyze the loop function at the physical masses directly.
We begin with a discussion of results for the ’diagonal’ sector implied by the particular choice $C=0$. The baryon octet and decuplet self energies are computed according to (\[result-loop-8\], \[result-loop-10\]) with (\[eliminate-mu\]). The values for the baryon octet and decuplet self energies are listed in the 2nd column of Tab. \[tab:3\]. Those numbers are to be compared with the various chiral moments $\Sigma^{(3)}_B$ of (\[loop-HB-3\], \[loop-HB-3-B\]), $\Sigma^{(4)}_B$ of (\[loop-HB-4\], \[loop-HB-4-B\]) and $\Sigma^{(5)}_B$ of (\[loop-HB-5\], \[loop-HB-5-B\]) for the octet and decuplet states respectively. We make two encouraging observations. First we see a clear hierarchy in the successive orders in the self energies for all octet and decuplet states. The fifth order terms are significantly smaller than the third order terms. Second, the expansion truncated at fifth order is characterized by a mean deviation from the exact expressions of about 8 MeV only.
We continue with a discussion of the ’offdiagonal’ sector implied by the particular choice $F=D=H=0$. The results of this case study are collected in Tab. \[tab:4\]. We confirm the pattern observed before for the diagonal case. A clear hierarchy in the successive orders in the self energies is observed. The expansion truncated at fifth order is characterized by a mean deviation of about 2 MeV only.
$B$ $\Sigma_B$ $\Sigma^{(3+4+5)}_B$ $\Sigma^{(3)}_B$ $\Sigma^{(4)}_B$ $\Sigma^{(5)}_B$
------------ ------------ ---------------------- ------------------ ------------------ ------------------
$N$ -56.6 -56.8 -46.5 -8.3 -2.0
$\Lambda$ -118.3 -118.2 -127.9 9.2 0.5
$\Sigma$ -140.2 -135.4 -423.8 260.1 28.3
$\Xi$ -193.2 -190.2 -380.0 174.5 15.2
$\Delta$ -115.4 -118.6 -50.9 -61.2 -6.5
$\Sigma^*$ -62.7 -64.7 -32.0 -36.0 3.3
$\Xi^*$ -4.7 -5.9 1.5 -13.5 6.2
$\Omega$ 54.2 53.8 43.5 4.5 5.8
: The self energies $\Sigma^{}_B$ in units of MeV are evaluated at the physical isospin averaged meson and baryon masses. The axial coupling constants are $F=D=H=0$ and $C=1.6$. []{data-label="tab:4"}
$B$ $Z_B$ $Z^{[3]}_B$ $Z^{[4]}_B$ $ Z^{[5]}_B$ $\bar \Sigma^{\rm bubble}_B/Z_B$ $\bar \Sigma^{[3]}_B$ $\bar \Sigma^{[4]}_B$ $ \bar \Sigma^{[5]}_B$
------------ ------- ------------- ------------- -------------- ---------------------------------- ----------------------- ----------------------- ------------------------
$N$ 1.118 0.463 1.226 1.167 -271.9 -500.8 -267.2 -263.3
$\Lambda$ 2.064 0.851 1.906 2.179 -222.4 -660.9 -250.9 -200.7
$\Sigma$ 2.507 0.615 2.433 2.300 -260.7 -1426.7 -289.9 -283.0
$\Xi$ 3.423 1.022 3.111 3.386 -223.4 -1071.7 -255.0 -219.8
$\Delta$ 1.570 0.757 1.514 1.615 -199.9 -297.7 -215.1 -196.4
$\Sigma^*$ 1.914 1.104 1.913 1.982 -169.8 -273.8 -182.2 -162.0
$\Xi^*$ 2.438 1.525 2.472 2.516 -139.5 -250.4 -148.3 -132.5
$\Omega$ 3.064 1.936 3.115 3.151 -121.2 -241.7 -127.1 -115.7
: The axial coupling constants are $F=0.45$ and $D =0.80$ together with $H = 9\,F-3\,D$ and $C=1.6$. The $\bar \Sigma^{[n]}_B$ as introduced in (\[def-Zn\]) are measured in units of MeV. Physical meson and baryon masses are used for $M_B$, $M_R$ and $m_Q$. []{data-label="tab:5"}
We turn to the effects of the wave-function factors $Z_B$. As was already demonstrated in Tab. \[tab:1\] there is a significant deviation from the chiral limit value $Z_B\to 1$ implied by the loop contribution to the baryon self energy. This has a significant effect on the set of Dyson equations (\[gap-equation-B\]). To illustrate this further we introduce $\bar \Sigma^{[n]}_B$ and $\bar Z^{[n]}_B$ with $$\begin{aligned}
&& Z^{[n]}_B = 1 -\sum_{k=3}^{n}\, \frac{\partial}{\partial M_B}\,\bar \Sigma_B^{ {\rm bubble}-k} \,, \qquad
\bar \Sigma^{[n]}_B = \sum_{k=3}^n \,\bar \Sigma_B^{ {\rm bubble}-k} / Z^{[n]}_B \,,
\label{def-Zn}\end{aligned}$$ and collect numerical values thereof in Tab. \[tab:5\]. We observe a convincing convergence pattern for all baryons. Note however, that due to the large third order terms for the baryon octet states significant result can be expected only at the accuracy level four and higher.
From this section we conclude that indeed a systematic decomposition of the baryon self energies into chiral moments is feasible and appears well converging. However, the sizes of the fifth order terms are a bit too large so that a full control of the baryon masses accurate at the few MeV level may require the consideration of the ’full’ fifth order contribution, which involves the computation of a class of two-loop diagrams.
Low-energy parameters from QCD lattice data
===========================================
0.3cm In the previous chapter we illustrated that the power counting domain (PCD) of the chiral expansion for the baryon octet and decuplet masses may be surprisingly large encompassing most likely the physical quark masses. In order to demonstrate such a behavior it is useful to reorganize the chiral expansion. If its various moments are expressed in terms of the physical meson and baryon masses the first few terms are able to reproduce the full one-loop expressions with increasing accuracy. We would like to challenge this picture by a realistic parameter set that includes all low-energy parameters relevant at N$^3$LO and that is adjusted to a QCD lattice data set on the baryon masses at different sets of unphysical quark masses.
In the previous analysis [@Lutz:2014oxa] a large set of QCD lattice data points were quite accurately reproduced and in part predicted. Unfortunetely, the underlying set of low-energy parameters can not be so easily used for our purpose. In principle one may envisage a matching of the scheme used in [@Lutz:2014oxa] with the one developed here. However, since such a matching would rely necessarily on an expansion in powers of $(\Delta/M)$, the extremely poor convergence properties of this expansion make a quantitative application of such a matching futile. Moreover, as was illustrated in Section 3.4 the effects of the baryon’s wave-function renormalization were not sufficently well treated in our previous work [@Lutz:2014oxa]. In any case we deem the scheme proposed here superior to the one in [@Lutz:2014oxa]. While our approach is strictly consistent with chiral constraints in the chiral regime with $m_Q < \Delta$ these constraints are realized in [@Lutz:2014oxa] only at a formal level to some order in $(\Delta/M)^n$.
The chiral extrapolation scheme
-------------------------------
0.3cm
We adjust the low-energy parameters to a set of QCD lattice data. While this can in principle be done at different chiral orders, we do so using the subtracted loop expressions (\[result-loop-8\], \[result-loop-10\]) in (\[gap-equation-B\]) supplemented by (\[def-tadpole\], \[eliminate-mu\]) and the finite volume corrections of the scalar loop expressions as worked out previously in [@Lutz:2014oxa]. The good convergence properties of our chiral expansion as formulated in terms of the physical meson and baryon masses we take as a reasonable justification of this strategy.
Moreover, despite the rapid convergence properties of the reordered chiral expansion we found that the fifth order contributions from the bubble-loop can still be sizable of the order of 20 MeV. Therefore it is a matter of convenience to perform our fits using the one-loop functions as detailed in Chapter 3. Therewith the finite volume corrections specific to the various chiral moments, whose derivation would require further tedious algebra, are not required. It should also be mentioned that the complete fifth order expression (N$^4$LO) would receive further contributions from a set of two-loop diagrams as explored for instance in [@Schindler:2007dr]. In a complete study such two-loop diagrams, however, also including the decuplet degrees of freedom, should be considered. This is beyond the scope of the present work and not yet available in the literature.
Fit 1 Fit 2 Fit 3
--------------------------- --------- --------- ---------
$10^3\,(L_4 - 2\,L_6)\, $ -0.0462 -0.0405 -0.0488
$10^3\,(L_5 - 2\,L_8)\, $ -0.0892 -0.1084 -0.1103
$10^3\,(L_8 + 3\,L_7)\, $ -0.4808 -0.4828 -0.4872
: Low-energy parameters from a fit to the baryon octet and decuplet masses of the PACS, LHPC, HSC, NPLQCD, QCDSF-UKQCD and ETMC groups as described in the text. All parameters $L_i$ are scale dependent given at $\mu =$ 770 MeV together with $f =92.4$ MeV (see (\[meson-masses-q4\])). []{data-label="tab:FitParametersA"}
It is pointed out that the values of the low-energy constants $L_4 -2\,L_6, L_5 -2\,L_8$ have a crucial impact on the description of the baryon masses from lattice QCD simulations [@Lutz:2014oxa]. In our approach we use the published pion and kaon masses from a given lattice ensemble. With (\[meson-masses-q4\]) the later translate into the quark masses that are used in our chiral formulae for the baryon masses. In turn the three combinations of Gasser and Leutwyler low-energy parameters as collected in Tab. \[tab:FitParametersA\] are determined from a fit to the baryon masses. Note however, that for any given choice of $f, L_4 - 2\,L_6$ and $L_5 -2\,L_8$ the value of $L_8 + 3\,L_7$ is determined by the physical eta-meson mass at the one-loop level (\[meson-masses-q4\]). With Tab. \[tab:FitParametersA\] significant results are obtained for the low-energy constants. In contrast their latest determination from the phenomenology of the meson sector suffers from substantial uncertainties [@Bijnens:2011tb; @Bijnens:2014lea]. For instance the value of the combination $L_5 -2\,L_8$ may be positive or negative. There is yet a further interesting issue to be discussed. From Tab. \[tab:FitParametersA\] one may infer the quark-mass ratio $m_s/m \simeq 26.1 \pm 0.1$, which comes close to the empirical value claimed in the PDG within a $5 \%$ uncertainty only [@PDG].
Three fit scenarios
-------------------
0.3cm From the many distinct fits we document three typical scenarios that all rely on the large-$N_c$ sum rules (\[res-FDCHs\], \[def-combinations\], \[ces-subleading\], \[Q4-subleading\]) as they are recalled in Chapter 2 at subleading order. This is supplemented by the renormalization scale-invariance conditions (\[ces-subleading-Gamma\]). While Fit 1 is characterized by insisting on the two identities $$\begin{aligned}
b_F + b_D = d_D/3 \,, \qquad \qquad d_0 + d_D/3 - b_0 = 2\,b_D \,,
\label{rescall-b-Nc}\end{aligned}$$ Fit 2 insists on only the first of the two equations in (\[rescall-b-Nc\]). Last, in Fit 3 all low-energy parameters $b_0, b_D, b_F$ and $d_0, d_D$ are kept independent. We remind the reader that given the imposed large-$N_c$ relations there are altogether only 8 independent low-energy parameters that drive the terms proportional to the square of the quark masses. They are complemented by 7 degrees of freedom that determine the symmetry conserving two-body counter terms.
How to fit the lattice data
---------------------------
0.3cm
The applied strategy how to arrive at a realistic parameter set is described in the following. We first identify the lattice data set used in our fits. Only published and documented results for QCD lattice simulations with three light flavours at pion and kaon masses smaller than $600$ MeV are considered. That leaves data sets from PACS, LHPC, HSC, NPLQCD, QCDSF-UKQCD and ETMC [@PACS-CS2008; @LHPC2008; @HSC2008; @NPLQCD:2011; @Bietenholz:2011qq; @Alexandrou:2013joa]. We are aware of the recent lattice ensembles of the CLS group with 2+1 flavors based on nonperturbatively improved Wilson fermions [@Bruno:2014jqa; @Bali:2016umi; @Bruno:2016plf]. Results for baryon masses are not available yet. Based on the published pion and kaon masses of the various ensembles [@Bruno:2016plf] we will attempt to make a prediction of the baryon masses as they follow from our sets of low-energy parameters.
Like in the previous work [@Lutz:2014oxa] we use the empirical values of the physical baryon octet and decuplet masses for a determination of the lattice scales. All of our parameter sets are tuned as to reproduce the isospin averaged baryon masses from the PDG [@PDG] within an error window of at most three MeV. It is not our purpose to show that QCD lattice simulations are consistent with the empirical baryon masses, rather we assume the latter and wish to extract from the lattice data the low-energy parameters of the chiral Lagrangian.
Fit 1 Fit 2 Fit 3 lattice group
------------------------------------------------------- -------- -------- -------- ----------------------------------
$a_{\rm PACS-CS}\, \hfill \mathrm{[fm]}$ 0.0943 0.0929 0.0925 0.0907(14) [@PACS-CS2008]
$a_{\rm LHPC} \, \hfill \mathrm{[fm]}$ 0.1318 0.1289 0.1285 0.1241(25) [@LHPC2008]
$a_{\rm HSC} \, \hfill \mathrm{[fm]}$ 0.1229 0.1218 0.1225 0.1229(7) [@HSC2008]
$a_{\rm QCDSF-UKQCD}\, \hfill \mathrm{[fm]}$ 0.0759 0.0758 0.0758 0.0765(15) [@Bietenholz:2011qq]
$a^{\beta =1.90}_{\rm ETMC}\, \hfill \mathrm{[fm]}$ 0.1030 0.1019 0.1016 0.0934(37) [@Alexandrou:2013joa]
$a^{\beta =1.95}_{\rm ETMC}\, \hfill \mathrm{[fm]}$ 0.0921 0.0920 0.0920 0.0820(37) [@Alexandrou:2013joa]
$a^{\beta =2.10}_{\rm ETMC}\, \hfill \mathrm{[fm]}$ 0.0680 0.0679 0.0680 0.0644(26) [@Alexandrou:2013joa]
systematic error
$\chi^2_{\rm PACS-CS}/N$ 1.7241 1.0507 0.8253 10 [MeV]{}
2.3080 1.4678 1.1703 5 [MeV]{}
$\chi^2_{\rm LHPC}/N$ 0.9029 2.1253 1.4668 20 [MeV]{}
6.8158 5.6362 3.7141 10 [MeV]{}
19.842 17.454 12.216 5 [MeV]{}
$\chi^2_{\rm HSC}/N$ 0.7954 0.7631 0.7367 10 [MeV]{}
1.0224 0.9916 0.9453 5 [MeV]{}
$\chi^2_{\rm NPLQCD}/N$ 0.4100 0.3185 0.4077 10 [MeV]{}
1.2859 0.9788 1.2473 5 [MeV]{}
$\chi^2_{\rm QCDSF-UKQCD}/N$ 0.6776 0.6741 0.7045 10 [MeV]{}
0.9174 0.9195 0.9353 5 [MeV]{}
$\chi^2_{\rm ETMC}/N$ 0.9744 0.9772 1.1405 10 [MeV]{}
1.2944 1.2673 1.5210 5 [MeV]{}
: Our determination of the lattice scale for PACS-CS, LHPC, HSC, NPLQCD, QCDSF-UKQCD and ETMC with $a_{\rm HSC} = a_{\rm NPLQCD}$. The set of lattice data fitted is described in the text. The corresponding low-energy parameters of Fit 1-3 are given in Tab. \[tab:FitParametersA\] - \[tab:FitParametersD\]. []{data-label="tab:lattice-scale"}
We do not implement discretization effects in our chiral extrapolation approach since the majority of the data sets is available at a single beta value only. As a consequence a systematic error analysis is not possible yet in our present study. In order to cope with this deficiency we supplement the statistical errors given by the lattice groups by a systematic error in mean quadrature. A lower limit for such an error may be put by the isospin splittings of the baryon octet and decuplet masses, which is in the range of 1-4 MeV. Surely the budget for the systematic error should further increase from discretization effects as well as from the absence of chiral N$^4$LO effects. Following [@Lutz:2014oxa] we perform fits at different ad-hoc values for the systematic error. We would argue that once this error is sufficiently large the $\chi^2$ per data point should be close to one. By this method we may estimate the net size of the systematic error in our chiral extrapolation approach.
We found considerable tension amongst the world lattice data set which prohibits a significant fit with a common systematic error estimate. A natural solution to this misery arises if a larger error budget is assigned to the data of LHPC. We note that this is the case even if we ignore the already previously in [@Lutz:2014oxa] questioned data on the baryon decuplet masses of this group. We would expect that discretization errors are largest for the baryon data of LHPC. Their studies are the only ones that are based on a mixed action framework with domain-wall valence quarks but staggered sea-quark ensembles generated by MILC [@Orginos:1999cr; @Orginos:1998ue; @MILC2001; @MILC2004]. In anticipation of the details of our fit results we find the systematic error to be about 10 MeV for all lattice groups but LHPC, for which our estimate comes at about 20 MeV.
To actually perform such fits is quite a computational challenge. For any set of the low-energy parameters eight coupled non-linear equations are to be solved for each lattice configuration considered. We chose to apply the evolutionary algorithm of GENEVA 1.9.0-GSI [@Geneva]. Any of our attempts to use a gradient approach as offered for instance by MINUIT did not lead to any competitive results. We submitted typical GENEVA runs with a population size of 8000 on 700 parallel CPU cores. The runtime of fits last to about a week and more.
In Tab. \[tab:lattice-scale\] we show the consequence of three different parameter sets for the spatial lattice scales. The values from the three fits are consistent with the corresponding values determined from the different lattice groups given their uncertainties. The spread implied by the different fits is much smaller than the uncertainty of the lattice scales given by the lattice groups with the exception of the LHPC data. As was emphasized in [@Lutz:2012mq; @Alexandrou:2013joa; @Lutz:2014oxa] the physical baryon masses pose a strong constraint on the precise value of the QCD lattice scale. The table illustrates the quality of the various fits by providing the chi-square ($\chi^2$) per number of fitted data point ($N$). Two values are provided in the table for all collaborations with the exception of LHPC, for which three cases are provided. While the upper value is computed with respect to a systematic error of 10 MeV, the lower one with respect to 5 MeV. For the LHPC the upper value corresponds to the additional 20 MeV. All $\chi^2/N$ values are close to one at the advocated estimates for the systematic error of 10 MeV for the PACS-CS, HSC, QCDSF-UKQCD, NPLQCD, ETMC and 20 MeV for the data of LHPC.
Baryon masses on QCD lattice ensembles
--------------------------------------
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Let us illustrate our results with a direct comparison to the lattice data. The following series of figures is based on Fit 3 and well illustrates our conclusions. In all figures the lattice data are shown only with their statistical errors as provided by the collaborations. Our results are presented with open symbols always that lie on top of the data points. First the PACS-CS and LHPC data are scrutinized with Fig. \[fig:lattice-1\] and Fig \[fig:lattice-2\], where the baryon octet and decuplet masses are compared with the results of Fit 3. Note that while the PACS-CS data are based on 32$^3$ lattices, the LHPC data on 20$^3$ ensembles. There are three comments we wish to make here. As was anticipated the description of the PACS-CS data is significantly better than the LHPC data. Note that we did not consider an additional set of masses from PACS-CS at $m_\pi \simeq 150$ MeV. The evaluation of finite volume effects is difficult to fully control, since the product $ m_\pi\, L \simeq 2 $ is unfavorably small. The considerable tension amongst the two data sets is most clearly illustrated by the results for the decuplet masses. For the $\Delta$, $\Sigma^*$ and $\Xi^*$ masses of LHPC one may speculate that the temporal lattice separation was not sufficiently large so that the asymptotic exponential mass was not reached yet in their mass determination. This possible explanation is less likely for the $\Omega$ mass, where we expect a significant underestimated mass from LHPC. Here a comparison with the results of PACS-CS may be instructive. For instance, the LHPC ensemble at the pion mass of about 347 MeV has an associated kaon mass of about 587 MeV. This is to be compared to the PACS-CS ensemble at pion mass 292 MeV, which comes with a kaon mass of about 586 MeV. It is striking to see that the $\Omega$ baryon masses of the two ensembles are split nevertheless by almost 100 MeV. We take this as a hint that there indeed must be significant discretization effects in the LHPC ensembles. We note that the chisquare values for the LHPC ensembles in Tab. \[tab:FitParametersA\] include the four baryon octet masses together with the $\Omega$ mass only. Also in addition the $\Delta, \Sigma^*$ and $\Xi^*$ masses were not considered in the chisquare of the previous study [@Lutz:2014oxa].
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We continue with Fig. \[fig:lattice-3\], where we present our results for the HSC ensembles on 16$^3$ and 24$^3$ lattices. For all ensembles presented a convincing reproduction of the lattice data is achieved. Additional studies on the ensemble at pion mass 390 MeV were generated by NPLQCD, for which we offer Fig. \[fig:lattice-4\]. Such data are at four different lattice volumes, however only for the baryon octet masses. The lattice data are reproduced well for all states with possibly some reservation for the $\Sigma$. Incidentally, for the latter state the plateau signals as shown in Fig. 9 of [@NPLQCD:2011] suffer from sizable fluctuations in particular on the 32$^3$ ensemble. If compared to the signals from the four octet states on the 24$^3$ lattices the plateau is much less pronounced and stable. See for instance the $\Lambda $ in Fig. 7 of [@NPLQCD:2011]. We note that the qualitative pattern of Fig. \[fig:lattice-3\] remains through all of our three fit scenarios.
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Consider the ensembles of QCDSF-UKQCD, that are generated on 16$^3$, 24$^3$ and 32$^3$ lattices. In Fig. \[fig:lattice-5\] the baryon masses are shown in application of the lattice scales taken from Fit 3 as given in Tab. \[tab:FitParametersA\]. An excellent description of all lattice points is achieved. For more discussions, in particular on some decuplet masses, we refer to the detailed previous study [@Lutz:2014oxa].
It remains to illustrate our results for the ensembles of the ETMC, which generated baryon masses at different lattice scales and volumes as summarized in Fig. \[fig:lattice-7\]. In the previous study [@Lutz:2014oxa] their baryon masses were predicted almost quantitatively based on the knowledge of the pion and kaon masses of the ensembles only. This came as a great surprise to the community and deserves further studies. With our current fits based on a further improved chiral extrapolation framework a full quantitative description is achieved, given, however, the assumption that the LHPC ensembles indeed suffer from significant discretization effects. In the two figures results for all ensembles of ETMC are included, also for those for which their baryon masses are so far not derived. With our figures such masses are to be taken as predictions of our chiral extrapolation studies which await confirmation or rejection.
Estimates for low-energy parameters
-----------------------------------
0.3cm
We turn to the low-energy parameters determined by our three fits. They fall into two classes. In Tab. \[tab:FitParametersB\] and Tab. \[tab:FitParametersC\] we collect parameters that are scale invariant and in Tab. \[tab:FitParametersD\] those that run on the renormalization scale $\mu$. Given our particular self consistent summation scheme all baryon masses arise as $\mu$ independent quantities. It is emphasized that our results are heavily relying on the large-$N_c$ sum rules presented in Chapter 2 in great detail. Even at subleading order in the $1/N_c$ expansion the number of free fit parameters is reduced to a great extent and only therefore significant results from the lattice data set can be deduced. Our prime interest are the parameters listed in Tab. \[tab:FitParametersB\] and Tab. \[tab:FitParametersC\] since they are of central importance for coupled-channel computations of low-energy meson-baryon scattering based on the chiral Lagrangian.
We refrain from providing statistical errors in the parameters being not relevant. The number of considered lattice data points of about 300 makes the statistical error negligible. Any uncertainty is driven by systematic effects that are not fully under control. The most reasonable we can do is to offer a set of distinct scenarios as we do with our Fit 1-3.
[l|rrr]{} & Fit 1 & Fit 2 & Fit 3\
$ M\;\;$ & 0.8796 & 0.8745 & 0.8692\
$\Delta $& 0.3510 & 0.3724 & 0.3673\
\
$ b_0\, \hfill \mathrm{[GeV^{-1}]}$ & -0.6784 & -0.6805 & -0.6911\
$ b_D\, \hfill \mathrm{[GeV^{-1}]}$ & 0.0788 & 0.0820 & 0.0761\
$ b_F\, \hfill \mathrm{[GeV^{-1}]}$ & -0.3281 & -0.3409 & -0.3281\
$ d_0\, \hfill \mathrm{[GeV^{-1}]}$ & -0.2714 & -0.2331 & -0.2595\
$ d_D\, \hfill \mathrm{[GeV^{-1}]}$ & -0.7479 & -0.7768 & -0.7533\
\
$F$ & 0.4893 & 0.4849 & 0.4858\
$D$ & 0.7408 & 0.7453 & 0.7442\
$C$ & 1.4815 & 1.4905 & 1.4884\
$H$ & 2.1809 & 2.1285 & 2.1395\
[l|rrr]{} & Fit 1 & Fit 2 & Fit 3\
$\bar g^{(S)}_0\,\hfill\mathrm{[GeV^{-1}]}$ & -7.9775 & -7.9905 & -8.0106\
$\bar g^{(S)}_1\,\hfill\mathrm{[GeV^{-1}]}$ & 0.2632 & 0.7972 & 0.7894\
$\bar g^{(S)}_D\,\hfill\mathrm{[GeV^{-1}]}$ & -1.0381 & -1.2850 & -1.3066\
$\bar g^{(S)}_F\,\hfill\mathrm{[GeV^{-1}]}$ & -4.4782 & -5.2778 & -4.6855\
$\bar h^{(S)}_1\,\hfill\mathrm{[GeV^{-1}]}$ & -3.3318 & -2.5412 & -3.2253\
$\bar h^{(S)}_2\,\hfill\mathrm{[GeV^{-1}]}$ & 0.0000 & 0.0000 & 0.0000\
$\bar h^{(S)}_3\,\hfill\mathrm{[GeV^{-1}]}$ & -8.1001 & -9.8693 & -9.0970\
$\bar h^{(S)}_4\,\hfill\mathrm{[GeV^{-1}]}$ & -3.9791 & -3.0050 & -2.9407\
$\bar h^{(S)}_5\,\hfill\mathrm{[GeV^{-1}]}$ & 0.2204 & 1.2208 & 1.2929\
$\bar h^{(S)}_6\,\hfill\mathrm{[GeV^{-1}]}$ & 3.9791 & 3.0050 & 2.9407\
\
$\bar g^{(V)}_0\,\hfill\mathrm{[GeV^{-2}]}$ & -0.0735 & -0.1456 & -0.3197\
$\bar g^{(V)}_1\,\hfill\mathrm{[GeV^{-2}]}$ & -6.7576 & -6.9246 & -6.7135\
$\bar g^{(V)}_D\,\hfill\mathrm{[GeV^{-2}]}$ & 8.8166 & 9.0872 & 9.0061\
$\bar g^{(V)}_F\,\hfill\mathrm{[GeV^{-2}]}$ & -2.0591 & -2.1625 & -2.1445\
$\bar h^{(V)}_1\,\hfill\mathrm{[GeV^{-2}]}$ & 3.9697 & 3.9756 & 3.9915\
$\bar h^{(V)}_2\,\hfill\mathrm{[GeV^{-2}]}$ & 9.9114 & 9.7755 & 9.9144\
$\bar h^{(V)}_3\,\hfill\mathrm{[GeV^{-2}]}$ & -9.9114 & -9.7755 & -9.6922\
Consider first Tab. \[tab:FitParametersB\] where the low-energy parameters that enter the baryon masses at N$^2$LO are listed. Conceptually the most crucial low-energy parameter are the chiral limit values of the baryon masses at $m=m_s = 0$. All of our three fits predict masses of around 875 MeV and 1238 MeV for octet and decuplet states respectively. Such values are somewhat larger than those obtained in the previous most comprehensive analysis [@Lutz:2014oxa]. This was to be expected since as the pion and kaon masses start to get smaller than $\Delta$ the approach used in [@Lutz:2014oxa] looses control and therefore the values of $M$ and $\Delta$ can not be trusted fully. Moreover, one should note that there is very little direct constraints on those limit values since lattice ensembles at small pion [*and*]{} kaon masses are not available so far.
It is interesting to compare the five $Q^2$ parameters in Tab. \[tab:FitParametersB\] with the values collected in Tab. \[tab:FitParameters:N2LO\], where the latter were determined from a N$^2$LO analysis of the physical baryon masses only. We recall that the values from Fit 1 are subject to the large-$N_c$ relations as recalled with $$\begin{aligned}
d_D = 3\,b_D + 3\,b_F \,, \qquad \qquad d_0 = b_0 + b_D - b_F \,.
\label{rescall-b-Nc-B}\end{aligned}$$ Only in Fit 3 all 5 parameters were adjusted in an independent manner. We would conclude that both tables present low-energy parameters reasonably close to each other. Also the spread of the low-energy parameters amongst the three different fits is comfortably small.
In Tab. \[tab:FitParametersB\] we also collected the axial coupling constants of the baryons. In all three fits they are subject to the large-$N_c$ constraint equations $$\begin{aligned}
C = 2\,D \,,\qquad \qquad H = 9\,F -3\,D\,.
\label{reacll-FDHC}\end{aligned}$$ With our fits we explored the impact of variations around the values $F = 0.45$ and $D = 0.80$ used in our N$^2$LO studies. Again we find a small spread amongst the three different fits. Our values are within a reasonable range for $F$ and $D$ that are required to reproduce the empirical axial-vector coupling constants of the baryon octet states [@Okun].
We continue with the set of symmetry preserving low-energy parameters that drive the leading chiral correction in the two-body meson baryon interaction. They are collected in Tab. \[tab:FitParametersC\]. For all three fit scenarios the 17 counter terms are parameterized by 7 operators only, which are detailed at length in Chapter 2. The reader may be reminded that the sum rules do depend on the values of the $b_0, b_D, b_F$ and $d_0, d_D$ counter terms. While Fit 1 is based on the large-$N_c$ scenario II of Chapter 2, Fit 2 and 3 on scenario III and IV respectively. It is interesting to confront our results to the leading order large-$N_c$ scenario I of Chapter 2. At leading order an additional 4 sum rules appear that take the form $$\begin{aligned}
&&\bar h_5^{(S)} = 3\,\bar g_1^{(S } + \bar g_D^{(S)}\,, \qquad\bar h_6^{(S)} = -3\,\bar g_D^{(S)} -\frac{9}{2}\,\bar g_1^{(S)} \,,\qquad
\nonumber\\
&& \bar g_D^{(V)} = - \frac{3}{2}\,\bar g_1^{(V)}\,, \qquad \quad \;\bar h_3^{(V)} = \frac{3}{2}\,\bar g_1^{(V)}\,.
\label{recall-gh-sum}\end{aligned}$$ We find it reassuring that all four relations are approximately realized by our numerical estimates displayed in Tab. \[tab:FitParametersC\]. Using the values for $\bar g_1^{(S)}, \bar g_D^{(S)}$ and $\bar g_1^{(V)}$ we roughly recover the numerical values for $\bar h_5^{(S)}, \bar h_6^{(S)}$ and $ \bar g_D^{(V)}, \bar h_3^{(V)} $. In turn we may state that the overall pattern of the symmetry conserving two-body counter terms is governed by 3 degrees of freedom only. This is an amazing success showing the huge predictive power of large-$N_c$ QCD in hadron physics.
[l|cccc]{} & Fit 1 & Fit 2 & Fit 3\
$c_0\,\hfill\mathrm{[GeV^{-3}]}$ & -0.0776 & -0.0837 & -0.0725\
$c_1\,\hfill\mathrm{[GeV^{-3}]}$ & -0.1133 & -0.1236 & -0.1336\
$c_2\,\hfill\mathrm{[GeV^{-3}]}$ & 0.1229 & 0.1408 & 0.1470\
$c_3\,\hfill\mathrm{[GeV^{-3}]}$ & 0.4464 & 0.4761 & 0.4216\
$c_4\,\hfill\mathrm{[GeV^{-3}]}$ & -0.1818 & -0.2158 & -0.2312\
$c_5\,\hfill\mathrm{[GeV^{-3}]}$ & 0.0929 & 0.0601 & 0.1037\
$c_6\,\hfill\mathrm{[GeV^{-3}]}$ & 0.1414 & 0.1695 & 0.1507\
$\zeta_0\,\hfill\mathrm{[GeV^{-2}]}$ & 0.0114 & -0.0018 & 0.0222\
$\zeta_D\,\hfill\mathrm{[GeV^{-2}]}$ & 0.1119 & 0.1139 & 0.1497\
$\zeta_F\,\hfill\mathrm{[GeV^{-2}]}$ & -0.1103 & -0.1076 & -0.1412\
\
$e_0\,\hfill\mathrm{[GeV^{-3}]}$ & -0.6170 & -0.6386 & -0.5801\
$e_1\,\hfill\mathrm{[GeV^{-3}]}$ & 0.2762 & 0.2055 & 0.1955\
$e_2\,\hfill\mathrm{[GeV^{-3}]}$ & 1.0919 & 1.2743 & 1.1096\
$e_3\,\hfill\mathrm{[GeV^{-3}]}$ & -0.2667 & -0.4670 & -0.3828\
$e_4\,\hfill\mathrm{[GeV^{-3}]}$ & 0.0827 & 0.1133 & 0.0487\
$\xi_0\,\hfill\mathrm{[GeV^{-2}]}$ & 0.2336 & 0.2197 & 0.3131\
$\xi_D\,\hfill\mathrm{[GeV^{-2}]}$ & 0.0046 & 0.0189 & 0.0256\
We note that a meaningful comparison of Tab. \[tab:FitParametersC\] with parameters from available coupled-channel studies like [@Lutz:2001yb], is not possible in a straight forward manner, since at present such computations do not yet consider the baryon decuplet degrees of freedom explicitly. Also a direct comparison with the results of [@Lutz:2014oxa] can only be expected at a qualitative level. It is not straight forward how to match the two distinct schemes in view of the extremely slow convergence of the $\Delta/M$ expansion. Nevertheless, it is assuring to see that similar patterns for the scalar and vector coupling constants emerge. Again the spread in the low-energy parameters as seen in Tab. \[tab:FitParametersC\] amongst the three different fits is comfortably small.
Finally we turn to Tab. \[tab:FitParametersD\], in which we collect all symmetry breaking low-energy constants that derive the quadratic quark mass terms in the baryon self energies. In all three fit scenarios the 12 low-energy constants $c_n$ and $e_n$ are parameterized by eight operators only. Again it is instructive to consider the three additional constraints that arise at the leading order large-$N_c$ scenario I as derived in Chapter 2. We recall the three sum rules $$\begin{aligned}
c_2 = - \frac{1}{2}\,e_1 \,,\qquad c_3 = \frac{1}{2}\,e_1 + \frac{1}{3}\,e_2 \,,\qquad c_4 = \frac{1}{3}\,e_1\,,
\label{recall-c-e}\end{aligned}$$ and find that the numerical estimates collected in Tab. \[tab:FitParametersD\] are qualitatively in line with (\[recall-c-e\]). Using the estimates for $e_1$ and $e_2$ one roughly recovers the values for $c_3$ but only the small magnitude of $c_2$ and $c_4$. Note that such a comparison is scale invariant only if the symmetry conserving counter terms in Tab. \[tab:FitParametersC\] would follow the additional sum rules (\[recall-gh-sum\]), which is not the case for any of the three fit scenarios. Nevertheless we may state that the overall pattern of the symmetry conserving two-body counter terms is governed by 5 degrees of freedom only.
It is left to discuss the wave-function renormalization terms $\zeta_0, \zeta_D,\zeta_F$ and $\xi_0, \xi_D$ as summarized in Tab. \[tab:FitParametersD\]. In all our three fit scenarios the two sum rules $$\begin{aligned}
\xi_D = 3\,\zeta_F + 3\,\zeta_D \,, \qquad \qquad \xi_0 = \zeta_0 + \zeta_D - \zeta_F \,,
\label{rescall-zeta-xi-Nc}\end{aligned}$$ are imposed. As compared to the previous study where the size of such counter terms were estimated from the baryon masses, we observed a significant reduction in the size of such terms. This is expected since in [@Lutz:2014oxa] the way such parameters are used was quite distinct as compared to the present more reliable approach.
We conclude that the spread in the low-energy parameters as advocated in Tab. \[tab:FitParametersB\]-\[tab:FitParametersD\] amongst the three different fits is comfortably small. Given the number of about 300 described lattice data points the number of fit parameters is reasonably small and significant results are established that characterize important low-energy properties of QCD.
[l||c|c|rrr]{} & [@Durr:2011mp] & [@Horsley:2011wr] & Fit 1 & Fit 2 & Fit 3\
$\sigma_{\pi N}$ & $39(4) ^{+ 18}_{- 7} $ & $ 31 (3)(4)$ & 48.81 & 48.38 & 47.56\
$\sigma_{\pi \Lambda}$ & $29(3) ^{+11}_{-5} $ & 24(3)(4) & 52.40 & 58.49 & 57.12\
$\sigma_{\pi \Sigma}$ & $ 28(3) ^{+19}_{-3}$ & 21(3)(3) & 20.55 & 20.37 & 21.21\
$\sigma_{\pi \Xi}$ & $16(2)^{+8}_{-3} $ & 16(3)(4) & 20.02 & 23.79 & 22.87\
\
$\sigma_{s N}$ & $\;\;34(14)^{+28}_{-24} $ & $ 71(34)(59)$ & 42.59 & 52.46 & 22.91\
$\sigma_{s \Lambda}$ & $\;\;90(13) ^{+24}_{-38} $ & 247(34)(69) & 452.26 & 441.84 & 435.88\
$\sigma_{s \Sigma}$ & $ 122(15) ^{+25}_{-36}$ & 336(34)(69) & 279.29 & 285.94 & 291.73\
$\sigma_{s \Xi}$ & $156(16)^{+36}_{-38} $ & 468(35)(59) & 640.47 & 638.52 & 657.13\
\
& [@MartinCamalich:2010fp] & [@Ren:2013oaa] & Fit 1 & Fit 2 & Fit 3\
$\sigma_{\pi \Delta}$ & $55(4)(18) $ & $28(1)(8) $ & 45.16 & 40.21 & 40.98\
$\sigma_{\pi \Sigma^*}$ & $39(3)(13) $ & $22(2)(9) $ & 22.68 & 22.99 & 22.47\
$\sigma_{\pi \Xi^*}$ & $22(3)(7) $ & $11(2)(6) $ & -2.35 & 2.15 & 1.86\
$\sigma_{\pi \Omega}$ & $\;\;5(2)(1) $ & $\;\;5(2)(2) $ & 2.96 & 0.74 & 0.88\
\
$\sigma_{s \Delta}$ & $\;\;56(24)(1) $ & $\;\;88(22)(3) $ & -313.38 &-285.82 & -307.68\
$\sigma_{s \Sigma^*}$ & $160(28)(7) $ & $243(24)(31) $ & 93.85 & 67.06 & 69.87\
$\sigma_{s \Xi^*}$ & $ 274(32)(9)$ & $391(24)(67)$ & 468.32 & 427.30 & 450.41\
$\sigma_{s \Omega}$ & $360(34)(26) $ & $528(26)(101) $ & 125.13 & 171.31 & 151.58\
Sigma terms from a chiral extrapolation
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The pion-nucleon sigma term $\sigma_{\pi N}$ and the strangeness sigma term $\sigma_{sN}$ are defined as follows $$\begin{aligned}
&&\sigma_{\pi N} = m\,\frac{\partial}{\partial m} m_N\,, \qquad \qquad
\sigma_{s N} = m_s\,\frac{\partial}{\partial m_s} m_N\,.
\label{def-sigmapiN}\end{aligned}$$ From the knowledge of the quark-mass dependence of the baryon masses such sigma terms can readily be determined [@Durr:2011mp; @Horsley:2011wr; @Ren:2013dzt; @MartinCamalich:2010fp; @Ren:2013oaa]. On the other hand the size of the pion-nucleon sigma term can be extracted from the pion-nucleon scattering data set. Recently the seminal value of $\sigma_{\pi N}= 45(8)$ MeV established long ago by Gasser, Leutwyler and Sainio in [@Gasser:1990ce] was questioned by an analysis of an updated data set using the Roy-Steiner equations in [@Hoferichter:2016ocj; @RuizdeElvira:2017stg]. A significantly larger value of $\sigma_{\pi N}= 58(5)$ MeV was obtained. This new result triggered further studies from the lattice community which provided a series of direct computations of the sigma terms close to the physical point [@Durr:2015dna; @Bali:2016lvx; @Abdel-Rehim:2016won; @Yang:2015uis]. All of them claim values that appear more consistent with the seminal result of Gasser, Leutwyler and Sainio in [@Gasser:1990ce] rather than the [*large*]{} sigma term scenario of [@RuizdeElvira:2017stg]. It is noteworthy to recall also the previous analysis [@Alvarez-Ruso:2013fza] that obtained $\sigma_{\pi N} =52(3)(8)$ MeV based on a flavour SU(2) extrapolation of a large selection of lattice data for the nucleon mass [@Procura:2006bj].
We consider our previous results on the sigma terms [@Semke:2012gs; @Lutz:2014oxa] outdated. In [@Semke:2012gs] the finite volume effects were not considered yet and only a partial set of lattice data were considered. More critically is the fact that both works are not fully consistent in the chiral regime with $m_\pi < \Delta $. While this does not appear to prohibit a reproduction of the lattice data set, the extrapolation down to the physical pion mass does suffer from significant uncertainties as is illustrated by our current results for the sigma terms. It should be noted also, that as long as the systematic error in the baryon masses on the various lattice ensembles is not available, a full quantitative control on the final error budget of our results is basically impossible.
In Tab. \[tab:sigmaterms\] we present our predictions for the pion- and strangeness sigma terms of the baryon octet and decuplet states based on our parameter sets Fit 1-3. The sigma terms of the baryon octet and decuplet states are defined by analogy with the definition of the sigma terms of the nucleon in (\[def-sigmapiN\]). Since a full estimate of the systematic uncertainties is beyond the scope of this work, we again illustrate uncertainties by providing sigma terms in three different fit scenarios.
Our values for the baryon octet states in Tab. \[tab:sigmaterms\] are compared with two lattice determinations [@Durr:2011mp; @Horsley:2011wr] that rely on a sizable extrapolation of the lattice data down to the physical quark masses. Such extrapolations are quite a challenge and may lead to significant uncertainties. Nevertheless, we note that our values for the non-strange sigma terms are in reasonable range of the lattice results. For the strangeness sigma terms those lattice studies come typically with a large error budget. Still, there appears to be a striking conflict amongst the values obtained by the BMW and QCDSF-UKQCD groups [@Durr:2011mp; @Horsley:2011wr]. Our results are neither close to the values of any of the two groups. A more significant observation is that a recent direct evaluation of the $\chi$QCD group with $\sigma_{\pi N} = 45.9(7.4)(2.8) $ MeV and $\sigma_{s N} = 40.2(11.7)(3.5) $ MeV in [@Yang:2015uis] predicted values in the range of our results. Note that the size of the nucleon’s strangeness content is compatible also with the lattice average $\sigma_{sN}= 40^{+10}_{-10}$ MeV advocated previously in [@Junnarkar:2013ac]
The sigma terms for the baryon decuplet states are compared with two previous extrapolation studies [@MartinCamalich:2010fp; @Ren:2013oaa]. While our results are in range of [@MartinCamalich:2010fp; @Ren:2013oaa] for the pion sigma terms, this is clearly not the case for the strangeness sigma terms. In particular we find striking the large and negative values for the isobar we predict in our study. This hints at a strong and non-linear dependence of this state on the strange quark mass.
[lc|cc|r]{} $\beta $ & $a_{\rm CLS}$ \[fm\] & $m_\pi$ \[MeV\] & $m_K$ \[MeV\] & $N_s$\
3.40 & 0.08636(98)(40) & 420 & 420 & 32\
& & 350 & 440 & 32\
& & 280 & 460 & 32\
& & 220 & 470 & 48\
\
3.55 & 0.06426(74)(17) & 420 & 420 & 32\
& & 280 & 460 & 48\
& & 200 & 480 & 64\
\
3.70 & 0.04981(56)(10) & 420 & 420 & 48\
& & 260 & 470 & 64\
Predictions for baryon masses in CLS ensembles
----------------------------------------------
0.3cm
We consider 9 ensembles of the CLS collaboration at three different $\beta$ values [@Bruno:2016plf]. In Tab. \[tab:CLS\] the characteristics thereof are recalled. Given our parameter sets we compute all baryon masses in the finite box as specified by $N_s$ and the lattice scale estimates of [@Bruno:2016plf].
-0.2cm
Our results are presented with Fig. \[fig:lattice-9\]. The baryon masses are shown based the scenario Fit 3. In order to minimize any possible uncertainty in the lattice scale determination of [@Bruno:2016plf], we show the baryon masses in units of the lattice scale. Here we assume the central value of the lattice scales as recalled in Tab. \[tab:CLS\]. As compared to the Fit 1 and Fit 2 no significant deviations from the masses of Fit 3 are observed in the octet masses. For the decuplet masses our solutions, in particular Fit 1 predicts baryon masses off by at most 5$\%$ from the masses of the Fit 3 scenario. We conclude that we obtained stable and significant results for the baryon masses on the CLS ensembles which await a critical evaluation of the CLS collaboration. The results of CLS may be of importance to unravel possible further systematic uncertainties in the analyzed QCD lattice data set.
Once the CLS collaboration make their results on the baryon masses available we will include their results in our global fit and study the impact of such data on the low-energy constants of QCD.
Summary and outlook {#sec:summary}
===================
We reconsidered the chiral extrapolation of baryon masses based on the three-flavour chiral Lagrangian formulated with the baryon octet and decuplet fields. The main achievements of our work are summarized:
- At N$^3$LO the number of relevant low-energy parameters is quite large. A significant parameter reduction was obtained by the application of large-$N_c$ sum rules. We reviewed all sum rules that are relevant for the chiral extrapolation of the baryon masses. So far unknown subleading terms in the $1/N_c$ expansion were established for the first time.
- A subtraction scheme for the one-loop contributions to the baryon self energies was devised that ensures consistent results in a chiral expansion with either $m_Q \sim M_\Delta -M_N$ or $m_Q \ll M_\Delta -M_N$ with $m_Q$ denoting a meson mass. The significant role played by effects from the baryon wave-function renormalization was emphasized. It was argued that such effects should be considered already at the N$^3$LO level.
- A reordering of terms in the chiral expansion of the baryon masses was suggested that makes the convergence properties more effective. The various moments are expressed in terms of physical meson and baryon masses. It was illustrated that the one-loop contributions to the baryon self energy if expanded in powers of $x=m_Q/M_B$ with $M_B$ and $m_Q$ a physical baryon and meson mass respectively is rapidly converging. Based on the analytic properties of the loop functions such an expansion was proven to converge up to $x=m_Q/M_B < 2$. Flavour breaking effects are considered by an expansion of $d=M_R/M_B -1$ around its chiral limit value $d_0$, where two different types of baryons $B,R$ are involved. The convergence condition $|d-d_0|< |x+d_0|$ was derived and shown to be satisfied by the physical meson and baryon masses in the chiral expansion of the baryon octet masses. For the baryon decuplet states such an expansion is not convergent and a further partial summation scheme is required. Explicit expressions up to chiral order five were derived for all baryon masses at the one-loop level. The novel chiral ordering was successfully tested for physical meson and baryon masses. This suggests a rather large PCD which includes the physical masses of the up, down and strange quarks.
- Results are obtained that are invariant under changes of the renormalization scale. Given the need to formulate the chiral expansion in terms of physical meson and baryon masses this is achieved with a particular rewrite of the contributions form the counter terms using physical masses.
- The set of low-energy parameters was adjusted to QCD lattice data at N$^3$LO, where the low-energy parameters are systematically correlated by large-$N_c$ sum rules. Results from PACS-CS, LHPC, HSC, NPLQCD, QCDSF-UKQCD and ETMC are considered. We observe considerable tension between the PACS-CS and the LHPC data set. The most natural resolution requires a reduction of the LHPC weight in our global fit indicating significant discretization effects. Predictions for baryon masses on ensembles from CLS as well as all low-energy constants that enter the baryon masses at N$^3$LO are made. For the nucleon we then obtain a sigma term of $\sigma_{\pi N} = 48(1)$ MeV and a strangeness content of $\sigma_{sN} = 38(15)$ MeV.
To further substantiate the claimed chiral low-energy parameters it is necessary to take further data on a QCD lattice in particular at unphysical quark masses. In order to consolidate the PCD the chiral extrapolation formulae should be extended to the two-loop level, where the effects of the baryon decuplet degrees of freedom should be considered explicitly. The low-energy parameters determined in our study should be scrutinized in future coupled-channel computations of low-energy meson baryon scattering that consider the baryon octet and decuplet fields simultaneously.
Acknowledgments {#acknowledgments .unnumbered}
===============
M.F.M. Lutz thanks Kilian Schwarz and Jan Knedlik for significant support on distributed computing issues. Particular thanks go to Walter Schön who is operating the HPC cluster at GSI with his department in an outstanding manner. Without the ongoing and constructive interactions with his group this work would not have been possible. We are grateful to Rüdiger Berlich of Gemfony scientific UG for help with their optimization library Geneva. John Bulava and Ulrich Sauerwein are acknowledged for critically reading the manuscript.
Appendix A {#appendix-a .unnumbered}
==========
We collect all kinematic coefficients that enter the chiral decomposition of the one-loop contributions to the baryon octet self energies. All such terms depend on the ratio $\Delta/M$ only. $$\begin{aligned}
&&\alpha_1 = \frac{(2\,M+\Delta)^4}{16\,M^2\,(M+\Delta)^2}\,, \qquad \alpha_3 =\frac{8\,M\,(M +\Delta) +3\,\Delta^2 }{8\,(M+\Delta)^2}\,,
\nonumber\\
&& \alpha_2 =\big(4\,M\,( M+\Delta) +3\,\Delta^2 \big)\,\frac{(2\,M+\Delta)^2}{16\,M^2\,(M+\Delta)^2}\,,\qquad
\alpha_4 = \frac{(2\,M+\Delta )^3}{8\,M\,(M+\Delta)^2}\,,
\nonumber\\
&& \alpha_5 = \frac{4\,M^2+\Delta\,M -\Delta^2}{4\,(M+\Delta)^2}\,,\qquad
\alpha_6 = \frac{M^2}{(M+\Delta)^2}\,,
\nonumber\\ \nonumber\\ \nonumber\\
&& \gamma_1 = \frac{2\,M+ \Delta}{M}\,\log \frac{\Delta\,(2\,M + \Delta)}{(M+ \Delta)^2} \,, \qquad \qquad
\nonumber\\
&& \gamma_2 = - \frac{2\,M^2+ 2\,\Delta\,M+ \Delta^2}{M\,(2\,M+ \Delta)}\,\log \frac{\Delta\,(2\,M + \Delta)}{(M+\Delta)^2}
-\frac{M}{2\,M+\Delta} \,,
\nonumber\\
&& \gamma_3 = \frac{M}{2\,M+ \Delta}\,,\qquad \qquad \gamma_5 = \frac{M\,(M+ \Delta)^2}{(2\,M+ \Delta)^3}\,,
\nonumber\\
&& \gamma_4 = \frac{M^3}{2\,(2\,M+ \Delta)^3} -2\,\frac{M\,(M+ \Delta)^2}{(2\,M+ \Delta)^3}\,\log \frac{\Delta\,(2\,M + \Delta)}{(M+\Delta)^2}\,,
\nonumber\\ \nonumber\\ \nonumber\\
&& \tilde \gamma_1 = \gamma_1- \frac{2\,M+ \Delta}{M}\,\log \frac{2\,\Delta}{M+\Delta} \,,
\nonumber\\
&& \tilde \gamma_2 = \gamma_2 + \frac{2\,M^2 + 2\,\Delta\,M + \Delta^2}{(2\,M+\Delta)\,M}\,\log \frac{2\,\Delta}{M} + \frac{2\,M + \Delta}{4\,M}
\nonumber\\
&& \qquad \qquad+\,2\,\big(\tilde \gamma_3 -\gamma_3\big)\, \log \frac{M+\Delta}{M}\,,
\nonumber\\
&& \tilde \gamma_3 = \gamma_3 - \frac{2\,M^2 + 2\,\Delta\,M + \Delta^2}{2\,M\,(2\,M + \Delta)}\,, \qquad \qquad
\tilde \gamma_5 = 0\,,
\nonumber\\
&& \tilde \gamma_4 = \gamma_4 + \frac{2\,M\,(M + \Delta)^2}{(2\,M+\Delta)^3}\,\log\frac{2\,\Delta}{M}
\nonumber\\
&& \qquad-\, \frac{4\,M^2 + \Delta\,(4\,M + 5\,\Delta)}{32\,M\,(2\,M + \Delta)}+ 2\,\big(\tilde \gamma_5 -\gamma_5\big)\, \log \frac{M+\Delta}{M}\,,
\nonumber\\ \nonumber\\
&& \tilde \alpha_1 = \Delta \,\frac{ \partial }{\partial \Delta} \, \alpha_1 \,\frac{2\,M+ \Delta}{2\,M} \,,
\nonumber\\
&& \tilde \alpha_2 = \Delta^2\,\frac{\partial }{\partial \Delta} \, \frac{\alpha_1 \,\tilde \gamma_2 }{\Delta}\,,\qquad \qquad\;\,
\tilde \alpha_3 = \Delta^2\,\frac{\partial }{\partial \Delta} \,\frac{\alpha_1 \,\tilde \gamma_3 }{\Delta}\, ,
\nonumber\\
&& \tilde \alpha_4 =\Delta\,\gamma_1\,\frac{\partial}{\partial \Delta}\, \alpha_1\,, \qquad \qquad \quad \tilde \alpha_5 = \Delta\,\frac{\partial}{\partial \Delta}\, \alpha_1\,\tilde \gamma_1\,,
\nonumber\\
&& \tilde \alpha_6 = \frac{\Delta^2\, \partial^2 }{\partial \Delta \,\partial \Delta} \,
\Bigg(\alpha_1 \,\frac{2\,M+ \Delta}{2\,M} \Bigg) \,, \qquad \qquad \tilde \alpha_7 = \Delta\,\frac{\Delta^2\,\partial^2 }{\partial \Delta\,\partial \Delta} \, \frac{\alpha_1 \,\tilde \gamma_2 }{\Delta}\,,
\nonumber\\
&& \tilde \alpha_8 = \Delta\,\frac{\Delta^2\,\partial^2 }{\partial \Delta \,\partial \Delta} \,\frac{\alpha_1 \,\tilde \gamma_3 }{\Delta}\, ,\qquad \qquad \qquad \qquad
\nonumber\\ \nonumber\\
&& \tilde \alpha_9 = \gamma_1 \,\frac{\Delta^2\,\partial ^2}{\partial \Delta \,\partial \Delta}\,\alpha_1\,, \qquad \qquad
\tilde \alpha_{10} = \frac{\Delta^2\,\partial^2}{\partial \Delta \,\partial \Delta}\,\alpha_1\,\tilde \gamma_1\,,
\nonumber\\
&& \tilde \alpha_{11} = -\frac{1}{4}\,\alpha_1\,\frac{M}{2\,M+\Delta} + \Big(\alpha_1-\alpha_2 \Big)\,\frac{(2\,M+ \Delta)\,M}{2\,\Delta^2}\,,\end{aligned}$$ While the $\alpha_i$ characterize the chiral expansion of the coefficients in front of $\bar I_{QR}$ and $\bar I_Q$ in (\[result-loop-8\]), the $\gamma_i$ follow from a chiral expansion of $\bar I_{QR}$ with $M_B = M$ and $M_R = M+ \Delta$ and $m_Q < \Delta$. The $\tilde \gamma_n$ follow from the corresponding $\gamma_n$ after subtractions from a chiral expansion of the anomalous term $f^{(d)}_0(x^2)\,f^{(d)}_1(x^2)$ in (\[IQR-x-delta\]). Finally the coefficients $\tilde \alpha_n$ characterize the central results (\[loop-HB-4\]) and \[loop-HB-5\]).
The symmetry breaking term in (\[def-tadpole\]) takes the form
$$\begin{aligned}
\Sigma^{(4-\chi)}_N \!\!\!\!&=&\!\!\! - 4\,B_0 \left( b^{\rm eff}_0\, (2\,m+m_s) + b^{\rm eff}_D\, (m+m_s) + b^{\rm eff}_F\, (m-m_s) \right)
\nonumber \\
\!\!\!\!&\phantom =& \!\!\!-4\,B_0^2\, \Big( c_0\, (2\,m^2 + m_s^2) + c_2\, (m^2+m_s^2) + c_3\, (m^2-m_s^2) \Big)
\nonumber \\
\!\!\!\!&\phantom =& \!\!\! - 2\,B_0\, \Big( \zeta_0\, (2\,m+m_s) + \zeta_D\, (m+m_s)
+ \zeta_F\, (m-m_s) \Big) \Big(M_N - M\Big) \,,
\nonumber \\
\Sigma^{(4-\chi)}_\Lambda \!\!\!\!&=&\!\!\! - 4\,B_0\, \Big(b^{\rm eff}_0\, (2\,m+m_s) + \frac{2}{3}\,b^{\rm eff}_D\, (m+2\,m_s) \Big)
\nonumber \\
\!\!\!\!&\phantom =& \!\!\!- 4\,B_0^2\, \Big( c_0\, (2\,m^2 + m_s^2) + \frac 23 \,c_1\, (m - m_s)^2 + \frac 23 \,c_2\, (m^2 + 2\,m_s^2) \Big)
\nonumber \\
\!\!\!\!&\phantom =& \!\!\!- 2\,B_0\, \Big(\zeta_0\, (2\,m+m_s) + \frac{2}{3}\,\zeta_D\, (m+2\,m_s) \Big) \Big(M_\Lambda - M\Big)\,,
\nonumber \\
\Sigma^{(4-\chi)}_\Sigma\!\!\!\!&=&\!\!\! - 4\,B_0\, \Big(b^{\rm eff}_0\, (2\,m+m_s) + 2\,b^{\rm eff}_D\,m \Big)
\nonumber \\
\!\!\!\!&\phantom =& \!\!\! - 4\,B_0^2\, \Big(c_0\, (2\,m^2+m_s^2) + 2\,c_2\, m^2 \Big)
\nonumber \\
\!\!\!\!&\phantom =& \!\!\!- 2\,B_0\, \Big(\zeta_0\, (2\,m+m_s) + 2\,\zeta_D\,m
\Big) \Big(M_\Sigma - M\Big) \,,
\nonumber \\
\Sigma^{(4-\chi)}_\Xi \!\!\!\!&=&\!\!\! - 4\,B_0\, \Big( b^{\rm eff}_0\, (2\,m+m_s) + b^{\rm eff}_D\, (m+m_s) - b^{\rm eff}_F\, (m - m_s) \Big)
\nonumber\\
\!\!\!\!&\phantom =& \!\!\!- 4\,B_0^2\left( c_0\, (2\,m^2+m_s^2) + c_2\,(m^2 + m_s^2) - c_3\,(m^2 - m_s^2) \right)
\nonumber\\
\!\!\!\!&\phantom =& \!\!\!- 2\,B_0\, \Big( \zeta_0\, (2\,m+m_s) + \zeta_D\,
(m+m_s) - \zeta_F\, (m - m_s) \Big) \Big(M_\Xi - M\Big) \,,
\nonumber\\ \nonumber\\
&& \!\!\!\!\! \!\!\! \!\!\!\!\! \!\!\! b^{\rm eff}_0 = c_6\, B_0\,(2\,m+m_s)\,, \qquad \qquad
b^{\rm eff}_D = c_4\, B_0\,(2\,m+m_s)\,, \qquad
\nonumber\\
&& \!\!\!\!\! \!\!\! \!\!\!\!\! \!\!\! b^{\rm eff}_F = c_5\, B_0\,(2\,m+m_s)\,,
\label{result-counter-terms-octet}\end{aligned}$$ with the low-energy parameters $c_i$. The renormalization scale dependence of the $c_i$ as implied by (\[def-tadpole\]) is $$\begin{aligned}
&& \mu^2\,\frac{d }{d \,\mu^2} \,c_i = -\frac{1}{4}\,\frac{ \Gamma_{c_i}}{(4\,\pi\,f )^2}\,,\end{aligned}$$ with $$\begin{aligned}
&& \Gamma_{c_0} = \frac{20}{3}\,b_0+ 4\,b_D -
\frac{1}{36}\, \Big( 30 \,\bar g_0^{(S)}+9 \,\bar g_1^{(S)}+26 \,\bar g_D^{(S)}\Big)
\nonumber\\
&& \qquad \qquad -\, \frac{M}{144}\, \Big(30\,
\bar g_0^{(V)}+9 \,\bar g_1^{(V)}+26 \,\bar g_D^{(V)}\Big) \,,
\nonumber\\
&& \Gamma_{c_1} = -
\frac{1}{24} \,\Big(4 \,\bar g_1^{(S)}+\bar g_1^{(V)}\, M \Big)\,,
\nonumber\\
&& \Gamma_{c_2} = \frac{2}{3}\,b_D + \frac{1}{16} \,\Big(4\, (\bar g_1^{(S)}+\bar g_D^{(S)})+M\, (\bar g_1^{(V)}+\bar g_D^{(V)})\Big) \,,
\nonumber\\
&& \Gamma_{c_3} = \frac{2}{3}\,b_F +\frac{1}{16} \,\Big(4\, \bar g_F^{(S)}+\bar g_F^{(V)}\, M\Big ) \,,
\nonumber\\
&& \Gamma_{c_4} = \frac{44}{9}\,b_D-\frac{1}{72} \,\Big( 36\, \bar g_1^{(S)}+52 \,\bar g_D^{(S)} + M\,( 9\, \bar g_1^{(V)} + 13\, \bar g_D^{(V)})
\Big)\,,
\nonumber\\
&& \Gamma_{c_5} = \frac{44}{9}\,b_F-\frac{13}{72} \,\Big(4\, \bar g_F^{(S)}+\bar g_F^{(V)}\, M\Big) \,,
\nonumber\\
&& \Gamma_{c_6} = \frac{44}{9}\,b_0+ \frac{1}{432}\,\Big(-264 \,\bar g_0^{(S)}+108\, \bar g_1^{(S)} +32\, \bar g_D^{(S)}
\nonumber\\
&& \qquad \qquad
+ \, M\,\big(-66 \,\bar g_0^{(V)}+27\, \bar g_1^{(V)} +8\, \bar g_D^{(V)} \big)\Big)\,.
\label{res-Gamma-ci}\end{aligned}$$ Large-$N_c$ sum rules for the low-energy parameters $c_n, e_n$ are detailed in (\[ces-subleading\]). Corresponding relations for the $\Gamma_{c_n}, \Gamma_{e_n}$ follow from (\[ces-subleading\]) by the substitution $c_n\to \Gamma_{c_n} $ and $e_n\to \Gamma_{e_n}$.
We derive the form of the anomalous scaling term, $c^{\rm ano}_i$, introduced in (\[def-c-e-ano\], \[c-e-running\]). The prescription (\[eliminate-mu\]) applied to the $(M_R -M_B)\,\bar I_Q$ terms in (\[result-loop-8\]) implies a renormalization of the symmetry breaking counter terms $$\begin{aligned}
&& c^{\rm ano}_i = \frac{1}{4}\,\frac{1}{(4\,\pi\,f )^2}\, \Gamma^{(1)}_{c_i}\,\gamma^{(1)}_c
+ \frac{1}{4}\,\frac{C^2}{(4\,\pi\,f )^2}\, \Big( \Gamma^{(2)}_{c_i}\gamma^{(2)}_c + \Gamma^{(3)}_{c_i}\gamma^{(3)}_c \Big) \,,
\qquad
\nonumber\\
&& \gamma^{(1)}_c = - 4 - \log \frac{M^2}{\mu^2} \,, \qquad \qquad
\gamma^{(2)}_c = -\frac{2}{3}\left(\frac{\partial \Delta\, \alpha_4}{\partial \Delta}\right) \log\frac{\mu^2}{(M+\Delta)^2} \,,
\nonumber\\
&& \gamma^{(3)}_c = -\,\frac{2}{3}\left(\frac{\partial \Delta \,\alpha_4}{\partial M}\right) \log \frac{\mu^2}{(M+\Delta)^2}
- \gamma^{(2)}_c\,.
\nonumber\\
&& \mu^2\,\frac{d }{d \,\mu^2} \,c^{\rm ano}_i = \frac{1}{4}\,\frac{-1}{(4\,\pi\,f )^2}\, \Gamma^{(1)}_{c_i}
+\frac{1}{6}\,\frac{C^2}{(4\,\pi\,f )^2}\,\Bigg\{ \Gamma^{(2)}_{c_i} \,\Big[ 1+ \Delta\,\frac{\partial}{\partial \Delta} \Big]
\nonumber\\
&& \qquad \qquad \; -\, \Gamma^{(3)}_{c_i} \,\Big[ 1 + \Big(1+\frac{\Delta}{M} \Big)\,\Delta\,\frac{\partial}{\partial \Delta }\Big]
\Bigg\}\,\alpha_4\,,
\label{res-c-ano}\end{aligned}$$ with $$\begin{aligned}
&& \Gamma^{(1)}_{c_0} =
- \frac{4}{3} \, b_D \left(D^2+3 \,F^2\right)-8\, b_F\, D\, F \,, \qquad
\Gamma^{(1)}_{c_1} = -\frac{64}{9} \,b_D \,D^2\,,
\nonumber\\
&& \Gamma^{(1)}_{c_2} = \frac{2}{3} \, b_D \left(5 \,D^2+9 \,F^2\right)+12\, b_F\, D\, F \,, \qquad
\nonumber\\
&& \Gamma^{(1)}_{c_3} = \frac{20}{3} \,b_D \,D \,F +\frac{2}{3}\, b_F \left(5\, D^2+9 \,F^2\right)\,, \qquad
\Gamma^{(1)}_{c_4} = \frac{32}{9} \,b_D \,D^2\,, \qquad
\nonumber\\
&& \Gamma^{(1)}_{c_5} = 0 \,, \qquad
\Gamma^{(1)}_{c_6} = -\frac{8}{3} \,b_D \,D^2\,,
\nonumber\\ \nonumber\\
&& \Gamma^{(2)}_{c_0} = - \frac{11}{9}\,d_D \,, \qquad
\Gamma^{(2)}_{c_1} = -\frac{10}{9}\,d_D\,, \qquad
\Gamma^{(2)}_{c_2} = \frac{8}{3}\,d_D\,, \qquad
\nonumber\\
&&\Gamma^{(2)}_{c_3} = -\frac{2}{3}\,d_D\,,\qquad \Gamma^{(2)}_{c_4} = -\frac{2}{9}\,\Big( 9\,d_0 + 8\,d_D\Big)\,, \quad
\nonumber\\
&& \Gamma^{(2)}_{c_5} = \frac{1}{9}\,\Big( 15\,d_0 + 19\,d_D\Big)\,, \qquad \Gamma^{(2)}_{c_6} = \frac{1}{9}\,\Big( 42\,d_0 + 19\,d_D\Big)\,,
\nonumber\\ \nonumber\\
&& \Gamma^{(3)}_{c_0} =-2\,b_D - \frac{5}{3}\,b_F \,, \qquad
\Gamma^{(3)}_{c_1} = -\frac{2}{9}\,\Big(6\,b_D + 15\,b_F \Big)\,, \qquad
\nonumber\\
&& \Gamma^{(3)}_{c_2} = 2\,b_D + 5\,b_F \,, \qquad \Gamma^{(3)}_{c_3} = \frac{1}{3}\,\Big(5\,b_D - 6\,b_F \Big)\,, \qquad
\nonumber\\
&&\Gamma^{(3)}_{c_4} = -\frac{2}{9}\,\Big(9\,b_0 - 3\,b_D + 15\,b_F \Big)\,, \qquad \Gamma^{(3)}_{c_5} = \frac{1}{9}\,\Big(15\,b_0 + 42\,b_F \Big)\,,\qquad
\nonumber\\
&& \Gamma^{(3)}_{c_6} = \frac{1}{9}\,\Big(42\,b_0 + 18\,b_D + 15\,b_F \Big)\,.\end{aligned}$$ We close this Appendix with explicit expressions of the fifth moment of the octet self energy. With $m_{QR}^2 = m_Q^2-(M_R-M_B)^2$ we find $$\begin{aligned}
&&\bar \Sigma^{{\rm bubble}-5}_{B \in [8]} = \!\! \sum_{Q\in [8], R\in [8]}
\left(\frac{m_{QR}}{4\,\pi\,f}\,G_{QR}^{(B)} \right)^2 \Bigg\{ \frac{\pi}{16}\,\frac{m^3_Q}{M_B^2}
- \frac{m^4_Q}{24\,M^3_B}
\nonumber\\
&& \qquad \quad +\,\Big(M_R-M_B\Big)^2\,\Bigg[ \frac{\pi}{4\,m_Q} + \frac{1}{2\,M_B}\,\Big( 2 + 3\,\log \frac{m_Q}{M_R} \Big)\Bigg] \Bigg\}
\nonumber\\
&& \; +\sum_{Q\in [8], R\in [10]}
\left(\frac{m_Q}{4\,\pi\,f}\,G_{QR}^{(B)} \right)^2 \, \Bigg\{ \frac{\tilde \alpha_{11}}{3}\,\frac{\Delta^3}{M^2}\,\log \frac{4\,\Delta^2}{(M+\Delta)^2}
\nonumber\\
&& \qquad \quad + \, \frac{1}{3}\, \Big( \alpha_1- \alpha_2\Big )\,\Bigg( \frac{2\,M+ \Delta}{2\,M}\,\frac{M_R-M_B}{\Delta_B^2}\, m_Q^2\,\log \frac{m_Q^2}{M_R^2}
\nonumber\\
&& \qquad \qquad \quad +\,\big(\gamma_1-\tilde \gamma_1 \big)\,\frac{\Delta_Q^2-\Delta\,\Delta_B }{\Delta_B}- \tilde \gamma_1\, \frac{\Delta_Q^2}{\Delta_B^2}\,\Big( M_R-M_B-\Delta_B\Big) \Bigg)
\nonumber\\
&& \qquad \quad -\,\frac{\tilde \alpha_{11}}{3\,M_B^2}\,\Bigg[ \big(M_R-M_B \big)^3\,\log \frac{m_Q^2}{M_R^2}
+ \Delta_Q^3\,\Big( \log \big( M_R-M_B + \Delta_Q \big)
\nonumber\\
&& \qquad \qquad \quad -\, \log \big(M_R-M_B - \Delta_Q\big) \Big)\Bigg]
\nonumber\\
&& \qquad \quad +\,\frac{m_Q^2\, \Delta_Q^2}{3\,\Delta^3_B} \,\Bigg[\Big(\alpha_2-\alpha_1 \Big)\, \Big( \tilde \gamma_2 +\tilde \gamma_3\,\log \frac{m_Q^2}{M_R^2} \Big)
- \alpha_1\,\Big( \tilde \gamma_4 + \tilde \gamma_5\,\log \frac{m_Q^2}{M_R^2} \Big) \Bigg]
\nonumber\\
&& \qquad \quad + \, \Big(M_R - M_B-\Delta_B \Big)^2\Bigg(\frac{\tilde \alpha_9}{6}\,\frac{\Delta_Q^2}{m_Q^2\,\Delta_B}
-\frac{\tilde \alpha_{10}}{6}\,\frac{\Delta_Q^2}{m_Q^2\,\Delta^2_B}\,\big(M_R-M_B \big)
\nonumber\\
&& \qquad \qquad \quad
- \frac{\tilde \alpha_6}{6\,\Delta_B^2\,m_Q^2}\,\Bigg[
\Big( \Delta_Q^2-\frac{1}{2}\,m_Q^2\Big)\,\big(M_R-M_B\big)\,\log \frac{m_Q^2}{M_R^2}
\nonumber\\
&& \qquad \qquad \quad
+\, \Delta_Q^3\,\Big( \log \big(M_R-M_B + \Delta_Q \big)-\log \big(M_R-M_B - \Delta_Q\big) \Big)
\Bigg]
\nonumber\\
&& \qquad\qquad \quad +\, \frac{1}{6\,\Delta^3_B}\,\Big(-\tilde \alpha_7\,\Delta_Q^2 + \tilde \alpha_8\,m_Q^2\,\log \frac{m_Q^2}{M_R^2}\Big)
\Bigg)
\Bigg\}\,.
\label{loop-HB-5} \end{aligned}$$
Appendix B {#appendix-b .unnumbered}
==========
We collect all kinematic coefficients that enter the chiral decomposition of the one-loop contributions to the baryon decuplet self energies. All such terms depend on the ratio $\Delta/M$ only. $$\begin{aligned}
&&\beta_1 = \frac{(2\,M+\Delta)^4}{16\,M\,(M+\Delta)^3}\,, \qquad \qquad \beta_3 =M\,\frac{8\,M\,(M +\Delta) +3\,\Delta^2 }{8\,(M+\Delta)^3}\,,
\nonumber\\
&& \beta_2 =\big(4\,M\,( M+\Delta) +3\,\Delta^2 \big)\,\frac{(2\,M+\Delta)^2}{16\,M\,(M+\Delta)^3}\,, \qquad
\beta_4 = \frac{(2\,M+\Delta )^3}{8\,(M+\Delta)^3}\,,
\nonumber\\
&& \beta_5 = \frac{4\,M^3+ 5\,\Delta\,M^2 +2\,\Delta^2\,M }{4\,(M+\Delta)^3}\,, \qquad
\beta_6 = \frac{M}{M+\Delta}\,,
\nonumber\\ \nonumber\\ \nonumber\\
&& \delta_1 = -\frac{M\,(2\,M+ \Delta)}{(M+\Delta)^2}\,\log \frac{\Delta\,(2\,M+\Delta)}{M^2}\,, \qquad
\nonumber\\
&& \delta_2 = \frac{M}{2\,M+ \Delta } +M\,\frac{2\,M^2 + 2\,\Delta\,M+\Delta^2}{(2\,M + \Delta )\,(M+ \Delta )^2}\,
\log \frac{\Delta\,(2\,M+ \Delta)}{M^2} \,,
\nonumber\\
&& \delta_3 = - \frac{M}{2\,M+\Delta } \,, \qquad \qquad \qquad \delta_5 = -\frac{M^3}{(2\,M+\Delta )^3}\,,
\nonumber\\
&& \delta_4 =- \frac{M\,(M+\Delta)^2}{2\,(2\,M+ \Delta)^3 }
+ \frac{2\,M^3 }{(2\,M + \Delta )^3}\,\log \frac{\Delta\,(2\,M+ \Delta)}{M^2} \,,
\nonumber\\ \nonumber\\ \nonumber\\
&& \tilde \delta_1 = \delta_1 +\frac{M\,(2\,M+ \Delta)}{(M+\Delta)^2}\, \log \frac{2\,\Delta}{M} \,,
\nonumber\\
&& \tilde \delta_2 = \delta_2 - \frac{M\,(2\,M^2 + 2\,\Delta\,M + \Delta^2)}{(2\,M+\Delta)\,(M+\Delta)^2}\,\log \frac{2\,\Delta}{M+\Delta}
\nonumber\\
&& \qquad -\, \frac{M\,(2\,M + \Delta)}{4\,(M +\Delta)^2}- 2\,\big(\tilde \delta_3 -\delta_3\big)\, \log \frac{M+\Delta}{M}\,,
\nonumber\\
&& \tilde \delta_3 = \delta_3 + \frac{M\,(2\,M^2 + 2\,\Delta\,M + \Delta^2)}{2\,(M +\Delta)^2\,(2\,M + \Delta)}\,, \qquad \qquad
\tilde \delta_5 = 0\,,
\nonumber\\
&& \tilde \delta_4 = \delta_4 - \frac{2\,M^3}{(2\,M+\Delta)^3}\,\log\frac{2\,\Delta}{M+\Delta}
\nonumber\\
&& \qquad +\, \frac{M\,(4\,M^2+4\,\Delta\,M+5\,\Delta^2)}{32\,(M+\Delta)^2\,(2\,M + \Delta)}
- 2\,\big(\tilde \delta_5-\delta_5\big)\, \log \frac{M+\Delta}{M}\,,
\nonumber\\ \nonumber\\
&& \tilde \beta_1 =\frac{M+\Delta}{M}\,\Delta\,\frac{\partial }{\partial \Delta} \,\beta_1 \,\frac{(2\,M+ \Delta)\,M}{2\,(M+\Delta)^2} \,,
\label{def-hat-alpha} \\
&& \tilde \beta_2 = \Delta^2\,\frac{\partial }{\partial \Delta} \, \frac{M+\Delta}{M}\,\frac{\beta_1 \,\tilde \delta_2 }{\Delta}\,, \qquad \qquad \quad \;
\tilde \beta_3 = \Delta^2\,\,\frac{\partial }{\partial \Delta} \, \frac{M+\Delta}{M}\,\frac{\beta_1 \,\tilde \delta_3 }{\Delta}\, ,
\nonumber\\
&& \tilde \beta_4 = \frac{\Delta}{M}\,\frac{(M+\Delta)^2}{M}\,\delta_1\,\frac{\partial}{\partial \Delta}\, \frac{M\,\beta_1}{M+\Delta}\,, \qquad
\tilde \beta_5 = \Big( 1+ \frac{\Delta}{M}\Big)\,\Delta\,\frac{\partial}{\partial \Delta}\,\beta_1\,\tilde \delta_1 \,,
\nonumber\\
&& \tilde \beta_6 = D_{\Delta \Delta}\,\frac{(2\,M+ \Delta)\,M}{2\,(M+\Delta)^2}\,\beta_1 \,, \qquad \qquad
\tilde \beta_7 = \frac{\Delta}{M+\Delta}\,D_{\Delta \Delta} \,
\frac{M+\Delta }{\Delta}\,\beta_1 \,\tilde \delta_2 \,,\qquad \quad
\nonumber\\
&& \tilde \beta_8 = \frac{\Delta}{M+\Delta}\,D_{\Delta \Delta} \,
\frac{M+\Delta }{\Delta}\,\beta_1 \,\tilde \delta_3\,,
\nonumber\\
&& \tilde \beta_9 = \delta_1\,\frac{M+\Delta}{M}\, D_{\Delta \Delta} \,\frac{M\,\beta_1}{M+\Delta} \,, \qquad \qquad
\tilde \beta_{10} =D_{\Delta \Delta} \,\beta_1\,\tilde \delta_1 \,,
\nonumber\\
&& \tilde \beta_{11} = -\frac{1}{4}\,\beta_1 \,\frac{M}{2\,M + \Delta}+ \Big( \beta_1- \beta_2\Big )\,\frac{(2\,M+ \Delta)\,M}{2\,\Delta^2} \,,
\nonumber\\ \nonumber\\
&& \qquad \qquad D_{\Delta \Delta} = \frac{(M+\Delta)^2}{M^2}\,\Big( \frac{\Delta^2\, \partial^2 }{\partial \Delta \,\partial \Delta}
+\frac{2\,\Delta}{M+\Delta}\,\frac{\Delta \,\partial }{\partial \Delta} \Big)\,,\end{aligned}$$ While the $\beta_i$ characterize the chiral expansion of the coefficients in front of $\bar I_{QR}$ and $\bar I_Q$ in (\[result-loop-10\]), the $\delta_i$ follow from a chiral expansion of $\bar I_{QR}$ with $M_B = M+ \Delta$ and $M_R = M$ and $m_Q < \Delta$. Again the $\tilde \delta_n$ follow from the corresponding $\delta_n$ after subtractions from a chiral expansion of the anomalous term $f^{(d)}_0(x^2)\,f^{(d)}_1(x^2)$ in (\[IQR-x-delta\]). Finally the coefficients $\tilde \alpha_n$ characterize the central results (\[loop-HB-4-B\]) and \[loop-HB-5-B\]).
Consider the symmetry breaking counter terms $$\begin{aligned}
\Sigma^{(4-\chi)}_\Delta \!\!\!\!&=&\!\!\! - 4\,B_0\, \Big( d^{\rm eff}_0\, (2\,m+m_s) + d^{\rm eff}_D\, m\Big)
\nonumber\\
\!\!\!\!&\phantom =& \!\!\! - 4\,B_0^2\, \Big( e_0\,(2\,m^2 + m_s^2) + e_2\, m^2 \Big)
\nonumber\\
\!\!\!\!&\phantom =& \!\!\! - 2\,B_0\, \Big( \xi_0\, (2\,m+m_s) +
\xi_D\, m\Big) \Big(M_{\Delta } - (M+\Delta)\Big) \,,
\nonumber \\
\Sigma^{(4-\chi)}_{\Sigma^*} \!\!\!\!&=&\!\!\! - 4\,B_0\, \Big( d^{\rm eff}_0\, (2\,m+m_s) + \frac{1}{3} \,d^{\rm eff}_D\, (2\,m+m_s) \Big)
\nonumber \\
\!\!\!\!&\phantom =& \!\!\!- 4\,B_0^2\, \Big( e_0\, (2 \,m^2 + m_s^2) + \frac 13 \,e_1\, (m - m_s)^2 + \frac 13\, e_2\,(2\,m^2 + m_s^2) \Big)
\nonumber \\
\!\!\!\!&\phantom =& \!\!\!- 2\,B_0\, \Big( \xi_0\,
(2\,m+m_s) + \frac{1}{3}\, \xi_D\, (2\,m+m_s) \Big)
\Big(M_{\Sigma^*} - (M+\Delta)\Big)\,,
\nonumber \\
\Sigma^{(4-\chi)}_{\Xi^*} \!\!\!\!&=&\!\!\! - 4\,B_0\, \Big( d^{\rm eff}_0\, (2\,m+m_s) + \frac{1}{3} \,d^{\rm eff}_D\, (m+2\,m_s) \Big)
\nonumber \\
\!\!\!\!&\phantom =& \!\!\!-4\,B_0^2\, \Big( e_0\, (2\,m^2 + m_s^2) + \frac 13\, e_1\, (m - m_s)^2 + \frac 13\, e_2\, (m^2 + 2\,m_s^2) \Big)\,,
\nonumber \\
\!\!\!\!&\phantom =& \!\!\!- 2\,B_0\, \Big( \xi_0\, (2\,m+m_s)
+ \frac{1}{3} \,\xi_D\, (m+2\,m_s) \Big) \Big(M_{\Xi^*} - (M+\Delta)\Big)\,,
\nonumber \\
\Sigma^{(4-\chi)}_\Omega \!\!\!\!&=&\!\!\! - 4\,B_0\, \Big( d^{\rm eff}_0\, (2\,m+m_s) + d^{\rm eff}_D\, m_s \Big)
\nonumber \\
\!\!\!\!&\phantom =& \!\!\! - 4\, B_0\, \Big( e_0\, (2\,m^2+m_s^2) + e_2\, m_s^2 \Big)
\nonumber \\
\!\!\!\!&\phantom =& \!\!\! - 2\,B_0\, \Big( \xi_0\, (2\,m+m_s) +
\xi_D\, m_s \Big) \,\Big(M_\Omega - (M+\Delta)\Big)\,,
\nonumber\\
&& \!\!\!\!\! \!\!\! \!\!\!\!\! \!\!\! d^{\rm eff}_0 = e_4 \,B_0\,(2\,m+m_s),\qquad \qquad d^{\rm eff}_D = e_3\, B_0\,(2\,m+m_s)\,,
\label{result-counter-terms-decuplet}\end{aligned}$$ with $$\begin{aligned}
&& \mu^2 \,\frac{d}{d\,\mu^2}\,e_i = -\frac{1}{4}\,\frac{\Gamma_{e_i}}{(4\,\pi\,f )^2} \,,
\nonumber\\
&& \Gamma_{e_0} = \frac{20}{3}\,d_0+2\,d_D - \frac{1}{18}\,\Big(15\, \tilde h_1^{(S)}+13 \,\tilde h_2^{(S)}+9\, \tilde h_3^{(S) }
\Big)
\nonumber\\
&& \qquad -\, \frac{1}{72}\,( M+\Delta ) \,\Big( 15 \,\bar h_1^{(V)}+13\,\bar h_2^{(V)} +9\, \bar h_3^{(V)} \Big) \,,
\nonumber\\
&& \Gamma_{e _1} = -\frac{1}{3} \,\tilde h_3^{(S)} - \frac{1}{12} \,( M+\Delta ) \,\bar h_3^{(V)} \,,
\nonumber\\
&& \Gamma_{e_2} = \frac{2}{3}\,d_D + \frac{1}{2}\,\Big(\tilde h_2^{(S)}+\tilde h_3^{(S)}\Big)+
\frac{1}{8}\,( M+\Delta )\, \Big( \bar h_2^{(V)}+ \bar h_3^{(V)} \Big)\,,
\nonumber\\
&& \Gamma_{e_3} = \frac{44 }{9}\,d_D -\frac{1}{9} \,\Big( 13 \,\tilde h_2^{(S)}+ 9\, \tilde h_3^{(S)}\Big)
- \frac{1}{36} \,( M+\Delta )\,\Big( 13\, \bar h_2^{(V)} +9\, \bar h_3^{(V)} \Big)\,,
\nonumber\\
&& \Gamma_{e_4} = \frac{44 }{9}\,d_0 +\frac{1}{54}\,\Big(-33 \,\tilde h_1^{(S)}+4 \,\tilde h_2^{(S)} \Big)
\nonumber\\
&& \qquad \qquad -\,\frac{1}{216}\,( M+\Delta )\,\Big( 33 \,\bar h_1^{(V)} -4\,\bar h_2^{(V)} \Big)\,.
\label{res-Gamma-ei}\end{aligned}$$ We derive the form of the anomalous scaling term, $e^{\rm ano}_i$, introduced in (\[def-c-e-ano\], \[c-e-running\]). The prescription (\[eliminate-mu\]) applied to the $(M_R -M_B)\,\bar I_Q$ terms in (\[result-loop-10\]) implies a renormalization of the symmetry breaking counter terms $$\begin{aligned}
&& e^{\rm ano}_i = \frac{1}{4}\,\frac{1}{(4\,\pi\,f )^2}\, \Gamma^{(1)}_{e_i}\,\delta^{(1)}_{e}
+ \frac{1}{4}\,\,\frac{C^2}{(4\,\pi\,f )^2}\,\Big( \Gamma^{(2)}_{e_i}\, \delta^{(2)}_{e} + \Gamma^{(3)}_{e_i}\, \delta^{(3)}_{e} \Big) \,,
\nonumber\\
&& \delta^{(1)}_e= -4 - \log \frac{(\Delta + M)^2}{\mu^2} \,, \qquad \qquad
\delta^{(2)}_e = \frac{1}{3}\left(\frac{\partial \Delta\, \beta_4}{\partial \Delta}\right)\log\frac{\mu^2}{M^2} \,,
\nonumber\\
&& \delta^{(3)}_e = \frac 13\left(\frac{\partial \Delta \,\beta_4 }{\partial M}\right)\log\frac{\mu^2}{M^2}
- \delta^{(2)}_e \,,
\nonumber\\
&& \mu^2\,\frac{d }{d \,\mu^2} \,e^{\rm ano}_i = \frac{1}{4}\,\frac{-1}{(4\,\pi\,f )^2}\, \Gamma^{(1)}_{e_i}
-\frac{1}{12}\,\frac{C^2}{(4\,\pi\,f )^2}\,\Bigg\{ \Gamma^{(2)}_{e_i} \,\Big[ 1+ \Delta\,\frac{\partial}{\partial \Delta} \Big]
\nonumber\\
&& \qquad \qquad \; -\, \Gamma^{(3)}_{e_i} \,\Big[ 1 + \Big(1+\frac{\Delta}{M} \Big)\,\Delta\,\frac{\partial}{\partial \Delta }\Big]
\Bigg\}\,\beta_4\,,
\label{res-e-ano}\end{aligned}$$ with $$\begin{aligned}
&& \Gamma^{(1)}_{e_0} = -\frac{10}{81} \, d_D\,H^2\,, \qquad
\Gamma^{(1)}_{e_2} = \frac{10}{27} \, d_D\,H^2\,, \qquad
\Gamma^{(1)}_{e _1} = \Gamma^{(1)}_{e_3} = \Gamma^{(1)}_{e_4} = 0\,,
\nonumber\\ \nonumber\\
&& \Gamma^{(2)}_{e_0} = 0\,, \qquad
\Gamma^{(2)}_{e_1} = - \frac{4}{3}\,d_D \,, \qquad \Gamma^{(2)}_{e_2} = 2\,d_D \,,
\nonumber\\
&& \Gamma^{(2)}_{e_3} = 2\,( d_0 + d_D )\,, \qquad
\Gamma^{(2)}_{e_4} = 2\, d_0\,,
\nonumber\\ \nonumber\\
&& \Gamma^{(3)}_{e_0} = 2\,(b_F - b_D)\,, \qquad
\Gamma^{(3)}_{e_1} = -4\,b_F \,, \qquad \Gamma^{(3)}_{e_2} = 4\,b_D\,,
\nonumber\\
&& \Gamma^{(3)}_{e_3} = 2\,(b_0 + 2\,b_F) \,, \qquad
\Gamma^{(3)}_{e_4} = 2\,\big(b_0 + b_D - b_F \big)\,.\end{aligned}$$ We close this Appendix with explicit expressions for the fifth moment of the decuplet self energy: $$\begin{aligned}
&& \bar \Sigma^{{\rm bubble}-5}_{B \in [10]} = \!
\sum_{Q\in [8], R\in [10]}
\left(\frac{m_{QR}}{4\,\pi\,f}\,G_{QR}^{(B)} \right)^2 \frac{5}{18}\,\Bigg\{
- \frac{m^4_Q}{M^3_B} \,\Big( \frac{17}{60} - \frac{1}{5}\,\log\frac{m_Q}{M_R}\Big)
\nonumber\\
&& \qquad \quad +\, \frac{13\,\pi}{40}\,\frac{m^3_Q}{M_B^2}
+\,\Big(M_R-M_B\Big)^2\,\Bigg[\frac{\pi}{2\,m_Q} + \frac{1}{M_B}\,\Big( 2 + 3\,\log \frac{m_Q}{M_R} \Big)\Bigg] \Bigg\}
\nonumber\\
&& \; + \,\sum_{Q\in [8], R\in [8]}
\left(\frac{m_Q}{4\,\pi\,f}\,G_{QR}^{(B)} \right)^2 \,\Bigg\{- \frac{\tilde \beta_{11}}{6}\,\frac{ \Delta^3}{(M+\Delta)^2}\,\log \frac{4\,\Delta^2}{M^2}
\nonumber\\
&& \qquad \quad - \, \frac{1}{6}\, \Big( \beta_1- \beta_2\Big )\,\Bigg( \frac{(2\,M+ \Delta)\,M}{2\,(M+ \Delta)^2} \,\frac{M_B-M_R}{\Delta_B^2}\, m_Q^2\,\log \frac{m_Q^2}{M_R^2}
\nonumber\\
&& \qquad \qquad \quad -\, \big(\delta_1-\tilde \delta_1 \big) \,\frac{\Delta_Q^2- \Delta\,\Delta_B}{\Delta_B}- \tilde \delta_1\, \frac{\Delta_Q^2}{\Delta_B^2}\,\Big( M_R-M_B+\Delta_B\Big) \Bigg)
\nonumber\\
&& \qquad \quad +\,\frac{\tilde \beta_{11}}{6\,M_B^2}\, \Bigg[ \big(M_B-M_R \big)^3\,\log \frac{m_Q^2}{M_R^2}
+ \, \Delta_Q^3 \,\Big( \log \big(M_R-M_B - \Delta_Q \big)
\nonumber\\
&& \qquad \qquad \quad -\, \log \big(M_R-M_B + \Delta_Q\big) \Big)\Bigg]
\nonumber\\
&& \qquad \quad +\,\frac{m_Q^2\, \Delta_Q^2}{6\,\Delta^3_B} \,\Bigg[\Big(\beta_2-\beta_1 \Big)\, \Big( \tilde \delta_2 +\tilde \delta_3\,\log \frac{m_Q^2}{M_R^2} \Big)
- \beta_1\,\Big( \tilde \delta_4 + \tilde \delta_5\,\log \frac{m_Q^2}{M_R^2} \Big) \Bigg]
\nonumber\\
&& \qquad \quad +\,\Big(M_R - M_B +\Delta_B \Big)^2 \Bigg(
\frac{\tilde \beta_9}{12}\,\frac{\Delta_Q^2}{m_Q^2\,\Delta_B} + \frac{\tilde \beta_{10}}{12}\,\frac{\Delta_Q^2}{m_Q^2\,\Delta^2_B}\,\big( M_R-M_B\big)
\nonumber\\
&&\qquad \qquad + \,\frac{\tilde \beta_6}{12\,\Delta^2_B\,m_Q^2}\,\Bigg[
\Big( \Delta_Q^2 - \frac{1}{2}\,m_Q^2\Big)\,\big( M_B-M_R\big)\, \log \frac{m_Q^2}{M_R^2}
\nonumber\\
&&\qquad \qquad \quad +\, \Delta_Q^3 \,\Big(
\log (M_R-M_B - \Delta_Q ) -\log (M_R-M_B + \Delta_Q ) \Big)\Bigg]
\nonumber\\
&& \qquad\qquad +\, \frac{1}{12\,\Delta^3_B}\,\Big( -\Delta_Q^2\,\tilde \beta_7
+ \tilde \beta_8\,m_Q^2\,\log \frac{m_Q^2}{M_R^2}\Big)
\Bigg)
\Bigg\} \,,
\label{loop-HB-5-B}\end{aligned}$$ with $m_{QR}^2 = m_Q^2-(M_R-M_B)^2$.
[^1]: We correct a misprint in [@LutzSemke2010]. The coupling constants $g^{(V)}_{0,1,F,D}$ should be multiplied by the factor $1/2$ in equations (32).
[^2]: We note that insisting on the set of equations (\[result:large-Nc-chi\]) obtained within the $\varepsilon$-expansion instead, would lead to significant inconsistencies with (\[res-bds\]) and (\[Q4-subleading\], \[Q4-leading\]).
|
{
"pile_set_name": "ArXiv"
}
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More art
Design a poster for The Imitation Game
THE BRIEF
Studiocanal and Poster Spy are bringing you a fantastic design opportunity. We’d like you to design a poster for The Imitation Game. The winning entry will be used by Studiocanal in a one-off competition to promote the Blu-Ray and Home entertainment release of the film. As we realise the deadline of the competition is quite near, we will accept already existing poster entires, meaning you can submit posters you’ve designed for The Imitation Game before the announcement of this competition.
DATES TO REMEMBER
Submit your entry by March 8th 2015
HOW TO ENTER
Simply create an account and upload your entry to our website. Your entry must be A3 dimensions with 300DPI resolution, but please upload a Web friendly version, if you win we’ll contact you for the hi-res file.
Title your entry ‘Piece name – The Imitation Game Competition’ i.e ‘Alan Turing – The Imitation Game Competition. Add your entry to the ‘Imitation Game Poster Competition’ category. Terms and Conditions.
THE CONTEST PRIZES
1st prize – A Blu-Ray player, a copy of The Imitation Game on Blu-Ray, a Print of the winning design + the winning design shared on all The Imitation Game social platforms to thousands of fans worldwide.
Runners up – 3 Runners up will receive a DVD copy of the The Imitation Game
ABOUT THE IMITATION GAME
Based on the real life story of legendary cryptanalyst Alan Turing, THE IMITATION GAME portrays the nail-biting race against time by Turing and his brilliant team of code-breakers, endorsed by Churchill himself, at Britain’s top-secret Government Code & Cypher School at Bletchley Park during the darkest days of World War II. The film spans the key periods of Turing’s life, from his unhappy teenage years at boarding school and the triumph of his secret wartime work on the revolutionary electro-mechanical ‘Bombe’, which was capable of breaking 3,000 Enigma-generated naval codes a day, to the tragedy of his post-war decline following his conviction for a now outdated criminal offence. A complicated and troubled man, whose contributions and genius significantly shortened the war, saving thousands of lives, Turing may have been the eventual victim of an unenlightened British Establishment, but his work and legacy live on…
Starring Academy, BAFTA and Golden Globe nominee Benedict Cumberbatch (Star Trek: Into Darkness, TV’s Sherlock) as Turing, Academy, BAFTA and Golden Globe nominee Keira Knightley (Begin Again, Atonement) as his confidante and equal, Joan Clarke, and featuring supporting turns from Matthew Goode (Stoker, Watchmen), Mark Strong (Tinker, Tailor, Soldier Spy, Welcome To The Punch), Rory Kinnear (Skyfall, TV’s Penny Dreadful) and Charles Dance (TV’s Game Of Thrones, Gosford Park), THE IMITATION GAME is at once a searing piece of British drama, a brilliantly taut thriller and a posthumous honour to arguably one of Britain’s most important, most brilliant men.
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{
"pile_set_name": "Pile-CC"
}
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Q:
Clicar em um link e exibir o valor dentro de um input
Olá, alguém sabe como eu poderia fazer isso, tenho 10 link, cada link corresponde a um elemento tipo link 1 = :D, link 2 = :S, link 3 = :$ e assim por diante, ai eu tenho um input type="text" name="mensagem" placeholder="digite sua mensagem..."/>, minha dúvida é o seguinte, como eu faria pra quando a pessoa clicasse em um desses link o valor que é informado neles mostrasse no input? sem ser pelo value="", vou exemplificar melhor <a href="javascript:void(0)">:D</a> <a href="javascript:void(0)">:S</a> <a href="javascript:void(0)">:$</a> ao clicar em um desses link quero que envie o valor correspondente ai link clicado para o input
A:
Crie um eventListener com click para cada <a>, que ao ser clicado, o texto correspondente será concatenado ao texto do input:
document.addEventListener("DOMContentLoaded", function(){
var els = document.body.querySelectorAll("a[href*='java']");
for(var x=0; x<els.length; x++){
els[x].addEventListener("click", function(){
var a_txt = this.textContent,
inpt = document.body.querySelector("#texto");
inpt.value += " "+a_txt;
});
}
});
<a href="javascript:void(0)">:D</a>
<a href="javascript:void(0)">:S</a>
<a href="javascript:void(0)">:$</a>
<br />
<input id="texto" type="text" value="olá!" />
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{
"pile_set_name": "StackExchange"
}
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The last couple of weeks have been really showcase for the diversity and brilliant spirit of Sheffield people.
Snow, Snow and more Snow
I have been out to thank the people who have helped to keep Sheffield moving. Not just Council staff but also the sturdy and hardy volunteers of Sheffield, who have helped to look after others and keep Sheffield on the move. It is really important that we now review the gritting situation and have a discussion with the people of Sheffield on how we can improve.
Me with one of Sheffield's gritting lorries - invaluable during the recent snow and icy weather
Listening to Sheffield
Great news that the people’s panel, which has helped steer the bids to Government for the Sustainable Communities Act, has been successful in getting all four schemes accepted :
Sheffield taking over the post office franchise
Growing local food on derelict land
Skills and Apprenticeship Model without having to go through national hoops for Sheffield
Asylum Seekers whose asylum case has been processed being able to work and contribute to society.
This is what happens when real people power takes over and local people have their say, not only does the Council listen, but it would appear the Government is listening as well.
Hail a Taxi
I was delighted to go to the Taxi Association driver’s annual meeting, on behalf of the Council, and help present some long service awards. Many times taxis do a very good job quietly, and do not get the recognition they deserve. I was therefore very happy to deliver a goodwill message from the City, as well as hand out the prizes to some of the taxi drivers.
Great Graduation
As Leader, I attended the graduation ceremony for students who have received brilliant education from the University of Sheffield, and celebrate in their success. I was really proud of such a good University and also the students who will now become ambassadors for this wonderful City.
A True Legend
I helped to unveil, with the Lord Mayor, the Walk of Fame plaque for Sean Bean. A great man and a great ambassador for the City, very shy and unassuming, but he really has put Sheffield on the map. I was really pleased that the people of Sheffield turned out to thank Sean for all he has done for the City, both Owls and Blades!
Food, Glorious Food
I met with organisations wishing to run the first ever Sheffield Food Festival. Really exciting that the festival will be coming, and celebrating Sheffield’s food and drink in June of this year. I’m really looking forward to the summer and experiencing with Sheffielders a wonderful festival.
Supporting Local Troops
The Lord Mayor and I attend the exercising the freedom of the City by the Local 38 Signal Regiment Volunteers Squadron within the City. Really pleased that people of Sheffield turned up to thank them for the work they do, whether they are regular or a member of the TA.
V & A Museum – Sheffield!
I was delighted that the partnership between Museum Sheffield and the Victoria and Albert Museum has been extended by another 5 years. On behalf of the city, I was able to showcase Sheffield to the Director of the V & A Sir Mark Jones, and looking forward to the exhibits which start again in 2011, with the first of the history of couture with such designers as Dior. It is marvellous to know that such an important Museum still rates Sheffield as a great international City to exhibit its important collections.
Keep the Cold at Bay
Free Insulation for Sheffielders - Promoting the scheme through the Sheffield Showcase
I was one of the people involved in a photo session to highlight the free insulation scheme which we have here within the City. A delightful and funny photo opportunity which showed that you don’t have to be cold in Sheffield and that you live in private accommodation, there are ways in which we can help you not only to keep warm but to reduce your bills as well and help save the environment. Further details (link to go in here and photo from Andy which was taken in the shop window)
As always the City Council and I are here to ensure that we listen and try to get things right for you first time so if you have any issues you would like me to be aware of please do not hesitate to contact me.
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{
"pile_set_name": "Pile-CC"
}
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Q:
Does A Program that is written with the Microsoft .NET framework compile/execute native code?
Newb question:
Does a Program that is written with the Microsoft .NET framework compile/execute native code?
I don't mean if there is a way not to have to install the .net framework on a machine. Simply put: does a .net application run on another layer like Java (i.e. bytecode).
A:
A .NET application must run over the Common Language Runtime (CLR).
The CLR is Microsoft's implementation of the CLI standard. (And there are other implementations of the CLR beside the Microsoft .NET Framework i.e.: Mono, Portable.NET).
The CLR executes a type of bytecode known as the Common Intermediate Language (CIL).
A:
Sort of. The .NET compiler compiles your source code into IL (an intermediate language) and packages it in an assembly (usually one .DLL or .EXE file) which you deploy. At run-time, it is hosted by a CLR (common language runtime) which is responsible for executing the code, enforcing security rules, and so on. The main desktop CLR for Windows (there are others like Mono and Silverlight) doesn't interpret the IL, but rather "JIT"s (just in-time compiles) the IL code into native code before executing methods (functions).
Note there are actually some performance advantages to just in-time compilation. For example, the CLR can optimize the native code it generates based on performance characteristics of the machine it is running on like type of CPU, CPU cache size, number of CPUs, RAM size, etc. Traditional compilers can't do this as they don't know what machine the code they generate will ultimately be executed on.
Also, assemblies can be "pre-JITted" using a tool called ngen. In this process the native code is compiled from the IL before the assembly is executed and cached on disk. That way, no JITting overhead is incurred at run-time.
|
{
"pile_set_name": "StackExchange"
}
|
Predictors of clinical outcomes in patients with neuropsychiatric systemic lupus erythematosus.
Neuropsychiatric systemic lupus erythematosus (NPSLE), a serious organ disorder with a variety of symptoms, has diverse therapeutic outcomes because of the variability of NPSLE manifestations. A comprehensive association study of NPSLE among clinical and immunopathogenic aspects and outcomes has not been conducted. We analyzed the laboratory data, NPSLE symptoms, and clinical outcomes at 1yr post-treatment and the profiles of 27 cytokines, chemokines and growth factors in cerebrospinal fluid (CSF) samples using the Bio-Plex Human 27-plex panel from 28 NPSLE patients. Univariate and multivariable competing risks regression analyses were used to determine the predictive factors of clinical response. We also tried to predict the outcome of NPSLE by the 27 cytokines/chemokines/growth factors using a weighted-voting (WV) algorithm. Of the two males and 26 females (92.9%), 16 were non-responders at 1yr post-treatment; in the final model, the independent predictors of non-responders were longer disease durations of SLE (odds ratio [OR]: 1.490, 95% confidence interval [CI]: 1.143-2.461, p=0.0003) and patients with more than one NPSLE symptom types (OR: 15.14, 95% CI: 1.227-452.1, p=0.0334). The pretreatment CSF interleukin (IL)-6, IL-10, interferon-gamma (IFN-γ) and tumor necrosis factor-alpha (TNF-α) levels were significantly higher in the non-responders (p=0.0207, p=0.0054, p=0.0242 and p=0.0077, respectively). We identified six "minimum predictive markers:" IL-10, TNF-α, IL-6, IFN-γ, IL-4 and IL-13 by a WV algorithm that showed the highest accuracy (70.83%) and highest Matthews correlation coefficient (54.23%). We have devised a numerical prediction scoring system that was able to separate the non-responders from responders. The patients with longer disease durations of SLE and those with more than one NPSLE symptom types had poorer outcomes. Our findings may indicate both the importance of making a diagnosis at an earlier phase for better therapeutic response and the usefulness of measuring multiple cytokines to predict NPSLE therapeutic outcomes.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
The effects of perioperative hypothermia and the duration of anesthesia on postoperative wound infection rate in clean wounds: a retrospective study.
To determine the effects of hypothermia and duration of anesthesia on the infection rate in clean wounds in dogs and cats. Retrospective clinical study. Seven hundred seventy-seven dogs and cats undergoing clean surgical procedures. Records of animals prospectively evaluated for postoperative wound infection were retrospectively evaluated for the prevalence of perioperative hypothermia. Body temperatures during the perioperative period and the duration of surgery and anesthesia were recorded. Data were analyzed to identify differences between animals with infected and uninfected wounds and multiple logistic regression modeling was used to evaluate the independent contribution of risk factors to the incidence of postoperative wound infection. No statistically significant differences were found in the analysis of temperature data between animals with infected and uninfected wounds. Duration of anesthesia was significantly greater in animals with wound infections (P = .01). Multiple logistic regression modeling identified duration of anesthesia as a risk factor for postoperative wound infection independent of the duration of surgery. In animals with clean surgical wounds, mild perioperative hypothermia is not a significant risk factor for postoperative wound infection. The duration of anesthesia, however, is a significant risk factor independent of the duration of surgery. To decrease the incidence of postoperative wound infection, the duration of anesthesia should be minimized. Surgical time, as well as the time required for ancillary diagnostic tests while under anesthesia should, therefore, be kept to a reasonable minimum.
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{
"pile_set_name": "PubMed Abstracts"
}
|
When healthy, Burfict stands alongside names like Lavonte David and Thomas Davis, so the thought of combining him with an already humming 6-0 machine is scary. Sunday, when the Steelers and Le'Veon Bell roll into town, we may get our first look at just how good Burfict is feeling.
|
{
"pile_set_name": "OpenWebText2"
}
|
High resolution NMR solution structure of the leucine zipper domain of the c-Jun homodimer.
The solution structure of the c-Jun leucine zipper domain has been determined to high resolution using a new calculation protocol designed to handle highly ambiguous sets of interproton distance restraints. The domain comprises a coiled coil of parallel alpha-helices in which most of the hydrophobic residues are buried at the highly symmetrical dimer interface; this interface extends over 10 helical turns and is the most elongated protein domain solved to date using NMR methods. The backbone fold is very similar to that seen in crystal structures of the GCN4 and Jun-Fos leucine zippers; however, in contrast with these crystal structures, the Jun leucine zipper dimer appears to be devoid of favorable intermolecular electrostatic interactions. A polar asparagine residue, located at the dimer interface, forms the sole point of asymmetry in the structure; furthermore, the side chain of this residue is disordered due to motional averaging. This residue, which is highly conserved in the leucine zipper family of transcription factors, provides a destabilizing influence that is likely to facilitate the rapid exchange of zipper strands in vivo.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
bcl-2 plays a critical role in growth and in spontaneous or induced apoptosis in myeloma cell lines.
The role of bcl-2 in spontaneous and drug-induced apoptosis in multiple myeloma (MM) is not yet established, particularly since the frequency of t(14:18) in MM is relatively low. In recent studies, we have investigated the steady-state levels of bcl-2 mRNA transcripts and bcl-2 protein in 8 MM cell lines and found inverse correlation between the levels of bcl-2 and sensitivity to dexamethasone (DEX)-induced apoptosis. Moreover, we have shown that bcl-2 was further down-regulated in DEX sensitive cell lines, but not in DEX resistance cell lines, in the course of DEX-induced apoptosis (Int J Oncol 8: 719-726, 1996). Herein, we report the results of transfection studies of 2 DEX sensitive MM cell lines, expressing relatively low levels of bcl-2, with a bcl-2 inducible gene construct expressed under the control of lac repressor operon. Thus, switching-on of bcl-2 by IPTG resulted in increased bcl-2 protein in the cells, enhancement of cell growth, and a decrease in spontaneous apoptosis, concomitant with increased resistance to DEX. Switching-off of bcl-2 protein expression by removal of IPTG resulted in restoration of sensitivity to DEX-induced apoptosis. We, therefore, conclude that bcl-2 plays a central role in cell growth and in spontaneous and induced apoptosis in MM cell lines.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
Q:
任意の辞書で「もしかして」検索機能を提供するライブラリまたはアルゴリズム
誤字を検出して正解の単語をサジェストする、いわゆる「もしかして」検索を実装しようとしています。
使用する正解の単語コーパス(以下『辞書』)を検索対象の項目ごとに切り替えて精度を上げる運用を考えています。
(例えば氏名の項目には『氏名データベース』から、注文の項目には『自社の取扱い商品名リスト』から生成した辞書をそれぞれ割り当てます)
オンプレミス環境で任意の辞書からレーベンシュタイン距離が1の誤字(挿入、置換、削除を1文字行って正解に合致する誤字)と正解を表示することが目的です。
日本語に対してこの校正用途で使用可能なライブラリまたはアルゴリズムは公開されているのでしょうか。
言語やOSは問いません。
自作のコードではgrepとループを繰り返す総当たり処理しか思いついていないため、項目数や辞書の単語数が増えてくると低速になることを懸念しております。
高速なライブラリがあれば試用したいのですがうまく見つけられないため質問させていただきました。
A:
PostgreSQLでは、拡張機能fuzzystrmatchでLevenshteinが提供されています。
https://www.postgresql.org/docs/10/static/fuzzystrmatch.html
また、Elasticsearchでも、可能と思われます。
https://www.elastic.co/guide/en/elasticsearch/reference/current/query-dsl-fuzzy-query.html
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{
"pile_set_name": "StackExchange"
}
|
Juanita Suazo Dubray
Juanita Suazo Dubray (born 1930) is a Native American potter from Taos Pueblo, New Mexico. She is a lifelong resident of Taos Pueblo and descends from an unbroken line of Taos Pueblo natives. Her mother Tonita made traditional micaceous pottery for utilitarian use. She became interested in the micaceous pottery tradition in 1980 after a career of working as a pharmaceutical technician.
She started making micaceous pottery at the age of 50 with the encouragement of a neighbor who gave her some clay. When she first started making pottery she made one-of-a-kind micaceous pots using different ancient designs and symbols. Eventually she began using more contemporary designs and symbols on her pots, making them out of both micaceous and white clay. She added an element of sculpture, producing many pieces with icons of corn, turtles, lizards, and kiva steps in relief. Her original corn design has become her most recognized symbol. She also often includes traditional ornamentation of rope fillets, tool-impressed rims and loop handles on her pots. Juanita has also produced sculptured objects including nativity scenes and storyteller dolls.
As a self-taught potter, Juanita has come a long way in mastering the skills of making traditional micaceous pottery, which are truly beautiful works of art. She has attended numerous shows and exhibitions including the Santa Fe Indian Market, Denver Indian Market, the San Ildefonso and San Juan Pueblo Eight Northern Indian Markets among others. In 1988 she received first place in the San Ildefonso Eight Northern Indian Market. In 1994 she was designated a Master Potter by the School of American Research and was invited to attend the school’s Micaceous Pottery Artists Convocation. She was one of ten master micaceous potters to attend. In June 2004 she also taught a workshop at the Taos Art School on making traditional Taos Pueblo micaceous pottery.
References and further reading
Anderson, Duane - All That Glitters: The Emergence of Native American Micaceous Art Pottery in Northern New Mexico. 1999.
External links
Juanita Suazo Dubray pottery at the Holmes Museum of Anthropology
Category:1930 births
Category:Living people
Category:Artists from New Mexico
Category:Native American potters
Category:Taos Pueblo artists
Category:American women ceramists
Category:American ceramists
Category:Native American women artists
Category:Women potters
Category:21st-century American women artists
Category:21st-century ceramists
|
{
"pile_set_name": "Wikipedia (en)"
}
|
import reducer from '../reducer';
describe('UPLOAD | containers | ModalStepper | reducer', () => {
describe('ADD_FILES_TO_UPLOAD', () => {
it('should add the files to the empty filesToUpload array and update the current step', () => {
const action = {
type: 'ADD_FILES_TO_UPLOAD',
filesToUpload: {
0: { name: 'test1', ok: true },
1: { name: 'test2', ok: false },
},
nextStep: 'test',
};
const state = {
currentStep: 'browse',
filesToUpload: [],
};
const expected = {
currentStep: 'test',
filesToUpload: [
{
abortController: new AbortController(),
file: { name: 'test1', ok: true },
fileInfo: {
alternativeText: '',
caption: '',
name: 'test1',
},
originalName: 'test1',
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 0,
tempId: null,
},
{
abortController: new AbortController(),
file: { name: 'test2', ok: false },
fileInfo: {
alternativeText: '',
caption: '',
name: 'test2',
},
originalName: 'test2',
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 1,
tempId: null,
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
it('should add the files to the (not empty) filesToUpload array and update the current step', () => {
const action = {
type: 'ADD_FILES_TO_UPLOAD',
filesToUpload: {
0: { name: 'test2', test: true },
1: { name: 'test3', test: false },
},
nextStep: 'test',
};
const state = {
currentStep: 'browse',
filesToUpload: [
{
abortController: new AbortController(),
file: { name: 'test1', ok: true },
fileInfo: {
alternativeText: '',
caption: '',
name: 'test1',
},
originalName: 'test1',
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 0,
tempId: null,
},
],
};
const expected = {
currentStep: 'test',
filesToUpload: [
{
abortController: new AbortController(),
file: { name: 'test1', ok: true },
fileInfo: {
alternativeText: '',
caption: '',
name: 'test1',
},
originalName: 'test1',
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 0,
tempId: null,
},
{
abortController: new AbortController(),
file: { name: 'test2', test: true },
fileInfo: {
alternativeText: '',
caption: '',
name: 'test2',
},
originalName: 'test2',
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 1,
tempId: null,
},
{
abortController: new AbortController(),
file: { name: 'test3', test: false },
fileInfo: {
alternativeText: '',
caption: '',
name: 'test3',
},
originalName: 'test3',
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 2,
tempId: null,
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
it('should work if the filesToUpload is empty', () => {
const action = {
type: 'ADD_FILES_TO_UPLOAD',
filesToUpload: {},
nextStep: 'test',
};
const state = {
currentStep: 'browse',
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 0,
tempId: null,
},
],
};
const expected = {
currentStep: 'test',
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 0,
tempId: null,
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('ADD_URLS_TO_FILES_TO_UPLOAD', () => {
it('should add the files to the empty filesToUpload array and update the current step', () => {
const action = {
type: 'ADD_URLS_TO_FILES_TO_UPLOAD',
nextStep: 'test',
};
const state = {
currentStep: 'browse',
filesToUpload: [],
filesToDownload: ['http://www.un.com/photo-1', 'http://www.deux.com/photo-2'],
};
const firstURL = new URL('http://www.un.com/photo-1');
const firstURLName = decodeURIComponent(
firstURL.pathname.substring(firstURL.pathname.lastIndexOf('/') + 1)
);
const secondURL = new URL('http://www.deux.com/photo-2');
const secondURLName = decodeURIComponent(
secondURL.pathname.substring(secondURL.pathname.lastIndexOf('/') + 1)
);
const expected = {
currentStep: 'test',
filesToDownload: [],
filesToUpload: [
{
file: null,
fileInfo: {
alternativeText: '',
caption: '',
name: firstURLName,
},
originalName: firstURLName,
originalIndex: 0,
fileURL: firstURL,
hasError: false,
errorMessage: null,
isUploading: false,
isDownloading: true,
tempId: 1,
},
{
file: null,
fileInfo: {
alternativeText: '',
caption: '',
name: secondURLName,
},
originalName: secondURLName,
originalIndex: 1,
fileURL: secondURL,
hasError: false,
errorMessage: null,
isUploading: false,
isDownloading: true,
tempId: 2,
},
],
};
const received = reducer(state, action);
expect(received.currentStep).toEqual(expected.currentStep);
expect(received.filesToDownload).toEqual(expected.filesToDownload);
expect(received.filesToUpload).toEqual(
expect.arrayContaining([
expect.objectContaining(expected.filesToUpload[0]),
expect.objectContaining(expected.filesToUpload[1]),
])
);
});
it('should add the files to the (not empty) filesToUpload array and update the current step', () => {
const state = {
currentStep: 'browse',
filesToDownload: ['http://www.trois.com/photo-3', 'http://www.quatre.com/photo-4'],
filesToUpload: [
{
abortController: new AbortController(),
file: { name: 'test1', ok: true },
fileInfo: {
alternativeText: '',
caption: '',
name: 'test1',
},
originalName: 'test1',
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 0,
tempId: null,
},
{
file: null,
fileInfo: {
alternativeText: '',
caption: '',
name: 'test1',
},
originalName: 'test1',
originalIndex: 1,
fileURL: 'test1',
hasError: false,
errorMessage: null,
isUploading: false,
isDownloading: true,
tempId: 2,
},
],
};
const action = {
type: 'ADD_URLS_TO_FILES_TO_UPLOAD',
nextStep: 'test',
};
const firstURL = new URL('http://www.trois.com/photo-3');
const firstURLName = decodeURIComponent(
firstURL.pathname.substring(firstURL.pathname.lastIndexOf('/') + 1)
);
const secondURL = new URL('http://www.quatre.com/photo-4');
const secondURLName = decodeURIComponent(
secondURL.pathname.substring(secondURL.pathname.lastIndexOf('/') + 1)
);
const expected = {
currentStep: 'test',
filesToDownload: [],
filesToUpload: [
{
abortController: new AbortController(),
file: { name: 'test1', ok: true },
fileInfo: {
alternativeText: '',
caption: '',
name: 'test1',
},
originalName: 'test1',
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 0,
tempId: null,
},
{
file: null,
fileInfo: {
alternativeText: '',
caption: '',
name: 'test1',
},
originalName: 'test1',
originalIndex: 1,
fileURL: 'test1',
hasError: false,
errorMessage: null,
isUploading: false,
isDownloading: true,
tempId: 2,
},
{
file: null,
fileInfo: {
alternativeText: '',
caption: '',
name: firstURLName,
},
originalName: firstURLName,
originalIndex: 2,
fileURL: firstURL,
hasError: false,
errorMessage: null,
isUploading: false,
isDownloading: true,
tempId: 3,
},
{
file: null,
fileInfo: {
alternativeText: '',
caption: '',
name: secondURLName,
},
originalName: secondURLName,
originalIndex: 3,
fileURL: secondURL,
hasError: false,
errorMessage: null,
isUploading: false,
isDownloading: true,
tempId: 4,
},
],
};
const received = reducer(state, action);
expect(received.currentStep).toEqual(expected.currentStep);
expect(received.filesToDownload).toEqual(expected.filesToDownload);
expect(received.filesToUpload).toEqual(
expect.arrayContaining([
expect.objectContaining(expected.filesToUpload[0]),
expect.objectContaining(expected.filesToUpload[1]),
expect.objectContaining(expected.filesToUpload[2]),
expect.objectContaining(expected.filesToUpload[3]),
])
);
});
});
describe('CLEAN_FILES_ERROR', () => {
it('should not change the filesToUpload property if it is empty', () => {
const action = {
type: 'CLEAN_FILES_ERROR',
};
const state = {
currentStep: 'test',
filesToUpload: [],
};
expect(reducer(state, action)).toEqual(state);
});
it('should remove the errors of all files from the filesToUploadArray', () => {
const action = {
type: 'CLEAN_FILES_ERROR',
};
const state = {
currentStep: 'test',
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: true,
errorMessage: 'error1',
isUploading: false,
originalIndex: 0,
},
{
abortController: new AbortController(),
file: { test: true },
hasError: true,
errorMessage: 'error2',
isUploading: false,
originalIndex: 1,
},
{
abortController: new AbortController(),
file: { test: false },
hasError: true,
errorMessage: 'error3',
isUploading: false,
originalIndex: 2,
},
],
};
const expected = {
currentStep: 'test',
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 0,
},
{
abortController: new AbortController(),
file: { test: true },
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 1,
},
{
abortController: new AbortController(),
file: { test: false },
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 2,
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('CLEAR_FILES_TO_UPLOAD_AND_DOWNLOAD', () => {
it('should empty the filesToDownload and filesToUpload arrays', () => {
const state = {
filesToDownload: ['1', '2'],
filesToUpload: ['3', '4'],
};
const action = {
type: 'CLEAR_FILES_TO_UPLOAD_AND_DOWNLOAD',
};
const expected = {
filesToDownload: [],
filesToUpload: [],
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('FILE_DOWLOADED', () => {
it('should update the corresponding file', () => {
const state = {
currentStep: 'browse',
filesToDownload: [],
filesToUpload: [
{
abortController: new AbortController(),
file: { name: 'test1', ok: true },
fileInfo: {
alternativeText: '',
caption: '',
name: 'test1',
},
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 0,
tempId: null,
},
{
file: null,
fileInfo: {
alternativeText: '',
caption: '',
name: 'test1',
},
originalIndex: 1,
fileURL: 'test1',
hasError: false,
errorMessage: null,
isUploading: false,
isDownloading: true,
tempId: 2,
},
],
};
const action = {
type: 'FILE_DOWNLOADED',
fileTempId: 2,
blob: 'test',
};
const expected = {
currentStep: 'browse',
filesToDownload: [],
filesToUpload: [
{
abortController: new AbortController(),
file: { name: 'test1', ok: true },
fileInfo: {
alternativeText: '',
caption: '',
name: 'test1',
},
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 0,
tempId: null,
},
{
file: 'test',
fileInfo: {
alternativeText: '',
caption: '',
name: 'test1',
},
originalIndex: 1,
fileURL: 'test1',
hasError: false,
errorMessage: null,
isUploading: false,
isDownloading: false,
tempId: 2,
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('ON_CHANGE', () => {
it('should change the data correctly', () => {
const action = {
type: 'ON_CHANGE',
keys: 'test',
value: 'test 1',
};
const state = {
fileToEdit: {
test: 'test',
isUploading: true,
},
currentStep: 'test',
};
const expected = {
fileToEdit: {
test: 'test 1',
isUploading: true,
},
currentStep: 'test',
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('ON_CHANGE_MODAL_TAB', () => {
it('should change the data correctly', () => {
const action = {
type: 'ON_CHANGE_MODAL_TAB',
to: 'selected',
};
const state = {
currentStep: 'list',
currentTab: 'browse',
};
const expected = {
currentStep: 'list',
currentTab: 'selected',
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('ON_CHANGE_URLS_TO_DOWNLOAD', () => {
it('should change the data correctly', () => {
const action = {
type: 'ON_CHANGE_URLS_TO_DOWNLOAD',
keys: 'test',
value: ['test 1', 'test 2'],
};
const state = {
filesToDownload: [],
currentStep: 'test',
};
const expected = {
filesToDownload: ['test 1', 'test 2'],
currentStep: 'test',
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('SET_FILE_TO_DOWNLOAD_ERROR', () => {
it('should update the specified file error', () => {
const state = {
currentStep: 'browse',
filesToDownload: [],
filesToUpload: [
{
abortController: new AbortController(),
file: { name: 'test1', ok: true },
fileInfo: {
alternativeText: '',
caption: '',
name: 'test1',
},
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 0,
tempId: null,
},
{
file: null,
fileInfo: {
alternativeText: '',
caption: '',
name: 'test1',
},
fileOriginalName: 'test1-test',
originalName: 'test1',
originalIndex: 1,
fileURL: 'test1',
hasError: false,
errorMessage: null,
isUploading: false,
isDownloading: true,
tempId: 2,
},
],
};
const action = {
type: 'SET_FILE_TO_DOWNLOAD_ERROR',
fileTempId: 2,
};
const expected = {
currentStep: 'browse',
filesToDownload: [],
filesToUpload: [
{
abortController: new AbortController(),
file: { name: 'test1', ok: true },
fileInfo: {
alternativeText: '',
caption: '',
name: 'test1',
},
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 0,
tempId: null,
},
{
file: null,
fileInfo: {
alternativeText: '',
caption: '',
name: 'test1',
},
originalIndex: 1,
originalName: 'test1',
fileOriginalName: 'test1-test',
fileURL: 'test1',
hasError: true,
errorMessage: 'test1-test',
isUploading: false,
isDownloading: false,
tempId: 2,
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('TOGGLE_SELECT_ALL', () => {
it('should select all files', () => {
const action = {
type: 'TOGGLE_SELECT_ALL',
};
const state = {
allowedTypes: [],
selectedFiles: [],
files: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'mySecondFile',
ext: '.png',
mime: 'image/png',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
};
const expected = {
allowedTypes: [],
selectedFiles: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'mySecondFile',
ext: '.png',
mime: 'image/png',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
files: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'mySecondFile',
ext: '.png',
mime: 'image/png',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
it('should deselect all files', () => {
const action = {
type: 'TOGGLE_SELECT_ALL',
};
const state = {
allowedTypes: [],
selectedFiles: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'mySecondFile',
ext: '.png',
mime: 'image/png',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
files: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'mySecondFile',
ext: '.png',
mime: 'image/png',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
};
const expected = {
allowedTypes: [],
selectedFiles: [],
files: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'mySecondFile',
ext: '.png',
mime: 'image/png',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
it('should add the unselect files of the current page', () => {
const action = {
type: 'TOGGLE_SELECT_ALL',
};
const state = {
allowedTypes: [],
selectedFiles: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
files: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'mySecondFile',
ext: '.png',
mime: 'image/png',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
};
const expected = {
allowedTypes: [],
selectedFiles: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'mySecondFile',
ext: '.png',
mime: 'image/png',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
files: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'mySecondFile',
ext: '.png',
mime: 'image/png',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
it('should add all files to the already selected files if not in the same page', () => {
const action = {
type: 'TOGGLE_SELECT_ALL',
};
const state = {
allowedTypes: [],
selectedFiles: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'mySecondFile',
ext: '.png',
mime: 'image/png',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
files: [
{
id: 3,
name: 'myThirdFile',
ext: '.png',
mime: 'image/png',
size: 4.22,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 4,
name: 'myFourthFile',
ext: '.png',
mime: 'image/png',
size: 3.44,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
};
const expected = {
allowedTypes: [],
selectedFiles: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'mySecondFile',
ext: '.png',
mime: 'image/png',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 3,
name: 'myThirdFile',
ext: '.png',
mime: 'image/png',
size: 4.22,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 4,
name: 'myFourthFile',
ext: '.png',
mime: 'image/png',
size: 3.44,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
files: [
{
id: 3,
name: 'myThirdFile',
ext: '.png',
mime: 'image/png',
size: 4.22,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 4,
name: 'myFourthFile',
ext: '.png',
mime: 'image/png',
size: 3.44,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
it('should deselect all files of the current page only event if not allowed', () => {
const action = {
type: 'TOGGLE_SELECT_ALL',
};
const state = {
allowedTypes: ['video'],
selectedFiles: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'mySecondFile',
ext: '.png',
mime: 'image/png',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 3,
name: 'myThirdFile',
ext: '.png',
mime: 'image/png',
size: 4.22,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 4,
name: 'myFourthFile',
ext: '.png',
mime: 'image/png',
size: 3.44,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
files: [
{
id: 3,
name: 'myThirdFile',
ext: '.png',
mime: 'image/png',
size: 4.22,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 4,
name: 'myFourthFile',
ext: '.png',
mime: 'image/png',
size: 3.44,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
};
const expected = {
allowedTypes: ['video'],
selectedFiles: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'mySecondFile',
ext: '.png',
mime: 'image/png',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
files: [
{
id: 3,
name: 'myThirdFile',
ext: '.png',
mime: 'image/png',
size: 4.22,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 4,
name: 'myFourthFile',
ext: '.png',
mime: 'image/png',
size: 3.44,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
it('should select the allowed files', () => {
const action = {
type: 'TOGGLE_SELECT_ALL',
};
const state = {
allowedTypes: ['image', 'file'],
selectedFiles: [],
files: [
{
id: 1,
name: 'myImage',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'myFile',
ext: '.png',
mime: 'application/pdf',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 3,
name: 'myVideo',
ext: '.png',
mime: 'video/mp4',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 4,
name: 'mySecondImage',
ext: '.png',
mime: 'image/jpg',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
};
const expected = {
selectedFiles: [
{
id: 1,
name: 'myImage',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'myFile',
ext: '.png',
mime: 'application/pdf',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 4,
name: 'mySecondImage',
ext: '.png',
mime: 'image/jpg',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
allowedTypes: ['image', 'file'],
files: [
{
id: 1,
name: 'myImage',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'myFile',
ext: '.png',
mime: 'application/pdf',
size: 2.24,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 3,
name: 'myVideo',
ext: '.png',
mime: 'video/mp4',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 4,
name: 'mySecondImage',
ext: '.png',
mime: 'image/jpg',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('GO_TO', () => {
it('should update the current step', () => {
const action = {
type: 'GO_TO',
to: 'test',
};
const state = {
currentStep: 'browse',
};
const expected = {
currentStep: 'test',
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('REMOVE_FILE_TO_UPLOAD', () => {
it('should remove the file from the filesToUpload array', () => {
const action = {
type: 'REMOVE_FILE_TO_UPLOAD',
fileIndex: 1,
};
const state = {
currentStep: 'test',
selectedFiles: [],
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: true,
errorMessage: 'error1',
isUploading: false,
originalIndex: 0,
},
{
abortController: new AbortController(),
file: { test: true },
hasError: true,
errorMessage: 'error2',
isUploading: false,
originalIndex: 1,
},
{
abortController: new AbortController(),
file: { test: false },
hasError: true,
errorMessage: 'error3',
isUploading: false,
originalIndex: 2,
},
],
};
const expected = {
currentStep: 'test',
selectedFiles: [],
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: true,
errorMessage: 'error1',
isUploading: false,
originalIndex: 0,
},
{
abortController: new AbortController(),
file: { test: false },
hasError: true,
errorMessage: 'error3',
isUploading: false,
originalIndex: 2,
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
it('should remove the file and add it to the selectedFiles', () => {
const action = {
type: 'REMOVE_FILE_TO_UPLOAD',
fileIndex: 1,
addToSelectedFiles: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
};
const state = {
currentStep: 'test',
currentTab: 'browse',
selectedFiles: [],
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: true,
errorMessage: 'error1',
isUploading: false,
originalIndex: 0,
},
{
abortController: new AbortController(),
file: { test: true, name: 'My File' },
hasError: true,
errorMessage: 'error2',
isUploading: false,
originalIndex: 1,
},
{
abortController: new AbortController(),
file: { test: false },
hasError: true,
errorMessage: 'error3',
isUploading: false,
originalIndex: 2,
},
],
};
const expected = {
currentStep: 'test',
currentTab: 'selected',
selectedFiles: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: true,
errorMessage: 'error1',
isUploading: false,
originalIndex: 0,
},
{
abortController: new AbortController(),
file: { test: false },
hasError: true,
errorMessage: 'error3',
isUploading: false,
originalIndex: 2,
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
it('should remove the file and not add to the selectedFiles if the input is not multiple', () => {
const action = {
type: 'REMOVE_FILE_TO_UPLOAD',
fileIndex: 1,
addToSelectedFiles: [
{
id: 2,
name: 'myFile2',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
};
const state = {
currentStep: 'test',
currentTab: 'browse',
selectedFiles: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: true,
errorMessage: 'error1',
isUploading: false,
originalIndex: 0,
},
{
abortController: new AbortController(),
file: { test: true, name: 'My File' },
hasError: true,
errorMessage: 'error2',
isUploading: false,
originalIndex: 1,
},
{
abortController: new AbortController(),
file: { test: false },
hasError: true,
errorMessage: 'error3',
isUploading: false,
originalIndex: 2,
},
],
};
const expected = {
currentStep: 'test',
currentTab: 'selected',
selectedFiles: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: true,
errorMessage: 'error1',
isUploading: false,
originalIndex: 0,
},
{
abortController: new AbortController(),
file: { test: false },
hasError: true,
errorMessage: 'error3',
isUploading: false,
originalIndex: 2,
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
it('should remove the file and add to the selectedFiles if the input is multiple', () => {
const action = {
type: 'REMOVE_FILE_TO_UPLOAD',
fileIndex: 1,
multiple: true,
addToSelectedFiles: [
{
id: 2,
name: 'myFile2',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
};
const state = {
currentStep: 'test',
currentTab: 'browse',
selectedFiles: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: true,
errorMessage: 'error1',
isUploading: false,
originalIndex: 0,
},
{
abortController: new AbortController(),
file: { test: true, name: 'My File' },
hasError: true,
errorMessage: 'error2',
isUploading: false,
originalIndex: 1,
},
{
abortController: new AbortController(),
file: { test: false },
hasError: true,
errorMessage: 'error3',
isUploading: false,
originalIndex: 2,
},
],
};
const expected = {
currentStep: 'test',
currentTab: 'selected',
selectedFiles: [
{
id: 1,
name: 'myFile',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
{
id: 2,
name: 'myFile2',
ext: '.png',
mime: 'image/png',
size: 146.25,
url: '/uploads/ba0c3352c4b14132aed3fcf3110b481c.png',
created_at: '2020-03-04T09:45:32.444Z',
updated_at: '2020-03-04T09:45:32.444Z',
},
],
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: true,
errorMessage: 'error1',
isUploading: false,
originalIndex: 0,
},
{
abortController: new AbortController(),
file: { test: false },
hasError: true,
errorMessage: 'error3',
isUploading: false,
originalIndex: 2,
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('RESET_PROPS', () => {
it('should return the initialState', () => {
const action = { type: 'RESET_PROPS' };
const state = { test: true };
const expected = {
allowedTypes: [],
selectedFiles: [],
files: [],
filesToDownload: [],
filesToUpload: [],
fileToEdit: null,
currentTab: null,
params: {
_limit: 10,
_start: 0,
_q: '',
filters: [],
_sort: null,
},
currentStep: 'list',
isFormDisabled: false,
isWarningDeleteOpen: false,
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('SET_CROP_RESULT', () => {
it('should update the fileToEditEntry with the passed data', () => {
const action = {
type: 'SET_CROP_RESULT',
blob: {
test: true,
},
};
const state = {
fileToEdit: {
originalIndex: 1,
file: null,
},
};
const expected = {
fileToEdit: {
originalIndex: 1,
file: {
test: true,
},
},
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('SET_FILE_ERROR', () => {
it('should update the specified file error', () => {
const action = {
type: 'SET_FILE_ERROR',
fileIndex: 1,
errorMessage: 'size limit exceeded',
};
const state = {
currentStep: 'test',
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: false,
errorMessage: null,
isUploading: true,
originalIndex: 0,
},
{
abortController: new AbortController(),
file: { test: true },
hasError: false,
errorMessage: null,
isUploading: true,
originalIndex: 1,
},
{
abortController: new AbortController(),
file: { test: false },
hasError: false,
errorMessage: null,
isUploading: true,
originalIndex: 2,
},
],
};
const expected = {
currentStep: 'test',
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: false,
errorMessage: null,
isUploading: true,
originalIndex: 0,
},
{
abortController: new AbortController(),
file: { test: true },
hasError: true,
errorMessage: 'size limit exceeded',
isUploading: false,
originalIndex: 1,
},
{
abortController: new AbortController(),
file: { test: false },
hasError: false,
errorMessage: null,
isUploading: true,
originalIndex: 2,
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('SET_FILE_TO_EDIT_ERROR', () => {
it('should update the fileToEdit error', () => {
const action = {
type: 'SET_FILE_TO_EDIT_ERROR',
errorMessage: 'size limit exceeded',
};
const state = {
fileToEdit: {
originalIndex: 1,
file: {
name: 'test1',
},
hasError: false,
errorMessage: null,
isUploading: true,
},
filesToUpload: [
{
originalIndex: 0,
file: {
name: 'test0',
},
},
{
originalIndex: 1,
file: {
name: 'test1',
},
},
{
originalIndex: 2,
file: {
name: 'test2',
},
},
],
};
const expected = {
fileToEdit: {
originalIndex: 1,
file: {
name: 'test1',
},
hasError: true,
errorMessage: 'size limit exceeded',
isUploading: false,
},
filesToUpload: [
{
originalIndex: 0,
file: {
name: 'test0',
},
},
{
originalIndex: 1,
file: {
name: 'test1',
},
},
{
originalIndex: 2,
file: {
name: 'test2',
},
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('SET_NEW_FILE_TO_EDIT', () => {
it('should set the fileToEdit key with the file at the passed index from the filesToUpload list', () => {
const action = {
type: 'SET_NEW_FILE_TO_EDIT',
fileIndex: 1,
};
const state = {
fileToEdit: null,
filesToUpload: [
{
originalIndex: 0,
file: {
name: 'test0',
},
},
{
originalIndex: 1,
file: {
name: 'test1',
},
},
{
originalIndex: 2,
file: {
name: 'test2',
},
},
],
};
const expected = {
fileToEdit: {
originalIndex: 1,
file: {
name: 'test1',
},
},
filesToUpload: [
{
originalIndex: 0,
file: {
name: 'test0',
},
},
{
originalIndex: 1,
file: {
name: 'test1',
},
},
{
originalIndex: 2,
file: {
name: 'test2',
},
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('SET_FILES_UPLOADING_STATE', () => {
it('should change all the isUploading keys of the filesToUpload to true', () => {
const action = {
type: 'SET_FILES_UPLOADING_STATE',
};
const state = {
currentStep: 'test',
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: false,
errorMessage: 'test',
isUploading: true,
originalIndex: 0,
},
{
abortController: new AbortController(),
file: { test: true },
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 1,
},
{
abortController: new AbortController(),
file: { test: false },
hasError: false,
errorMessage: null,
isUploading: false,
originalIndex: 2,
},
],
};
const expected = {
currentStep: 'test',
filesToUpload: [
{
abortController: new AbortController(),
file: { ok: true },
hasError: false,
errorMessage: null,
isUploading: true,
originalIndex: 0,
},
{
abortController: new AbortController(),
file: { test: true },
hasError: false,
errorMessage: null,
isUploading: true,
originalIndex: 1,
},
{
abortController: new AbortController(),
file: { test: false },
hasError: false,
errorMessage: null,
isUploading: true,
originalIndex: 2,
},
],
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('SET_FILE_TO_EDIT', () => {
it('should add a file to edit', () => {
const action = {
type: 'SET_FILE_TO_EDIT',
fileId: 13252341,
};
const state = {
currentStep: 'test',
fileToEdit: null,
selectedFiles: [],
files: [
{
id: 13252341,
alternativeText: 'My first picture',
caption: null,
name: 'picture1',
updated_at: '2020-03-30T10:48:26+02:00',
created_at: '2020-03-30T10:48:26+02:00',
},
{ id: 5564723, alternativeText: 'My second picture', caption: '', name: '' },
],
};
const expected = {
currentStep: 'test',
selectedFiles: [],
files: [
{
id: 13252341,
alternativeText: 'My first picture',
caption: null,
name: 'picture1',
updated_at: '2020-03-30T10:48:26+02:00',
created_at: '2020-03-30T10:48:26+02:00',
},
{ id: 5564723, alternativeText: 'My second picture', caption: '', name: '' },
],
fileToEdit: {
id: 13252341,
abortController: new AbortController(),
file: {
name: 'picture1',
created_at: '2020-03-30T10:48:26+02:00',
},
fileInfo: {
alternativeText: 'My first picture',
caption: null,
name: 'picture1',
},
hasError: false,
errorMessage: null,
isUploading: false,
},
};
expect(reducer(state, action)).toEqual(expected);
});
it('should add a selected file to edit', () => {
const action = {
type: 'SET_FILE_TO_EDIT',
fileId: 13252341,
};
const state = {
currentStep: 'test',
fileToEdit: null,
files: [],
selectedFiles: [
{
id: 13252341,
alternativeText: 'My first picture',
caption: null,
name: 'picture1',
updated_at: '2020-03-30T10:48:26+02:00',
created_at: '2020-03-30T10:48:26+02:00',
},
{ id: 5564723, alternativeText: 'My second picture', caption: '', name: '' },
],
};
const expected = {
currentStep: 'test',
files: [],
selectedFiles: [
{
id: 13252341,
alternativeText: 'My first picture',
caption: null,
name: 'picture1',
updated_at: '2020-03-30T10:48:26+02:00',
created_at: '2020-03-30T10:48:26+02:00',
},
{ id: 5564723, alternativeText: 'My second picture', caption: '', name: '' },
],
fileToEdit: {
id: 13252341,
abortController: new AbortController(),
file: {
name: 'picture1',
created_at: '2020-03-30T10:48:26+02:00',
},
fileInfo: {
alternativeText: 'My first picture',
caption: null,
name: 'picture1',
},
hasError: false,
errorMessage: null,
isUploading: false,
},
};
expect(reducer(state, action)).toEqual(expected);
});
});
describe('SET_PARAM', () => {
it('should set the _start param to 0 if the pagination limit changed', () => {
const action = {
type: 'SET_PARAM',
param: {
name: '_limit',
value: 50,
},
};
const state = {
params: {
_start: 10,
},
};
const expected = {
params: {
_start: 0,
_limit: 50,
},
};
expect(reducer(state, action)).toEqual(expected);
});
it('should add filter to params', () => {
const action = {
type: 'SET_PARAM',
param: {
name: 'filters',
value: {
name: 'mime',
filter: '_contains',
value: 'image',
},
},
};
const state = {
params: {
_start: 10,
filters: [],
},
};
const expected = {
params: {
_start: 0,
filters: [
{
name: 'mime',
filter: '_contains',
value: 'image',
},
],
},
};
expect(reducer(state, action)).toEqual(expected);
});
it('should not add filter to params if it is already exist', () => {
const action = {
type: 'SET_PARAM',
param: {
name: 'filters',
value: {
name: 'mime',
filter: '_contains',
value: 'image',
},
},
};
const state = {
params: {
_start: 0,
_limit: 50,
filters: [
{
name: 'mime',
filter: '_contains',
value: 'image',
},
],
},
};
const expected = {
params: {
_start: 0,
_limit: 50,
filters: [
{
name: 'mime',
filter: '_contains',
value: 'image',
},
],
},
};
expect(reducer(state, action)).toEqual(expected);
});
});
});
|
{
"pile_set_name": "Github"
}
|
A motorcycle such as the 2008 Kawasaki ZX6R featured in this video could probably beat a Tesla Model S under ideal conditions with a highly experienced rider on board the bike, but most of the time, a motorcycle will be no match for the Model S in low-speed, straight-line acceleration.
*Editor's Note: This video contains some very NSFW elements, including foul language.
We think that this video rather accurately captures how difficult it is to accelerate as rapidly as the Model S, even when the other vehicle in question is a sub-1,000 sport bike designed for speed.
|
{
"pile_set_name": "Pile-CC"
}
|
obviously a 258 will be better on gas but i sure love my warmed 401. i get 10 in town and 12-13 highway with th400 (no overdrive) 35 mts and 4.10 gearing. not bad mpg considering. my truck came from colorado and had almost no rust. floorboards will be rusty wherever. the only thing i would (will) change is adding fuel injection. i think the 74+ trucks have tons more parts. bjsoffroad.com. also, the 80+ tcases might not be able to handle brutal v8 power.
obviously a 258 will be better on gas but i sure love my warmed 401. i get 10 in town and 12-13 highway with th400 (no overdrive) 35 mts and 4.10 gearing. not bad mpg considering. my truck came from colorado and had almost no rust. floorboards will be rusty wherever. the only thing i would (will) change is adding fuel injection. i think the 74+ trucks have tons more parts. bjsoffroad.com. also, the 80+ tcases might not be able to handle brutal v8 power.
so are there three engine options. the 258, 360, and 401? are the tranny and t case the same for both V8s?
are 4.10 stock gearing? i beleive i read in the axle section they have d44 front and rear, so they have a large gear range, all the way to 5.13, right?
4.10 for manual tranny i believe. the th400 was up til 79 with bw qt. after that im think its the tf727 with new process t cases. the 360 could be had with 2 or 4 barrel carb. j20 has hd 44 and dana 60 rear. i love my truck. ive had 3 xjs, 3 zjs (2 of which were 5.9), and other non jeeps. i personally LOVE the J truck. people are always honking and looking at it. i will never sell it
looks like i answered my own question about power. so i know the power of the engines, i know the axles and ratios of different j-10 trucks, i know potential milage. now the question is, if i do a J-10 project, would it be worth my time to swap the engine?
the power numbers on these engines arnt great, as expected for 70's technology, and they arnt efficient, also expected. if i got my hands on a newer v8 drive train, or even a good 6cyl drivetrain, would a swap be the best option, or are the stock v8s better than they seem?
|
{
"pile_set_name": "Pile-CC"
}
|
Last week (17-18 July 2018), at the Beyond Blocks Summit in Seoul, South Korea, Ran Neu-Ner, CNBC’s “Crypto Trader”, did an interview with Michael Arrington, a partner at XRP-denominated cryptoasset hedge fund “Arrington XRP Capital”, during which they talked about XRP.
Arrington, who announced his hedge fund on 28 November 2017 at Consensus: Invest 2017 conference in New York, said at the time that his crypto-focused fund would be entirely denominated in XRP. In the blog post about the announcement, Arrington explained what this means:
“Investors contribute XRP to the fund, not dollars or other fiat currency.”
“All distributions, fees, etc. will also generally be paid in XRP (with some exceptions for LPs desiring different currency distributions).”
He described his reasoning for denominating the fund in XRP as follows:
“First, having a hedge fund denominated in a cryptocurrency makes things far easier for investors who already hold a lot of cryptocurrency. No need to convert back to fiat and then later back to a cryptocurrency as we make investments. Everyone saves fees and time that way. Second, XRP, developed by Ripple, is particularly useful for us. While we don’t have a commercial relationship with Ripple (they are not investors in our fund, for example), we are still able to use their super-fast and secure settlement infrastructure, as anyone else can. That means non-U.S. investors in our fund will have an easier time investing in us and making redemptions later. No need to rely on ancient fiat methods for cross-border currency transfers that are slow and laden with fees. We’ll pay our own fees and salaries out in XRP as well.”
During the interview with the CNBC Crypto Trader, Arrington was asked why he had chosen to denominate his fund in XRP. Arrington replied:
“XRP is a really really good way to move money. So, we denominate our fund in XRP because it's a fantastic way to move money cross-border very quickly at almost zero cost. So, there's a lot of tribalism in cryptocurrency… The one thing they all agree on is they all hate XRP because it's centralized, they think it's corporate-managed, etc. I mean, none of that is really true. But what it is is it's a fantastic way to move money. And while the other more decentralized cryptocurrencies sort of find their way toward becoming more efficient, in the mean time, XRP is fantastic. So, from a hedge fund point of view, it's great to denominate ourselves in XRP.”
Interface Image Credit: Image Courtesy of Beyond Blocks
|
{
"pile_set_name": "OpenWebText2"
}
|
Thermal behavior of a lipid-protein membrane model and the effects produced by anesthetics and neurotransmitters.
Despite decades of intense research to understand the phenomenon of anesthesia and its membrane-related changes in neural transmission, where lipids and proteins have been proposed as primary targets of anesthetics, the involved action mechanisms remain unclear. Based on the overall agreement that anesthetics and neurotransmitters induce particular modifications in the plasma membrane of neurons, triggering specific responses and changes in their energetic states, we present here a thermal study to investigate membrane effects in a lipid-protein model made of 1,2-dimyristoyl-sn-glycero-3-phosphocholine and albumin from chicken egg white under the influence of neurotransmitters and anesthetics. First, we observe how ovalbumin, ovotransferrin, and lysozyme (main albumin constituents from chicken egg white) interact with the lipid membrane enhancing their lipophilic character while exposing their hydrophobic domains. This produces a lipid separation and a more ordered hybrid lipid-protein assembly. Second, we measured the thermotropic changes of this assembly induced by acetylcholine, γ-aminobutiric acid, tetracaine, and pentobarbital. Although the protein in our study is not a receptor, our results are striking, for they give evidence of the great importance of non-specific interactions in the anesthesia mechanism.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
Q:
Bash extract string from file to use as variable
What bash basic have I forgotten? I'm just trying to build a filename up in a script with VERSION and BUILD info...
So, dead-easy if hardcoded - this all makes sense:
VERSION=1.0.1
BUILD=45
NAME=Product-$VERSION-$BUILD.zip
echo $NAME
> Product-1.0.1-45.zip
But, what if the VERSION is provided via a (single) line in a file with contents just "1.0.1":
VERSION=$(<version.txt)
echo $VERSION
> 1.0.1
BUILD=45
NAME=Product-$VERSION-$BUILD.zip
echo $NAME
> -45.zip-1.0.1
?????? "-45.zip-1.0.1"?
Ok, I though it might be some left over newline or end of file character, so I've tried:
VERSION=$(cat version.txt)
VERSION=$(cat version.txt | tr -d '\n')
VERSION=$(sed -n '1p' version.txt)
Same effect. Using quotes around NAME="..." no joy (I had thought there was some interpolation going on...)
And, this is all on a Mac with:
bash --version
GNU bash, version 3.2.57(1)-release (x86_64-apple-darwin15)
Copyright (C) 2007 Free Software Foundation, Inc.
Thank you.
A:
Try:
VERSION=$(tr -d '\r' < version.txt)
as version.txt seems to have DOS line endings.
|
{
"pile_set_name": "StackExchange"
}
|
Q:
how to make a div transparent without affecting the child in CSS 3?
how to make a div transparent without affecting the child in CSS 3
here's my HTML code:
<div id="icon">
<ul>
<li><a href=""><img src="Iconpaper.png"></a></li>
<li><a href=""><img src="Movies.png"></a></li>
<li><a href=""><img src="Phone.png"></a></li>
<li><a href=""><img src="Stocks.png"></a></li>
<li><a href=""><img src="Love.png"></a></li>
</ul>
</div>
<div id="search">
SEARCH
</div>
</div>
and here's the CSS:-
#header{
background-color:#000;
width:1349px;
height:60px;
position:fixed;
z-index:2;
opacity:0.7;
}
#icon{
float:left;
padding:10px;
}
li{
display:inline;
}
#header img{
width:35px;
height:35px;
}
#search{
float:right;
color:#e5e5e5;
padding:20px;
font-size:20px;
}
so, I want to make the #header div tranparent and fixed without affecting the #icon and #search div.
A:
Instead of using opacity, use rgba() like background: rgba(0,0,0,.7) where a stands for alpha/opacity. So change the below block of code like
#header{
background-color: rgba(0,0,0,.7); /* 0.7 Opacity for black */
width:1349px;
height:60px;
position:fixed;
z-index:2;
}
|
{
"pile_set_name": "StackExchange"
}
|
Advertisement New poll shows change in presidential race in Wisconsin Share Shares Copy Link Copy
There has been a shakeup in the presidential race in Wisconsin.The new Marquette Law School poll released Thursday shows a shift in both parties.The candidates have barely campaigned in Wisconsin, but we're seeing voters here are shifting their support.On the Democratic side. Hillary Clinton and Bernie Sanders are now in a statistical tie. Clinton is leading by just two points, 45-43 among Wisconsin voters, but well within the margin of error.She held 9 point lead over Sanders in the last poll in November. Martin O'Malley is at just 1 percent.In the Republican race, Donald Trump is now in the lead, with 24 percent.Trump was tied for second last time with 19 percent. He's followed by Marco Rubio, Ted Cruz and Ben Carson.Cruz had the biggest gain, jumping 7 points over the last poll to 16 percent, while Carson plummeted from first place in November with 22 percent down to 8 percent this time. Rubio is at 18 percent. The poll's director expects it all to change again before Wisconsin voters go to the polls.“I think we'll (see) dramatic changes after Iowa and after New Hampshire, and we'll know much better in mid-February what the situation will look like as the race comes to Wisconsin in April,” Marquette Law School Poll Director Charles Franklin said.Clinton and Trump each have only very small leads, but when voters were asked who they thought would win the nomination, those two run away with it.Nearly 49 percent of Republicans think Trump will win, and more than 65 percent of Democrats believe Clinton will be the party's nominee.Unlike the presidential primaries, Wisconsin's U.S. Senate race shows only a slight change in the numbers, and it’s a race that is not very close at this point.VIDEO: MU poll has Feingold ahead in U.S. Senate raceThe poll has former U.S. Sen. Russ Feingold, the Democrat, leading the incumbent Republican U.S. Sen. Ron Johnson, by a 50-to-37 point margin.That's a 2 percentage increase in Feingold's lead since November.The poll's director said the bigger surprise may be Johnson's lack of name recognition among voters.“It's hovered in the 30s and 40 percent who say they don't know enough to have an opinion about him. But I think it reflects on the fact that people are more focused on the presidential politics than on the Senate race at this point,” Franklin said.
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{
"pile_set_name": "OpenWebText2"
}
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Evaluation of vector competence for West Nile virus in Italian Stegomyia albopicta (=Aedes albopictus) mosquitoes.
West Nile virus (WNV) is a zoonotic arboviral pathogen transmitted by mosquitoes in a cycle that involves wild birds as reservoir hosts. The virus is responsible for outbreaks of viral encephalitis in humans and horses. In Europe, Culex pipiens (Diptera: Culicidae) is considered to be the main vector of WNV, but other species such as Stegomyia albopicta (=Aedes albopictus) (Diptera: Culicidae) may also act as competent vectors of this virus. Since 2008 human cases of WNV disease have been reported in northeast Italy. In 2011, new areas of southern Italy became involved and a first outbreak of WNV lineage 1 occurred on the island of Sardinia. On the assumption that a potential involvement of St. albopicta in WNV transmission cannot be excluded, and in order to evaluate the competence of this species for the virus, an experimental infection of an St. albopicta laboratory colony, established from mosquitoes collected in Sardinia, was carried out. The results were compared with those obtained in a colony of the main vector Cx. pipiens. The study showed St. albopicta collected on Sardinia to be susceptible to WNV infection, which suggests this Italian mosquito species is able to act as a possible secondary vector, particularly in urban areas where the species reaches high levels of seasonal abundance.
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{
"pile_set_name": "PubMed Abstracts"
}
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In drug discovery research, proper evaluation of incorporation, metabolism and excretion of a drug or the like in the hepatic tissue of a living body is extremely important. Further, for simply carrying out large-scale drug screening, or from an ethical point of view, an in vitro test method has been demanded. As a means for such a test, cultured cells are used, and their culture is preferably carried out under conditions reflecting those in a living body as much as possible. For example, as a culture system for hepatocytes, one which can excellently reproduce the proper polarity of the hepatic tissue of a living body, wherein, for example, the cell membrane is clearly differentiated between the blood vessel side and the bile canaliculus membrane side, is demanded
For example, Patent Document 1 describes that it is thought that, by binding a binding protein or an adhesion protein to a microscale substrate and culturing hepatocytes thereon, formation of a bile canaliculus is promoted. Further, Patent Document 2 describes that, by culturing small hepatocytes on a polycarbonate porous sheet covered with collagen, a bile canaliculus-like structure was formed on Day 30 of the culture.
In the above-described three-dimensional culture methods, preparation of hepatocytes having the polarity from the primary cultured cells takes several weeks to several months.
On the other hand, in cases where the collagen gel sandwich method (Non-patent Document 1: LeCluyse et al., Am J Physiol Cell Physiol, 1994, vol. 266, pp. 1764-1774) is used, formation of a bile canaliculus and the bile component excretion activity begins to be detected about 3 or 4 days after deposition of a collagen gel. However, even in the cases where the collagen gel sandwich method is used, several days are required before the bile component excretion activity is obtained. Further, metabolites cannot be continuously analyzed in such cases since a bile duct having an outlet, as is the case in a living body, is required for the continuous analysis. There is also a problem in that the number of bile canaliculi is too small and the activity is too low, to be used in drug screening.
Further, in Non-patent Document 2 (Tissue Engineering vol.13 Number 8 2007 2105-2117) and Non-patent Document 3 (Acta Biomaterialia 5 2009 613-620), it is shown that, when hepatocytes are to be cultured on gas-permeable PDMS (polydimethylsiloxane), adhesion of the cells can be maintained for 3 days by coating the surface of the PDMS with PEM or by forming thin pillars having a diameter of 1 to 3 μm. However, the adhesion cannot be maintained for a long time and hence those cultured cells are problematic in view of stable use in a test. Further, it has been generally thought that PDMS is not suitable for adherent culture of hepatocytes.
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{
"pile_set_name": "USPTO Backgrounds"
}
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1. Field of the Invention
The present invention relates to a dispensing apparatus and more particular to a dispensing apparatus having a dispensing assembly and a slidable locking cap for restraining the dispensing assembly in a closed position.
2Description of the Related Art
Dispensing devices, especially those for lawn care products such as a combination of lawn fertilizer and weed control, are known, as exemplified by U.S. Pat. No. 5,996,858. Lawn products are often particulate or granular, but may be liquid, and these are spread by a consumer holding the device in an open condition while walking at a prescribed rate along a predetermined path. These devices have rotatable spouts fitted to a plastic molded container having an integral handle. Some have covers, other breakaway tabs and some have both.
The lawn product must be handled in a recommended manner and the dispensing devices ought to be tightly closed and kept in a safe place. Cost, ease of use and reliable structure are also of concern when designing such dispensing devices.
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{
"pile_set_name": "USPTO Backgrounds"
}
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Been away for a good while now after getting married. For some reason I felt the need to draw these two. These where one of my favorite OTP's from way back. I love them <3
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{
"pile_set_name": "OpenWebText2"
}
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Smoking habits of final-year Galician medical students.
Smoking habits among final-year Galician medical students have been studied using a questionnaire complying with the recommendations of the W.H.O. and the U.I.C.C. Aspects reported include the prevalence of the smoking habit, the characteristics of smoker, drug and habit, and health problems attributed to smoking. The prevalence rate was high (61.9%); average consumption by smokers was 16 cigarettes/day; most smokers smoked cigarettes with medium-to-high nicotine and medium-to-low tar contents; and the proportion of ex-smokers was small. Smokers were found to be well aware of the dangers of smoking, and their failure to relinquish the habit is attributed to lack of social support. The role of Medical Faculties in the fight against smoking is discussed, and it is suggested that priority should be given to anti-smoking campaigns among secondary school students (14-17 year-olds) and university undergraduates, since 60% of smokers acquired the habit during the former period and 21% during the latter.
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{
"pile_set_name": "PubMed Abstracts"
}
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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<html><head><title>Python: package debugging</title>
</head><body bgcolor="#f0f0f8">
<table width="100%" cellspacing=0 cellpadding=2 border=0 summary="heading">
<tr bgcolor="#7799ee">
<td valign=bottom> <br>
<font color="#ffffff" face="helvetica, arial"> <br><big><big><strong>debugging</strong></big></big></font></td
><td align=right valign=bottom
><font color="#ffffff" face="helvetica, arial"><a href=".">index</a><br><a href="file:e:\vslprf\dlr\languages\ironpython\tests\debugging\__init__.py">e:\vslprf\dlr\languages\ironpython\tests\debugging\__init__.py</a></font></td></tr></table>
<p><tt>-------------------------------------------------------------------------------<br>
INTRODUCTION<br>
This test plan addresses debugging test coverage for the 2.x series of <br>
IronPython interpreter releases.<br>
<br>
EDITORS NOTES<br>
Throughout this document you will find references to documentation in<br>
other packages similar to "See documentation for debugging.pdb_module". This simply<br>
means that relative to this package (i.e., debugging), you should follow<br>
the 'pdb_module (package)' link at the bottom of this page.<br>
<br>
-------------------------------------------------------------------------------<br>
FEATURE GOALS<br>
The goals of IP's debugging feature is to provide IronPython users with <br>
complete use of CPython's existing debugger functionality, the "pdb" and<br>
"bdb" modules respectively, while also providing a great interactive debugging <br>
experience using Microsoft tools such as mdbg and the Visual Studio IDE.<br>
<br>
-------------------------------------------------------------------------------<br>
PRIMARY TESTING CONCERNS<br>
- new builtin module attributes added to IP to support CPython's "bdb" and "pdb"<br>
modules<br>
- compatibility with CPython's use of the "bdb" and "pdb" modules<br>
- what happens breakpoint-wise when IP steps into .NET code from "pdb"?<br>
- .NET applications hosting IP should be able to debug Python code<br>
- the experience of debugging IP under Microsoft's mdbg and Visual <br>
Studio tools is what existing CSharp and VB.Net would expect; but still<br>
Pythonic<br>
- "-D" command-line flag<br>
<br>
-------------------------------------------------------------------------------<br>
PRIMARY TESTING FOCUS<br>
Our principal testing focus will be on testing that IP's support of the<br>
"pdb" module is completely compatible with that of CPython by running existing<br>
CPython tests, and also by creating a new generic side-by-side testing framework.<br>
<br>
The secondardy focus will be testing that debugging IP under mdbg is a<br>
pleasant experience. This will initially be acheived by using the CLR Team's<br>
existing debugging test framework, but in the long run we will move to a<br>
new generic, side-by-side testing framework which can be reused for other <br>
side-by-side testing areas.<br>
<br>
-------------------------------------------------------------------------------<br>
REFERENCES<br>
* IronPython Test Plan Internal IP SharePoint site<br>
* Feature Specifications None...<br>
* Development Documents None...<br>
* Schedule Documents None...<br>
* CPython pdb module <a href="http://docs.python.org/library/pdb.html">http://docs.python.org/library/pdb.html</a><br>
* CPython bdb module <a href="http://docs.python.org/library/bdb.html">http://docs.python.org/library/bdb.html</a><br>
* pdb tutorial <a href="http://onlamp.com/pub/a/python/2005/09/01/debugger.html">http://onlamp.com/pub/a/python/2005/09/01/debugger.html</a><br>
* MDbg.exe <a href="http://msdn.microsoft.com/en-us/library/ms229861.aspx">http://msdn.microsoft.com/en-us/library/ms229861.aspx</a><br>
* Debugging IP in Visual Studio <a href="http://devhawk.net/2008/05/08/Debugging+IronPython+Code+In+Visual+Studio.aspx">http://devhawk.net/2008/05/08/Debugging+IronPython+Code+In+Visual+Studio.aspx</a><br>
* Bug queries <a href="http://ironpython.codeplex.com/WorkItem/AdvancedList.aspx">http://ironpython.codeplex.com/WorkItem/AdvancedList.aspx</a><br>
and set the component to "Debugging"<br>
* Build drop location Updated at <a href="http://ironpython.codeplex.com/SourceControl/ListDownloadableCommits.aspx">http://ironpython.codeplex.com/SourceControl/ListDownloadableCommits.aspx</a><br>
on weekdays<br>
* source file tree $/.../dlr/Debugging/ and also $/.../dlr/.../IronPython/*<br>
<br>
-------------------------------------------------------------------------------<br>
PERSONNEL<br>
Program Manager: hpierson<br>
Developer: dinov<br>
Tester: dfugate<br>
<br>
-------------------------------------------------------------------------------<br>
TESTING SCHEDULE<br>
<br>
Phase I - Test Plan and Enabling Existing Tests<br>
- Write test plan for IronPython Debugging feature<br>
- Enable any existing CPython test cases for "pdb" and "bdb" in SNAP<br>
- Enable any existing CPython test cases for Python features supporting <br>
"pdb" and "bdb" in SNAP<br>
<br>
Phase II - Examine Coverage of Existing Cases and Write High-priority Cases<br>
- Verify that developer tests for new additions to IP <br>
supporting "pdb" and "bdb" modules are sufficient. Write more test<br>
cases if not<br>
- Write additional test cases for the "pdb" module if CPython's test cases <br>
are insufficient<br>
- Examine our existing mdbg test (cases) looking for holes. Write new test<br>
cases if needed<br>
- Author a few manual sanity test cases for verifying IP can <br>
be debugged under the Visual Studio IDE. These should be folded into<br>
the CodePlex test pass signoff procedure for major releases<br>
<br>
Phase III - Design and Implement Side-by-Side Testing Framework<br>
- Based on the needs of test cases added in the previous phase either:<br>
1. Design a side-by-side testing infrastructure to be used with testing<br>
IP's CPython debugging compatibility OR<br>
2. Look for existing side-by-side testing frameworks we could reuse.<br>
The pexpect package might be useful here<br>
- Implement (or add existing) side-by-side testing framework<br>
<br>
Phase IV - Implement High-priority Cases<br>
- Implement test cases for additions to IP which support the<br>
"pdb" module IF NEEDED<br>
- Implement test cases for the "pdb" module IF NEEDED<br>
- Implement test cases for mdbg IF NEEDED<br>
<br>
Phase IV - Write Lower Priority Cases<br>
- Write test cases around stepping into (hosted) Python code from a <br>
.NET application<br>
- Write test cases around stepping into .NET code from an ipy.exe<br>
process<br>
- Write performance test cases<br>
<br>
Phase V - Implement Lower Priority Cases<br>
- Implement test cases around stepping into (hosted) Python code from a <br>
.NET application<br>
- Implement test cases around stepping into .NET code from an ipy.exe<br>
process<br>
- Implement performance test cases<br>
<br>
Phase VI - Future<br>
- Develop test cases for the "bdb" module if CPython's test cases are<br>
insufficient<br>
- Automate manual sanity Visual Studio debugging tests<br>
- Migrate existing mdbg tests to the new side-by-side testing framework<br>
- Low-resource test cases and implementation<br>
- Reliability test cases and implementation<br>
- Scalability test cases and implementation<br>
- Stress test cases and implementation<br>
- Internationalization test cases and implementation<br>
<br>
Phase P - All Public Releases<br>
- Verify all user documentation with respect to debugging<br>
- Setup testing - verify pdb.py and all supporting modules are installed by the MSI<br>
- Generate code coverage report and verify block coverage as greater<br>
than 80%<br>
<br>
-------------------------------------------------------------------------------<br>
FEATURE HISTORY<br>
2.0: Tests implemented for IronPython under mdbg. Scenarios which still <br>
need to be covered are:<br>
* Attach scenario with and without the -D option<br>
* Step into/out when there is no pdb file for IP <br>
binaries<br>
* Multiple statements in one line (e.g., "x = 1;y=2"<br>
* if x and \n y: print 1<br>
* dict/tuple spanning multiple lines<br>
* break/continue, explicit raise<br>
* other multi-line statement scenarios such as:<br>
if True: print 1<br>
if True:\n print 1<br>
* MdbgInterop<br>
able to break into the C# code from Python<br>
able to break back into Python code from C#<br>
<br>
2.6B2: First release of IronPython to include support of CPython's pdb module.<br>
Only works if -X:Frames or -X:FullFrames option supplied to ipy.exe.<br>
No pdb-related tests running in SNAP at this point, but we are running<br>
all of CPython's tests WRT supporting functions in the sys module.<br>
Debugging test plan completely rewritten in the form of pydoc strings,<br>
and made public.<br>
<br>
-------------------------------------------------------------------------------<br>
FEATURES:<br>
- sys.settrace, sys.gettrace, and sys.call_tracing. NOTE: while each of these<br>
three builtin module members needs to be tested within unit tests on their<br>
own, the real use case here is through the "bdb" and "pdb" modules<br>
- ipy.exe's generation of PDBs<br>
- ipy.exe's PDB visualizers<br>
<br>
-------------------------------------------------------------------------------<br>
FILES AND MODULES:<br>
<br>
- FILES LIST:<br>
* everything under Microsoft.Scripting.Debugging, although the DLR <br>
officially owns this<br>
* sys.cs<br>
* IronPython.Runtime.PythonTracebackListener<br>
- REGISTRY, INI SETTINGS: None<br>
- SETUP PROCEDURES: <br>
CPython standard library must be installed and present in sys.path to be <br>
usable<br>
- DE-INSTALLATION PROCEDURES<br>
N/A<br>
- DATABASE SETUP AND PROCEDURES<br>
N/A<br>
- NETWORK DOMAIN/TOPOLOGIES CONFIGURATION PROCEDURES<br>
N/A<br>
- PERFORMANCE MONITORING COUNTERS SETUP AND CONFIGURATIONS<br>
N/A<br>
<br>
-------------------------------------------------------------------------------<br>
OPERATIONAL ISSUES<br>
N/A. This feature of IP is not being monitored/maintained by operational <br>
staff, and IP is provided on an as-is basis.<br>
<br>
-------------------------------------------------------------------------------<br>
SCOPE OF TEST CASES<br>
We'll be getting most of our test coverage on the debugging feature of <br>
IP by unit testing the CPython 'pdb' module. Doing this thoroughly<br>
should guarantee we hit nearly all blocks of code supporting debugging in <br>
IP DLLs. This will be validated and verified through monthly code <br>
coverage runs. As an aside, this should in theory hit most of the DLR's<br>
Microsoft.Scripting.Debugging.dll as well.<br>
<br>
As IP currently has no tie-in into the Visual Studio IDE, this is <br>
arguably far less important to test than our support of the 'pdb' module or <br>
even mdbg. As a result, the Microsoft toolset testing emphasis will involve<br>
exahaustively covering all aspects of mdbg. That said, some of our users do in<br>
fact have VS Pro installed implying that we should perform at least minimal,<br>
manual sanity tests before every major public release of IP. Should we<br>
ever provide visualizers for our debug symbols we'll need much more <br>
comprehensive and automated tests for VS of course.<br>
<br>
-------------------------------------------------------------------------------<br>
ACCEPTANCE CRITERIA<br>
- no debugging related feature should be checked into the internal source <br>
repository without some form of unit test hooked into SNAP checked in as<br>
well<br>
- we should not publically advertise the existance of any new debugging features<br>
in an IP release unless:<br>
- if the feature is CPython-based; the majority of it's corresponding <br>
CPython unit test cases have been enabled in SNAP and pass<br>
- if the feature is novel to IP; block coverage should be greater<br>
than 70%<br>
- the feature needs to be documented in some form other than a blog<br>
- performance of the feature needs to be "within reason"<br>
- if the feature is not CPython-based; it needs a Pythonic feel to it<br>
- at least half of all bugs opened on the feature since its inception are<br>
fixed<br>
<br>
-------------------------------------------------------------------------------<br>
KEY FEATURE ISSUES<br>
- no spec on debugging IP from mdbg, VS, or what debugging symbols <br>
should be generated for various Python constructs<br>
- insufficient test resources to adequately test this feature<br>
- insufficient resources to implement all debugging features called out in this<br>
test plan<br>
- existing mdbg tests are based on CLR infrastructure and require a Perl <br>
installation. We cannot redistribute this publically<br>
- existing mdbg tests in SNAP are flakey<br>
<br>
-------------------------------------------------------------------------------<br>
TEST APPROACH<br>
- DESIGN VALIDATION<br>
We have no part in the design of the "pdb" and "bdb" standard modules. <br>
<br>
As for debugging under mdbg...there is no current design document on <br>
debugging Python sessions. Generally speaking test will simply ensure that<br>
whatever mdbg functionality exists with regard to IP is "Pythonic",<br>
but at the same time familiar to CSharp and VB developers.<br>
<br>
- DATA VALIDATION<br>
pdb/bdb: at a very low-level, all we need to validate is that parameters passed<br>
to a trace function we set via sys.settrace are as expected. In particular,<br>
the first parameter passed in is the current stack frame which we have a <br>
very solid chance of getting wrong.<br>
<br>
mdbg/VS: need to validate that generation of PDB symbols "make sense"<br>
with respect to whatever Python source is being compiled. There are at <br>
least two ways to accomplish this:<br>
1. Create a regression test in which we compare the generated PDB of a <br>
known Python script to an expected PDB file. The Python script should<br>
exhaustively cover everything that's possible in the Python grammar.<br>
Testing in this manner is not really maintainable in the long run as we<br>
expect the PDB generated for a given Python script to change over time<br>
reflecting optimizations and new features added to IP<br>
2. Test that the behavior of mdbg, given a known Python script, does not <br>
regress. Again, this Python script should exhaustively cover everything<br>
that's possible in Python's grammar, but this time around we'll also<br>
need to cover everything that's possible under mdbg<br>
<br>
- API TESTING<br>
We'll exhaustively cover the entire "pdb" standard module without ever <br>
touching the CSharp APIs directly. Prior coverage runs have shown that <br>
(generally speaking) any block of code that is not directly hittable through <br>
the Python API is likely dead code. Also, testing "bdb" module is lower <br>
priority as "pdb" uses this for its own implementation. The final <br>
justification for this is that there is actually very little in terms of <br>
debugging APIs in IP DLLs. Most of the debugging support is built<br>
directly into the DLR's Microsoft.Scripting.Debugging.dll.<br>
<br>
For mdbg/VS, we'll exhaustively cover all mdbg commands.<br>
<br>
- CONTENT TESTING<br>
All debugging documentation should be thoroughly reviewed by Test before any<br>
public release of IronPython. Careful attention will be given to duplicating<br>
exactly any command fed into ipy.exe or mdbg.exe, and this should be <br>
automated entirely if feasible.<br>
<br>
- LOW-RESOURCE TESTING<br>
Use of the debugging feature has a few side effects which might be interesting<br>
from a limited resources perspective. First and foremost, use of the -X:Frames<br>
and -X:FullFrames IP console flags imply that IP will consume more <br>
memory than under normal circumstances. We should check that IP does not <br>
consume "too much" extra memory. Next, use of the debugging flag, '-D', in<br>
conjunction with the '-X:SaveAssemblies' flag will generate <br>
Snippets.debug.scripting.pdb in the %TMP% directory. What occurs if the drive<br>
containing %TMP% is full?<br>
<br>
NOTE: while this is an interesting test area to explore, there are no current<br>
plans to test it. We should perform general low-resource testing of <br>
IP before tackling it for this specific feature.<br>
<br>
- SETUP TESTING<br>
The only option of IP's MSI installer capable of affecting<br>
the debugging feature is the ability to selectively install CPython's standard<br>
library. As we generate the list of CPython modules to include in the MSI<br>
dynamically, it would be worthwhile to always check that pdb.py is included.<br>
<br>
NOTE: IronPython currently has no automated tests for the MSI. Once we<br>
do, we need to add a check to ensure pdb.py is always included. For the time<br>
being this will have to be done manually.<br>
<br>
- MODES AND RUNTIME OPTIONS<br>
We should focus our efforts on testing IP with the following modes:<br>
* -D -X:Frames<br>
* -D -X:FullFrames<br>
* -D -X:Frames -X:SaveAssemblies<br>
* -D<br>
* -X:Frames<br>
* <br>
using both debug and release IP assemblies. Also note that this<br>
needs to be performed for both Python interactive sessions and Python scripts<br>
passed into ipy.exe (e.g., "ipy.exe test_str.py"). Last but<br>
not least, there's the %PYTHONDEBUG% environment variable to consider.<br>
<br>
- INTEROPERABILITY<br>
Of primary concern is that IP produces an identical experience as<br>
CPython when given input which utilizes the pdb module. This will be <br>
accomplished via side-by-side testing and verification that the output of <br>
IP is the same as CPython given an identical input.<br>
<br>
We will also verify that IP can be debugged from mdbg and the Visual<br>
Studio IDE.<br>
<br>
- INTEGRATION TESTING<br>
* Silverlight support of debugging?<br>
* breaking into .NET code from pdb<br>
* breaking into COM from pdb<br>
* breaking into IronRuby from pdb<br>
* breaking into Python code from DLR hosting APIs<br>
* breaking into Python code from IronRuby<br>
<br>
- BETA TESTING<br>
The second beta release of IronPython 2.6 will support the debugging feature<br>
in the form of very limited pdb module support with the -X:Frames flag <br>
passed to ipy.exe. As with all beta releases of IP, this will be <br>
released on CodePlex to the general public. We will then use feedback<br>
from the IronPython Community to determine the amount of effort that goes <br>
into fully testing this feature.<br>
<br>
- ENVIRONMENT/SYSTEM - GENERAL<br>
The %PYTHONDEBUG% environment variable may have some impact on this feature.<br>
Other than this, the VS IDE will of course need to be installed for testing<br>
the VS debugging experience.<br>
<br>
- CONFIGURATION<br>
Need .NET 2.0 Service Pack 1 installed to run IP, and .NET 3.5<br>
Service Pack 1 to build the feature.<br>
<br>
- USER INTERFACE<br>
IP provides no user interfaces.<br>
<br>
- PERFORMANCE & CAPACITY TESTING<br>
Minimally, we need to run one or more tests in the perf lab under the -X:Frames<br>
and -X:FullFrames test modes. We should also measure the end-to-end run time<br>
of a complete, yet minimal, debugging sample utilizing the pdb module in the <br>
lab. The focus here will simply be on ensuring there are no perf regressions<br>
which are greater than 15% for any given checkin, and also that overall <br>
performance of the debugging feature remains palatable to our userbase.<br>
<br>
In terms of capacity testing we should look at:<br>
- if perf gets affected when breaking into deeply nested functions (e.g., <br>
recursive functions)<br>
- anything else?<br>
<br>
- PRIVACY<br>
Does %TMP%\Snippets.debug.scripting.pdb contain sensitive customer data? If <br>
so, does IP disclose the existence of this file?<br>
Is remote debugging supported? If so, what safeguards are in place?<br>
<br>
- RELIABILITY<br>
Most end-users are expected to enter into debugging sessions for short <br>
periods of time to diagnose issues with Python code. From this perspective<br>
the so-called "up time" of debugging sessions is less important than the <br>
overall sporadic failure frequency. We can get a good sense of how often <br>
sporadic failures occur by automatically running debugging tests in SNAP <br>
for every IP checkin.<br>
<br>
- SCALABILITY<br>
Does debugging still work correctly when stepping into deeply nested (e.g., 1000)<br>
functions?<br>
<br>
- STRESS TESTING<br>
- gcstress<br>
- MDA<br>
- assemblies in the GAC<br>
- call pdb functions multiple times and look for memory leaks<br>
- what happens when stepping into unreasonably deeply nested functions?<br>
<br>
- VOLUME TESTING<br>
App building exercise or try utilizing pdb from some of our internal Python <br>
tools. It would be interesting to use this from gopackage when exceptions <br>
are encountered. <br>
<br>
- INTERNATIONAL ISSUES<br>
As Python is not a localized language and available only in English, we <br>
simply need to confirm that nothing gets localized. This can be done by<br>
running a simple debugbing test against non-English OSes such as Deutsche<br>
Vista.<br>
<br>
- ROBUSTNESS<br>
We'll need a dedicated test or two in the stress lab to ensure there are no<br>
memory leaks. Also, we'll need to keep an eye out for sporadic failures of<br>
debugging tests in SNAP.<br>
<br>
- ERROR TESTING<br>
What happens when invalid commands are fed to the pdb debugger? Is this <br>
handled identically to CPython?<br>
<br>
Is there any conceivable way to fully break debugging without actually <br>
breaking ipy.exe in general? What happens under the mode <br>
"-D -X:SaveAssemblies" when the current user doesn't have write <br>
permissions on %TMP%? What happens if MS.Scripting.Debugging.dll is <br>
removed outright?<br>
<br>
- USABILITY<br>
There are three major usability issues with debugging:<br>
* IP offers no visualizer for the VS IDE<br>
* we're largely incompatible with CPython's pdb module<br>
* debugging Python code from .NET apps isn't currently possible<br>
<br>
Test will depend on feedback from the IronPython Mailing List and blogs to<br>
determine more usability issues. Resource permitting, we may also do <br>
app building exercises.<br>
<br>
The usability goal of this feature is that there are no complaints about<br>
the IP debugging experience from our users.<br>
<br>
- ACCESSIBILITY<br>
As this feature provides no new user interfaces to IronPython. and simply <br>
emits output to the stdout stream of command prompts, there should be no <br>
need to invest into accessibility testing.<br>
<br>
- USER SCENARIOS<br>
It's anticipated that users of this feature will be limited almost exclusively to<br>
developers. Expert Python users will likely prefer using the pdb<br>
module or debugging their applications directly via the "-i" ipy.exe <br>
option. Existing Microsoft customers with little Python background will <br>
probably be more comfortable with the VS IDE debugging experience. Due to <br>
this we must make sure both experiences are great!<br>
<br>
The types of applications being debugged will likely:<br>
* be non-trivial<br>
* consist of many different modules/packages<br>
* make heavy use of the CPython standard library and/or third party Python<br>
packages<br>
* be debugged often during the application development phase<br>
* be debugged infrequently in a production environment when something goes <br>
awry<br>
<br>
With these constraints in mind, we should try to debug existing major third<br>
party Python applications and/or add debugging support to our own internal<br>
Python tools.<br>
<br>
- BOUNDARIES AND LIMITS<br>
What happens when stepping into a recursive function at the maximum recursion<br>
level?<br>
<br>
- OPERATIONAL ISSUES<br>
None<br>
<br>
- SPECIAL CODE PROFILING AND OTHER METRICS<br>
Overall block coverage of all assemblies with "ipy" or "IronPython" in their<br>
names should be above 80% and file coverage should stay above 97%. Visual <br>
Studio's mstest will be used to measure code coverage.<br>
<br>
-------------------------------------------------------------------------------<br>
TEST ENVIRONMENT<br>
<br>
- OPERATING SYSTEMS<br>
32-bit Windows XP<br>
32-bit Windows 2003<br>
64-bit Windows 2003<br>
32-bit Windows Vista<br>
64-bit Windows Vista<br>
32-bit Windows Vista (Deutsche)<br>
- NETWORKS<br>
General Intranet network connection required for SNAP.<br>
May be other special network needs if remote debugging is/becomes a supported scenario.<br>
- HARDWARE<br>
- MACHINES<br>
At least two machines of every OS variety called out above with at least<br>
10 gigs of free hard disk space, 2 gigs of RAM, and a modern CPU<br>
- SOFTWARE<br>
* Visual Studio 2008 Team System Service Pack 1 installed to run the <br>
test suite<br>
* PowerShell 1.0 to run any supporting test scripts<br>
* CPython for side-by-side tests<br>
* mdbg<br>
<br>
-------------------------------------------------------------------------------<br>
UNIQUE TESTING CONCERNS FOR SPECIFIC FEATURES<br>
It should be relatively easy to drive pdb or mdbg via the command line in an<br>
automated fashion, but the same cannot be said about the VS IDE debugging <br>
experience. We'll need to reuse the VS team's automation infrastructure and <br>
ensure any machines running these tests in SNAP are never locked at the <br>
username/password screen which would cause the test to fail. Also, should <br>
visualization ever be a supported scenario, we may have no other option than to <br>
test this manually (note - this needs to be investigated).<br>
<br>
-------------------------------------------------------------------------------<br>
AREA BREAKDOWN<br>
- CPython's "pdb" module<br>
See debugging.pdb_mod.<br>
<br>
- mdbg tool support<br>
See debugging.mdbg_tool.<br>
<br>
- VS IDE<br>
See debugging.vs.<br>
<br>
- sys module extensions<br>
- sys.settrace<br>
settrace(function) <br>
Set the system's trace function, which allows you to implement a Python <br>
source code debugger in Python. The function is thread-specific; for a <br>
debugger to support multiple threads, it must be registered using <br>
settrace() for each thread being debugged.<br>
<br>
Trace functions should have three arguments: frame, event, and arg. frame <br>
is the current stack frame. event is a string: 'call', 'line', 'return', <br>
'exception', 'c_call', 'c_return', or 'c_exception'. arg depends on the <br>
event type.<br>
<br>
The trace function is invoked (with event set to 'call') whenever a new <br>
local scope is entered; it should return a reference to a local trace <br>
function to be used that scope, or None if the scope shouldn't be traced.<br>
<br>
The local trace function should return a reference to itself (or to another <br>
function for further tracing in that scope), or None to turn off tracing <br>
in that scope.<br>
<br>
The events have the following meaning:<br>
'call'<br>
A function is called (or some other code block entered). The global <br>
trace function is called; arg is None; the return value specifies the <br>
local trace function.<br>
'line'<br>
The interpreter is about to execute a new line of code (sometimes <br>
multiple line events on one line exist). The local trace function is <br>
called; arg is None; the return value specifies the new local trace <br>
function.<br>
'return'<br>
A function (or other code block) is about to return. The local trace <br>
function is called; arg is the value that will be returned. The trace <br>
function's return value is ignored.<br>
'exception'<br>
An exception has occurred. The local trace function is called; arg is <br>
a tuple (exception, value, traceback); the return value specifies the <br>
new local trace function.<br>
'c_call'<br>
A C function is about to be called. This may be an extension function <br>
or a builtin. arg is the C function object.<br>
'c_return'<br>
A C function has returned. arg is None.<br>
'c_exception'<br>
A C function has thrown an exception. arg is None.<br>
<br>
Note that as an exception is propagated down the chain of callers, an <br>
'exception' event is generated at each level.<br>
<br>
- sys.gettrace<br>
Get the trace function as set by settrace().<br>
<br>
- sys.call_tracing<br>
call_tracing(func, args) -> object<br>
<br>
Call func(*args), while tracing is enabled. The tracing state is<br>
saved, and restored afterwards. This is intended to be called from<br>
a debugger from a checkpoint, to recursively debug some other code.<br>
<br>
-------------------------------------------------------------------------------<br>
TEST CASE STRUCTURE<br>
Test cases will be stored directly in the pydoc strings of the functions <br>
implementing the tests. In turn, the modules containing these test case <br>
functions can be found under the "debugging" test package. Generating pydoc for<br>
the "debugging" test package and all sub-modules/sub-packages will generate <br>
this test plan.<br>
<br>
-------------------------------------------------------------------------------<br>
SPEC REVIEW ISSUES<br>
There is no IronPython spec for this feature. Any issues observed in the pdb <br>
module, which acts as a spec, and reproducible under CPython should be reported <br>
to <a href="http://bugs.python.org">http://bugs.python.org</a>.<br>
<br>
-------------------------------------------------------------------------------<br>
TEST TOOLS<br>
One of the following:<br>
- reuse CLR's debugging test infrastructure. NOTE: this is only suitable for <br>
mdbg tests<br>
- write our own new side-by-side testing infrastructure entirely in Python<br>
so that we can eventually contribute pdb tests back to CPython<br>
- write our own new side-by-side testing infrastructure in any<br>
language using any framework. <a href="http://sourceforge.net/projects/pexpect/">http://sourceforge.net/projects/pexpect/</a> could<br>
be useful as would be PowerShell<br>
- re-use some internal tool that might not be redistributable on CodePlex<br>
<br>
which will minimally need to support the following features:<br>
- ability to ignore lines (matching some regular expression) entirely<br>
- ability to substitute strings in lines<br>
- ability to run arbitrary commands (e.g., not limited to "ipy.exe ..." or "mdbg ...")<br>
- ability to match the current output against a reference output stored on disk<br>
- ability to run two or more arbitrary commands and compare their output against each other<br>
<br>
As per usual, the plan is to automate all tests using the SNAP checkin system<br>
and VS's mstest tool.<br>
<br>
-------------------------------------------------------------------------------<br>
SMOKE TEST (ACCEPTANCE TEST, BUILD VERIFICATION, ETC.)<br>
<br>
pdb acceptance test<br>
ipy.exe -c "import pdb"<br>
<br>
mdbg<br>
TODO (July 30, 2009)<br>
<br>
Visual Studio IDE<br>
TODO (July 30, 2009)<br>
<br>
<br>
-------------------------------------------------------------------------------<br>
AUTOMATED TESTS<br>
pdb and mdbg tests will be 100% automated in SNAP.<br>
<br>
<br>
-------------------------------------------------------------------------------<br>
MANUAL TESTS<br>
Setup testing will be manual for now, and we'll eventually move to automated <br>
testing in SNAP using PowerShell support scripts.<br>
<br>
Visual Studio IDE testing is also manual for now. Sometime in the <br>
future we'll migrate to using the VS team's automation technologies.<br>
<br>
Manual testing will only occur for major IP releases and the <br>
instructions will be documented on the internal IP website under the <br>
"Release Process" wiki.<br>
<br>
<br>
-------------------------------------------------------------------------------<br>
REGRESSION TESTS<br>
Regression tests will be added to existing test modules under the "debugging" <br>
package before any CodePlex or internal bug dealing with debugging is closed.<br>
As such, the majority of these regressions will be automated and run on every<br>
developer or test checkin. Developers should preferably add a regression test<br>
for every bug fix, and Test will verify the sufficiency of the test, extending<br>
it if necessary.<br>
<br>
-------------------------------------------------------------------------------<br>
BUG BASHES<br>
While considered to be extremely useful, we have no current plans for internal <br>
bug bashes on this feature. Quite simply put, we need more IronPython headcount <br>
and/or interest from the rest of Visual Studio Languages to accomplish this.<br>
<br>
-------------------------------------------------------------------------------<br>
BUG REPORTING<br>
All bug reports on this feature which do not include information consided to be<br>
Microsoft confidential are to be filed at <br>
<a href="http://ironpython.codeplex.com/WorkItem/AdvancedList.aspx">http://ironpython.codeplex.com/WorkItem/AdvancedList.aspx</a> under the "Debugging"<br>
component using the bug template found at <br>
<a href="http://ironpython.codeplex.com/Wiki/View.aspx?title=IronPython%20Bug%20Template">http://ironpython.codeplex.com/Wiki/View.aspx?title=IronPython%20Bug%20Template</a>.<br>
Bugs will be triaged on a weekly basis by the entire IronPython Team.<br>
<br>
-------------------------------------------------------------------------------<br>
PLAN CONTINGENCIES<br>
Without at least one additional SDET or other test tasks getting dropped, only <br>
phases I and II of this plan are implementable prior to the release of <br>
IP 2.6 RTM.<br>
<br>
-------------------------------------------------------------------------------<br>
EXTERNAL DEPENDENCIES<br>
We depend on the DLR for their implementation of Microsoft.Scripting.Debugging.dll <br>
which forms the basis of our support of the CPython pdb module. This plan <br>
assumes that this DLL has been adequately tested.<br>
<br>
There are no teams/projects we know about which are taking a dependency on <br>
IP's debugging functionality.<br>
<br>
-------------------------------------------------------------------------------<br>
HEADCOUNT REQUIREMENTS<br>
At least two FTE IronPython SDETs will be needed to implement this test plan <br>
fully: one to handle general, day-to-day IP test operations<br>
(i.e., passes/investigations/issues/regressions, etc), and another to work exclusively on the <br>
debugging feature. A loose approximation is that the SDET working full-time<br>
on debugging would need anywhere from one to three months to completely <br>
implement all aspects of this plan. This estimate varies considerably <br>
depending upon how much emphasis is to be given to pdb versus mdbg versus the <br>
VS IDE. Having a second full-time SDET on the debugging feature would have a<br>
not positive effect as the division of labor between testing command-line IP<br>
debugging support and VS IDE support is quite clear.<br>
<br>
-------------------------------------------------------------------------------<br>
PRODUCT SUPPORT<br>
IP is not a supported product in the conventional Microsoft sense. <br>
Support for IP is freely given directly by the IP Team via the <br>
IronPython Mailing List.<br>
<br>
-------------------------------------------------------------------------------<br>
DROP PROCEDURES<br>
All developer checkins must go through the SNAP checkin system => IronPython<br>
sources are always in a "good" state. Test will build IP from sources<br>
using developer instructions.<br>
<br>
-------------------------------------------------------------------------------<br>
RELEASE PROCEDURES<br>
See the IP "Release Process" wiki on the internal IP website.<br>
<br>
-------------------------------------------------------------------------------<br>
ALIAS/NEWSGROUPS AND COMMUNICATION CHANNELS<br>
Major changes around IP debugging support should be announced on the <br>
IronPython Mailing List, users@lists.ironpython.com.<br>
<br>
-------------------------------------------------------------------------------<br>
REGULAR MEETINGS<br>
- FEATURE TEAM MEETINGS<br>
There is no feature team for debugging.<br>
- PROJECT TEST TEAM MEETINGS<br>
IronPython weekly team meeting. Day and time are subject to change.<br>
We'll triage debugging work items during this meeting and discuss IP <br>
debugging issues as necessary.<br>
- FEATURE TEAM TEST MEETINGS<br>
There is no feature test team for debugging.<br>
<br>
-------------------------------------------------------------------------------<br>
DECISION MAKING PROCEDURES<br>
Decisions on this feature will be driven by the following criteria:<br>
- Microsoft business needs<br>
- IronPython Community feature requests<br>
- Previous decisions made by CPython. E.g., the pdb module<br>
- Existing debugging support in Microsoft products such as VS<br>
In the event a conscensus cannot be reached by the team on something, Jim<br>
Hugunin's input should be sought.<br>
<br>
Miscellaneous Procedures:<br>
- the gopackage tool is responsible for validating all source pushes to <br>
CodePlex<br>
- at least two IP team members need to sanity check public builds<br>
before they can be released<br>
- full test pass signoff on this feature will be needed for every public, signed<br>
release<br>
- bug triages will be performed with all three software disciplines in attendance<br>
- development design should be reviewed both by the PM and Test disciplines<br>
<br>
-------------------------------------------------------------------------------<br>
NOTES<br>
<br>
MDBG TEST CASE WRITING TIPS<br>
- use different language structures as the last line in the Python file<br>
- when only one line lives inside a block of code, but the code should not be<br>
stepped through<br>
- correct step-through: no extra step-throughs or lack thereof<br>
-</tt></p>
<p>
<table width="100%" cellspacing=0 cellpadding=2 border=0 summary="section">
<tr bgcolor="#aa55cc">
<td colspan=3 valign=bottom> <br>
<font color="#ffffff" face="helvetica, arial"><big><strong>Package Contents</strong></big></font></td></tr>
<tr><td bgcolor="#aa55cc"><tt> </tt></td><td> </td>
<td width="100%"><table width="100%" summary="list"><tr><td width="25%" valign=top><a href="debugging.mdbg_tool.html"><strong>mdbg_tool</strong> (package)</a><br>
</td><td width="25%" valign=top><a href="debugging.pdb_mod.html"><strong>pdb_mod</strong> (package)</a><br>
</td><td width="25%" valign=top><a href="debugging.vs.html"><strong>vs</strong> (package)</a><br>
</td><td width="25%" valign=top></td></tr></table></td></tr></table>
</body></html>
|
{
"pile_set_name": "Github"
}
|
Regulation of GTP cyclohydrolase I gene expression and tetrahydrobiopterin content in cultured sympathetic neurons by leukemia inhibitory factor and ciliary neurotrophic factor.
Cultures of neonatal rat superior cervical ganglia (SCG) were used to test the hypothesis that the cytokines leukemia inhibitory factor (LIF) and ciliary neurotrophic factor (CNTF) control GTP cyclohydrolase I (GTPCH) gene expression and 5,6,7,8-tetrahydrobiopterin (BH4) content as traits of the noradrenergic phenotype. Treatment for 7 days with 1 ng/ml of LIF was found to produce the characteristic switch in the SCG neurotransmitter phenotype reported by others, as evidenced by a 60% decline in tyrosine hydroxylase. (TH) activity and a 75% increase in choline acetyltransferase activity. This LIF treatment paradigm decreased BH4 levels in a concentration-dependent manner, with a maximal decline of 60% observed at 1 ng/ml. Analysis of the time course of this response indicated that LIF decreased BH4 levels by 60% following 3-7 days of treatment. Treatment of cultures with CNTF (2 ng/ml) resulted in a decline in BH4 levels that was of equal magnitude and followed the same time course as that produced by LIF. The LIF-dependent decline in BH4 levels resulted from a reduction in GTPCH enzyme activity, which decreased by 75% following 7 days of treatment. Nuclease protection assays of RNA extracted from cells treated for 7 days with 2 ng/ml of LIF or CNTF detected a 78-96% reduction in GTPCH mRNA content relative to beta-actin mRNA content. Concomitant decreases in TH and GTPCH gene expression in response to LIF or CNTF demonstrate a coordinated regulation of gene expression for this BH4-dependent enzyme and the rate-limiting enzyme in the synthesis of its essential cofactor, BH4. Moreover, these results indicate that GTPCH gene expression in SCG neurons should be regarded as a trait of the noradrenergic phenotype.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
As wireless communication systems such as cellular telephones, satellite, and microwave communication systems become widely deployed and continue to attract a growing number of users, there is a pressing need to accommodate a large and variable number of communication subsystems transmitting a growing volume of data with a fixed resource such as a fixed channel bandwidth accommodating a fixed data packet size. Traditional communication system designs employing a fixed resource (e.g., a fixed data rate for each user) have become challenged to provide high, but flexible, data transmission rates in view of the rapidly growing customer base. Various standards and interoperability requirements are developed on an on-going basis for present and future communications networks. The use of standards ensures that equipment available in the marketplace operates correctly with equipment from a variety of manufacturers and service providers, and in a variety of locales so that to a user carrying the equipment from place to place and even from country to country, the use of the equipment remains convenient and the details of the operations of the network are virtually transparent to the user.
For example, the third Generation Partnership Project Long Term Evolution (“3GPP LTE”) is the name generally used to describe an ongoing effort across the industry to improve the Universal Mobile Telecommunications System (“UMTS”) for mobile communications. The improvements are being made to cope with continuing new requirements and the growing base of users. Goals of this broad-based project include improving communication efficiency, lowering costs, improving services, making use of new spectrum opportunities, and achieving better integration with other open standards, and backwards compatibility with some existing infrastructure that is compliant with earlier standards. The project envisions a packet-switched communications environment with support for such services as Voice over Internet Protocol (“VoIP”) and Multimedia Broadcast/Multicast Service (“MBMS”). MBMS may support services where base stations transmit to multiple user equipment (“UE”) simultaneously, such as mobile televisions or radio broadcasts, for example. The 3GPP LTE project is not itself a standard-generating effort, but will result in new recommendations for standards for the UMTS.
The UMTS Terrestrial Radio Access Network (“UTRAN”) includes multiple Radio Network Subsystems (“RNS”), each of which contains at least one Radio Network Controller (“RNC”). However, it should be noted that the RNC may not be present in the actual implemented systems incorporating Long Term Evolution (“LTE”) or UTRAN (“E-UTRAN”). LTE may include a centralized or decentralized entity for control information. In UTRAN operation, each RNC may be connected to multiple Node Bs, which are the UMTS counterparts to Global System for Mobile Communications (“GSM”) base stations. Generally, in this document, a base station (“BS”) is one example of a “network entity,” but many other devices that can send and receive over-the-air interface of the network are also considered a “network entities,” including other UE devices, for example. In E-UTRAN systems, the eNode B may be, or is, connected directly to the access gateway (“aGW,” sometimes referred to as the services gateway “sGW”). Each Node B may be in radio contact with multiple UE (generally, user equipment includes mobile transceivers or cellular phones, although other devices such as fixed cellular phones, mobile web browsers, laptops, personal digital assistants (“PDAs”), MP3 players, and gaming devices with transceivers may also be UE)) via the radio Uu interface. In this document, the abbreviation for user equipment (“UE”) will be synonymous with the abbreviation for mobile station (“MS”), and MS will be used primarily. Mobile stations may also be cellular phones, PDAs, MP3 players, mobile web browsers, mobile PCs and the like.
The wireless communication systems as described herein are applicable to, as non-limiting examples, existing wireless systems, such as 3G (“3rd Generation mobile communications”), or future systems such as 3GPP LTE compatible wireless communication systems. As a method of improving performance in such systems, use of a relay has been proposed. A network including the relay function is typically referred to as a “multiple access relay network,” or as a MARC (“multiple access relay channel”). The relay concept is that in addition to a direct transmission between a mobile station or UE and a network entity such as a base station, a relay may be used that also receives the transmission of the UE and forwards or retransmits the message, or some form of the message, to the network entity. This relay signaling would be particularly significant when a mobile station or UE signal path to a base station is less than would be desired due to obstructions such as buildings, distance, signal noise, the number of other UE in the cell or area, etc; in these situations a relay signal may be used to increase the reception at the base station and hence, the system performance. A relay may be used at any time to increase the accuracy of the reception at the network entity by providing additional signal diversity, or, redundancy. The relay is a station that listens for UE messages transmitted towards the network entity or BS, the relay then transmits a version of the signals forward towards the BS. In this manner, the BS will receive the information, or a form of the information, from the UE in the uplink direction at least twice, once from the UE itself, and once from the relay. Because signal coding operations can remove errors when multiple signals carrying the same information are received (due to signal diversity, or redundancy), when a relay is used in this manner the BS can then eliminate or reduce reception errors that might otherwise occur due to signal noise or distance from the UE.
Coding schemes are used in communications systems. Two types of codes are of particular interest. Because the communications are performed in a relatively noisy (signal noise) environment, error correcting codes are used. Recursive systematic convolutional (“RSC”) codes are a common coding scheme. In these codes, a portion of the input is present in the output stream; also, the output is fed back into the convolution, so the code is recursive. In these codes, each m bit information symbols is input into an encoder and transformed into an n bit symbol, where n is greater than or equal to m, the code rate is m/n; and the transformation is a function of the last k information symbols, k is the constraint length of the code.
Recent work has also focused on the turbo codes. Developed in the early 1990s, the turbo codes provide a coding scheme that performs near the theoretical Shannon limit. A turbo code requires two RSC codes and an interleaver. The decoders for turbo coders use a soft decision process, that is, a probability function for each bit is developed based on the likelihood the original bit was a “0” or a “1.” Because the decoder uses two decoders and a likelihood or estimate is made by each, an iterative process is used to change the hypotheses until the two decoders come up with the same likelihood estimates for m bits of the data payload, then the process is complete. Turbo coders are used because they provide an error correcting code that provides maximal information transfer over a communications link in the presence of data corrupting noise (for example low signal to noise ratio (“SNR”) or high error rate conditions).
As contemplated currently, the relay station in a relay system may simply be a UE with a different or perhaps a better signal path to the base station. The relay may be closer to the base station, or be in a path with less noise, fewer obstructions, etc. In some contemplated system arrangements, a user who allows his MS to act as a relay would receive system credit in exchange for the relay services his MS performs, which would then lower the costs of his own use of the system. In a practical device, the UE would only act as a relay if the device had plenty of charge remaining, and a good path to the BS. This feature could be disabled to conserve or extend battery life, and if the UE was busy transmitting its own data, the relay function would not be available until the device again was idle and had sufficient resources available to act as a relay.
In areas where signaling is known to be problematic due to noise, obstruction or distance to the nearest BS, a dedicated relay device could be used; however, in most scenarios under consideration the relay is simply an additional MS that has resources available to act as a relay. By helping other UE, each user receives a better signal and, if credit is provided, cheaper service when they use the system; and, so all of the users would benefit by having their UE act as relay stations from time to time.
FIG. 1 depicts a simple mobile network including a relay station 13. In FIG. 1, the network entities such as base stations or node B stations 17, NB are operatively coupled together and also coupled to MME/UPE entities 18. A plurality of mobile stations MS/UE are communicating with a base station NB. In addition, a relay station RS is receiving the signals from the mobile stations MS/UE and then relaying the received signals to the base station NB. The base stations are interconnected with an X2 interface or communication link. The base stations are also connected by an S1 interface or communication link to an evolved packet core (“EPC”) including, for instance, a mobility management entity (“MME”) and a user plane entity (“UPE”), which may form an access gateway (“aGW,” a system architecture evolution gateway). The S1 interface supports a multiple entity relationship between the mobility management entities/user plane entities and the base stations and supports a functional split between the mobility management entities and the user plane entities. Note that although two UEs are shown and the relay station RS is receiving signals from two UEs, this illustration is simplified for ease of understanding and in fact many UE signals may be received by the relay and the relay will combine these received signals and relay information to the base station NB.
The actual implementation of such a function in the communications system continues to provide challenges. Several coding schemes have been considered for the relay. In a paper entitled “Joint Network Channel Coding for the Multiple Access Relay Channel”, Hausl et al., SECON '06, Vol. 3, September 2006, pp. 817-822, a joint network channel coding scheme, referred to hereafter as “JNCC”, is proposed. In this scheme the relay station and the UEs all use a RSC codling scheme. In another paper, entitled “A Joint Network Channel Coding Scheme for Relay Based Communications,” Heiu et al, CCECE 2007, April 2007, pp. 904-907, a similar scheme is proposed. In a paper entitled “Capacity Approaching Turbo Coding and Iterative Decoding for Relay Channels,” Zhang et al., IEEE Transactions on Communications, Vol. 53, No. 11, 2005, pp. 1895-1905; a system is proposed where the UE, if the link to the relay is less than perfect, use a turbo code at the UE and this could be used to help the relay recover the information; however, only a single UE environment is addressed.
FIG. 2 depicts a simplified view of a JNCC system with a base station BS receiving signals from a user equipment 11, a user equipment 15, and a relay station 13. The relay station 13 also receives transmitted signals from 11 and 15. In FIG. 2, the two UEs referenced as 11 and 15 respectively transmit their information to a network entity, base station 17 with the assistance of relay station 13. In addition, the relay station 13 receives transmissions of both the UEs. Again, although only two UEs are shown transmitting signals received by the relay, many UEs would be transmitting signals received by the relay in a real system.
In FIG. 2, the definitions of the signal links and their corresponding signal to noise ratios (“SNR”) are as follows: gUBi: path loss of link from a UE to the base station BS, also referred to as the “direct link”; SNRUBi is its SNR; gURi: path loss of link from a UE to relay; SNRURi is its SNR; gRB: path loss of link from the relay to BS; SNRRB is its SNR.
In the following figures, some definitions are used to depict the coding and transmit operations: SU,i: Systematic bits of UE i after channel coding PU,i: Parity bits of UE i after channel coding PUT,i: Transmitted parity bits of UE i after channel coding PUP,i: Punctured parity bits of UE i after channel coding SR: Systematic bits at relay after network coding PR: Parity bits at relay after network coding
FIG. 3 depicts a block diagram of the encoding used in the UE of the JNCC scheme. In FIG. 3, the channel code at the UEs is a recursive systematic convolutional (RSC) code. The network code in the relay is also a RSC code with the same parameters as the RSC code used in UEs. Only the code lengths may be different.
In FIG. 3, symbols SU,j in data stream 35 are input to RSC channel encoder 31, and the output 37 are encoded data symbols SU,j and parity symbols PU,j These symbols are then punctured using standard code puncturing in block 33 and the output 39 are punctured, encoded RSC code symbols and corresponding parity bits.
FIG. 4 depicts the process of a UE in the first time slot, time slot 1. In time slot 1, channel encoder (RSC) (31 in FIG. 3) encodes the systematic bits SU,i into encoded block [SU,i PU,i]. After puncturing (block 33 in FIG. 3) only SU,i and PUT,i (39 in FIG. 3) are transmitted. At the same time, the BS 17 and relay 13 listen. Note that these processes of FIG. 3 occur in both UE 11 and UE 15 in FIG. 4.
FIG. 5 depicts the processes of the relay station 13 of FIG. 4 in the JNCC scheme in time slot 2. In time slot 2, it was assumed that the relay station RS can perfectly decode the transmitted information by UEs. At first, the relay station 13 decodes RSC encoded signals 51, 65 received from both UEs 11, 15 and recovers systematic bits SU,i referenced as 55 and 69; the decoding is done by RSC decoders 53, 67 in FIG. 5. Then the relay 13 interleaves SU,i, i=1, 2 together in interleaver 57 into a new long information block 59, which is denoted by SR. After that, the relay station encodes SR by a RSC code encoder 71 (acting as a network coding), structure of the RSC encoder is the same as in UEs and outputs encoded signals 61, which includes symbols and parity bits. Finally, after puncturing in puncturing block 73, only the newly generated parity bits PR 64 are transmitted from the relay to the network entity or BS.
FIG. 6 depicts simply the transmission of the parity PR from the relay station 13 to the BS 17 in time slot 2.
FIG. 7 illustrates, in a block diagram, the iterative network and channel decoder at the BS used in the JNCC scheme.
Some definitions are needed to comprehend the blocks and operations in the FIG. 7:
yUBi, i=1, 2: what BS received from a user equipment i in time slot 1;
yRB: what BS received from the relay station RS in time slot 2;
{circumflex over (x)}UBi, i=1, 2: estimated information of user equipment i after decoding at BS;
Le−(ui)=i=1, 2: output, the extrinsic information of channel decoder;
Le|(ui)=i=1, 2: output, the extrinsic information of network decoder.
The iterative decoder consists of two soft input soft output (“SISO”) channel decoders 81, 89 and one SISO network decoder 85. First, the channel decoders 81, 89 calculate extrinsic information Le−(ui), i=1, 2 of user equipment i based on received signal yUBi from UE i. A value of zero is inserted for the punctured bits PUP before decoding. The log-likelihood ratios (LLRs) Le−(ui) are interleaved and mixed in the same way as the interleaving performed in the network encoder at the relay station. The LLRs after the mixture are a priori knowledge for the network decoder.
The network decoder obtains additional information about the parity bits PR from the relay station by received signal yRB at the BS. The network decoder in the base station of FIG. 7 calculates extrinsic information Le|(ui) i=1, 2 about SR (which is also SU); this information is fed back to the channel decoders 81 and 89 after de-mixture and de-interleaving by functions 83, 87. After several iterations as indicated by functions 91, 93 and the switch SW1, the channel decoder at BS can combine all the available information from both the relay station and the UEs to obtain the data estimates {circumflex over (x)}UBi, i=1, 2.
The JNCC scheme illustrates that joint network-channel coding can improve system throughput. Information transmitted from UEs to BS and from the relay station to the BS forms a distributed turbo code, which explores the space diversity gain. In addition, network coding at the relay makes it possible for two UEs to help each other; so that once one of the two UEs is under a bad channel condition, the other UE may help its decoder to recover its original information through network decoder.
The known schemes of the prior art assume that the relay station can recover the UE information perfectly, but in practical communication systems this is often not the case. A continuing need thus exists for an improved coding method and apparatus to provide a robust relay coding scheme when the data estimates at the relay for signals received from the UEs is less than perfect; e.g. when there are estimation errors at the relay station, such as would typically occur in practical communications systems.
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1. Field of the Invention
The present invention relates to building panels, particularly for the construction of houses. The invention is particularly concerned with a framework or skeleton panel which is formed as a grid of intersecting members, usually of wood-based material. The term "panel" will be used herein to include such a panel framework, and does not imply that this is a finished panel with insulation and/or facing sheets.
2. Prior Art
It is known to construct houses, and other buildings, from panels which are factory made, and which usually contain insulation. Examples of patents showing such panels are as follows:
U.S. Pat. No. 4,671,032, which issued Jun. 9, 1987 to Reynolds;
U.S. Pat. No. 4,765,105, which issued Aug. 23, 1988 to Tissington et al.;
U.S. Pat. No. 4,894,974, which issued Jan. 23, 1990 to Mayhew et al.
U.S. Pat. No. 5,157,892, issued Jun. 9, 1987 to Ryther; and
U.S. Pat. No. 5,167,700, issued Apr. 8, 1997 to Wright et al.
Applicant has had considerable experience both with the panels of the last-mentioned '700 patent, of which he is co-inventor, and with those of the Tisssington et al. patent. Both these patents are concerned with factory made panels having a framework made of wood members, and insulated with rigid foam insulation injected between the wood members in the factory. In the last-mentioned patent, dimensional lumber is used to provide strength, while in the Tissington et al patent it is preferred to use board such as oriented strand board (OSB). OSB is cheaper than standard dimensional lumber and is more resistant to warping. These panels have been used to construct over one thousand buildings of many different types, with great success.
Panels of the type shown in the Tisssington et al. patent and in the '700 patent have great potential in export markets, since buildings can be erected with these panels using largely unskilled labor. However, it has become apparent that a serious drawback of these and similar panels, i.e panels fully assembled and insulated in the factory, is that the bulkiness of the insulation leads to high shipping costs which are disadvantageous for export markets. The shipping costs could be much reduced if it were possible to ship a kit of structural members which could easily be assembled into a panel on site, without the need to ship the insulation.
The present invention accordingly is concerned with a panel in the form of a framework which can be shipped in disassembled form, without any insulation. The basic structural members of the panel occupy about one-fifth of the volume occupied by a fully assembled and insulated, factory produced panel. The structural members of the panel can easily be assembled on site by unskilled workers to form a rigid panel framework. Insulation, and facing sheets for example of plywood, OSB, and many other materials, can be added in accordance with local requirements and availability.
The present invention makes use of novel structural members which can easily be put together to form a grid. Panels formed as grids of crossing, interlocking members, are not new per se, and the Mayhew and Ryther patents, as well as the '700 patent aforesaid, show such panels. However, the prior art panels have various drawbacks.
One drawback of many of the prior art designs is that the grid forming members, as for example in Mayhew et al. and Ryther, are too thin for their edges to reliably receive nails for the facing sheets.
Another drawback has been the need to use structural members additional to those of the basic panel itself. Firstly, such panels have generally needed some kind of rails or studs or side pieces to improve the appearance of any exposed edges of the panels, which otherwise show the ends of the lateral members. Such rails or studs are shown for example at 240 in FIG. 2 of Mayhew, and as 28 in FIG. 1 of Ryther. Secondly, the grid forming members in many cases have not been stiff enough to be used exclusively to form the panel; in Mayhew et al. the members 240 are in the nature of studs which add strength and stiffness. Accordingly, these prior constructions all require the use of members other than the basic grid forming members to complete the panel framework.
One special feature of this invention is that a panel framework can be entirely formed from a plurality of structural members of novel design, which can be all identical or can be of only two different designs. These basic members are used not only for the horizontal and vertical members of the panel grid, but also form its four edges, i.e. the side edges and end (e.g. top and bottom) edges of the panel, where they provide smooth relatively uninterrupted edge surfaces, while producing a panel of good strength and rigidity. The panel also has adequate nail receiving surfaces on both sides, even when formed of relatively thin material such as 3/4 inch thick OSB. Insulation and facing sheets can be added after assembly.
Furthermore, the novel structural members can also be used to produce beams and joists needed for building a house, and also floor panels which need higher strength than the basic wall panels. In fact it is possible to construct houses almost entirely from panels, joists and other parts produced from these one or two types of structural member, along with facing sheets, and insulation if required, which can be obtained locally. This avoids the need to organise shipments of the many different structural members usually needed to make a house, and avoids problems which frequently occur if there is a shortage or breakage of one or two structural members of a specialized design.
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Q:
Another third party directing developers to Stack Overflow for tech support and more
In this question a user has come to Stack Overflow and posted a feature request in the mistaken belief that Stack Overflow is some sort of general communication channel for the company concerned. Looking at their developer page I can see how confusion might arise, as they list Stack Overflow along with their Twitter account under the heading:
Community
Connect with the Wattpad developer community to stay informed, receive support, and participate in events.
In this particular case I've explained to the user in question that feature requests to a third party developer are off-topic for Stack Overflow, but I can see this problem recurring in the future unless the third party company clarifies their web site in order to make it clear that Stack Overflow isn't a general communication forum for their product.
A:
There is now a page addressing this situation in the Help Center, primarily addressed to the third-party themselves.
I think an appropriate action in cases like this is to leave a comment on the off-topic / low quality question clearly linking to that official page. Ideally, this serves multiple purposes:
The person asking the question will understand that it is the company that is being criticized for sending them here, not them for following.
If they succeed in finding an alternative means of contact, they may become our advocate, pointing back to the guidelines.
If the company is in fact actively monitoring the tag, they will see the comment themselves, and hopefully clarify their links.
If a large or sustained influx of poor questions comes from a particular source, then a more official contact might be necessary.
A:
There are three total questions on the tag in question. In all honesty I think it's a wasted effort to contact every single company that does this.
When/if it becomes a problem for a specific tag (that is, we get more than a single off topic question on it - let's say 10) then the site should be contacted.
I'm not saying it's a bad thing that you opened a meta issue for this - but 35 people viewing this and the whole discussion all over doesn't seem particularly worth it given there is only 1 misbehaving question and 3 total questions on the tag.
That said - I pinged their head of product (he answered one of the questions on the tag), so they'll see it next time they visit Stack Overflow.
A:
A response from the perspective of a product owner. In the past I encouraged people to use SO for questions about the standard interfaces that our product supports, and discouraged them from using it for product-specific questions. But that distinction really doesn't work well; firstly people aren't always sure about what's standard and what's product-specific, secondly it's a blurry line anyway because you always have cases that end up being a discussion about whether the product implements the standard correctly. So our position is now that we're happy for people to ask product-specific questions on SO, and it has a couple of benefits: firstly many of them are answered by other users before we even get to see them, secondly we're under no contractual or moral obligation to follow it through to a successful resolution. The main disadvantage is that it's not on our tracking system, which is only really a problem if there's actually a product bug being reported. But we still point people primarily to our own product support site.
As for feature requests (getting back to the question...) the boundaries are very fuzzy. A "how do I do X" question very easily blends into a "please could you provide a way of doing X" request. If you allow one and not the other, you're in danger of blocking people whose only offence is to phrase their question in the wrong way - something for which StackOverflow has a notorious reputation.
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Blade of the Phantom Master
{{Infobox animanga/Print
| type = manga
| author = Youn In-wan
| illustrator = Yang Kyung-il
| publisher = Daewon C.I. (South Korea) Shogakukan (Japan)
| demographic = Seinen
| magazine = Young Champ (South Korea), Monthly Sunday Gene-X (Japan)
| first = 2001
| last = 2007
| volumes = 17 + 1 Shin Angyo Onshi Gaiden
| chapter_list =
}}
, translated as "New Secret Royal Agent", is a serial South Korean-Japanese manhwa and anime film created by Youn In-wan and illustrated by Yang Kyung-il. The series takes place in a world reminiscent of ancient Korea, and follows the Korean-folktale-inspired adventures of Munsu, one of the few remaining guardians against corruption and tyranny, as he seeks to find those responsible for the destruction of his country. It was serialized from 2001 to 2007 in South Korea (as Shin amhaengosa) and in Japan (as Shin Angyō Onshi), and was adapted into an animated theatrical-release film in 2004 in a first-of-its-kind collaboration between Japan and South Korea. In 2007, an English-language version of the film was released in the United States by ADV Films (licensed for $130,000) under the title Blade of the Phantom Master. In 2008, the anime became one of over 30 ADV titles transferred to Funimation.
PlotBlade of the Phantom Master takes place in the fictional land of Jushin, modeled after feudal Korea. In Jushin, there once lived secret government agents called the amheng osa (or angyō onshi in the Japanese version), who traveled the countryside in disguise. They were charged by the king with finding and punishing corrupt government officials, and bringing justice to the country's citizens.
At the start of the series, Jushin has been destroyed, fractured into numerous fiefdoms and kingdoms, many of which are ruled by corrupt and tyrannical warlords. Blade of the Phantom Master follows the adventures of one of the remaining amheng osa, Munsu, as he continues to wander the countryside and deals with the chaos caused by Jushin's fall.
Though initially episodic in nature, it becomes apparent as the series progresses that Munsu's travels are not random. In truth, Munsu is searching for the man responsible for assassinating his best friend, the king of Jushin, an act that led to the fall of the country.
But as Munsu grows closer to reaching his goal, he encounters old friends and comrades from his past, some who have since switched their allegiance to his enemy. Through them, it is revealed that Munsu was not always an amheng osa and is himself partly responsible for the king's death and subsequent fall of Jushin.
In addition to the overarching plotline, the series also uses the exploits of Munsu and his companions to retell various Korean folk stories.
Amheng Osa
In Blade of the Phantom Master, amheng osa bear bronze medallions, given to them by the king and emblazoned with between one and three horses. The greater the number of horses, the higher the rank of the amheng osa. Amheng osa of first mahai rank have one horse emblazoned onto their medallions, which allows them to wield basic magic to fight ordinary soldiers. The most powerful medallions feature three horses, and allow the bearers, third mahai (, 三馬牌), to perform summonings and regenerate injuries.
Despite being made for use by amheng osa, the mahai medallions will also work for normal people, so long as their convictions and willpower in executing justice are sufficiently strong. Hong Gildong, for example, successfully wielded a fourth mahai medallion. After the fall of Jushin, both first and second mahai medallions were rendered useless; only third and fourth mahai medallions still functioned.
Amheng osa are also prohibited from having families, but they are allowed a single travel partner called a 'Sando', who doubles as a bodyguard. Sando tend to be individuals of great fighting prowess or intelligent beasts.
Characters
Munsu (文秀/문수)
The anti-heroic protagonist of the series, former military general, and a third mahai amen osa from the fallen kingdom of Jushin. Despite the common perception held by Jushin's former citizens that amen osa are virtuous and bearers of justice, Munsu usually comes across as somewhat amoral and does not believe in helping people who refuse to help themselves. When he does help others, his methods almost always involve excessive bloodshed, lying, torture, and other questionable acts.
Munsu suffers from a curse that resembles asthma, which can only be alleviated by the inhaler-like charm he wears around his neck. This curse originates from during the Jushin period, where he convinced Aji Tae to switch the curse which was originally suffered by his lover Kye Wol Hyang unto him in hopes of relieving her pain. However, this was ineffective; not only did she die in the end while he retained the curse, Munsu actually fell directly into Aji Tae's scheme. In volume 11, Munsu confessed to Wonsul that despite claims that he was her killer, the truth was that Kye Wol Hyang killed herself by running into his sword while he was holding it right into her heart. He blames himself for her death and believes that he is her killer. When asked by Hong Gildong, he refused to deny that he was her sister's killer although his life was at stake. He went against the entire Hwalbindang after consuming a special drug that removed his asthma for a period of time, and managed to kill most of them. However, the drug had negative side effects when it wore off, and conveniently Aji Tae appeared while Munsu was at his most weak and wounded moment. Seeing his sworn enemy, his condition worsened and he started vomiting more blood, falling into a more critical state. Munsu swears that he will not die despite reality and that he will find Aji Tae in the end.
Before passing out, he asks Bang Ja to use an acupuncture needle from his pocket in order to prevent his death, but as soon as Bang Ja did it, Munsu's heart stopped beating. Everyone lost hope and believed that he was dead; however, after a few days despite the humid weather, Munsu's body did not decay. Later it was discovered that the needle contained mandrake extract and Munsu was affected with the infamous hallucinogen, allowing him to escape death. But being affected by the mandrake's poison means he will forever live in a fake world of his most desired dreams where he happily living with his loved one. Volume 11 shows the most treasured moments in Munsu's life and more about his past, including his relationship with Kye Wol Hyang.
After waking up from his dream-world, Munsu realizes that the mandrake extract has cancelled out his curse and he realizes that he only has a few more days to live. Munsu calls in favors from his allies and launches a massive attack on Aji Tae's castle. Although Munsu is victorious in killing his nemesis, he succumbs to his ailments and dies. In the last chapter, Munsu is reunited with his lover and friends in the afterlife.
Sando/Chun Hyang (山道/春香/산도/춘향)
A beautiful girl with prodigious fighting skill. She acts as Munsu's 'Sando', or bodyguard. When she was kidnapped by a corrupt lord who wanted to make her his personal bodyguard, her lover embarked on a futile quest to become an amen osa. He died in the process, but not before making Munsu aware of her plight. After Munsu frees her, she decides to become his bodyguard in memory of her dead lover, and takes the title "Sando" as her new name.
Despite her fearsome natural fighting ability, Sando is quiet and shy, with a high moral stance. As a result, she is often in conflict with the amoral Munsu over his questionable methods. She has made it clear that if he ever becomes truly evil, she will no longer protect him. She also has a great fear of heights, and will refuse to cross bridges set over deep mountain gorges or valleys. Munsu finds this extremely peculiar, seeing as to how she often leaps several stories into the air during combat.
Together with Munsu and Bang Ja, Sando helps fight corruption. Although she is still hesitant about Munsu's methods, she learns to trust him, and Munsu in turn relies on her more than ever.
Later in the series, she is defeated in combat and leaves Munsu in shame to pursue greater strength. She learns the power of using her 'ki' from a friend of Aji Tae, attaining the strength she desires. She becomes devastated after she hears about the "death" of Munsu from Aji Tae and he manipulates her into becoming his latest bodyguard.
When Munsu storms the castle to kill Aji Tae, she originally fights him, chopping off one of his arms. However, Munsu is able to help her remember their memories and friendship. Together, they fight Aji Tae, and Sando is the one who kills him. When Munsu dies in the castle, Sando grieves.
After the two-month time-skip, it is revealed from Bang Ja's letters that Sando has parted ways and is still using her fighting skills to extinguish evil.
Bang Ja (房子/방자)
Munsu's unwanted but good-intentioned servant. Once the servant and apprentice of a first mahai onshi, his former master released him from service after Jushin's destruction. When his master and his sando were later killed in a rebel uprising against a corrupt lord, Bang Ja began roaming the country as a thief. He believes that amen osa should be virtuous and heroic, which is why Munsu's behavior often shocks him.
He is a third-rate Magician who summons animals to do his bidding, and he deeply takes his role as a Bang Ja seriously. This often leads to his being manipulated and bullied by Munsu, who often beats him or sends him on inane/impossible errands.
He was responsible for the main death of Won Hyo. After Sando left the group and Munsu almost died, Bang Ja used Yuui Tae's acupuncture needle on Munsu so that he lives. Bang Ja finds it difficult that Munsu is in a coma state situation that he is a lifeless body. After Yeongsil received the false information about the Mandrake cure, Bang Ja and Yeongsil traveled together to an icy mountain encountering Sando. Having joined Aji Tae, Sando attacked Bang Ja and Yeongsil. In order to save his life, Yeongsil injects Bang Ja with a drug that makes Bang Ja appear dead. Fortunately, Bang Ja recovers when he hears Munsu's voice.
In the battle at Aji Tae's castle, Bang Ja helps Munsu create a diversion. After Aji Tae's defeat and Munsu's death, Bang Ja writes a letter to Munsu, recommitting himself to fight for the ideal world that Munsu had talked about.
Kye Wol Hyang (桂月香/계월향)
Is Munsu's deceased lover and sister of Hong Gildong. She is Munsu and Hae Mo Su's childhood friend. She has an illness that resembles asthma, which can only be alleviated by the inhaler-like charm he wears around his neck. Munsu couldn't stand and watch Kye Wol Hyang suffer so he asked Aji Tae to perform a ritual to pass Kye Wol Hyang's illness to Munsu. Later it is known that Kye Wol Hyang committed suicide but Munsu still blames himself for her death even when Hong Gildong asks for the truth.
Won Sul (元述/원술)
A master swordsman from Jushin, who was once a subordinate of Munsu. However, when Jushin fell he began serving Aji Tae, growing Yang Gwi Bi, a plant with narcotic properties, to ship to the west in exchange for weaponry. His weapon, Saruhyondo, is a sword with a blade forged from his killing 'ki', or killing intent. Aside from being impossibly sharp and hard, the blade is also extremely malleable, re-shaping itself into any killing form Wonsul can imagine. As it is made of pure killing ki, the blade is also invisible to the naked eye. Wonsul can manifest the blade so long as he has something to act as a hilt, such as a stick or his signature dragon's head sword hilt.
While working for Aji Tae, Wonsul was defeated and killed by Sando, while temporarily confused by her possession of Aji Tae's lucky charm. His death, however, proved temporary, as he was later resurrected by Aji Tae. Now effectively a zombie of sorts, Wonsul retained his mind and skill, but his body was like a living corpse, continuing to decay. Furthermore, his re-animated form proved extremely hard to kill, since it was already technically dead - even when decapitated, he still remained conscious and fully aware. He went on to serve as Munsu's sando in Chun Hyang's stead. When Munsu went against the Hwalbindang, Wonsul remained by his side. As their battle with the Hwalbindang comes, Aji Tae made his appearance, upon which Wonsul requested that the former end his state of living death. At first Aji Tae appears to oblige, disintegrating Wonsul's body. However, Aji Tae then states that so long as even part of his body remains intact, he wants Wonsul to remain alive, and "see everything through to the end". At this, Wonsul's head, the only remaining part of his body, begins to cry.
Later, when Munsu recovers from his mandrake-induced coma and prepares for a final battle with Aji Tae, Wonsul is dispatched to attack. Despite having been turned into an immense, grotesque mass of flesh (he is initially mistaken for one of Kaidaiten's demons), Munsu recognises his old friend and grants Wonsul his wish, exploding a nearby ammunition dump and engulfing the monstrosity in the blast. Back in his fortress, Aji Tae comments that Wonsul is finally dead.
After Munsu's death, Won Sul jokes with Munsu in the afterlife.
Aji Tae (阿志泰/아지태)
A former scholar from Jushin and the man Munsu holds responsible for the destruction of the country. Many of Munsu's former allies and comrades have since switched their loyalties to Aji Tae, having been coerced by his power or duped by his charisma. His motives and purpose remain unknown. He possesses a large range of magical abilities, among them the ability to resurrect the dead, explode people with a mere glance, shapeshifting, and teleportation.
During the Junshin period, Aji Tae was General Munsu's second-in-command. At that time, he was smaller in size and sported short black hair and glasses. Despite his innocent exterior, however, the Jushin Aji Tae was already convinced of the inferiority and unworthiness of mankind, and was already plotting his conquest of Jushin.
As of volume 15, he has succeeded in conquering most of the former Jushin territories, having gathered together a formidable force of supernatural allies. This includes the resurrected Kaidaiten and its demon brood, an army of undead, black magic practitioners from the West, and Munsu's former bodyguard Sando.
Series origins
Much of the premise for and characters of Blade of the Phantom Master were drawn from the classic Korean tale, The Legend of Chun Hyang. Youn said many Korean readers of the comic did not like his dark portrayal of the light-hearted classic tale, and he was sometimes told he had "bad taste." He explained that Blade of the Phantom Mask used the original, lesser-known version of The Legend of Chun Hyang, which is far more tragic, as its basis. He sought to not only draw on the beauty of the original novel, but also to arrange its message to fit modern times. Youn also drew upon other classic Korean stories, such as Amhaengeosa (Secret royal inspector), and historical figures like Heo Jun for inspiration.
The model for Munsu was the historical figure Park Mun-su, from Korea's Joseon Dynasty period. According to Youn, he was originally a military officer in charge of training the army, and was active as an amen osa for only one year. However, his legacy was considerable, including not only seeking and punishing corrupt officials, but also stopping the invasion of the Korean peninsula by foreigners and saving the king from a coup d'état. Sando is based largely on Ju Non-gae, a figure from the Japanese-Korean Seven-Year War. Following the capture of Hanyang (now Seoul) by Toyotomi Hideyoshi's troops in 1592, Non-gae avenged the death of her lover, a soldier, by willingly giving up her life to cause the death of a Japanese general. The holiday Uiambeolje commemorates her spirit of patriotic self-sacrifice.
When developing the idea of using a story about amen osa, Youn said he worried that Japanese readers might find the idea too foreign. He later learned that Japan had similar people, called mito koumon, in its history, and eventually found that many places around the world had individuals of similar positions in their own histories. He felt this universality of such heroes who seek out and report corrupt government officials showed that good and evil don't differentiate between countries, races, or cultures. Youn admits to being influenced his portrayal of amen osa by Richō Angyōki (李朝暗行記), a Japanese manga by Natsuki Sumeragi. While a bit embarrassed at being so affected by a foreigner's portrayal of Korean history, he was impressed and surprised by the manga's historical accuracy.
Media
Comic
The Blade of the Phantom Master comic was serialized from 2001 to 2007. In Japan, the series ran from April 2001 April to September 2007 as manga in Monthly Sunday Gene-X. It was also published as manhwa in South Korea's Young Champ. The work was collected into 17 graphic novel volumes, which were published by Shogakukan in Japan and Daiwon C.I. in South Korea. As of 2005, these collections have sold over 2 million copies between the two countries. Translation of the comic from Korean to Japanese was provided by Manabu Okazaki. Many chapters included special author's notes to give background on Korean folktales and historical figures referenced in the story, and to explain instances in which the author chose to deviate from generally accepted fact in his portrayals. For instance, in volume 4, Youn provided information on Hwanung, a sage from the Korean legend, Dangun Shinhwa. He feared his portrayal of Hwanung as a summoned creature dressed in S&M gear might cause misunderstandings among readers of the comic, and explained that his development of the character in the comic was influenced by interesting but unsupported statements from the internet, whereas the Hwanung of legend holds a very high status in Korea, on a par with "that of Jesus Christ in Western society."
Japanese editions of the comic volumes also included omake-style humorous shorts detailing a variety of Youn and Yang's cross cultural and comic writing adventures, entitled "From Korea - Hello!!"
Youn and Yang maintained their residences in Incheon, South Korea throughout most of the writing and publication of the series, often requiring the services of translators for dealings with their Japanese editor, Akinobu Natsume, especially early on, and necessitating multiple business trips to Japan. Youn studied Japanese and his proficiency improved as the comic progressed. He admitted, however, that it "took two hours while staring at a dictionary" to read his first Japanese-language fan letter.
Japanese editions of volume 8 of the comic were packaged with a bonus booklet entitled Osa-logy. It contained a short side story by the series authors, plus humorous comic shorts by guest authors and artists. Contributors included Airi Kawauchi (河内愛里 Kawauchi Airi), Minoru Murao, Itō Shin (真伊東 Shin Itō), and Kazuhiko Shimamoto. Also included were interviews between author Youn and actress Yoon Son-ha, and between Youn and the manga authors CLAMP (creators of The Legend of Chun Hyang, among other titles). A guidebook entitled Amenosa, This Reality and Mission (アメンオサ、その真実と使命 Amenosa, sono shinjitsu to shimei, 공식 가이드북) was also published, containing color art galleries by artist Yang, plus story summaries and character data. A "gaiden"-style volume of two side stories was also released for sale.
Since its original releases in South Korea and Japan, the comic has been licensed and published in French as Le Nouvel Angyo Onshi by Pika Édition, in Hungarian as Árnybíró by Mangafan, in German as Shin Angyo Onshi by Carlsen Comics, in Thai as Dtòo Laa Gaan Tá-mil Chà-bàp Pí-sèt (ตุลาการทมิฬ ฉบับพิเศษ) by Vibulkij, in Indonesian as Shin Angyo Onshi by Level Comics, and in Chinese by Jonesky (Hong Kong) and Sharp Point Press (Taiwan). No English-language adaptations have been published or announced as licensed.
Animated film
In 2004, Japanese studio Oriental Light and Magic and Korean studio Character Plan collaborated to create an animated film adaptation of the comic, entitled Phantom Master: Dark Hero from the Ruined Empire. The project represented the first time Korean and Japanese creators had ever collaborated on an animated film, and funding was shared by sources from both nations. It was distributed by The Klockworx in Japan and Cinema Service in Korea. The film was co-directed by Ahn Tae-gun and Jōji Shimura, and produced by Yang Jae-hye, Lee Sang-don, Bunsho Kajiya, Lee Don-ki, and Shukuchi Kanda. It featured a musical score from composer Kow Otani and theme songs performed by BoA. Vocal tracks were recorded in both Korean and Japanese, though Korean actor Ji Sung's narration was retained in its original language for the Japanese release and augmented with native subtitles. Character Plan president Yang Jee-hye said his company was able to learn new skills and technologies, both of which have been maintained during Japan's long history of film-making, from Oriental Light and Magic, who completed about 70% of the work on the film.Phantom Master: Dark Hero from the Ruined Empire was shown at the Sixth Bucheon International Animation Festival, 6 November 2004, in Bucheon, South Korea, at which it served as the opening film. It was released into theaters simultaneously in Japan and Korea on 26 November 2004, and had an encore run at the Seoul Ani Cinema for three weeks beginning 17 February 2005. Its North American debut was at the Fantasia Festival in Montreal, Quebec, Canada on 15 July 2005, where it was shown in Korean with English subtitles. ADV Films released the movie to DVD in North America in 2007, with a choice of Japanese or English audio and optional English subtitles. The movie has also been locally released in Poland as Ostatni Strażnik Magii by Vision Film's Anime Gate imprint and in Russia as Povelitel' Prizrakov (, lit. Lord of the Ghosts) by MC Entertainment. The film was re-released on DVD by Funimation Entertainment on June 30, 2009 under the title Blade of the Phantom Master: Shin Angyo Onshi'' with the ADV movie trailer for the film as a special feature. The film features the English language track and the Japanese language track with English subtitles.
The film is an adaptation of early comic chapters, covering the stories of Munsu's desert encounter with Mong Ryong, his subsequent quest to free Sando, and one of the pair's early adventures together.
Webtoon
On November 18, 2017, this work is rebooted and started serializing to Naver Webtoon three times a week. Because this comic is rebooted, it reconstructed the coloring and the cut arrangement newly in the webtoon style. It is collaborating with a company named YLAB on a webtoon project called Super String.
References
External links
Category:ADV Films
Category:2001 manhwa
Category:2001 manga
Category:2004 anime films
Category:Animated films based on manhwa
Category:Animated films based on manga
Category:Adventure anime and manga
Category:Fantasy anime and manga
Category:Funimation
Category:Japanese films
Category:Seinen manga
Category:South Korean animated films
Category:Sharp Point Press titles
Category:Odex
Category:South Korean webtoons
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Bo Vesterdorf
Bo Vesterdorf (born 1945) is a Danish judge who has been President of the European Court of First Instance.
Vesterdorf began his career as a lawyer-linguist at the European Court of Justice before becoming Administrator in the Danish Ministry of Justice, examining magistrate, and Legal Attaché in the Permanent Representation of Denmark to the European Communities.
He was a Temporary Judge at the Østre Landsret (Danish Court of Appeal), Head of the Constitutional and Administrative Law Division in the Ministry of Justice, Director of the Administration Department in the Ministry of Justice, and a university lecturer. He also served as a member of the Steering Committee on Human Rights at the Council of Europe, and subsequently as a member of its Bureau. In 2004 he became a member of the "Ad hoc committee on judicial training" at the Academy of European Law, Trier, Germany. He was a judge at the European Court of First Instance from 25 September 1989 and its president from 4 March 1998 to 17 September 2007.
Vesterdorf has been Commander 1st Degree of the Danish Royal Order of the Dannebrog since 20 June 2006. On 1 November 2007 he was appointed Senior Legal Consultant at Plesner Law Firm in Copenhagen. He is an external fellow at University College London's Faculty of Law and is attached to St Gallen University, Switzerland and Fordham Law School, New York. In May 2008 he was made Doctor of Laws honoris causa by St Gallen University.
External links
BusinessWeek profile
Bo Vesterdorf CV
Category:1945 births
Category:Living people
Category:Presidents of the General Court (European Union)
Category:Danish jurists
Category:Danish expatriates in the United Kingdom
Category:Danish judges of international courts and tribunals
Category:Danish officials of the European Union
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Q:
CSS: Floated element after the content in code
I need to have a floated element after the content/text that's supposed to flow around it in my code for SEO reasons. Usually floats are done like so:
CSS:
#menu {
float: right;
width: 180px;
padding: 10px;
background: #fcc;
margin: 0 0 15px 15px;
}
HTML:
<div id="menu">This is a right float. The long text flows around it.</div>
<div id="content"><p>This is a long text. Lorem ipsum dolor sit amet,
consectetuer adipiscing elit. Praesent nec risus.
Praesent adipiscing aliquet magna. Proin bibendum velit
vitae tortor. Vestibulum a dui quis urna feugiat viverra.
Vestinbulum diam dui, ullamcorper in, rhoncus at, facilisis at,
lorem. Phasellus turpis metus, sodales sit amet, laoreet nec,
aliquet sit amet, tortor. Vivamus massa orci, gravida sit amet,
dictum quis, euismod a, est. Aenean pretium facilisis nunc.</p>
<p>Nulla eros mauris, egestas eget, ullamcorper sed, aliquam ut,
nulla. Phasellus facilisis eros vel quam. Etiam rutrum turpis
a nibh. Integer ipsum. Vestibulum lacus diam, varius in,
blandit non, viverra sit amet, sapien. Sed porta sollicitudin
nibh. Nam eget metus nec arcu ultricies dapibus.</p></div>
But I need to have the HTML like this:
<div id="content"><p>This is a long text. Lorem ipsum dolor sit amet,
consectetuer adipiscing elit. Praesent nec risus.
Praesent adipiscing aliquet magna. Proin bibendum velit
vitae tortor. Vestibulum a dui quis urna feugiat viverra.
Vestinbulum diam dui, ullamcorper in, rhoncus at, facilisis at,
lorem. Phasellus turpis metus, sodales sit amet, laoreet nec,
aliquet sit amet, tortor. Vivamus massa orci, gravida sit amet,
dictum quis, euismod a, est. Aenean pretium facilisis nunc.</p>
<p>Nulla eros mauris, egestas eget, ullamcorper sed, aliquam ut,
nulla. Phasellus facilisis eros vel quam. Etiam rutrum turpis
a nibh. Integer ipsum. Vestibulum lacus diam, varius in,
blandit non, viverra sit amet, sapien. Sed porta sollicitudin
nibh. Nam eget metus nec arcu ultricies dapibus.</p></div>
<p id="menu">This is a right float. Because it's placed below the text in code,
it also appears that way.</p>
Basically, I need this HTML to look like the previous example (HTML and CSS). How can I do this?
The width of the floated element is constant, but the height can change. The content has to flow around it. The reason I need to have it this way is because the floated element is the menu, which doesn't contain any important text and is usually the same for many pages, so the content should be topmost in the code.
A:
Simple you have add the following css
#content {
float: left;
width: 300px; /* put here the width you want */
}
demo: http://jsfiddle.net/qTDLr/1/
Edit: make sure that the sum of #content and #menu width is less than the container width.
A:
This recent question may be the same
Wrap text around right floated column where left column appears first in html
the solution involves floating a empty "spacer" div right , this spacer is first in source, it should have the width and height of the content to be in the right side - in the link a solution including a bit of jQuery to get the height - the position the actual menu over the top of the floated spacer
a JS fiddle example produced from that link : HERE
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Mayor John Tory said Monday that he believes the city is making progress in tackling gridlock, but some drivers still haven’t gotten the message about not obstructing busy downtown streets.
The mayor made the comments following a four-day enforcement blitz by Toronto police last week that targeted drivers who block rush-hour routes in the city’s core.
According to police, over the course of the initiative, which focused on the area bounded by Bloor St., Front St., Parliament St. and Dufferin St., officers issued 1,467 tickets and towed 298 vehicles.
The crackdown between last Tuesday and Friday was the third such blitz police have carried out since January 2015, when Tory announced a zero-tolerancepolicy for blocking rush-hour routes.
Speaking to reporters at the intersection of Front and York Sts. on Monday morning, Tory said the high number of tags and tows showed that “we’re making some progress” on improving traffic conditions, “but that we’ve got a long way to go.”
Tory, who made fighting gridlock a central plank of his 2014 mayoral campaign, said “it’s obvious that some people still haven’t got the message in terms of changing their behaviours.”
“People just have to know they can’t just walk into a Tim Hortons to get a cup of coffee, or can’t just go in to get their dry cleaning. It disrupts thousands of people literally when they do that, to convenience themselves for a few minutes, and we just can’t have that kind of behaviour continuing,” he said.
The mayor didn’t provide any empirical evidence that the crackdowns have helped alleviate congestion. He said the city only recently started to track traffic flow using sophisticated data and it was too soon to draw conclusions.
But he stated that stepped-up enforcement would serve as a strong deterrent to drivers who illegally block streets. “I think when you have your car towed away it would be unlikely, unless you’re really dumb, that you’d do that again.”
According to the police, officers gave out fewer tickets last week than the previous rush-hour blitz, which took place over five days last October. During that crackdown police issued 2,078 tickets and towed 406 vehicles.
Between January and August of this year, police gave out 54,206 tickets for rush-hour offences and towed 12,595 vehicles. That’s fewer than the 56,494 tickets they issued over the same period in 2015, but they towed fewer cars during the first eight months of last year — a total of 11,234.
Loading... Loading... Loading... Loading... Loading... Loading...
Both years saw significant increases compared with the first eight months of 2014, when police wrote 42,152 rush-hour tickets and towed 5,790 vehicles.
Although the traffic blitzes have become a feature of the first two years of Tory’s administration, the mayor asserted that in the long term, the “real solution” to Toronto’s congestion problems depends on adding capacity to the transit system and facilitating active transportation such as cycling and walking.
Before his press conference Monday, the mayor took a ride in a news helicopter to observe traffic patterns from the sky. He said that he checked in on the newly installed Bloor St. bike lane pilot project and that “traffic seemed to be moving fairly well” along the street.
Read more about:
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Blogging our outdoor adventures!
Menu
Cross-country Skiing
On the eve of a big snowstorm (we’re expecting 16″-20″ of snow tomorrow!) we finally got around to blogging about our fun time at the Nansen Ski Club’s Warming Hut Grand Opening. The Nansen Ski Club is America’s oldest ski club. Yup, you heard that right. The oldest and longest running ski club is…
On the weekend before last, we headed over to the Notch-Way Cross Country Ski Trail in Franconia, NH. The northern trailhead is just off Route 141, while the southern trailhead can be found at Cannon Mountain. With such a warm winter and little snowfall, we knew that we would be able to walk along the…
The temps might be cold, but if you bundle up, keep active, and stay in the woods, you can stay very comfortable. For this adventure, Andrew and I went to explore the newest cross-country ski center in the White Mountains of New Hampshire: Ski Hearth Farm in Sugar Hill. We learned about this place from an…
Neither one of us has ever been on the trails at Great Glen Trails and we finally checked it out last weekend. We wanted to get out on our skis, but the snow in the backcountry was too crusty, so we had to go to a groomed place and Great Glen is just down the…
For several months now, Andrew has been raving about the scallops at Dimillo’s on the Water in Portland, ME with a promise that he’d take Lindsay there someday. Yesterday was the day, our Saturday was wide open with no other responsibilities, so we grabbed our skis and jumped in the truck. From Northern New Hampshire, we…
On Sunday, we jumped out of bed early and headed over to the Green Mountain State to meet up with some friends. We planned to meet Amanda and Will at Willoughby State Forest CCC Road on the south end of Lake Willoughby that is the main access point for the Bartlett Mt Ski Area. Andrew…
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Q:
Wrong value for form in laravel
I have a privacy function.If public = 1, the post is public, else if is 0, the post is private.I have this toggle :
<label class="toggle" style="right: 185px">{{ Form::checkbox('public') }}<i class="no-rounded privancy"></i></label>
The toggle is set on public by default, but at submit, in database I receive NULL in column public. If I press the button on private, in database I Receive 1, and 1 is for PUBLIC. How it's working?How can I make this working because I need this.
A:
If you look at code that generates the checkbox, you'll see it can take up to 4 arguments, the third being whether or not it is checked by default, and what the value is. The value is 1 by default. So when you check it, it will return 1.
public static function checkbox($name, $value = 1, $checked = null, $options = array())
{
return \Collective\Html\FormBuilder::checkbox($name, $value, $checked, $options);
}
Just change your form to value of 2 to return 2 when checked.
Form::checkbox('public', 2)
And as pointed out in your comments, an unchecked checkbox will not be submitted so you will have to check in the controller when you save.
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Video: J'Leon Love Expects Tough Fight From Periban
Ryan Burton catches up with super middleweight contender J'Leon Love to discuss his upcoming fight with Marco Antonio Periban on Saturday night at the MGM Grand in Las Vegas. The fight will be part of the Showtime Pay-Per-View undercard to the Floyd Mayweather Jr. vs. Marcos Maidana welterweight unification. Love talks about the style of Rubio, what he needs to do against Rubio and more.
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1st Session, 42nd Parliament, 64-65 Elizabeth II, 2015-2016
HOUSE OF COMMONS OF CANADA
BILL C-6
An Act to amend the Citizenship Act and to make consequential amendments to another Act
Her Majesty, by and with the advice and consent of the Senate and House of Commons of Canada, enacts as follows:
R.S., c. C- 29
Citizenship Act
2014 , c. 22 , s. 3 ( 1 )
1 ( 1 ) The portion of paragraph 5 ( 1 )(c) of the Citizenship Act before subparagraph (i) is replaced by the following:
(c) is a permanent resident within the meaning of subsection 2 ( 1 ) of the Immigration and Refugee Protection Act , has, subject to the regulations, no unfulfilled conditions under that Act relating to his or her status as a permanent resident and has
2014 , c. 22 , s. 3 ( 1 )
( 2 ) Subparagraph 5 ( 1 )(c)(i) of the Act is replaced by the following:
(i) been physically present in Canada for at least 1 , 095 days during the five years immediately before the date of his or her application, and
2014 , c. 22 , s. 3 ( 1 )
( 3 ) Subparagraph 5 ( 1 )(c)(ii) of the Act is repealed.
2014 , c. 22 , s. 3 ( 1 )
( 4 ) Subparagraph 5 ( 1 )(c)(iii) of the Act is replaced by the following:
(iii) met any applicable requirement under the Income Tax Act to file a return of income in respect of three taxation years that are fully or partially within the five years immediately before the date of his or her application;
2014 , c. 22 , s. 3 ( 1 )
( 5 ) Paragraph 5 ( 1 )(c. 1 ) of the Act is repealed.
2014 , c. 22 , s. 3 ( 1 )
( 6 ) Paragraphs 5 ( 1 )(d) and (e) of the Act are replaced by the following:
(d) if under 55 years of age at the date of his or her application, has an adequate knowledge of one of the official languages of Canada; (e) if under 55 years of age at the date of his or her application, demonstrates in one of the official languages of Canada that he or she has an adequate knowledge of Canada and of the responsibilities and privileges of citizenship; and
( 7 ) Section 5 of the Act is amended by adding the following after subsection ( 1 ):
Length of physical presence — calculation
( 1 . 001 ) For the purpose of subparagraph ( 1 )(c)(i), the length of physical presence is calculated in the following manner: (a) for every day during which the person was physically present in Canada as a temporary resident or protected person under the Immigration and Refugee Protection Act before becoming a permanent resident, the person accumulates half of a day of physical presence, up to a maximum of 365 days; and (b) for every day during which the person has been physically present in Canada since becoming a permanent resident, the person accumulates one day of physical presence.
2014 , c. 22 , s. 3 ( 2 )
( 8 ) Subsection 5 ( 1 . 1 ) of the Act is repealed.
2014 , c. 22 , s. 3 ( 5 )
( 9 ) Subsection 5 ( 2 ) of the Act is amended by adding “and” at the end of paragraph (a) and by repealing paragraphs (c) and (d).
2014 , c. 22 , s. 3 ( 6 )
( 10 ) Paragraph 5 ( 3 )(a) of the Act is replaced by the following:
(a) in the case of any person, the requirements of paragraph ( 1 )(d) or (e);
2014 , c. 22 , s. 3 ( 6 )
( 11 ) Paragraph 5 ( 3 )(b) of the Act is amended by adding “or” at the end of subparagraph (ii) and by repealing subparagraph (iii).
2014 , c. 22 , s. 3 ( 6 )
( 12 ) Subsection 5 ( 3 ) of the Act is amended by adding “and” at the end of paragraph (b) and by repealing paragraph (b. 1 ).
( 13 ) Section 5 of the Act is amended by adding the following after subsection ( 3 ):
Disabled persons
( 3 . 1 ) For the purposes of this section, if an applicant for citizenship is a disabled person, the Minister shall take into consideration the measures that are reasonable to accommodate the needs of that person.
( 14 ) Subsection 5 ( 4 ) of the Act is replaced by the following:
Special cases
( 4 ) Despite any other provision of this Act, the Minister may, in his or her discretion, grant citizenship to any person to alleviate cases of statelessness or of special and unusual hardship or to reward services of an exceptional value to Canada.
2014 , c. 22 , s. 7 ( 2 )
2 Subsections 9 ( 2 . 1 ) and ( 2 . 2 ) of the Act are replaced by the following:
Exception
( 2 . 1 ) No application for renunciation may be made if the Minister has provided the applicant with a notice referred to in subsection 10 ( 3 ) or has commenced an action under subsection 10 . 1 ( 1 ) for a declaration in respect of the applicant until the Minister provides the applicant with his or her decision under subsection 10 ( 5 ) or a final judgment has been rendered in that action, as the case may be.
Processing of application suspended
( 2 . 2 ) If an application for renunciation is made and the Minister subsequently provides the applicant with a notice referred to in subsection 10 ( 3 ) or commences an action under subsection 10 . 1 ( 1 ) for a declaration in respect of the applicant, the processing of that application is suspended until the Minister provides the applicant with his or her decision under subsection 10 ( 5 ) or a final judgment has been rendered in that action, as the case may be.
2014 , c. 22 , s. 8
3 Subsection 10 ( 2 ) of the Act is repealed.
2014 , c. 22 , s. 8
4 Subsections 10 . 1 ( 2 ) and ( 3 ) of the Act are replaced by the following:
Effect of declaration
( 3 ) A declaration made under subsection ( 1 ) has the effect of revoking a person’s citizenship or renunciation of citizenship.
2014 , c. 22 , s. 8
5 Sections 10 . 3 and 10 . 4 of the Act are repealed.
2014 , c. 22 , s. 8
6 Section 10 . 6 of the Act is replaced by the following:
No appeal from interlocutory judgment
10 . 6 Despite paragraph 27 ( 1 )(c) of the Federal Courts Act , no appeal may be made from an interlocutory judgment made with respect to a declaration referred to in subsection 10 . 1 ( 1 ) or 10 . 5 ( 1 ).
2014 , c. 22 , s. 9 ( 2 )
7 Subsection 11 ( 1 ) of the Act is amended by striking out “and” at the end of paragraph (d), by adding “and” at the end of paragraph (c) and by repealing paragraph (e).
2014 , c. 22 , s. 12 ( 1 )
8 Paragraph 14 ( 1 )(a) of the Act is replaced by the following:
(a) subparagraph 5 ( 1 )(c)(i), in the case of an application for citizenship under subsection 5 ( 1 );
2014 , c. 22 , s. 17
9 ( 1 ) The portion of section 21 of the English version of the Act before paragraph (c) is replaced by the following:
Periods not counted as physical presence
21 Despite anything in this Act, no period may be counted as a period of physical presence for the purpose of this Act during which a person, under any enactment in force in Canada, (a) has been under a probation order; (b) has been a paroled inmate; or
( 2 ) Paragraph 21 (c) of the Act is replaced by the following:
(c) has served a term of imprisonment.
R.S., c. 30 ( 3 rd Supp.), s. 11 ( 1 )
10 ( 1 ) The portion of paragraph 22 ( 1 )(a) of the English version of the Act before subparagraph (iii) is replaced by the following:
(a) while the person, under any enactment in force in Canada, (i) is under a probation order, (ii) is a paroled inmate, or
R.S., c. 30 ( 3 rd Supp.), s. 11 ( 1 )
( 2 ) Subparagraph 22 ( 1 )(a)(iii) of the Act is replaced by the following:
(iii) is serving a term of imprisonment;
2014 , c. 22 , s. 19 ( 2 )
( 3 ) Subsection 22 ( 1 ) of the Act is amended by adding “or” at the end of paragraph (e. 2 ) and by replacing paragraphs (f) and (g) with the following:
(f) if, during the 10 years immediately before the person’s application, the person ceased to be a citizen under paragraph 10 ( 1 )(a), as it read immediately before the coming into force of section 8 of the Strengthening Canadian Citizenship Act , or under subsection 10 ( 1 ) or 10 . 1 ( 3 ).
11 The Act is amended by adding the following after section 23 . 1 :
Seizure
23 . 2 The Minister may seize and detain any document that is provided to him or her for the purposes of this Act if he or she has reasonable grounds to believe that it was fraudulently or improperly obtained or used or that the measure is necessary to prevent its fraudulent or improper use.
12 Subsection 27 ( 1 ) of the Act is amended by adding the following after paragraph (i. 1 ):
(i. 2 ) prescribing the procedures to be followed in relation to a document that may be seized under section 23 . 2 , including in relation to its seizure, storage, return and disposition;
2014 , c. 22 , s. 26
13 The portion of paragraph 27 . 2 (c) of the Act before subparagraph (i) is replaced by the following:
(c) with regard to the requirements of paragraphs 5 ( 1 )(d) and (e),
Transitional Provisions
Presence in Canada — pending applications
14 Paragraphs 5 ( 1 )(c) and 14 ( 1 )(a) of the Citizenship Act , as they read immediately before the day on which subsection 1 ( 1 ) comes into force, apply to a person whose application for citizenship was made on or after June 11 , 2015 but before the day on which that subsection comes into force and has not been finally disposed of before the day on which that subsection comes into force.
Presence in Canada — pending applications (subsections 1 ( 1 ) and ( 2 ))
15 If subsection 1 ( 1 ) comes into force before subsection 1 ( 2 ), then paragraph 5 ( 1 )(c) of the Citizenship Act , as it read immediately before the day on which subsection 1 ( 2 ) comes into force, applies to a person whose application for citizenship is made on or after the day on which subsection 1 ( 1 ) comes into force but before the day on which subsection 1 ( 2 ) comes into force and has not been finally disposed of before the day on which subsection 1 ( 2 ) comes into force.
Intention to reside in Canada — citizenship granted
16 Paragraph 5 ( 1 )(c. 1 ) of the Citizenship Act , as it read immediately before the day on which subsection 1 ( 5 ) comes into force, is deemed never to have applied to a person whose application for citizenship was made on or after June 11 , 2015 and who was granted citizenship before the day on which that subsection comes into force.
Intention to reside in Canada — pending applications
17 Paragraph 5 ( 1 )(c. 1 ) of the Citizenship Act , as it read immediately before the day on which subsection 1 ( 5 ) comes into force, does not apply to a person whose application for citizenship was made on or after June 11 , 2015 but before the day on which that subsection comes into force and has not been finally disposed of before the day on which that subsection comes into force.
Knowledge of Canada and official language — pending applications
18 Paragraphs 5 ( 1 )(d) and (e) of the Citizenship Act , as enacted by subsection 1 ( 6 ), apply to a person whose application for citizenship was made on or after June 11 , 2015 but before the day on which that subsection comes into force and has not been finally disposed of before the day on which that subsection comes into force.
Knowledge of Canada and official language (minors) — pending applications
19 Paragraphs 5 ( 2 )(c) and (d) of the Citizenship Act , as they read immediately before the day on which subsection 1 ( 9 ) comes into force, do not apply to a person whose application for citizenship was made on or after June 11 , 2015 but before the day on which that subsection comes into force and has not been finally disposed of before the day on which that subsection comes into force.
Citizenship deemed not to have been revoked
20 A person whose citizenship was revoked under subsection 10 ( 2 ) of the Citizenship Act , as it read immediately before the day on which section 3 comes into force, is deemed never to have had their citizenship revoked.
Intention to reside in Canada — citizenship granted (resumption)
21 Paragraph 11 ( 1 )(e) of the Citizenship Act , as it read immediately before the day on which section 7 comes into force, is deemed never to have applied to a person whose application for resumption of citizenship was made on or after June 11 , 2015 and who was granted citizenship before the day on which that section comes into force.
Intention to reside in Canada — pending applications (resumption)
22 Paragraph 11 ( 1 )(e) of the Citizenship Act , as it read immediately before the day on which section 7 comes into force, does not apply to a person whose application for resumption of citizenship was made on or after June 11 , 2015 but before the day on which that section comes into force and has not been finally disposed of before the day on which that section comes into force.
Persons serving term of imprisonment — pending applications
23 Paragraph 21 (c) and subparagraph 22 ( 1 )(a)(iii) of the Citizenship Act , as enacted by subsections 9 ( 2 ) and 10 ( 2 ), respectively, apply to a person whose application has not been finally disposed of before the day on which section 9 comes into force.
Prohibition on Taking Oath of Citizenship
Prohibition — taking oath
24 Subsection 22 ( 6 ) of the Citizenship Act applies to a person who made an application under subsection 5 ( 1 ) or ( 2 ) or 11 ( 1 ) of that Act before June 11 , 2015 and who is required under that Act to take the oath of citizenship to become a citizen but has not done so before the day on which this section comes into force.
2001 , c. 27
Consequential Amendments to the Immigration and Refugee Protection Act
2014 , c. 22 , s. 42
25 Subparagraph 40 ( 1 )(d)(iii) of the Immigration and Refugee Protection Act is replaced by the following:
(iii) subsection 10 . 1 ( 3 ) of the Citizenship Act , in the circumstances set out in section 10 . 2 of that Act.
2014 , c. 22 , s. 43
26 Paragraph 46 ( 2 )(c) of the Act is replaced by the following:
(c) subsection 10 . 1 ( 3 ) of the Citizenship Act , other than in the circumstances set out in section 10 . 2 of that Act.
Coming into Force
Order in council
27 ( 1 ) Subsections 1 ( 1 ), ( 3 ) and ( 7 ) and section 8 come into force on a day to be fixed by order of the Governor in Council.
Order in council
( 2 ) Subsections 1 ( 2 ) and ( 4 ) come into force on a day to be fixed by order of the Governor in Council.
Order in council
( 3 ) Subsections 1 ( 6 ), ( 9 ) and ( 10 ) and section 13 come into force on a day to be fixed by order of the Governor in Council.
Order in council
( 4 ) Sections 11 and 12 come into force on a day to be fixed by order of the Governor in Council.
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Q:
Qt with PyQt. Is it possible to view the object hierarchy of a running window?
I am currently working on a project using PyQt5, and am using several windows that will dynamically change their widgets, depending on the data I supply.
For the purposes of debugging, would it be possible to view the object structure of a window as it is running? I am using Qt Designer to design many of my windows, but as the contents change while the program is running, Qt Creator cannot show me the structure of my windows at all times in my program.
Is it possible to view the object hierarchy, such as in the Object Inspector in Qt Creator? Or perhaps is it possible to make the invisible widgets, like layouts and spacers, visible while running?
A:
I don't know if it's possible to do this in Qt Creator while the application is running, but you can definitely insert statements into the source code which will print out the entire object hierarchy. Just pick your base object and recursively print the output of QWidget.children().
One problem is when to print this so that you neither miss newly-added widgets nor completely overwhelm the terminal (so a timer is not the best idea). If your application responds to that data that you supply by calling a specific slot or function, which seems like the points at which the tree changes, that would be a perfect time to do this. You can start from the QApplication object, and walk the tree down from there.
If you don't respond to data that way, there is a more involved but OK solution. You can instead intercept all QChildEvents and print the new object hierarchy at that point. This can be done by installing a filter object on the root object you're interested in as soon as it's created, which would then install itself on any new children. This could then print the full object tree, starting from the root. Check out this answer for more details on how to create this kind of filter object. it's in C++, but the code should be straightforward to translate to Python.
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Today, Brazil’s Marcelo Melo is the new individual No. 1 in the Emirates ATP Doubles Rankings. You’d have to turn the clock back more than three years to September 3, 2012 to find the last time someone not named Bryan held down the top spot. That’s when Max Mirnyi and Daniel Nestor closed out an 18-week run atop the doubles charts.
The man they call “Girafa” (he’s 6-foot-8, 192 lbs.) has found success in 2015 regardless of whom he’s teamed up with, including Mirnyi, Ivan Dodig, Julian Knowle, Bruno Soares, Raven Klaasen and Lukasz Kubot. We’re talking five titles with three different partners.
“I think for Brazil it's going to be huge,” said countryman Soares. “It's very important for us, for everything that myself, he and Andre [Sa] have been doing for doubles and tennis in Brazil for the past seven or eight years. We've been representing Brazil worldwide for such a long time at the biggest events. For him now to achieve No. 1 in the world is something really special for him and for us.”
“It’s amazing for Brazil,” echoed Serbia’s Nenad Zimonjic, himself a former No. 1. “Guga [Gustavo Kuerten] was No. 1 in singles, and now Marcelo is going to be No. 1 in doubles. It’s a great achievement for him. Now with a couple of different partners he’s shown how well he can play. This is a reflection of the whole season. It’s one thing that nobody can take away from you. I’m really happy for him. It’s also good for our sport to have more No. 1s.”
With Dodig, Melo reached semi-finals at the Australian Open, Indian Wells and Monte-Carlo, and the duo captured its second ATP World Tour team title in Acapulco. Then came Roland Garros, where, cheered on by Kuerten, Melo would team with Dodig to capture his first Grand Slam title, beating the two-time former champions and No. 1-ranked pairing of Mike Bryan/Bob Bryan 6-7(5), 7-6(5), 7-5 in a thrilling final. Melo/Dodig had fallen to the Bryans in the 2013 Wimbledon final 3-6, 6-3, 6-4, 6-4.
While Dodig honed his singles game on the Challenger circuit, Melo didn’t miss a beat. Teaming with Klaasen, the first-time pairing reeled off back-to-back titles in Tokyo and Shanghai, an ATP World Tour Masters 1000 event. But he wasn’t done yet. In Vienna, he took the court for the first time with Kubot, and the tandem went all the way to the Erste Bank Open title, coming back from a set and 2-4 down to beat second seeds Jamie Murray/John Peers 4-6, 7-6(3), 10-6. Melo, 32, is now 18-18 overall in career finals.
“I'm living the dream, playing three tournaments — winning 500, 1000 and 500 [Emirates ATP Rankings] points again,” said Melo, who’s already qualified for the Barclays ATP World Tour Finals, along with Dodig. "There was a lot of pressure on my shoulders to become No. 1. This is a tough achievement. I am a really lucky guy to be No. 1 with the Bryans still around.”
In 2009, the former 16s and 18s Brazilian champion reached the Roland Garros mixed doubles final with American Vania King, becoming the first Brazilian to reach a Grand Slam final since his compatriot Kuerten. He is coached by his older brother and former touring pro Daniel Melo, who won the Brasil Open doubles title with Enzo Artoni in 2001, the year he rose to a career-high No. 151 in the Emirates ATP Rankings.
“Marcelo and I go back a long way,” said Soares. “We've known each other since we were six, seven years old. We grew up together. We're from the same city [Belo Horizonte], we're from the same club. It's a boy's dream. Once you start playing tennis and start understanding, you have a couple of dreams: winning big tournaments, winning a Slam and maybe one day getting to No. 1. It feels like such a faraway dream and it's just amazing that a guy I know, who is so close to me, achieved that this year. I feel very happy for him and I think he's going to keep doing amazing things in tennis and for Brazil.”
“The Bryans are still around — the best team in history,” said fellow doubles specialist Marcin Matkowski. “For Marcelo to be ranked No. 1 ahead of them is a great accomplishment.”
“For anyone to overcome the Bryans is incredible,” echoed Britain’s Murray.” He’s been playing really well for a long time now. I think he fully deserves to get to No. 1. It’s definitely a very difficult thing to do. Not many people have overcome the Bryans since I’ve been on tour the last eight, nine years.”
As a pair, the Bryans remain the No. 1 team in the calendar-year Emirates ATP Doubles Race To London, although that hold is also under threat from Jean-Julien Rojer and Horia Tecau, who have 6,220 points, a mere 65 fewer than the Bryans heading into this week's BNP Paribas Masters in Paris, where the winning team will collect 1000 points.
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Q:
What's the isospin of photons?
What's the isospin of photons? Why PDG book says $0, 1(1^{--})$ for its $I(J^{PC})$? What does $0, 1$ mean here? Is it that the isospins aren't determined and can be 0 or 1?
A:
It's a (known) linear combination of 0 and 1. The electromagnetic field operator can be written as something like
$$A_\mu = B_\mu\cos\theta_W + W_\mu^3\sin\theta_W$$
where $B_\mu$ is the $U(1)$ hypercharge operator and $W_\mu^3$ is the measured component of the weak isospin operator. $B_\mu$ is not associated with any weak isospin, so that's where the 0 comes from, but $W_\mu^3$ is, so that's the 1.
By the way, it's worth mentioning (as Ron pointed out) that weak isospin is not the same thing as just isospin. The latter corresponds to a particular $SU(2)$ subgroup of the $SU(6)$ flavor "symmetry," but weak isospin corresponds to its own completely separate $SU(2)$ symmetry group. Basically they are completely different physical properties that just happen to share the same group structure. Some physicists have developed an unfortunate habit of calling any property that follows this group structure "isospin" (unless it is actual spin).
Since the photon does not have any up/down flavor, it exists in the trivial representation of non-weak isopsin $SU(2)$, and thus its actual isospin is zero.
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{
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Breakthrough OLAP performance on Cassandra and Spark
Prerequisite Knowledge
Working familiarity with Apache Cassandra and Apache Spark, and analytical/BI architectures and databases in general. This is more of an architectural talk so API knowledge is not needed.
Description
Apache Cassandra is rock-solid and widely deployed for OLTP and real-time applications, but is typically not thought of as an OLAP database for analytical queries. This talk will show architectures and techniques for combining Apache Cassandra and Spark to yield a 10-1000x improvement in OLAP analytical performance. We will then introduce a new open-source project that combines the above performance improvements with the ease of use of Apache Cassandra, and compare it to implementations based on Hadoop and Parquet.
First, the existing Cassandra Spark connector allows one to easily load data from Cassandra to Spark. We’ll cover how to accelerate queries through different caching options in Spark, and the tradeoffs and limitations around performance, memory, and updating data in real time. We then dive into the use of columnar storage layout and efficient coding techniques that dramatically speed up I/O for OLAP use cases. Cassandra features like triggers and custom secondary indexes allow for easy data ingestion into columnar format.
Next, we explore how to integrate this new storage with Spark SQL and its pluggable data storage API. Future developments will enable extreme analytical database performance, including smart caching of column projections, a columnar version of Spark’s Catalyst execution planner, and how vectorization makes for fast cache- and GPU-friendly calculations (see Spark’s Project Tungsten).
FiloDB is a new open-source database using the above techniques to combine very fast Spark SQL analytical queries with the ease of use of Cassandra. We will briefly cover interesting use cases, such as:
Easy exactly-once ingestion from Kafka for streaming and IoT applications
Evan Chan
Tuplejump
Evan Chan is a distinguished software engineer at Tuplejump. Evan loves to design, build, and improve bleeding-edge distributed data and backend systems using the latest open source technologies. He has led the design and implementation of multiple big data platforms based on Storm, Spark, Kafka, Cassandra, and Scala/Akka, including a columnar real-time distributed query engine. Evan is an active contributor to the Apache Spark project, a DataStax Cassandra MVP, and cocreator and maintainer of the open source Spark Job Server. He is a big believer in GitHub, open source, and meetups and has given talks at various conferences, including Spark Summit, Cassandra Summit, FOSS4G, and Scala Days.
Apache Hadoop, Hadoop, Apache Spark, Spark, and Apache are either registered trademarks or trademarks of the Apache Software Foundation in the United States and/or other countries, and are used with permission. The Apache Software Foundation has no affiliation with and does not endorse, or review the materials provided at this event, which is managed by O'Reilly Media and/or Cloudera.
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{
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}
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Q:
Hudson - job is stuck, how to kill it?
I have a job running under Hudson that has not progressed from "Started by user anonymous". How can I stop it? I tried restarting the Hudson server but it just resumed the job on startup.
It can't be killed by the normal cancel build button.
Thanks.
A:
Hudson was waiting for SVN to respond - SVN was waiting for the permission for my id to use the repository. Once this was there Hudson started working again.
I would presume that in this instance there would have been an SVN process I would have needed to kill in order to get Hudson to respond again.
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{
"pile_set_name": "StackExchange"
}
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Q:
Django: How to get parameters from QuerySet
Consider the following Django model:
class SomeModel(models.Model):
some_var = models.IntergerField()
Whats the best way to get an array of a models parameters from a search results?
Example (not working of course):
a = SomeModel.objects.all().some_var
would give something like [3, 4, 1, 9, 1, 2]
A:
There is existing queryset method called values_list https://docs.djangoproject.com/en/1.10/ref/models/querysets/#values-list
a = SomeModel.objects.all().values_list('some_var', flat=True)
We are using flat=True so that it will give flat list
Entry.objects.values_list('id').order_by('id')
[(1,), (2,), (3,), ...]
Entry.objects.values_list('id', flat=True).order_by('id')
[1, 2, 3, ...]
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{
"pile_set_name": "StackExchange"
}
|
package com.saintdan.framework.tools;
import com.saintdan.framework.constant.CommonsConstant;
import com.saintdan.framework.param.BaseParam;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Map;
import java.util.TreeMap;
import java.util.stream.Collectors;
import org.apache.commons.lang3.StringUtils;
import org.springframework.data.domain.PageRequest;
import org.springframework.data.domain.Sort;
import org.springframework.data.domain.Sort.Direction;
/**
* Query helper.
*
* @author <a href="http://github.com/saintdan">Liao Yifan</a>
* @date 5/8/16
* @since JDK1.8
*/
public class QueryHelper {
public static PageRequest getPageRequest(BaseParam param) {
return PageRequest.of(param.getPageNo() == null ? 0 : param.getPageNo() - 1,
param.getPageSize(), QueryHelper.getSort(param.getSortBy()));
}
/**
* Get default {@link Sort}.
*
* @return {@link Sort}
*/
public static Sort getDefaultSort() {
return Sort.by(Direction.ASC, "id");
}
/**
* Get {@link Sort}
*
* @param param sort param
* @param direction {@link Sort.Direction}
* @return {@link Sort}
*/
public static Sort getSort(String param, Sort.Direction direction) {
return Sort.by(direction, param);
}
/**
* Get {@link Sort}
*
* @param map sort map
* @return {@link Sort}
*/
public static Sort getSort(TreeMap<String, Sort.Direction> map) {
List<Sort.Order> orderList = new ArrayList<>();
for (Map.Entry<String, Sort.Direction> entry : map.entrySet()) {
Sort.Order order = new Sort.Order(entry.getValue(), entry.getKey());
orderList.add(order);
}
return Sort.by(orderList);
}
/**
* Get {@link Sort}
*
* @param sortBy sortedBy
* @return {@link Sort}
*/
public static Sort getSort(String sortBy) {
return StringUtils.isBlank(sortBy) ? getDefaultSort()
: Sort.by(Arrays.stream(sortBy.split(CommonsConstant.COMMA)).map(
(orders) -> getOrder(orders.split(CommonsConstant.COLON)))
.collect(Collectors.toList()));
}
/**
* Get {@link Sort.Order}
*
* @param orders orders
* @return {@link Sort.Order}
*/
private static Sort.Order getOrder(String[] orders) {
return new Sort.Order(Sort.Direction.fromString(orders[1]), orders[0]);
}
}
|
{
"pile_set_name": "Github"
}
|
Monday, 9 November 2015
Bentley
A very kind lady sent me Wilson Bentley's book called "Snowflakes in photographs" - thank you! I was thrilled! I no longer need to search through internet for snowflake photos, I have all I need right there in that book.
Wilson Bentley is one of the first known photographers of snowflakes. I am inspired by many of the samples in his book… this is the first one that came off my shuttles. I was thinking of him and I was looking to create a bit of a bolder design because I wished to name my new snowflake design after him. I also wanted it to be special in his honour and that's when I came up with the idea of giving it a crystal centre, in a star shape. There is often a little star at the heart of real snowflakes so this seemed perfect. I can't quite catch it in my photos unfortunately but the Swarovski crystals look wonderful and sparkly at the heart of this snowflake. I've just ordered different ones with an AB coating and I think they'll look even better.
Of course, I know that not everyone likes to tat with beads (or even have any to hand) so Bentley can also be made without beads and I will provide both versions.
I wanted really straight "arms" to my snowflake so I used lock chains and also in the centre where, like in Snowdrop, I wanted to emphasise the hexagonal shape which is a feature of real snowflakes.
I added a silver filament to my cotton thread
and when I pressed it, it made the picots at the tip go a bit funny…
I need to sort that out but was too impatient!
Below is the snowflake photograph
that inspired Bentley
Trying to show you the sparkly centre star;
This will look lovely hanging on a tree when the
light catches the crystals…
Very icy.
Without crystals: With crystals:
Again this is not a difficult design to tat. I've even done away with the SCMR which I used at first to be able to throw the decorative rings at the tips of the snowflake. Instead, I used a chain joined back which I have decided I actually prefer. I think the resulting join is better and lays flatter than when using a SCMR. I think SCMRs can sound daunting to new tatters but if you just think of it as a chain joined back at its beginning, then anybody can do that.
Ahhhh, this may be your best snowflake yet!! As a tatter hesitant to use beads, I really appreciate that you thought about providing two different version. However I'm also really drawn to the crystal star version and would actually tat it. Superb is definitely the word for this pattern.
Another beautiful snowflake! I look forward to trying it both with and without the center crystal. The easier the techniques, the more eager I am to try a pattern. I know I will have to look up (and practice) any of the techniques I don't use often, which can be a hindrance. Thank you for making your patterns so user-friendly :)
Another gorgeous snowflake, I love your snowflakes and you get your patterns to look like snowflakes, I look forward to tatting this pattern with or without beads I enjoy using beads but I never over do the beads I like to see the tatting as well.Margaret
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{
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