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Protease-activated receptors in human airways: upregulation of PAR-2 in respiratory epithelium from patients with asthma.
Protease-activated receptors (PARs), which are G protein-coupled receptors that are activated after proteolytic cleavage of the amino terminus of the receptor, are likely to play a major role in airway inflammation. PARs are activated by endogenous proteases, including thrombin (PAR-1, -3, and -4) and tryptase (PAR-2 and -4), both of which are present in inflamed airways. The purpose of this study was to compare the expression and distribution of PARs in biopsy specimens obtained from asthmatic and normal subjects and to examine the effect of inhaled corticosteroids on PAR expression. Biopsy specimens were obtained from 10 normal and 20 asthmatic patients, and sections were stained for PAR-1, -2, -3, and -4 through use of specific antibodies. Staining was scored semiquantitatively for both intensity and distribution. Staining for all PARs was seen on the epithelium and smooth muscle in biopsy specimens from both normal and asthmatic subjects. In the epithelium, PAR-1 and -3 staining appeared to be apically concentrated, whereas PAR-2 and -4 staining was more diffuse. In normal subjects, epithelial staining intensity of PAR-1 and -3 was significantly greater than for PAR-4 (P < .05). Staining for PAR-1, -3, and -4 in biopsy specimens from asthmatic subjects was similar to that in specimens from normal subjects, irrespective of whether the former were using inhaled corticosteroids. However, PAR-2 staining in asthmatic epithelium was significantly increased in comparison with normal epithelium. Expression of PARs in airway smooth muscle did not differ between groups. Asthma per se is associated with increased PAR-2 expression in bronchial epithelium. Importantly, staining was not influenced by inhaled corticosteroids. These results suggest that PAR-2 might be involved in airway inflammation.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
#include <stdio.h>
#include <stdlib.h>
#include <errno.h>
#include <string.h>
/** Our old friend die from ex17. */
void die(const char *message)
{
if (errno) {
perror(message);
} else {
printf("ERROR: %s\n", message);
}
exit(1);
}
// a typedef creates a fake type, in this
// case for a function pointer
typedef int (*compare_cb) (int a, int b);
/**
* A classic bubble sort function that uses the
* compare_cb to do the sorting.
*/
int *bubble_sort(int *numbers, int count, compare_cb cmp)
{
int temp = 0;
int i = 0;
int j = 0;
int *target = malloc(count * sizeof(int));
if (!target)
die("Memory error.");
memcpy(target, numbers, count * sizeof(int));
for (i = 0; i < count; i++) {
for (j = 0; j < count - 1; j++) {
if (cmp(target[j], target[j + 1]) > 0) {
temp = target[j + 1];
target[j + 1] = target[j];
target[j] = temp;
}
}
}
return target;
}
int sorted_order(int a, int b)
{
return a - b;
}
int reverse_order(int a, int b)
{
return b - a;
}
int strange_order(int a, int b)
{
if (a == 0 || b == 0) {
return 0;
} else {
return a % b;
}
}
/**
* Used to test that we are sorting things correctly
* by doing the sort and printing it out.
*/
void test_sorting(int *numbers, int count, compare_cb cmp)
{
int i = 0;
int *sorted = bubble_sort(numbers, count, cmp);
if (!sorted)
die("Failed to sort as requested.");
for (i = 0; i < count; i++) {
printf("%d ", sorted[i]);
}
printf("\n");
free(sorted);
}
int main(int argc, char *argv[])
{
if (argc < 2) die("USAGE: ex18 4 3 1 5 6");
int count = argc - 1;
int i = 0;
char **inputs = argv + 1;
int *numbers = malloc(count * sizeof(int));
if (!numbers) die("Memory error.");
for (i = 0; i < count; i++) {
numbers[i] = atoi(inputs[i]);
}
test_sorting(numbers, count, sorted_order);
test_sorting(numbers, count, reverse_order);
test_sorting(numbers, count, strange_order);
free(numbers);
return 0;
}
|
{
"pile_set_name": "Github"
}
|
sqrt(200))*5*3).
-14*sqrt(17)/25
Simplify (sqrt(76) + (sqrt(76)*-3 - sqrt(76))*-3 + sqrt(76) - 6*sqrt(76)*-3 - (3*sqrt(76) + -3 + (4*sqrt(76) + 2 - sqrt(76))))**2.
104*sqrt(19) + 51377
Simplify -2*(((sqrt(2662)*1)/(-4*sqrt(8)))**2 + (sqrt(891) + 4*(-1 + sqrt(891) + sqrt(891)))**2 + (sqrt(891) - (-2*sqrt(891) - sqrt(891)))*1).
-4621299/32 + 1224*sqrt(11)
Simplify (-3*-1*4*(sqrt(112) + sqrt(112) + 1 + -2 - (5 + sqrt(112) + 3)))**2.
-10368*sqrt(7) + 27792
Simplify (-4 + (sqrt(567) + -1)*-5 - (5 + sqrt(28) + (sqrt(168)/sqrt(3))/sqrt(8))*5)**2.
2880*sqrt(7) + 25776
Simplify (-2*-5*sqrt(104)*-3*3)/(((sqrt(64) + 2*sqrt(64) - sqrt(64))*-4)/((-2*sqrt(64) - sqrt(64))/sqrt(8))).
-135*sqrt(13)/4
Simplify (6*(2*sqrt(2176)*-3 + sqrt(2176))*5)/((sqrt(2) - (sqrt(288) - sqrt(288)*-1)) + sqrt(6)/sqrt(3)*1 - (sqrt(32)*2*4 + sqrt(32))).
600*sqrt(17)/29
Simplify (6*(0 + 2*sqrt(2448) + sqrt(2448) + sqrt(2448) + -3 + (sqrt(2448) - (sqrt(2448) + 1)) + 3 + (sqrt(2448) + -1)*-5 + sqrt(2448))*5)**2.
14400
Simplify -6*(sqrt(7488) + (sqrt(7488) - (1*sqrt(7488) + sqrt(7488))) + sqrt(52) + sqrt(52) - (sqrt(4212)*2 - sqrt(52)))/(4*sqrt(144)*2)*-2.
-15*sqrt(13)/4
Simplify ((sqrt(77) - (sqrt(77) + (-1*sqrt(77) - sqrt(77))))*-6 + 3*sqrt(77)*-5)/((sqrt(210)/(5*sqrt(10)))/sqrt(3)).
-135*sqrt(11)
Simplify 1*(-6*-4*(2 + 3 + 4*(0 + sqrt(2700) + -3)))**2.
-967680*sqrt(3) + 24911424
Simplify (2*(sqrt(605) + sqrt(605)*2 + -2 + (1 + (sqrt(605) - 1*sqrt(605)) - sqrt(605))))**2 + (0 + (sqrt(500) + 2 + -2)*-3)**2.
-176*sqrt(5) + 14184
Simplify ((-4*((sqrt(125) - (sqrt(125) + sqrt(125)*-1)) + -2 - sqrt(125) - (4 + 0 + sqrt(125))) + -2)*-1 + 2)*-1.
20 + 20*sqrt(5)
Simplify ((-4 + (5 + 4*sqrt(500) + sqrt(500) - (5 + 0 + sqrt(500))))*-4 + 3)**2.
-6080*sqrt(5) + 128361
Simplify 5 + (2 + 3 + (sqrt(1573) - ((1 + sqrt(1573))*4 + sqrt(1573))) + -5)**2 + -1.
352*sqrt(13) + 25188
Simplify -3 + (-1*sqrt(51)*3)/(sqrt(3) + sqrt(48) + sqrt(96)/sqrt(2)) - ((sqrt(17) - (sqrt(17)*2 + 5) - ((-1*sqrt(2057))**2 - sqrt(17))) + -3).
-sqrt(17)/3 + 2062
Simplify (sqrt(2448) - (-4 + sqrt(2448))**2) + 5 + -1 - (sqrt(1836)*1)/(sqrt(3) - -1*(-1*sqrt(3) + sqrt(3))).
-2460 + 102*sqrt(17)
Simplify ((0 + sqrt(28) + (sqrt(28) - (2 + sqrt(28))) + sqrt(28))*6 - (-1 + sqrt(28)/sqrt(4) + 5)*3)**2.
-1008*sqrt(7) + 3663
Simplify ((1*sqrt(77) + sqrt(77))*5*-2*5)/(sqrt(49)/(3*sqrt(7)) - (sqrt(21)*2)/sqrt(3)) + 1.
1 + 60*sqrt(11)
Simplify (sqrt(152) + (6*-1*sqrt(152) - sqrt(152)))/sqrt(8)*-5 + -2*sqrt(57)/sqrt(3) + sqrt(133)/sqrt(28).
57*sqrt(19)/2
Simplify 4 + ((sqrt(33)/(-2*sqrt(3)) - sqrt(11)) + 1*sqrt(275))**2 + ((sqrt(2112)*-2 + sqrt(2112))/((sqrt(36)*-2)/sqrt(12)))**2.
1259/4
Simplify 2 + sqrt(77)/(-6*(sqrt(11)*1 + sqrt(11)) - sqrt(11)) + -5 + 5 + sqrt(77)/sqrt(11).
2 + 12*sqrt(7)/13
Simplify (sqrt(153) + 3*sqrt(153)*-2)/(sqrt(9) + (sqrt(81) - (sqrt(81) + sqrt(81)*-2 + sqrt(81)))) - (sqrt(170)*1*-4)/(sqrt(10) - sqrt(40)*5).
-61*sqrt(17)/36
Simplify (sqrt(28) + -2 - -3*sqrt(175) - 4*(sqrt(448) + 1 + 3)**2)*-5.
1195*sqrt(7) + 9290
Simplify (((-1*sqrt(132)*-1 - sqrt(132)) + sqrt(132))*-2*-6)/(4*(sqrt(300) - sqrt(12)) + (sqrt(12) - sqrt(588)*3)).
-3*sqrt(11)
Simplify -3*((3*sqrt(16)/sqrt(32))/(3*1*sqrt(256) + sqrt(256)) + 5).
-15 - 9*sqrt(2)/128
Simplify (((sqrt(18) - (sqrt(2178) - sqrt(18)))*1 - sqrt(18)) + sqrt(450)*3)/((-1*-1*sqrt(108) + sqrt(108) + sqrt(108))/(2*sqrt(12)*-6 + sqrt(12))).
-55*sqrt(2)/3
Simplify 2 + -4 + -3*(sqrt(180) + -5*1*sqrt(180))**2*5 + 4.
-43198
Simplify ((1*sqrt(238)*-6)/sqrt(7)*-3)/((-1*sqrt(512) + sqrt(512) - sqrt(512))/(sqrt(12)/sqrt(27) + sqrt(4))).
-3*sqrt(17)
Simplify 2*((4*5*(sqrt(684)*-2)**2 + -3)*2 + -2).
218864
Simplify 3*(sqrt(13) + sqrt(52)/sqrt(4) + -2 + (sqrt(13) + 0)*-4 + sqrt(13) - (-6*(sqrt(117) - (sqrt(117)*-1 - sqrt(117))))/sqrt(9)) + 1.
-5 + 51*sqrt(13)
Simplify ((((sqrt(143) - sqrt(143)*1)*4 + sqrt(143)*-1*4)*-3)/((sqrt(1584) - 2*sqrt(1584) - sqrt(1584)) + -2*(sqrt(11) + sqrt(77)/sqrt(7))))**2.
117/49
Simplify (-1*(2 + sqrt(832))*2*5 - (((sqrt(832) - -2*sqrt(832)) + sqrt(832))*4 + sqrt(832) + -1 + 1)*-5)**2*3.
-72000*sqrt(13) + 14041200
Simplify (sqrt(99)*3*2 + sqrt(99) + -5*(sqrt(99) - -4*sqrt(99)))/(-2*(sqrt(36)/(sqrt(4) + sqrt(12)/sqrt(3)) + sqrt(9) + (sqrt(45)*1)/sqrt(5))).
18*sqrt(11)/5
Simplify (6*sqrt(88)*-4 - (sqrt(88) - (sqrt(88) + -4*sqrt(88)*6)))/((6*(sqrt(32) + sqrt(8)) - ((sqrt(72) - 2*sqrt(72)) + sqrt(72) + sqrt(72)))*5).
-16*sqrt(11)/25
Simplify (-1*sqrt(117) + sqrt(117) + 5 - (sqrt(117) + 3*(-3 + sqrt(117)) + sqrt(117) + sqrt(117))**2) + -2 + ((1*(sqrt(234) + sqrt(26)))/sqrt(2)*-1)**2.
-4082 + 324*sqrt(13)
Simplify (-4*(sqrt(99) - sqrt(99)*-4) + -1*sqrt(99)*-3)/(4*sqrt(324)*3).
-17*sqrt(11)/72
Simplify 4 + (((sqrt(240) - 2*sqrt(240))*4)/sqrt(4))/((sqrt(12) - sqrt(96)/sqrt(512))*3).
-32*sqrt(5)/21 + 4
Simplify (sqrt(24)/sqrt(2)*-1)/sqrt(6)*3 + ((sqrt(10)/sqrt(5))**2 + 4 - -3*sqrt(72)).
6 + 15*sqrt(2)
Simplify 2*(-1 + 1 + 2 + -4*(3 + sqrt(108)) + -3)*5.
-240*sqrt(3) - 130
Simplify (sqrt(144)/(3*4*sqrt(8)))/(sqrt(6) - (sqrt(486) - 2*sqrt(486)) - (sqrt(864) - sqrt(864)*1)).
sqrt(3)/120
Simplify (-1*(sqrt(847) + -1 + sqrt(847)) + -2)**2 - (-2 + sqrt(77)/(-3*sqrt(11)*2)).
265*sqrt(7)/6 + 3391
Simplify (1 + sqrt(448) + 1 + 0 + sqrt(448)*-4 + -5)**2 + 3 + -2.
144*sqrt(7) + 4042
Simplify 5*(sqrt(245) + -1 + 2)**2*-6 - (-1*-2*sqrt(245) + -5)**2*-1.
-6375 - 560*sqrt(5)
Simplify 5 + sqrt(125)*5 + sqrt(20)*2 + sqrt(20) - (((sqrt(180) - -1*sqrt(180)) + 4 - (sqrt(180) + 0 + -2*sqrt(180)))**2 + 3).
-1634 - 113*sqrt(5)
Simplify -4 + ((sqrt(110) - (-6*-1*sqrt(110) + sqrt(110))) + 2*sqrt(110)*6)/(-5*sqrt(50)/sqrt(5) - sqrt(90)/(sqrt(9)*-2)) + 2.
-4*sqrt(11)/3 - 2
Simplify (-6*-4*(-6*((-2 + (sqrt(68) - (0 + sqrt(68))) - sqrt(68)) + sqrt(68)) + -2)*3)**2.
518400
Simplify (-4*(((sqrt(140) - -1*sqrt(140))/sqrt(5))/(3*sqrt(63)))/(-1*3*sqrt(2) + sqrt(504)/sqrt(7)))**2.
128/729
Simplify -3 + 4 + sqrt(176) + 0 - ((-4*(sqrt(1331) - (sqrt(1331) + -2)))**2 + (2 + sqrt(1331) + 2)**2).
-1410 - 84*sqrt(11)
Simplify (3*(1 + 1 + 1 + (sqrt(539) - (-2*sqrt(539) + -3) - sqrt(539)) + sqrt(539) + -5 + -2))**2.
-378*sqrt(11) + 43668
Simplify 2 + -5*(1 + (6*(sqrt(1300)*4 + sqrt(1300)) - (-4 + sqrt(1300) + 1))**2).
-5466548 - 8700*sqrt(13)
Simplify -6*(2 + -5*(sqrt(200)*1*4 + sqrt(200)*-1*1 + 4)**2)*-6.
-326808 - 43200*sqrt(2)
Simplify -4*((sqrt(931)*-2 + sqrt(931) + sqrt(931))*-6*-6 - (1*sqrt(19)*3 + sqrt(114)/(sqrt(6) - (sqrt(6) + sqrt(6)*-3))))**2.
-7600/9
Simplify (-6*-2*sqrt(700)*-6 + ((sqrt(700) - -2*sqrt(700))*4)**2*3)*-4*-5.
-14400*sqrt(7) + 6048000
Simplify (-3 + 3*sqrt(1620))**2 + (((sqrt(1250) + sqrt(50))*-3)/sqrt(10)*-2)**2.
-324*sqrt(5) + 21069
Simplify 3 + -6*-2*(sqrt(19) + sqrt(475) + 2 + sqrt(114)/(sqrt(6)*1 + sqrt(6)) - -5*(-3 + sqrt(19) + sqrt(684))).
-153 + 498*sqrt(19)
Simplify ((4 + (sqrt(500) - 1*sqrt(500) - sqrt(500)) - (-2*sqrt(500) + 3)) + 2)**2 + -2*(sqrt(245)*-2)**2 + -4 + -4.
-1459 + 60*sqrt(5)
Simplify (((sqrt(102)/sqrt(6) - sqrt(17)) + -5 - sqrt(17) - 6*sqrt(17)*1) + 4 + (sqrt(153) + 1)*5 + sqrt(153) + -4 + sqrt(153)*-3)**2.
68
Simplify 4*(0 + sqrt(405) + 1)**2 - -6*((sqrt(5) + -1)*-4 + -2).
48*sqrt(5) + 1636
Simplify (sqrt(896)*3 - sqrt(56) - sqrt(56))/(sqrt(48)/(sqrt(6)*-1 - sqrt(6))) - 2*(-6*(3 + sqrt(847)) + sqrt(847)).
36 + 90*sqrt(7)
Simplify 1*(-2 + (sqrt(110) - (sqrt(110) + 4*1*sqrt(110)))/(sqrt(90)*4 - sqrt(10)))*6.
-12 - 24*sqrt(11)/11
Simplify -1*-5*sqrt(2057)*1 + -2 - (-4 + 5 + sqrt(833) + sqrt(833)*1 + 0)**2.
-3335 + 27*sqrt(17)
Simplify 1*(-2 + (0 + ((sqrt(1216) + 1 + sqrt(1216))*4 + (0 + 1*sqrt(1216) - sqrt(1216)))*-3)**2).
4608*sqrt(19) + 700558
Simplify (sqrt(228)/((sqrt(24)/sqrt(2) + sqrt(12))*2) + ((sqrt(171) - 1*sqrt(171)) + sqrt(19))*-5 + -5 + -1 + sqrt(1539) + -1 + -5)**2.
-102*sqrt(19) + 7795/16
Simplify (((sqrt(363)*-1 - sqrt(363))/sqrt(11) - sqrt(33)) + (sqrt(825) + sqrt(33) + sqrt(33))*-1)/(sqrt(176) + 1*sqrt(176) - sqrt(176) - -2*sqrt(99)).
-sqrt(3)
Simplify 2 + (sqrt(44)/sqrt(16) + (sqrt(396)*1)**2 + -5 - 1*((sqrt(176) + sqrt(11))*-2 - 6*(2*sqrt(11) - sqrt(11)))).
33*sqrt(11)/2 + 393
Simplify (-6*(sqrt(2448) - (-3 + sqrt(2448) + -2))*1 + (sqrt(2448) - (sqrt(2448) + 2*sqrt(2448) + sqrt(2448))) + 3 + (4 + sqrt(2448))*5)**2.
-336*sqrt(17) + 9841
Simp
|
{
"pile_set_name": "DM Mathematics"
}
|
The role of basic sciences in diagnostic oral radiology.
Although it is generally taken for granted that dental education must include both basic science and feature-based knowledge components, little is known about their relative roles in visual interpretation of radiographs. The objectives of this study were twofold. First, we sought to compare the educational efficacy of three learning strategies in diagnostic radiology: one that used basic scientific (pathophysiologic) information, one that used feature lists structured with an organizational tool, and one that used unstructured feature lists. Our second objective was to determine whether basic scientific information provides conceptual coherence or is merely a simple means for organizing feature-based knowledge. Predoctoral dental and undergraduate dental hygiene students (n=96) were randomly assigned into three groups (basic science, structured algorithm, and feature list) and were taught four confusable intrabony entities. The students completed diagnostic and memory tests immediately after learning and one week later, and these data were subjected to a 3x2 repeated measures ANOVA. For the diagnostic test, students in the basic science group outperformed those assigned to the feature list and structured algorithm groups on immediate and delayed testing (p<0.05). A main effect of learning condition was found to be significant. On the memory test, performance was similar across all three groups, and no significant effects were found. The results of this study support the critical role of basic scientific knowledge in diagnostic radiology. This study also refutes the organized learning theory and provides support for the conceptual coherence theory as a possible explanation for the process by which basic science aids in diagnosis.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
Q:
Why is this only fading In and not fading out
I have an image on the UIButton that I wish to glow in when I click button and glow out when I click it again.
Everytime I click, it doesn't glow out, it only glows in making it brighter
.
I have tried UIView animateWithDuration as well as CATransition and CABasicAnimation..
Something is wrong. Probably something basic that I should know about.
I'd appreciate the help.
Heres my code:
-(void)didTapButton:(UIButton *)button {
button.selected = !button.selected;
UIColor *glowColor = [self.arrayOfGlowColor objectAtIndex:button.tag];
UIImageView *imageView = button.imageView;
UIGraphicsBeginImageContextWithOptions(imageView.bounds.size, NO, [UIScreen mainScreen].scale);
[imageView.layer renderInContext:UIGraphicsGetCurrentContext()];
UIBezierPath *path = [UIBezierPath bezierPathWithRect:CGRectMake(0,0,imageView.bounds.size.width,imageView.bounds.size.height)];
[glowColor setFill];
[path fillWithBlendMode:kCGBlendModeSourceAtop alpha:1.0];
UIImage *imageContext_image = UIGraphicsGetImageFromCurrentImageContext();
UIView *glowView = [[UIImageView alloc] initWithImage:imageContext_image];
glowView.center = imageView.center;
[imageView.superview insertSubview:glowView aboveSubview:imageView];
glowView.alpha = 0;
glowView.layer.shadowColor = glowColor.CGColor;
glowView.layer.shadowOffset = CGSizeZero;
glowView.layer.shadowRadius = 10;
glowView.layer.shadowOpacity = 1.0;
/*
[UIView animateWithDuration: 1.0 animations:^(void) {
glowView.alpha = (button.selected) ? 1.0 : 0.0f;
}];
NSLog(@"glowView.alpha:%f",glowView.alpha);
NSLog(button.selected ? @"YES" : @"NO");
*/
/*
if (button.selected) {
CATransition *fadeIn = [CATransition animation];
fadeIn.duration = 1.0;
fadeIn.startProgress = 0.0f;
fadeIn.endProgress = 1.0f;
[fadeIn setType:kCATransitionFade];
fadeIn.timingFunction = [CAMediaTimingFunction functionWithName:kCAMediaTimingFunctionEaseIn];
[fadeIn setFillMode:@"extended"];
[glowView.layer addAnimation:fadeIn forKey:nil];
}
if (!button.selected) {
CATransition *fadeOut = [CATransition animation];
fadeOut.duration = 1.0;
fadeOut.startProgress = 1.0f;
fadeOut.endProgress = 0.0f;
[fadeOut setType:kCATransitionFade];
fadeOut.timingFunction = [CAMediaTimingFunction functionWithName:kCAMediaTimingFunctionEaseIn];
[fadeOut setFillMode:@"extended"];
[glowView.layer addAnimation:fadeOut forKey:nil];
}
*/
if (button.selected) {
//Create a one-way animation that fades in the glow.
glowView.layer.opacity = 1.0;
CABasicAnimation *glowFadeInAnim = [CABasicAnimation animationWithKeyPath:@"opacity"];
glowFadeInAnim.fromValue = [NSNumber numberWithDouble:0.0];
glowFadeInAnim.toValue = [NSNumber numberWithDouble:1.0];
glowFadeInAnim.repeatCount = 1;
glowFadeInAnim.duration = 1.0;
glowFadeInAnim.autoreverses = FALSE;
glowFadeInAnim.fillMode = kCAFillModeForwards;
glowFadeInAnim.removedOnCompletion = NO;
glowFadeInAnim.timingFunction = [CAMediaTimingFunction functionWithName:kCAMediaTimingFunctionEaseIn];
[glowView.layer addAnimation:glowFadeInAnim forKey:nil];
}
if (!button.selected) {
glowView.layer.opacity = 1.0;
CABasicAnimation *glowFadeOutAnim = [CABasicAnimation animationWithKeyPath:@"opacity"];
glowFadeOutAnim.fromValue = [NSNumber numberWithDouble:1.0];
glowFadeOutAnim.toValue = [NSNumber numberWithDouble:0.0];
glowFadeOutAnim.repeatCount = 1;
glowFadeOutAnim.beginTime = 2;
glowFadeOutAnim.duration = 2.0;
glowFadeOutAnim.autoreverses = FALSE;
glowFadeOutAnim.fillMode = kCAFillModeForwards;
glowFadeOutAnim.removedOnCompletion = NO;
glowFadeOutAnim.timingFunction = [CAMediaTimingFunction functionWithName:kCAMediaTimingFunctionEaseOut];
[glowView.layer addAnimation:glowFadeOutAnim forKey:nil];
glowView.layer.opacity = 0.0;
}
NSLog(@"glowView.opacity:%f",glowView.layer.opacity);
NSLog(button.selected ? @"YES" : @"NO");
}
A:
If you create a new glowView every time the button is pressed and add it to the button, then obviously it will just keep getting brighter, as more and more of them are being added to the button. You need to create the glowView once, for example in your viewDidLoad method, and store it as an instance variable so you don't lose it:
@interface MyViewController : UIViewController {
UIView *_glowView;
}
...
- (void)viewDidLoad {
[super viewDidLoad];
_glowView = ... // Initialise it here
...
[imageView.superview insertSubview:_glowView aboveSubview:imageView];
}
Then in your didTapButton: method, you handle the tap as you do (adding or removing the _glowView, but make sure you don't set it to nil so the reference to it is always retained). This way, you only create and add it once, and the problem should be solved.
|
{
"pile_set_name": "StackExchange"
}
|
Effect of the abrasive properties of sedges on the intestinal absorptive surface and resting metabolic rate of root voles.
Recent studies on grasses and sedges suggest that the induction of a mechanism reducing digestibility of plant tissues in response to herbivore damage may drive rodent population cycles. This defence mechanism seems to rely on the abrasive properties of ingested plants. However, the underlying mechanism has not been demonstrated in small wild herbivores. Therefore, we carried out an experiment in which we determined the joint effect of abrasive sedge components on the histological structure of small intestine as well as resting metabolic rate (RMR) of the root vole (Microtus oeconomus). Histological examination revealed that voles fed with a sedge-dominated diet had shorter villi composed from narrower enterocytes in duodenum, jejunum and ileum. Reduction in the height of villi decreased along the small intestine. Activity of the mucus secretion increased along the small intestine and was significantly higher in the ileum. The intestinal abrasion exceeded the compensatory capabilities of voles, which responded to a sedge-dominated diet by a reduction of body mass and a concomitant decrease in whole body RMR. These results explain the inverse association between body mass and the probability of winter survival observed in voles inhabiting homogenous sedge wetlands.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
Stats
Eurofighter Typhoon Fighter-Bomber
Apparently the nations of Europe aren’t planning on going to war with each other anytime soon. If they did, they would be fighting against each other with the exact same aircraft, I guess it comes down to the pilot’s skill at that point.
The Eurofighter Typhoon, or Europe’s answer to the 5th Generation fighter aircraft concept, is finally emerging on the world stage as a prominent export fighter aircraft. While people consistently try to compare this jet with the F-22 Raptor, it really doesn’t compete in many areas. The Eurofighter Typhoon’s primary attributes are its maneuvering and speed capabilites, while it falls short in the deep penetration role. There is only 1 pilot in the world who has flown both the F-22 Raptor and the Eurofighter Typhoon, and..
|
{
"pile_set_name": "Pile-CC"
}
|
Last May, Mississippi Governor Phil Bryant introduced the state’s new “default” license plate — the one that would automatically be given to anybody who needs one — and it included the state seal with the phrase “In God We Trust” on it.
Bryant had signed a bill to put the Christian phrase on the seal in 2014, so this was the next phase in pushing God on all the citizens in the state. The plates went into circulation at the beginning of this year.
That alone was a problem, but the bigger issue was this: If you wanted to avoid promoting God by getting a different background on your license plate, it was going to cost you money. Which, in a way, was like a tax on non-Christian residents.
The American Humanist Association’s Legal Director David Nioseissued a warning about the new plates in a letter sent to Bryant last year, saying that the change raised a number of constitutional concerns.
Unlike on our money, he wrote, the religious phrase here was front and center… and large. It was clearly a promotion of religion. Niose called on Bryant to make sure there were free alternative plates for residents that didn’t include religious propaganda.
Bryant never responded.
Yesterday, the AHA sent another letter to Department of Revenue Commissioner Herb Frierson and Attorney General Jim Hood offering a “final warning.”
“Mississippi’s law violates the First Amendment rights of atheists in accordance with firmly settled Supreme Court precedent,” explained Monica Miller, American Humanist Association senior counsel. “The Supreme Court has made clear that the state cannot force motorists to display an ideological message they deem unacceptable on their license plates,” Miller added.
Today’s letter notes that “[b]eyond violating the Free Speech rights of nontheistic Mississippians, compelling such citizens to display ‘In God We Trust’ or pay a penalty contravenes the Religion Clauses of the First Amendment.”
Miller notes in her letter that license plates saying “In God We Trust” aren’t the same as the phrase appearing on paper money — in case that’s the argument officials want to use. She says that several courts have ruled that the phrase on currency isn’t considered “compelled speech” — if atheists paid with cash, no one would reasonably mistake them for trying to proselytize — but license plates are more personal. Furthermore, unlike currency, you have to display your plate to the public.
In a separate case she cites, Miller says that an “In God We Trust” license plate in South Carolina was deemed constitutional only because “it was not the default plate and the department offered many others at no additional cost, one in particular bearing the opposite viewpoint.”
She’s basically setting up the arguments the AHA would use in a lawsuit if it came to that. But Mississippi has options available to avoid a lawsuit. The only question is whether they’ll take the easy route and just make a secular license plate available at no additional cost… or whether pushing a religious plate on everyone is a hill on which they’re prepared to fight.
If you don’t comply with this reasonable request, you should understand that you face potential litigation.
I would add that even outside the legal questions, forcing a religious phrase on everyone, even in Mississippi, is an idea that Christians ought to oppose. They would be up in arms if the phrase was an obvious reference to a non-Christian God. If the seal said “In God We Don’t Trust,” would they remain silent? Would they just accept the plate? Or would they argue that the government has no right to force an atheistic perspective on them?
Just because “In God We Trust” has been around for decades doesn’t mean it’s okay for politicians can slap the phrase everywhere they find space. Tradition doesn’t make something right, and this religious motto has always been a bad tradition.
By the way, Mississippi’s Lt. Governor Tate Reeves addressed the AHA’s letter in a Facebook post yesterday, dismissing it completely and saying that “in Mississippi we do trust God.”
I love how he calls them an “out-of-state” group, as if an in-state group making the exact same request would get better reception.
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{
"pile_set_name": "Pile-CC"
}
|
Connect with Us
Coupeville Notes
"The last time a movie company wanted to film along Coupeville's historic waterfront, its offer was resoundingly rejected after a series of contentious public meetings. The majority at the time - many who had weathered previous film shoots in Coupeville - felt movie crews caused too much disruption for too little compensation. But many others likened the rejection to killing the golden goose.Now the town is working on a way to make movies worth its while.At a public meeting hosted last Wednesday by Coupeville's Ad Hoc Film Committee chairman Jack McPherson, the town may have found some answers. The one thing that seems to be bringing people together is that even those who are not in favor of it would concede if the town would benefit, McPherson said.That's benefits as in an up-front fees to be paid into a town fund ranging anywhere from $1,000 to $5,000 per day, depending on the level of activity, he said. The Ad Hoc Film Committee was formed last summer, shortly after producers of A Leonard Cohen Afterworld were told to find another town to film in. The movie was eventually shot in Langley and quickly tanked.After that, the mayor's thought was we should get some folks together, gather information and find out what people do want, McPherson said.The results of the committees findings will eventually be forwarded to the town council and used to craft a town ordinance to address filming in Coupeville - if and when Hollywood beckons again.Currently, the town has an ordinance that covers permits and parades, McPherson said. But it doesn't cover something as complex as shutting down streets and painting buildings, he added. Hopefully we'll take the information and produce a better ordinance. That's why the committee was formed, to give the town council info they can work with.Compensating merchants will be a separate issue, according to McPherson.The mayor pointed out the town can only authorize the use of rights of way in the town, he said. If they (movie companies) want to use individual buildings or businesses, they have to work with those affected.About 35 people attended Wednesday's meeting, McPherson said, adding that filming fans and critics were well represented. We're not gonna give anything away, McPherson said. We felt that in Coupeville, we subject ourselves to stringent historical review, sign and zoning ordinances, and if someone has come in and produces something that benefits from that, its not going to be for nothing.--------------------COUPEVILLE NOTESPublic invited to plan Ebey's futureAnyone interested in the future of Ebey's Landing National Historical Reserve will have a chance to shape its new general management plan during public meetings in Coupeville and Seattle next week.The purpose for the meetings are to guide future management efforts for the 17,000-acre Reserve, said manager Rob Harbour.People who have experienced the Reserve's rolling farmland, scenic pathways and quiet beaches know what a gem this place is, Harbour said. The idea for a Reserve started with local citizens. Now citizen involvement can help provide a clear sense of direction for the years to come.Ebey's Landing National Historical Reserve is managed by a trust board under a partnership with the town of Coupeville, Island County, Washington State Parks and the National Parks Service.Initial public meetings, called scoping meetings, will be held in Seattle June 20, from 6:30 to 8:30 p.m., at the REI Flagship store at 222 Yale Ave. N., in the second-floor meeting room.Coupeville will be the location of the second meeting June 21, from 2:30 to 5:30 p.m. and again from 7-9 p.m. at the Coupeville Recreation Hall, 901 N.W. Alexander St.Fire hall's future debatedIs $188,000 too much to spend to bring Coupeville's Fire Hall back up to code?That's a question Coupeville's Town Council considered at at its meeting last Tuesday, and a decision the town would like a little help in making.We're anxious to get the word out to as many people as possible and see what they want to do with it, Town Planner Larry Cort.The town recently paid $3,200 for a structural and historical review of the 1937-era building, the results of which are now available at Town Hall.The building is one of the 52 designated historic properties in Coupeville and has been evaluated four times in the past. Each time, it was determined the fire hall needed significant improvements to bring it up to code.Some who attended last Tuesday's council meeting thought the fire hall deserved restoration.In the first place, I think this town is too eager to tear down old buildings, resident Janet Enzman said. For example the old courthouse, which was torn down, fit this town to a T.Enzman, who also conducts walking tours of Coupeville for the Island County Historical Museum, said the old fire hall/museum is . I think its a fun building and it's important to preserve buildings from the past, she said. It's a funky old building but it has character.Others, like councilman Frank Tippets, aren't so sure.Based on the information in the report, it's a very high cost to make it sound, compared to what a new building would cost, Tippets said, adding, I would characterize it's historical value as marginal, based on my interpretation of the report. The town has three options, Tippets said: sell the building, demolish it and do something else with the property, or restore it.To date, Mayor Conard said, several people have expressed interest in purchasing the old fire hall but no firm offers have come forward.After receiving comments and suggestions from the public, Conard will bring a recommendation back to the council concerning the fire hall's fate.To comment on the proposals for the fire hall, contact Coupeville Town Hall, either by calling 678-4461, or writing to Town Planner Larry Cort or Mayor Nancy Conard at: Town of Coupeville, P.O. Box 725, Coupeville 98239; or by e-mail to Cort at: lcort@whidbey.net or to Conard at: mayor@whidbey.net."
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{
"pile_set_name": "Pile-CC"
}
|
import Notify from 'heyui/src/plugins/notify';
import utils from 'heyui/src/utils/utils';
import locale from 'heyui/src/locale';
const prefixCls = 'h-modal';
let Default = {
middle: false
};
function Confirm(content, title) {
return new Promise((resolve, reject) => {
let param = {
type: prefixCls,
content: `<div><i class="h-icon-warn yellow-color" style="font-size:28px;vertical-align: -8px;"></i> ${content}</div>`,
buttons: ['cancel', 'ok'],
events: {
ok: (n) => {
n.close();
resolve();
},
cancel: (n) => {
n.close();
reject(new Error('cancel'));
}
},
title,
className: 'h-modal-comfirm h-modal-type-default',
hasMask: true,
closeOnMask: true,
hasCloseIcon: false,
timeout: 0
};
param = utils.extend({}, Default, param, true);
return Notify(param);
});
}
function confirm(content, title) {
if (!title) {
title = locale.t('h.confirm.title');
}
return Confirm(content, title);
}
confirm.config = (options) => {
if (options.middle) {
Default.middle = true;
}
};
export default confirm;
|
{
"pile_set_name": "Github"
}
|
Q:
Como mandar um string para um servidor web?
Eu preciso mandar uma string para um servidor, que no caso será uma página do meu site. Eu preciso mandar um txt com a string para lá, apenas isso. Alguém sabe com fazer isso no Android do jeito mais simples possível? Agradeço desde já!
A:
Crie esta classe em seu projeto:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.net.URLEncoder;
import java.util.ArrayList;
import org.apache.http.HttpEntity;
import org.apache.http.HttpResponse;
import org.apache.http.NameValuePair;
import org.apache.http.client.ClientProtocolException;
import org.apache.http.client.HttpClient;
import org.apache.http.client.entity.UrlEncodedFormEntity;
import org.apache.http.client.methods.HttpGet;
import org.apache.http.client.methods.HttpPost;
import org.apache.http.client.methods.HttpUriRequest;
import org.apache.http.impl.client.DefaultHttpClient;
import org.apache.http.message.BasicNameValuePair;
import org.apache.http.protocol.HTTP;
public class RestClient {
private ArrayList <NameValuePair> params;
private ArrayList <NameValuePair> headers;
private String url;
private int responseCode;
private String message;
private String response;
public String getResponse() {
return response;
}
public String getErrorMessage() {
return message;
}
public int getResponseCode() {
return responseCode;
}
public RestClient(String url)
{
this.url = url;
params = new ArrayList<NameValuePair>();
headers = new ArrayList<NameValuePair>();
}
public void AddParam(String name, String value)
{
params.add(new BasicNameValuePair(name, value));
}
public void AddHeader(String name, String value)
{
headers.add(new BasicNameValuePair(name, value));
}
public void Execute(RequestMethod method) throws Exception
{
switch(method) {
case GET:
{
//add parameters
String combinedParams = "";
if(!params.isEmpty()){
combinedParams += "?";
for(NameValuePair p : params)
{
String paramString = p.getName() + "=" + URLEncoder.encode(p.getValue(),"UTF-8");
if(combinedParams.length() > 1)
{
combinedParams += "&" + paramString;
}
else
{
combinedParams += paramString;
}
}
}
HttpGet request = new HttpGet(url + combinedParams);
//add headers
for(NameValuePair h : headers)
{
request.addHeader(h.getName(), h.getValue());
}
executeRequest(request, url);
break;
}
case POST:
{
HttpPost request = new HttpPost(url);
//add headers
for(NameValuePair h : headers)
{
request.addHeader(h.getName(), h.getValue());
}
if(!params.isEmpty()){
request.setEntity(new UrlEncodedFormEntity(params, HTTP.UTF_8));
}
executeRequest(request, url);
break;
}
}
}
private void executeRequest(HttpUriRequest request, String url)
{
HttpClient client = new DefaultHttpClient();
HttpResponse httpResponse;
try {
httpResponse = client.execute(request);
responseCode = httpResponse.getStatusLine().getStatusCode();
message = httpResponse.getStatusLine().getReasonPhrase();
HttpEntity entity = httpResponse.getEntity();
if (entity != null) {
InputStream instream = entity.getContent();
response = convertStreamToString(instream);
// Closing the input stream will trigger connection release
instream.close();
}
} catch (ClientProtocolException e) {
client.getConnectionManager().shutdown();
e.printStackTrace();
} catch (IOException e) {
client.getConnectionManager().shutdown();
e.printStackTrace();
}
}
private static String convertStreamToString(InputStream is) {
BufferedReader reader = new BufferedReader(new InputStreamReader(is));
StringBuilder sb = new StringBuilder();
String line = null;
try {
while ((line = reader.readLine()) != null) {
sb.append(line + "\n");
}
} catch (IOException e) {
e.printStackTrace();
} finally {
try {
is.close();
} catch (IOException e) {
e.printStackTrace();
}
}
return sb.toString();
}
public void AddParam(String name, long value) {
params.add(new BasicNameValuePair(name, value + ""));
}
public enum RequestMethod {
GET(1), POST(2);
public int action;
private RequestMethod(int action) {
this.action = action;
}
}
}
Depois é só usar o seguinte código dentro de uma Thread:
RestClient client = new RestClient("http://site");
client.AddParam("nome_parametro1", valor);
client.AddParam("nome_parametro2", valor2);
try {
client.Execute(RestClient.RequestMethod.GET);
String resposta = client.getResponse();
} catch (Exception e) {
e.printStackTrace();
}
|
{
"pile_set_name": "StackExchange"
}
|
Mass spectrometry for rapid characterization of microorganisms.
Advances in instrumentation, proteomics, and bioinformatics have contributed to the successful applications of mass spectrometry (MS) for detection, identification, and classification of microorganisms. These MS applications are based on the detection of organism-specific biomarker molecules, which allow differentiation between organisms to be made. Intact proteins, their proteolytic peptides, and nonribosomal peptides have been successfully utilized as biomarkers. Sequence-specific fragments for biomarkers are generated by tandem MS of intact proteins or proteolytic peptides, obtained after, for instance, microwave-assisted acid hydrolysis. In combination with proteome database searching, individual biomarker proteins are unambiguously identified from their tandem mass spectra, and from there the source microorganism is also identified. Such top-down or bottom-up proteomics approaches permit rapid, sensitive, and confident characterization of individual microorganisms in mixtures and are reviewed here. Examples of MS-based functional assays for detection of targeted microorganisms, e.g., Bacillus anthracis, in environmental or clinically relevant backgrounds are also reviewed.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
In the search for a workable ankle arthroplasty, various designs have been tried. As seen below in Table 1, certain published results relating to conventional total ankle arthroplasty were disappointing for both patients and surgeons (the typical clinical series of Table 1 includes 20-40 patients followed for an average of five years or less; only general observations can be made from this data).
TABLE 1Good-to-Excellent Satisfaction Rates After Total Ankle Replacements-Conventional Designs# ofAvg. F/UDeviceAuthor/YearAnkles(months)Satisfaction RateSmithDini/80212746%ICLHGoldie/82183660%TPRJensen/92235969%Bath & WessexCarlsson/93526081%TPRKumar/88376052%LCSBuechel/92407285%SmithKirkup/85188461%MayoKitaoka/9616010819%
As Table 1 reveals, patient satisfaction with conventional, cemented ankle implants has ranged from 19 percent to 85 percent (see, e.g., Dini A A, Bassett F H: Evaluation of the early result of Smith total ankle replacement. Clin Orthop 1980; 146:228-230; Goldie I F, Herberts P: Prosthetic replacement of the ankle joint. Reconstr Surg and Traumat 1981; 18:205-210; Jensen N C, Kroner K: Total ankle joint replacement: A clinical follow-up. Orthopedics 1992; 15:236-240; Carlsson A S, Henricson A, Linder L, Nilsson J A, Redlund-Johneur: A survival analysis of 52 Bath-Wessex ankle replacements. The Foot 1994; 4:34-40; Kumar D J R: Total ankle arthroplasty. A review of 37 cases. J Tn Med Assoc 1988; 81:682-685; Buechel F F, Pappas M, Iorio U: NJ low contact stress total ankle replacement: Biomechanical rationale and review of 23 cementless cases. Foot Ankle 1988; 8:270-290; Kirkup J: Richard Smith ankle arthroplasty. J Roy Soc Med 1985; 78:301-304; Kitaoka H B, Patzer G L: Clinical results of the Mayo total ankle arthroplasty. J Bone Joint Surg 1996; 78A: 1658-1664).
It is believed that length of follow-up was a major factor with patient satisfaction, as patients with longer follow-ups generally had declining degrees of satisfaction. As seen below in Table 2, the rates of radiographic loosening with these conventional implants were quite substantial, ranging from 22 percent to 75 percent (see, e.g., Goldie I F, Herberts P: Prosthetic replacement of the ankle joint. Reconstr Surg and Traumat 1981; 18:205-210; Jensen N C, Kroner K: Total ankle joint replacement: A clinical follow-up. Orthopedics 1992; 15:236-240; Carlsson A S, Henricson A, Linder L, Nilsson J A, Redlund-Johneur: A survival analysis of 52 Bath-Wessex ankle replacements. The Foot 1994; 4:34-40; Kumar D J R: Total ankle arthroplasty. A review of 37 cases. J Tn Med Assoc 1988; 81:682-685; Kirkup J: Richard Smith ankle arthroplasty. J Roy Soc Med 1985; 78:301-304; Kitaoka H B, Patzer G L: Clinical results of the Mayo total ankle arthroplasty. J Bone Joint Surg 1996; 78A: 1658-1664; Helm R, Stevens J: Long-term results of total ankle replacement. J Arthroplasty 1986; 1:271-277; Bolton-Maggs B G, Sudlow R A, Freeman M A R: Total ankle arthroplasty. A long-term review of the London Hospital experience. J Bone Joint Surg 1985; 67B: 785-790). Of note, it is believed that some of the major factors implicated with loosening were: 1) highly constrained designs; and 2) cement fixation (it might have been the use of cement alone, or the combination of the use of cement to create adequate space for cementation, which was a major contributing factor to increased loosening rates).
TABLE 2Radiographic Loosening After Total Ankle Replacement-Conventional DesignsAvg. F/UDeviceAuthor/Year# of Ankles(months)Loosening RateICLHGoldie/82183622%ICLHHe1m/86145457%TPRJensen/92235952%Bath & WessexCarlsson/93526067%TPRKumar/88376026%ICLHBolton-416632%Maggs/85SmithKirkup/85188439%MayoKitaoka/9616010875%
Further, conventional total ankle arthroplasty has also been plagued with unusually high wound problems. The soft tissues around the ankle region, especially in rheumatoid and elderly patients, provide a relatively thin envelope for arthroplasty containment. Problems with superficial and deep infections, resection arthroplasties, attempted re-implantations or arthrodeses and, occasionally, below-knee amputations have dampened the enthusiasm of many orthopaedic surgeons involved with conventional total ankle replacement. In this regard, see Table 3 below, relating to published “long-term”results after conventional ankle arthrodesis.
TABLE 3Published “Long-Term” Results After Conventional Ankle ArthrodesisAvg.Author/# ofF/UMajor **ContinuedHindfootYearPatients(years)ComplicationsPainDJDSaid/7836824%*>50%Mazur/79128*25%100%Morrey/8041848%76% 50%Ahlberg/81411232%68% 44%Boobbyer/81 58921%**Morgan/851011010%**Lynch/8862734%**Glick/96348 6%**
While somewhat better short term results associated with conventional implants have stimulated interest in total ankle replacement, such conventional implants have shown their deficiencies. For example, one conventional prosthesis (the AGILITY ankle replacement) has shown an overall high rate of satisfaction in early follow up but with evident problems (see, e.g., Pyevich M T, Saltzman C L, Callaghan J J, Alvine F G: Total ankle arthroplasty: A unique design. Two to twelve-year follow-up. J. Bone Joint Surg., Vol 80-A(10):1410-1420, October, 1998; Saltzman C L, Moss T, Brown T D, Buckwalter J A Total Ankle Replacement Revisited. JOSPT 30(2):56-67, February, 2000; Saltzman C L, Alvine F G, Sanders R W, Gall R J. Challenges with Initial Use of a Total Ankle. Clinical Orthopaedics and Related Research (Accepted)).
One issue in this regard is the large amount of bone that is typically resected during conventional surgery. This creates a problem if revision is required because the subsequent lack of bone makes revision or conversion to a fusion problematic. The difficulties caused by having to resect a large amount of bone will become more apparent over time as with longer follow up the need for revision becomes more common.
Another issue with this conventional AGILITY ankle replacement is the limited range of motion it allows after surgery. It is believed that in approximately fifty percent of the cases the patient's plantarflexion contracture remained with patients not being able to dorsiflex significantly beyond neutral position.
A second conventional prosthesis (the STAR), while believed to not require as much bone resection, has articular contact surfaces that are flat in the medial-lateral direction, thus making edge loading necessary when resisting the varus/valgus loads imposed upon the ankle during ordinary ambulation (see, e.g., Kofoed H, Danborg L: Biological fixation of ankle arthroplasty. Foot 1995; 5:27-3 1; Kofoed H, Toben S: Ankle arthroplasty for rheumatoid arthritis and osteoarthritis: Prospective long-term study of cemented replacements. J Bone Joint Surg 1998; 80B:328-332).
Further still, additional papers include the following: Morgan C D, Henke J A, Bailey R W, Kaufer H: Long-term results of tibiotalar arthrodesis. J Bone Joint Surg 1985; 7A:546-550; Glick T M, Morgan D D, Myerson M S, Sampson T O, Mann J A: Ankle arthrodesis using an arthroscopic method: Long-term follow-up of 34 cases. Arthroscopy 1996; 12:428-434; Money B F, Wiedeman G P: Complications in long-term results of ankle arthrodeses following trauma. J Bone Joint Surg 1980; 62A:777-784; Ahlberg A, Henricson A S: Late results of ankle fusion. Acta Orthop Scand 1981; 52:103-105; Mazur J M, Schwartz E, Simon S R: Ankle arthrodesis; long-term follow-up with gait analysis. J Bone Joint Surg 1979; 61A:964-975; Boobbyer G N: The long-term results of ankle arthrodesis. Acta Orthop Scand 1981; 52:107-110; Said B, Hunka L, Siller T N: Where ankle fusion stands today. J Bone Joint Surg 1978; 60B:211-214; Lynch A F, Bourne R B, Rorabeck C H: The long-term results of ankle arthrodesis. J Bone Joint Surg 1988; 70B:113-116.
Moreover, issued patents include the following: U.S. Pat. No. 6,183,519, entitled Ankle Prosthesis; U.S. Pat. No. 5,957,981, entitled Adjustable Prosthesis Joint; U.S. Pat. No. 5,824,106, entitled Ankle Prosthesis; U.S. Pat. No. 5,800,564, entitled Ankle Prosthesis With Angle Adjustment; U.S. Pat. No. 5,766,259, entitled Total Ankle Prosthesis And Method; U.S. Pat. No. 5,728,177, entitled Prosthesis With Foam Block Ankle; U.S. Pat. No. 5,312,216, entitled Artificial Joint Prosthesis; U.S. Pat. No. 5,156,630, entitled Ankle Joint Prosthesis Fixable In More Than One Orientation; U.S. Pat. No. 5,019,109, entitled Multi-Axial Rotation System For Artificial Ankle; U.S. Pat. No. 4,778,473, entitled Prosthesis Interface Surface And Method Of Implanting; U.S. Pat. No. 4,755,185, entitled Prosthetic Joint; U.S. Pat. No. 4,659,331, entitled Prosthesis Interface Surface And Method Of Implanting; U.S. Pat. No. 4,470,158, entitled Joint Endoprosthesis; U.S. Pat. No. 4,442,554, entitled Biomechanical Ankle Device; U.S. Pat. No. 4,360,931, entitled Prosthetic Ankle; U.S. Pat. No. 4,340,978, entitled New Jersey Meniscal Bearing Knee Replacement; U.S. Pat. No. 4,309,778, entitled New Jersey Meniscal Bearing Knee Replacement; U.S. Pat. No. 4,166,292, entitled Stressed Reinforced Artificial Joint Prosthesis; U.S. Pat. No. 4,156,944, entitled Total Ankle Prosthesis; U.S. Pat. No. 4,069,518, entitled Total Ankle Prosthesis; U.S. Pat. No. 4,021,864, entitled Ankle Prosthesis; U.S. Pat. No. D242,957, entitled Total Ankle Prosthesis; U.S. Pat. No. 3,987,500, entitled Surgically Implantable Total Ankle Prosthesis; and U.S. Pat. No. 3,975,778, entitled Total Ankle Arthroplasty.
Among those benefits and improvements that have been disclosed, other objects and advantages of this invention will become apparent from the following description taken in conjunction with the accompanying figures. The figures constitute a part of this specification and include an illustrative embodiment of the present invention and illustrate various objects and features thereof.
|
{
"pile_set_name": "USPTO Backgrounds"
}
|
Author: Marshall Schott
Depending on style, the ingredients for a typical 5 gallon batch of beer costs between $25 to $35, a bit more for those who use malt extract. Broken down, that’s roughly $0.50 to $0.75 per bottle. Now, as my accountant wife is wont to remind me, this obviously doesn’t include equipment and energy costs (this homebrew break-even calculator is fun). All in all, that’s not too bad, but wouldn’t it be nice to get that number even lower without impacting the quality of the beer? Of course it would!
For whatever reason, when I first considered purchasing ingredients in bulk, I felt a little anxious. I’m not sure if it was the commitment to using certain types of hops and grains, the fact I’d have to figure out a place to store my extra wares, or the fear that I’d be stuck to brewing only a few certain styles using what I had on hand. But after crunching the numbers, I was certain bulk was the way to go, as it would allow to me brew more beer more often for less money. There are absolutely some necessary equipment purchases when transitioning from pre-milled homebrew shop kits to buying in bulk, but in my experience, the costs are recovered within just a few months of brewing. While the price of bulk ingredients is hugely dependent on your source, nearly every homebrew shop I know of offers discounts on bulk grains. If yours doesn’t, look elsewhere, you’ll find something. To illustrate this difference, here’s what Tiny Bottom Pale Ale purchased separately from my local shop would cost versus the bulk price:
TBPA from LHBS
Grain: $18
Hops: $4
Yeast: $8
Total: $30 + tax
TBPA from Ingredients Purchased in Bulk
Grains: $10
Hops: $2.25
Yeast: $0.00 (previously harvested from starter)
Total: $12.25
I left off the price of DME for making starters, as I don’t use enough to justify purchasing entire sacks worth, but it’s possible some places will offer a discount if this is something you’re interested in. All in all, by purchasing in bulk and reusing yeast, I’ve essentially cut the price of brewing a batch of beer in half. Not too shabby. As I mentioned before, there are a few things to consider before jumping into bulk purchasing ingredients.
STORAGE
If you brew large batches often, you might be able to get away with storing your bulk grains in the sack they come in, but for most of us, a 50-55 lb sack lasts quite awhile, meaning we need a hospitable place to store them. I like to keep 4 base grains on hand at all times, which I purchase by the sack, as this gives me more stylistic options. My preferred storage option for entire sacks of grain is the 60 lbs Vittles Vault, which can be stacked to save room. These containers can easily store an entire 55 lbs of grain. I tend to fill and store them in the upright position, though this doesn’t allow for stacking.
If you prefer them to be in their proper position, I’d suggest filling when upright then repositioning them once the bag is empty.
For grains I may not use as often, stuff like Wheat and Victory malts, I’ll either split a sack with a friend or pick them up in increments of 20-25 lbs. I store these mid-sized amounts of grain in 5 gallon buckets with Gamma Lids attached to the top for an airtight seal.
You could definitely get away with using standard bucket lids, but I’ve found the Gamma lids to be far more durable and super convenient. As for the buckets, you can’t really beat the price at your local big box home improvement store.
I also like to keep a bunch of specialty grains on hand in amounts of 10 lbs or less, for these I use 2 gallon paint pails with their respective lids, which seal tighter than is probably necessary. I also use one of these buckets for measuring out grain on my scale.
I always try to load up on these grains during sales or when I’m placing orders for other stuff, usually to help push me into the free shipping zone. A sack of something like C60 would last me over a year, so even at full price, these grains don’t impact my bottom line much. For those grains I use in tiny amounts and only want 2 lbs max on hand at any given time, I repurpose Costco nut containers with screw on lids, they’ve worked just fine.
To keep stuff organized on the grain side of things, I use a sturdy 4-tier shelving unit for all the buckets and pails. In the past, I’ve stacked the Vittles Vaults next to the shelving unit, which worked great, but since I added another fermentation freezer, I now store them under my workbench in the upright position.
Obviously, the amount of grain one decides to keep stocked is subjective, I like the freedom to brew any number of styles whenever I want without having to take a trip to the homebrew shop. However, even for the small-batch apartment brewer, a single sack of 2-row on hand can do wonders for your pocketbook over time.
Bulk hops tend to cost significantly less than those purchased from a shop, even after the costs of shipping. I use a relatively inexpensive vacuum sealer and store them in a small freezer to keep them fresh for 2+ years, if they last that long. I like to use vacuum sealer bags that come in a roll because they’re cheaper and allow me to cut them to whatever size I need, a single purchase lasts me well over a year.
Yeast… that’s an easy one. I buy a vial then harvest multiple pitches from starters, I’ve gone as far as 17 generations without issue at this point. Lately, I’ve been pulling off 1 quart of starter into 32 oz Ball Jars and throwing them right into my little yeast fridge, the yeast remaining under the starter beer until next use. This has been working great.
That’s about it as far as storage goes. There are a few extra pieces of equipment you’ll need in order to get the full benefit of buying ingredients in bulk.
REQUIRED GEAR
All grain purchased in bulk, at least as far as I’m aware, is uncrushed, meaning you’ll probably want to invest in a solid mill. This will be the biggest investment most people make when transitioning to buying in bulk, but it definitely comes with some other benefits, namely determining your own mill gap in order to get more consistent efficiency. I use a Monster Mill MM3 attached to a low speed/high torque drill, it’s amazing, blasting through 10 lbs of grain in less than a minute.
To measure out grains, I use a battery powered baker’s scale with one of the 2 gallon pails I previously mentioned. In over 2 years of use, I’ve yet to have to replace the batteries.
I measure out my hop and mineral amounts using a small blade scale, this is also battery powered.
Besides that, you’ve likely already got anything else you might need– an old measuring cup to scoop your grains, some plastic cups to hold hops and minerals, etc.
BENEFITS OF BUYING IN BULK
Hands down, what I enjoy most about keeping bulk ingredients on hand is the fact I can brew whenever I want— no waiting for the shop to open then showing up and realizing they’re all out of Victory malt or Centennial hops, I can honestly design a recipe right now then go outside and brew it. Saving some coin is nice, as well, and really starts to add up over time. There’s no way I’d be able to brew as often as I do if I didn’t stock bulk ingredients.
WHERE TO SHOP
You might be wondering how to go about getting good deals on bulk ingredients, here’s where I share my sources. First off, if you’re not already harvesting yeast from starters, that should be your first step. Next, you may want to ease into bulk purchasing by starting with hops. I probably purchase 80% of my hops from Hops Direct in 1 lb increments, the smallest amount they sell. If you know other homebrewers, consider purchasing as a group and splitting the hops, it makes shipping less expensive and you get a wider variety. Farmhouse Brewing Supply and Yakima Valley Hops are other vendors I like to buy hops from, particularly because they sell hops in smaller amounts and have a pretty robust selection. For grain, MoreBeer is my go-to source, but only when I’m near an acutal store– 2-row goes for about $38 while continental base malts (like German Pils) run closer to $55 per sack, which is still only about $1 per pound. While I usually wait for sales to pick up speciality malts, I’ll occasionally just add 5-10 lbs to a MoreBeer order or stop by the HBS on my way home from work, it doesn’t amount to much since I use a lot in my brewing.
Ultimately, purchasing ingredients in bulk has saved me more money than any other upgrade since I started homebrewing, allowing me to brew more beer more often. If you have any questions this post failed to answer, please don’t hesitate to ask. Cheers!
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{
"pile_set_name": "OpenWebText2"
}
|
Q:
Summation by parts of $\sum_{k=1} ^n \frac{2k+1}{k(k+1)}$
Let $\{f_k\}$ and $\{g_k\}$ be sequences of real numbers. The formula for summation by parts is given by:
$\sum_{k=m} ^n f_k \Delta g_k=(f_{n+1}g_{n+1}-f_mg_m)-\sum_{k=m} ^n g_{k+1}\Delta f_k$,
where $\Delta f_k=f_{k+1}-f_k$.
Letting $f_k=2k+1$ and $g_k=-\frac{1}{k}$. One then computes $\Delta f_k=2$ and $\Delta g_k=\frac{1}{k(k+1)}$. Therefore, using the partial summation formula, we have
\begin{align*}
\sum_{k=1} ^n f_k \Delta g_k=\sum_{k=1} ^n \frac{2k+1}{k(k+1)}&=-\frac{2n+3}{n+1}+3+\sum_{k=1} ^n \frac{2}{k+1} \\
&=\frac{n}{n+1}+2(H_n-1)\\
&=2H_n-\frac{n+2}{n+1},
\end{align*}
where $H_n$ denotes the $n^{th}$ harmonic number.
I have check my answer multiple times, but I am convinced it is incorrect. Could anyone point out a flaw in my reasoning?
Here is the full solution:
Let $f_k=2k+1$ and $g_k=-\frac{1}{k}$. One then computes $\Delta f_k=2$ and $\Delta g_k=\frac{1}{k(k+1)}$. Therefore,
\begin{align*}
\sum_{k=1} ^n f_k \Delta g_k=\sum_{k=1} ^n \frac{2k+1}{k(k+1)}&=-\frac{2n+3}{n+1}+3+\sum_{k=1} ^n \frac{2}{k+1} \\
&=\frac{n}{n+1}+2(H_{n+1}-1)\\
&=2H_n+\frac{n}{n+1}-2\frac{n}{n+1}\\
&=2H_n-\frac{n}{n+1}.
\end{align*}
A:
It does look to be your final conversion to harmonic numbers is at fault. In particular,
$$\begin{align*}
\sum_{k=1}^n \frac1{k+1}&=\sum_{k-1=1}^n \frac1{k-1+1}\\
&=\sum_{k=2}^{n+1} \frac1{k}\\
&=H_{n+1}-1\\
&=H_n+\frac1{n+1}-1\\
&=H_n-\frac{n}{n+1}
\end{align*}$$
|
{
"pile_set_name": "StackExchange"
}
|
They've enthralled or terrified generations of kids, and now they're giant worldwide blockbusters. So what are the best animated features of all time? Using an obscure system of weights and measures, TIME's Richard Corliss has compiled and annotated the countdown, from No. 25 (Lady and the Tramp) to No. 1 (see for yourself). Are your favorites on the list? Let the great debate commence; we know it'll be animated.
Lady and the Tramp
It’s said that when he first watched a rough cut of his studio’s next feature cartoon, Walt Disney absolutely disapproved of one scene: when the Cocker Spaniel Lady and the roguish mutt Tramp dig into a plate of spaghetti on a romantic night and catch ends of the same strand, their faces coming closer to a kiss as they nibble. This, of course, is the moment — played to the strains of Peggy Lee and Sonny Burke’s Neapolitan ballad “Bella Notte” — that immediately entered the DNA of millions of moviegoers and is still cherished more than a half-century later.
Disney’s 15th animated feature, and its first released in CinemaScope, was one of its more modest productions in a decade when the studio had mixed results with its ambitious adaptations of such famous tales as Alice in Wonderland, Peter Pan and Sleeping Beauty. Returning to the core Disney values of humor and heart, veteran directors Clyde Geronimo, Hamilton Luske and Wilfred Jackson gave Lady and the Tramp the pedigree of a winner that delights every new generation of children.
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{
"pile_set_name": "Pile-CC"
}
|
Q:
Django + PostgreSQL: database representation of JSONField is changing
PostgreSQL 9.4.12
Django 1.10.7
With this minimal class :
from django.contrib.postgres.fields import JSONField
class Foobar(models.Model):
extra_data = JSONField(blank=True, default="")
I run manage.py shell_plus :
In [2]: a=Foobar.objects.create()
In [3]: a.extra_data={}
In [4]: a.save()
In [6]: a.extra_data
Out[6]: {}
In [7]: a.refresh_from_db()
In [8]: a.extra_data
Out[8]: '{}'
In [9]: a.save()
In [10]: a.refresh_from_db()
In [11]: a.extra_data
Out[11]: '"{}"'
What could be the reason the JSONField value is quoted at each database save?
A:
Found it. This is a known incompatibility between django-jsonfield and django.contrib.postgres.fields.JSONField that cannot be used in same project.
cf https://bitbucket.org/schinckel/django-jsonfield/issues/57/cannot-use-in-the-same-project-as-djangos
|
{
"pile_set_name": "StackExchange"
}
|
"We didn't mean to auto-draft,” Justin C. Cliburn said. “But the Internet in Baghdad wasn't the most reliable."
It was August of 2006. Cliburn was a specialist stationed at Camp Liberty in Baghdad, part of a security force (SECFOR) of Oklahoma Army National Guardsmen from the 1st Battalion, 158th Field Artillery regiment. His squad’s role was to escort civilian training contractors to Iraqi police stations, Cliburn serving as a Humvee gunner.
He also served, reluctantly and incongruously, as a first-year fantasy commissioner.
“That season the guy who was supposed to run our league was stationed down in Diwaniyah [at Camp Echo],” Cliburn recalled. “He had next-to-no internet access, so I took over.”
And still the league began with technical difficulties.
“Yeah, internet cut out right before our draft began,” said Kevin Pyle, a founding member of the OklahomIraqis League. “Every team was auto-picked. Not Yahoo’s fault. That was Iraq.”
“I really lucked out, though,” said Cliburn. “Got LaDainian Tomlinson at No. 3.”
View photos Members of the fantasy league take in a tour at AT&T Stadium. More
Despite an inauspicious beginning, the league has held together through battle, tragedy and distance. The bond shared by the group led to the push for a 10-year reunion for the SECFOR mission, spearheaded by a fantasy league and its commissioner. The event took place over Labor Day weekend, culminating with a draft party at Cowboys Stadium.
“We kinda had a wake-up call, a year and a half, two years ago,” Pyle said. “One of our brothers who was over there with us took his own life. About half of us made it to the services and we all mentioned that we have to get together at times other than this. That's part of why we thought it would be so great to get all of us together – not just the league, the full 152 of us that were over there in 2006.”
[For more info on post-traumatic stress disorder, visit the National Center for PTSD]
While not all 152 soldiers made it to the reunion, eight of 10 original members of the league are still involved. The league has also grown substantially, with three conferences this season, each with 14 owners.
Of course, Cliburn’s league wasn’t the only group of active fantasy players in Iraq back in ’06 – nor, in all likelihood, was it the most hardcore. But very few commissioners have ever documented the lifetime of a league as thoroughly and faithfully as Cliburn. In so doing, he’s strengthened the connections between those who served together in the 158.
“I'm just gonna go out there and say it,” said Pyle. “I think Justin is one of the greatest commissioners ever. He connects us in-season, out-of-season. We're always communicating with each other. Justin was having to play peacekeeper in the league those first three or four years — I was dealing with issues that I didn't realize at the time, and wasn’t alone.
View photos Several original league members, including Cliburn (front row, second from the right. Okiraqi.org) More
Story continues
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{
"pile_set_name": "OpenWebText2"
}
|
Conversations about binge drinking among vocational community college students: the relation with drinking attitudes and intentions and the moderating role of conversation partner popularity.
Objective: The association between conversational valence (i.e. how positive/negative people perceive their conversations to be) and binge-drinking attitudes and intentions has been well established. However, too few studies have recognised a potential reciprocal association as well as the potential role of the conversation partner. In order to address these gaps, this study explored whether conversational valence and binge-drinking attitudes and intentions were reciprocally associated and whether this association was moderated by conversation partner popularity. Design: Vocational community college students (N = 112, Mage = 18.09) participated in a two-wave study (one month between the waves). Methods. Binge-drinking attitudes and intentions, and popularity were measured at baseline. At the second wave, conversational valence, and binge-drinking attitudes and intentions were assessed. Results: In revealing that only conversational valence was indicative of binge-drinking attitudes and intentions, it was shown that conversational valence and binge-drinking attitudes and intentions were not reciprocally associated. Furthermore, it was shown that conversation-partner popularity moderated the association between conversational valence and binge-drinking attitudes. Conclusion: Conversational valence was shown to be indicative of binge-drinking attitudes and intentions, and not vice versa. Furthermore, after talking to a popular conversation partner, adolescents' attitudes towards binge drinking became more positive.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
Last week, octogenarian Margaret Priebe became something of a viral sensation when the St. Petersburg Times ran a piece on the 85-year-old, who claims she's one of Metallica's oldest fans. Over the weekend, Priebe got to meet the members of her favorite band after getting a special backstage invite from the thrash legends.
Priebe was welcomed backstage for a meet-and-greet prior to the band's Oct. 3 set, and each member of Metallica spent time with Priebe as she told stories about her favorite Metallica LP, 1999's 'S&M.' When meeting Kirk Hammett, the guitarist joked that Priebe is finally giving his mother some competition for title of the band's oldest fan, while drummer Lars Ulrich yelled out, "The number one Metallica fan" when he met Priebe.
According to reports, frontman James Hetfield dedicated the band's song 'Nothing Else Matters' to Priebe before a sell-out crowd of more than 18,000 people. Before that, though, when Hetfield met with Priebe backstage, he leaned down and asked, "Mind if I hug you?" Priebe didn't mind, and Hammett told her to "Keep it metal!" Priebe was all smiles as she got the entire band to autograph her copy of 'Death Magnetic.'Following the meet-and-greet with Metallica, Priebe told reporters the band members "were just like what I'd thought they'd be -- very nice." She was led through the arena to her seat, and fans burst into applause at the sight of her. Fans asked to take pictures with her, while she defiantly waved the devil horns.
Priebe's love for Metallica started years ago, when she heard a song from 'S&M' on the radio. According to reports, she had never heard such a racket before but loved every minute of it. Last year, she battled cancer with help from her MP3 player, which is loaded with tracks from Metallica, Judas Priest and Ozzy Osbourne. Priebe is now cancer-free, but hasn't given up on her love of metal.
"I like Metallica ... there's nothing wrong with them," Priebe says. "People think I'm weird. But I'm sorry, I like it loud. Lars is cute, but I like 'em all."
|
{
"pile_set_name": "OpenWebText2"
}
|
An electric cutter for all surgical prostheses.
A new electric cutter for surgical prostheses has been developed and was compared with surgical scissors for efficacy. This comparison of the two methods was done by cutting the edges of nine popular prostheses. It was concluded from gross and microscopical results after pulling both edges of the grafts cut by the two methods that the electric cutter is much more effective for surgical prostheses.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
Q:
Stack Overflow doesn't display correctly when using Tor Browser
I use Tor browser for nearly all of my internet browsing, including Stack Overflow. This wasn't a problem for me until about a week or two ago, when Stack Overflow produced two different errors when using Tor Browser.
One, it would sometimes display without using any styles. The pages displayed in a linear fashion, and there were no fonts other than Times New Roman, no pictures, and no color, just like in this question.
The second problem happens 100% of the time when problem one happens, and sometimes it happens on its own. When I try to log into Stack Overflow, I enter my Stack Exchange account information, hit enter or click login, and nothing happens.
These problems do not happen all of the time, but as I said, when problem one happens, problem two always follows it. I have tried accessing this from multiple machines, using multiple script settings, and the same problem happens. I am also a member of the Tor Stack Exchange, and sometimes, when I am logged into one Stack Exchange, and click over to the other in Tor Browser, the one will display with errors and the other will work perfectly.
I believe this is a bug, but if anyone knows a solution on my end, please tell me. (And please don't just tell me to stop using Tor.)
A:
There are two problems here:
Tor Browser is not officially supported; any breakage in styling and functionality is at your own risk.
There has been a history of abusive users using Tor to bypass restrictions placed on their accounts. As a result of recent extreme misbehaviour, many Tor exit nodes have been IP blocked. If you cannot connect at all, your request most probably came through such an exit node.
It is unlikely that the Stack Exchange team is going to ease up on these two restrictions.
|
{
"pile_set_name": "StackExchange"
}
|
The young JRR Tolkien’s dark retelling of a Finnish epic poem, which features a young man sold into slavery who unknowingly seduces his sister before killing himself, is to be published later this month for the first time.
The Story of Kullervo was written in 1915, while Tolkien was studying at Oxford. Thought to be his first work of prose fantasy, it sees the young writer who would go on to pen The Lord of the Rings retell part of the 19th-century Finnish poem the Kalevala. The author himself described it as “the germ of my attempt to write legends of my own”. The unfinished manuscript, which lies in the Bodleian Library in Oxford, has previously only appeared in an academic paper by the US Tolkien scholar Verlyn Flieger, with its release on 27 August by HarperCollins its first mainstream publication.
The work tells the story of the son of Kalervo, “Kullervo the hapless”, as Tolkien calls him. An orphan with supernatural powers, Kullervo is brought up in the home of a dark magician, Untamo, who killed his father, kidnapped his mother and tries to kill the boy three times. When Kullervo is sold into slavery, he swears revenge, but unknowingly commits incest with his twin sister – who kills herself when she discovers what they have done.
“And before he could leap up and grasp her she sped across the glade (for they abode in a wild dwelling …) like a shivering ray in the dawn light scarce seeming to touch the green dewy grass till she came to the triple fall and cast her over it down its silver column to the ugly depths,” writes Tolkien. “And her last wail he heard and stood heavy bent on the brink as a lump of rock till the sun rose and thereat the grass grew green and the birds sang and the flowers opened and midday passed and all things seemed happy: and Kullervo cursed them, for he loved her.”
Tolkien’s narrative breaks off shortly after this point, with the rest of the story, in which Kullervo then kills himself, told by the author in outline. In Stuart D Lee’s A Companion to JRR Tolkien, he compares the “straightforward prose” of Tolkien’s version of the tragic end of Kullervo with the “much more dramatic” end of Túrin in The Silmarillion. In Kullervo, Tolkien writes of the suicide of the young man: “The sword says if it had joy in the death of Untamo how much in death of even wickeder Kullervoinen. And it had slaid many an innocent person, even his mother, so it would not boggle over Kullervo. He kills himself and finds the death he sought for.”
In The Silmarillion, by contrast, Tolkien writes: “And from the blade rang a cold voice in answer: ‘Yea, I will drink thy blood gladly, that so I may forget the blood of Beleg my master, and the blood of Brandir slain unjustly. I will slay thee swiftly.’ Then Túrin set the hilts upon the ground, and cast himself upon the point of Guthrang, and the black blade took his life.”
HarperCollins called Kullervo “perhaps the darkest and most tragic of all JRR Tolkien’s characters”, adding that he was “the clear ancestor of Túrin Turambar, tragic incestuous hero of The Silmarillion”.
“In addition to it being a powerful story in its own right, The Story of Kullervo – published here for the first time with the author’s drafts, notes and lecture-essays on its source-work, The Kalevala – is a foundation stone in the structure of Tolkien’s invented world,” said the publisher.
“I was immensely attracted by something in the air of the Kalevala,” Tolkien wrote in 1955 to WH Auden. “I never learned Finnish well enough to do more than plod through a bit of the original, like a schoolboy with Ovid … But the beginning of the legendarium … was in an attempt to reorganise some of the Kalevala, especially the tale of Kullervo the hapless, into a form of my own.”
In 1914, he wrote of how he was “trying to turn one of the stories – which is really a great story and most tragic – into a short story … with chunks of poetry in between”.
John Garth, in his Tolkien and the Great War, calls the tale “a strange story to have captured the imagination of a fervent Roman Catholic: Kullervo unwittingly seduces his sister, who kills herself, and then he too commits suicide”.
But Garth suggests that “the appeal perhaps lay partly in the brew of maverick heroism, young romance, and despair”.
“The deaths of Kullervo’s parents may have struck a chord, too,” adds Garth, alluding to the deaths of both of Tolkien’s parents by the time he was 12. “An overriding attraction, though, was the sounds of the Finnish names, the remote primitivism, and the Northern air.”
The Story of Kullervo is the latest in a handful of previously unpublished works from Tolkien that have been released in recent years, including his translation of Beowulf, his poem The Fall of Arthur, and the unfinished Middle-earth story The Children of Húrin.
|
{
"pile_set_name": "OpenWebText2"
}
|
/*
* Licensed to the Apache Software Foundation (ASF) under one
* or more contributor license agreements. See the NOTICE file
* distributed with this work for additional information
* regarding copyright ownership. The ASF licenses this file
* to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing,
* software distributed under the License is distributed on an
* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied. See the License for the
* specific language governing permissions and limitations
* under the License.
*/
package org.apache.datasketches.quantiles;
import static org.apache.datasketches.quantiles.PreambleUtil.COMPACT_FLAG_MASK;
import static org.apache.datasketches.quantiles.PreambleUtil.EMPTY_FLAG_MASK;
import static org.apache.datasketches.quantiles.PreambleUtil.ORDERED_FLAG_MASK;
import static org.apache.datasketches.quantiles.PreambleUtil.READ_ONLY_FLAG_MASK;
import static org.apache.datasketches.quantiles.PreambleUtil.insertFamilyID;
import static org.apache.datasketches.quantiles.PreambleUtil.insertFlags;
import static org.apache.datasketches.quantiles.PreambleUtil.insertK;
import static org.apache.datasketches.quantiles.PreambleUtil.insertMaxDouble;
import static org.apache.datasketches.quantiles.PreambleUtil.insertMinDouble;
import static org.apache.datasketches.quantiles.PreambleUtil.insertN;
import static org.apache.datasketches.quantiles.PreambleUtil.insertPreLongs;
import static org.apache.datasketches.quantiles.PreambleUtil.insertSerVer;
import java.util.Arrays;
import org.apache.datasketches.Family;
import org.apache.datasketches.memory.WritableMemory;
/**
* The doubles to byte array algorithms.
*
* @author Lee Rhodes
* @author Jon Malkin
*/
final class DoublesByteArrayImpl {
private DoublesByteArrayImpl() {}
static byte[] toByteArray(final DoublesSketch sketch, final boolean ordered,
final boolean compact) {
final boolean empty = sketch.isEmpty();
//create the flags byte
final int flags = (empty ? EMPTY_FLAG_MASK : 0)
| (ordered ? ORDERED_FLAG_MASK : 0)
| (compact ? (COMPACT_FLAG_MASK | READ_ONLY_FLAG_MASK) : 0);
if (empty && !sketch.isDirect()) { //empty & on-heap
final byte[] outByteArr = new byte[Long.BYTES];
final WritableMemory memOut = WritableMemory.wrap(outByteArr);
final int preLongs = 1;
insertPre0(memOut, preLongs, flags, sketch.getK());
return outByteArr;
}
//not empty || direct; flags passed for convenience
return convertToByteArray(sketch, flags, ordered, compact);
}
/**
* Returns a byte array, including preamble, min, max and data extracted from the sketch.
* @param sketch the given DoublesSketch
* @param flags the Flags field
* @param ordered true if the desired form of the resulting array has the base buffer sorted.
* @param compact true if the desired form of the resulting array is in compact form.
* @return a byte array, including preamble, min, max and data extracted from the Combined Buffer.
*/
private static byte[] convertToByteArray(final DoublesSketch sketch, final int flags,
final boolean ordered, final boolean compact) {
final int preLongs = 2;
final int extra = 2; // extra space for min and max values
final int prePlusExtraBytes = (preLongs + extra) << 3;
final int k = sketch.getK();
final long n = sketch.getN();
// If not-compact, have accessor always report full levels. Then use level size to determine
// whether to copy data out.
final DoublesSketchAccessor dsa = DoublesSketchAccessor.wrap(sketch, !compact);
final int outBytes = (compact ? sketch.getCompactStorageBytes() : sketch.getUpdatableStorageBytes());
final byte[] outByteArr = new byte[outBytes];
final WritableMemory memOut = WritableMemory.wrap(outByteArr);
//insert preamble-0, N, min, max
insertPre0(memOut, preLongs, flags, k);
if (sketch.isEmpty()) { return outByteArr; }
insertN(memOut, n);
insertMinDouble(memOut, sketch.getMinValue());
insertMaxDouble(memOut, sketch.getMaxValue());
long memOffsetBytes = prePlusExtraBytes;
// might need to sort base buffer but don't want to change input sketch
final int bbCnt = Util.computeBaseBufferItems(k, n);
if (bbCnt > 0) { //Base buffer items only
final double[] bbItemsArr = dsa.getArray(0, bbCnt);
if (ordered) { Arrays.sort(bbItemsArr); }
memOut.putDoubleArray(memOffsetBytes, bbItemsArr, 0, bbCnt);
}
// If n < 2k, totalLevels == 0 so ok to overshoot the offset update
memOffsetBytes += (compact ? bbCnt : 2 * k) << 3;
// If serializing from a compact sketch to a non-compact form, we may end up copying data for a
// higher level one or more times into an unused level. A bit wasteful, but not incorrect.
final int totalLevels = Util.computeTotalLevels(sketch.getBitPattern());
for (int lvl = 0; lvl < totalLevels; ++lvl) {
dsa.setLevel(lvl);
if (dsa.numItems() > 0) {
assert dsa.numItems() == k;
memOut.putDoubleArray(memOffsetBytes, dsa.getArray(0, k), 0, k);
memOffsetBytes += (k << 3);
}
}
return outByteArr;
}
private static void insertPre0(final WritableMemory wmem,
final int preLongs, final int flags, final int k) {
insertPreLongs(wmem, preLongs);
insertSerVer(wmem, DoublesSketch.DOUBLES_SER_VER);
insertFamilyID(wmem, Family.QUANTILES.getID());
insertFlags(wmem, flags);
insertK(wmem, k);
}
}
|
{
"pile_set_name": "Github"
}
|
Domination 1914 - Meat Grinder
Hey so I’m working on modifying Domination 1914 No Man’s Land to make it better match my vision of WW1 and balance some gameplay issues the former has. I’ll be happy for suggestions, tips and when the time comes beta testers.
Here are just a few things I am looking to tweak
1 Slow US entry into the war - I plan to do this by making the US unable to build anything until they’ve researched a couple “Declare War” category techs
2 While we are on the US, the current map makes attacking Mexico too desirable. By militarizing the Mexican border I hope to make this a less desirable option.
3 Make naval warfare more important. The current game quickly has the centrals give up at sea. I want to strengthen the German U Boat - particularly giving them a tech they can accomplish that gives them a free u boat every turn. Also I want to add blockade as a power that warships have making water ways more important.
4 Give the defense the advantage they had in the real war. I have a few new defensive units in mind - Machine guns and a barbed wire suicide defense unit for starters - that’ll make taking a defensive position a strong position. Particularly on the narrow western front.
5 Add a ranged attack for artillery. This will take the form of rockets with a range of 1 that target defensive structures. I’d love to allow for it to target units as well but only if casualties are randomized (I don’t know how to do this). This will counterbalance the defense’s advantage and prevent just massive stack building.
6 Significantly increase the importance of technology. I want to make tanks a game changing tech for example but also I want the game to be as much a tech race as anything else as in the real war, technological advancements created the only real opportunities on the western front. That means making tanks and late fighters stronger and increasing the effect of every other tech.
7 Revamp communism. I want it to start slowly and pick up steam from two things - 1 it can get a Lenin tech that’ll radically reduce unit costs thus ushering in the revolution. Further Russia will have booby trap Communism techs that if these are researched weaken the country significantly. Example - Land Communism raises cost of infantry, cavalry and conscripts by a PU each. Industrial communism makes poison gas and heavy artillery and light artillery all impossible or much more expensive.
8 Booby trap techs for France and Germany. These I’ll call Pacifism or Strike techs and there will be onebper category. These will weaken the nation but not as much as communism does Russia. Strike Land May raise the cost of infantry half by 0.5 PU’s
9 Nation specific adjustments. British soldiers cost more until they research a special British tech - conscription. Germany gets a submarine advantage. France’s propaganda tech replaced with Paris reserves gives 5 infantry instead of 3 (WW1 fans will see where these come from)
And yeah that basically goes over the major themes I’m hoping for. I’ll be very happy if I can create a meat grinder on the western front, a more influential tech development, more focus on naval war, and a more historical and dynamic US and Communist involvement in the war.
Stretch goals - after I create a balanced version of the above that meets my goals I’d like to create an expanded game where Japan China and Mexico are added in (Japan as cobliegerent with the allies against Germany and at war with China who is cobelligerent to Germany against Japan. Mexico would be neutral until some trigger is figured out that would have them enter the war on the side of the Centrals (at some cost to Germany)
So yeah I have a lot on my mind. I’m not looking to create something as involved as Total World War but I am hoping to create a unique and uniquely WW1 experience.
@scallen1 I think Russian communism is often got wrong. The political flip was, wargame wise, bloodless, so I don't this needs to be represented or you need to have "Communists" as a player. Just would be the normal Russians player that, at some point, becomes communist (and it can still be called just Russians) and, gameplay wise, it should just, at that point, become unable to attack the Alliance (meaning the Central Powers) anymore, and have a bunch of white rebels spawning. Basically flipping the game behaviour from now, in that the other Russia would be the whites, not the reds.
A similar matter is with the Austro really. They were far more powerful than Italy (you can see that in whatever statistics comparing Italy with the Austro-Hungarian Empire) when they got beated up with ease, since they basically crumbled internally and morally (pretty much what happened to Italy in WW2, instead).
@scallen1 Sounds cool. I would definitely try to get input from some of the NML veterans. If you have questions about how to make some of these changes just post here on the forums and folks should be able to help ya out. Good luck!
@cernel yeah how to handle internal pressure is something I want to really figure out.
A trigger that the Centrals could accomplish that turns Russia Neutral is a possibility.
My ideal may be this.
1 - actions taken by Russia and/or the the centrals spark revolution.
2 - the revolution immediately weakens Russia
3 - Russian player can declare neutrality (ceding to the revolution) or try to put it down. In a game where the centrals can win, alternate history paths are as important as historicity
Creating a similar system in Germany France Austria, Turkey, and Italy (with them being less vulnerable than Russa) is also desirable. I want a system where political instability can weaken a country’s ability to wage offensive war at least.
But I’m gonna start in the direction I layer out. This can be an iterative process.
First step for me is the easy stuff - make Mexico and Switzerland much harder to invade.
Second step is to create a good meat grinder western front with artillery barrages and defense having a huge advantage.
That second step will be the hardest and I’ll approach my other goals once this has been accomplished.
One possible way to create an artillery garage is actually to do away with the artillery unit and only have artillery shell units. Alternatively, artillery could be a unit with no attack but that can build artillery shells which are suicide units that attack.
Positives of this strategy
Makes the cost of artillery primarily be it’s shells. This matches reality.
Creates the ability to launch attacks the way I want.
Downside - it will require one annoying thing - a barrage token. I can make it so artillery create these automatically and for free every turn. The barrage token would then enter battle as a normal unit with 0 attack 0 defense and 1 HP to make the engine handle the suicide attack if the shells appropriately.
Second downside - still not random casualties. I really really want randomized casualties.
@scallen1 So the best approach for artillery bombardment is have some artillery unit that generates say an artillery shell each round that then can move 1 territory (if not used then triggers remove them unless you want to stockpile). You could then have it have be a suicide unit with an AA attack against only certain units and if you put on random AA casualties then you'll get random instead of selected casualties. @Hepps is planning to do something like this for GD so I'll leave it to him to see if he already has some example XML laying around. Otherwise I can provide an example.
For random casualties, you need to use an AA type attack and set this property:
I had been searching through the forum and had decided on something similar to this but hadn't yet gotten the random casualties element. The AA attribute with specified units actually makes it better. Because as I got down to planning out shell types I wanted to have 3 types reminiscent of reality (shrapnel, gas and explosive). I had some good ideas but making it so they each can only affect certain types of units and hit those randomly will make me so happy.
Just so anyone interested (and the idea I had might make this interesting to people trying to do something similar in the future)
Artillery are essentially factories with production 1 and can only produce shells. I plan to allow stockpiling but shells cost money. Shells can move 1 but to prevent them from being able to be fired from a place without artillery I am adding another unit. This unit is a Bombardment token. Its free, max one per territory, automatically generates at the end of any turn an artillery is in a region without a bombardment token. It supports 999 or whatever shells and gives them their dice. It will have movement 1 but die at the end of every turn so it can never be used except when attacking from the territory it was born in (with artillery) The only gap in this is that artillery can move out of a territory but the shells and bombardment token will be able to attack from the original territory. I'm ok with this. It can be a player enforced rule but its so non critical to the game that I'm ok with it being player enforced.
So yeah plan is to make shrapnel shells that affect only infantry like units (including cavalry and machine guns) and also barbed wire (gonna double check my WW1 knowledge that they actually did cut barbed wire) They will have a low attack value but get two dice from bombardment tokens
Explosive shells affect everything making them more capable of hitting much more valuable targets than shrapnel. I think they'll be higher attack but only one die.
Gas shells affect the same units as shrapnel save they don't affect barbed wire (barbed wire is cheap and weak so an improvement). Gas shells roll 2 die at a high attack but will be expensive. such that they're less efficient than shrapnel but if you have the PU's to put into them they pack a big punch.
Artillery support for infantry is taken away. I'm gonna replace it with air support (which the game already has) and tank support after you research both armour (unlocking tanks) and combined arms (unlocking tank support)
Thats teh plan right now. I'm gonna use your AA plan but unless on playtesting stockpiling becomes a problem, I will allow it.
@scallen1 Not sure you need another unit to achieve this. I think you could have the artillery provide say +1 movement (like naval/air bases do in Global 40) to shells so that only if the artillery starts in the same territory as the shells can they be moved. You could also make it so artillery only move during non-combat move so that they essentially must start with the shells in the same territory, fire them to attack during combat move, and then could move to another territory to prepare shells for next turn.
@redrum Thats a good idea however - assuming I go with allowing stockpiling I would like to be able to build shells in factories.
However there is a problem I foresee in your plan. Gas in standard Domination NML if sent into battle without any units just suicides without even rolling. To do a gas attack you need to send at least one unit. So the bombardment token serves the purpose of being that one unit. I want you to be able to throw shells without thowing any real units into the fight.
@cernel So I've come to a decision that I plan to stick with through playtesting
Continental powers (everyone but the UK and US) are subject to techs that are slight booby traps (the worst raises the price of infantry to 3.5 PUs)
Russia has a special tech in its own category so it can be intentionally chosen wherein they declare neutrality. This I imagine a player would use if the Eastern front is broken through and they'd rather deny the Centrals the opportunity to take their land and PUs.
I'll note - any balanced game is gonna have the centrals more powerful than they historically were. So I'm not gonna weaken Austria Hungary in any way other than making the same booby trap of discontent available to them as to Germany and France and Italy and Russia and the Ottomans
Also if you haven't read below I've gotten great advice on how to make an effective ranged artillery system.
@scallen1 I think the Russian defection was a bonus to the Alliance (CP), so I don't think it can be well represented as an option for the Entente player. The Alliance cheaply got a whole lot of territory out of the Russian capitulation, even tho that didn't benefit them as much as it would be represented in the game, and still had to significantly expend to secure those gains.
Also, I want to point out there are two main stages.
The first stage is when Russians nevermore make any offensive and become military weaker, but are still at war with the Alliance (and were indeed invaded by the Germans). Here the Alliance should have the option to turn Russians neutral, leaving Russians all the territories they currently own (option not taken historically, because the Germans wanted more than that, and it can be argued they were greedy, and should have taken it, instead). On the other hand, since the Russians cannot attack anymore, that option is not really needed, as the Alliance player can just ignore them from now on, with no fear of being invaded.
The second stage is when the Russians formally capitulate, go neutral, and give a lot of territories to the Germans, except that almost all those territories were already mostly out of Russians control, having been taken over by the White (anti-communist) rebels. Here it would make sense for the Alliance to still have the option to not make peace, thus going into total war with Russians, but the Alliance player should virtually never have a convenience to go that way.
Hey so I’m working on modifying Domination 1914 No Man’s Land to make it better match my vision of WW1 and balance some gameplay issues the former has. I’ll be happy for suggestions, tips and when the time comes beta testers.
Here are just a few things I am looking to tweak
1 Slow US entry into the war - I plan to do this by making the US unable to build anything until they’ve researched a couple “Declare War” category techs
While I agree with your goal... I think you'd be better served by making the USA have substantial negative income modifiers while they are at peace rather than zero production capability. The result would be an ever increasing reserve of PU for the first X number of turns. Resulting in the US literally dropping 10 BB the moment they enter the war. This would seriously diminish your goal to make the battle for the Atlantic a more lengthy affair and more dynamic experience.
2 While we are on the US, the current map makes attacking Mexico too desirable. By militarizing the Mexican border I hope to make this a less desirable option.
The suggestion previously given to make Mexico a Neutral nation would be a much cleaner approach and offer you many more game-play options later in a game.
A couple ideas for ya to achieve some of your goals. They might have been touched on by others but here are my thoughts.
Start USA neutral and give USA a peacetime economy and production until they officially enter the war on the allied side. Perhaps 25% of normal income and only basic production ability. And no tech research. Maybe movement restrictions close to the war as well. Basically make USA very limited and force them to think hard about their moves and purchases during this period.
Create some conditions to allow USA to enter the war. Ideally they should be based on Centrals conquests and or a combination of Entente position. You can even create a scenario where USA sea vessels can be accidently sunk by the Centrals. This would require some creative new units owned by Entente but (just a technicality, so they can actually be sunk before USA is at war). Maybe a non combat sea transport that can be randomly killed if the sea zone containing it is attacked by Centrals. If this vessel is sunk USA automatically enters the war. Design it so Centrals may have to avoid the attack into a so called shipping lane to prevent such a thing from happening. But must not provide Entente a exploitation at same time.
Mexico should simply enter war on Centrals side if USA attacks them. Or can go further by creating some prerequisite condition as well that can allow Centrals to pull them into the war on their side.
Russia was manipulated by Germany historically. A master move by them. Lenin was exiled by Russia for stirring up discontent and a revolutionary sentiment. The Kaiser bankrolled Lenin and sent him back to Russia to continue his plans. This succeeded beyond Germany's wildest dreams. Try to replicate this scenario somewhat. Allow communists to form in Russia and allow Centrals to supply them with additional funds in form of user actions. Possibly allow them to share tech and give units if territories are bordering Germany and Communist.
@rogercooper Personal preference. I've always just disliked the politics ui in tripleA. And I like how theres a randomness aspect to tech. I'm using multiple techs to get US into the war and a couple bad rolls could delay their entrance. This doesn't seem popular here but I like randomness in these games - particularly on large maps where one random event doesn't change the entire game just one aspect of the war.
Also if you've played 1914 No Man's land you'll notice that Mexico is an intentionally tempting target for the US. I want to make it something the US would have to send a real army to attack. (a stretch goal for this project is to make Mexico an inactive team that becomes active if Germany does several things to get them into the war)
@cernel Taking away russia's ability to attack might be a better option than declaring neutrality because it leaves an option to Germany and Austria Hungary. This would then have to be made something acheived by Germany. Which makes sense. Also - instead of totally taking away their ability to attack I could just make offensive units (basically in my version of the game this meas artillery and artillery ammunition) either unpurchasable or very expensive. This would then allow russia to continue to focus on defending itself but as I am designing the game Germany could withdraw the vast majority of their army from the Eastern front if this occurs and just build up trenches and barbed wire with some machine guns and infantry to man it.
However in game, Russia declaring Neutrality could help the Entente because you'd do it only when the line was completely broken and Germany is about to take your capital.
The political aspects of this game and balancing are very up in the air. The critical thing to me is the Artillery barrage, defensive advantage aspect of the game and that that defensive aspect can be mitigated by tech.
@hepps The Mexico neutral nation idea is a goal. But I'm prioritizing the combat changes first. So militarizing the border is a band-aid.
If I go all the way to putting all my stretch ideas into a game, it'll be a second game because it'll involve a lot more alternative history possibilities than the game I'm making first which has historicity as a major goal.
Start USA neutral and give USA a peacetime economy and production until they officially enter the war on the allied side. Perhaps 25% of normal income and only basic production ability. And no tech research. Maybe movement restrictions close to the war as well. Basically make USA very limited and force them to think hard about their moves and purchases during this period.
I like the version of US entry I'm building. I think of spending on tech tokens as the US leadership trying to encourage the US population to support war. The US will be encouraged to be spending all of its income on getting itself into the war though depending on which "Enter the war" tech they unlock first, they might want to start producing units before they've gotten everything set up for war.
Create some conditions to allow USA to enter the war. Ideally they should be based on Centrals conquests and or a combination of Entente position. You can even create a scenario where USA sea vessels can be accidently sunk by the Centrals. This would require some creative new units owned by Entente but (just a technicality, so they can actually be sunk before USA is at war). Maybe a non combat sea transport that can be randomly killed if the sea zone containing it is attacked by Centrals. If this vessel is sunk USA automatically enters the war. Design it so Centrals may have to avoid the attack into a so called shipping lane to prevent such a thing from happening. But must not provide Entente a exploitation at same time.
It would be nice to give Germany the option of avoiding Unrestricted Submarine Warfare and thus keep the US out of the war but nah I'm not about that. I'd have to make USW something so desirable that the German player would choose it despite its consequences. As for German conquests bringing the US into the war, for balance I would have to make this highly probable that the German player would achieve these conquests - which I would considerable undesirable - and it really doesn't bare any historicity. So no, us inevitable entrance but slow entrance is the way I'm going.
Mexico should simply enter war on Centrals side if USA attacks them. Or can go further by creating some prerequisite condition as well that can allow Centrals to pull them into the war on their side.
This is a stretch goal. After I accomplish making my new artillery system and make my Meat Grinder high historicity game I want to expand on it with one with solid alternate history options. This will include making Japan, Mexico, and China potential full combatants in the war. (I have ideas written out called "late politics" and some early WW2 techs that would be unlockable late in the game)
Russia was manipulated by Germany historically. A master move by them. Lenin was exiled by Russia for stirring up discontent and a revolutionary sentiment. The Kaiser bankrolled Lenin and sent him back to Russia to continue his plans. This succeeded beyond Germany's wildest dreams. Try to replicate this scenario somewhat. Allow communists to form in Russia and allow Centrals to supply them with additional funds in form of user actions. Possibly allow them to share tech and give units if territories are bordering Germany and Communist.
A German political tech they can attempt is called Lenin in my game and it significantly weakens Russia's ability to wage offensive war (it doesn't noticably change their defensive abilities)
To all - anyone know of a way to have a tech add a territory to your country.
Example I want - Serbia I'm going to give free tech tokens to but all they can use them on is bringing Greece and Romania into the war (on their side). So every turn Serbia rolls their tech tokens and if they get a hit (will be designed so they should quickly hit both) Greek territory and units will go from Neutral to being Serb or Romanian territory and units will do the same.
I'll probably figure this out but if anyone already has an XML example of how to attach a territory and its units mid game to a new owner that'd be great
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Q:
White screen of death after server move
I am moving my expression engine site and database to a new server. Everything seems to be directed correctly but when I access admin.php I get a blank page. Any thoughts?
A:
If you are seeing a white screen there's an error happening and you need to display that error to be able to know how to proceed. (See the EE user guide about Blank Pages.)
To show that error, edit your folder's index.php file and replace $debug = 0 with $debug = 1. Revisit your site and you should see the error.
If you see something like this:
A Database Error Occurred
Unable to connect to your database server using the provided settings.
Then follow this answer on another question.
If that doesn't help, try the solutions offered in this answer.
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It's all about location! This beautiful cabin is located 6 miles west of Sturgis and 6 miles from Deadwood, in the middle of Boulder Canyon, across from the Boulder Canyon Golf Course!
This spacious, newer home has a large, fully equipped kitchen with large center island and dining area - seats 10. Open to the …
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Copper Claim Lodge is located in Boulder Canyon, just 5 miles from historic Deadwood and 7 miles from Sturgis. Sleeps up to 13 with 4 bedrooms (1 King master suite, 2 Queens, Single over Full Bunks and futon) and 3 bathrooms. A pull-out sofa in the family room and a quality air-bed is available for extra sleeping …
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Great location, easy access to Interstate or Main St. Set up in the front yard and enjoy watching the bikes roll by. 3 bedrooms, 2 baths. Easily sleeps 6 +, and can be set up for more. Very large yard for friends to pitch a tent, or hook up an RV. Single attached garage to keep your bikes safe when you aren't out …
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This 4 bedroom home has all new queen beds. It is nestled in the pine trees of the foothills with easy access to I-90. Located only 8 miles from sturgis, it is a magnificent place to stay for the motorcycle rally. This vacation home is also only 40 minutes from Historic Deadwood, Lead, and the scenic Spearfish Canyon…
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An American is 12 times more likely to be murdered by a firearm than an Indian, according to an IndiaSpend analysis of data.
An American is 12 times more likely to be murdered by a firearm than an Indian, according to an IndiaSpend analysis of data collated by GunPolicy, a database managed by the University of Sydney and funded by the United Nations.
The US experienced its worst-ever mass shooting at a gay night club in Orlando, Florida, leading to 49 deaths, renewing a debate on easy gun ownership in the USA.
India has a firearm homicide rate of 0.3 (per 100,000 population) against the US’ 3.4. A firearm is used in no more than 10% of homicides in India, against 60% in the US.
India’s homicide rate is comparable to countries that are far richer, such as Finland, France and Netherlands. The bulk of gun homicides–6.7 of 10 cases–are reported from India’s two most populous states, Uttar Pradesh and Bihar, which are together home to nearly 400 million people. It also appears clear that India’s strict gun-ownership laws help: more than eight of 10 Indian gun homicides are from unlicensed arms.
The world’s highest gun-homicide rate of 66.6–222 times as high as India’s–is claimed by the South American country of Honduras, which has half the population of Delhi and is as large as Telangana.
Japan, South Korea, Luxembourg and Hong Kong reported almost zero rates of gun homicide.
The data further reveal that six of the top 10 countries reporting the highest firearm-driven homicide rates are in the Americas–North as well as South.
Brazil topped the list (95%) in terms of proportion of homicides committed with a firearm, followed by Venezuela (90%) and Honduras (83%).
Of the world’s 50 most violent cities, 41 are in Latin America, including 21 in Brazil, according to this 2015 report by Mexico Citizens Council for Public Security, an NGO. Venezuela’s capital Caracas had the highest murder rate in the world last year and was ranked as the most violent city.
Source: GunPolicy, National Crime Records Bureau
85% of firearm homicides in India are from unlicensed arms
As many as 3,655 people were murdered with guns in India in 2014, of which 3,115 (85%) were killed by unlicensed arms, according to the National Crime Records Bureau (NCRB).
Obtaining a gun licence is far more difficult in India than in the United States, but illegal smuggling of guns is rampant in India, especially in states sharing borders with other countries, such as Bihar, as this April 2015 report in Firstpost detailed.
“You don’t have to buy with a licence because guns are so easily available from illegal sources,” Binalakshmi Nepram, secretary general of the Control Arms Foundation of India, told The Hindustan Times. “We feel saddened about what happened in America, but we are also aware that a similar situation can happen in India.”
National Crime Records Bureau
UP, Bihar account for 67% of all firearm-related murders in India
As many as 2,443 people were killed by firearms in Uttar Pradesh and Bihar: 1,510 and 933, respectively, accounting for 67% of total killings (3,655) by arms.
UP is India’s hub for illegal arms, and 24,583 firearms were confiscated in UP in 2014, accounting for 44% of all arms so taken into police custody in India; 62% of these were unlicensed, improvised and crude country-made fire arms, IndiaSpend reported in October 2015.
National Crime Records Bureau
Notes:
The data on country-wise homicide rates have been collated by GunPolicy; data from different years are included.
We have taken the most recent data for each country (but not older than 2008) and omitted some countries, which would have been in the top 10 except that their data were more than 10 years old.
Data on homicide rates may vary depending upon the year, but the trends largely remain the same.
The data include only murders committed by a firearm, not suicides and other unintentional deaths.
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1671 in music
The year 1671 in music involved some significant musical events.
Events
March 3 – Opening of the Paris Opera, with an opera by Robert Cambert.
Philippe Quinault, Molière and Pierre Corneille, collaborate with Jean-Baptiste Lully on a court entertainment.
Arcangelo Corelli settles in Rome after spending four years studying violin in Bologna.
Maurizio Cazzati is dismissed from his post as Maestro di Cappella in San Petronio, Bologna, as a result of controversy over his alleged failure to enforce the rules of counterpoint, and returns to Mantua where he spends the rest of his career as Maestro di Cappella da Camera to Duchess Isabella.
Ignazio Albertini arrives in Vienna with a letter of recommendation from Johann Heinrich Schmelzer.
Published popular music
Classical music
Johann Georg Ahle – Neues Zehn Geistlicher Arien
Giovanni Legrenzi – Op. 8, a collection of sonatas
Andreas Hammerschmidt – Sechsstimmige Fest- und Zeit-Andachten
Guilliaume-Gabriel Nivers – Antiphonarium romanum
Heinrich Schütz – Meine Seele erhebt den Herren, SWV 494
Denis Gaultier – Pièces de Luth sur trois différents modes nouveaux
Opera
Robert Cambert – Pomone
Antonio Pietro Degli – L'inganno fortunato
Antonio Draghi – L'avidità di Mida
Domenico Freschi & Gasparo Sartorio – Iphide greca
Births
February 19 – Charles-Hubert Gervais, composer (died 1744)
May 21 – Azzolino Bernardino della Ciaja, organist, harpsichordist, composer and organ builder (died 1755)
June 8 – Tomaso Albinoni, composer (died 1751)
June 16 – Johann Christoph Bach, musician and composer (died 1721)
June 30 – Teodorico Pedrini, priest, missionary, musician and composer (died 1746)
September – Antoine Forqueray, viola da gamba virtuoso and composer (died 1745)
probable – Robert Valentine, recorder player and composer (died 1747)
Deaths
date unknown – Daniel Farrant, composer, viol player and instrument maker (born 1575)
References
Music
Category:17th century in music
Category:Music by year
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First published in June 2015.
With tensions growing in Europe, Asia and the Middle East, a new generation of nuclear weapons technology is making nuclear warfare a very real prospect. And with very little fanfare, the US is embarking on the privatization of nuclear war under a first-strike doctrine.
“On August 6, 2003, on Hiroshima Day, commemorating when the first atomic bomb was dropped on Hiroshima (August 6 1945), a secret meeting was held behind closed doors at Strategic Command Headquarters at the Offutt Air Force Base in Nebraska. Senior executives from the nuclear industry and the military industrial complex were in attendance. This mingling of defense contractors, scientists and policy-makers was not intended to commemorate Hiroshima. The meeting was intended to set the stage for the development of a new generation of “smaller”, “safer” and “more usable” nuclear weapons, to be used in the “in-theater nuclear wars” of the 21st Century.
“Nuclear war has become a multibillion dollar undertaking, which fills the pockets of US defense contractors. What is at stake is the outright “privatization of nuclear war”.
US-NATO weapons of mass destruction are portrayed as instruments of peace. Mini-nukes are said to be “harmless to the surrounding civilian population”. Pre-emptive nuclear war is portrayed as a “humanitarian undertaking”.
US nuclear doctrine is intimately related to “America’s War on Terrorism” and the alleged threat of Al Qaeda, which in a bitter irony is con- sidered as an upcoming nuclear power.
Click image to order Michel Chossudovsky’s book
Under the Obama administration, Islamic terrorists are said to be preparing to attack US cities. Proliferation is tacitly equated with “nuclear terrorism”. Obama’s nuclear doctrine puts particular emphasis on “nuclear terrorism” and on the alleged plans by Al Qaeda to develop and use nuclear weapons.
…
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State legislatures had a busy week passing electronic privacy laws. Will Congress follow?
First, the Texas legislature unanimously passed HB 2268, which requires state law enforcement to obtain a search warrant before accessing emails and other forms of electronic communications content from service providers. This law is necessary because the federal Electronic Communications Privacy Act ("ECPA") -- which most state electronic privacy laws are modeled after -- hasn't kept up with changes in technology. First enacted in 1986, ECPA allows law enforcement to bypass the warrant requirement to obtain the contents of communications that have been in electronic storage for more than 180 days. This archaic dividing line makes no sense in an age where people store emails and other documents in their inboxes and in the cloud forever. And as the Sixth Circuit Court of Appeals ruled in 2010 in United States v. Warshak, a nonwarrant requirement violates the Fourth Amendment's prohibition against unreasonable searches.
We've repeatedly asked Congress to update ECPA to bring it in line with the 21st century and despite a number of false starts, it seems real ECPA reform could happen in 2013. Even the Department of Justice recently indicated before a congressional committee that a warrant requirement made sense. But rather than wait on the sidelines for Congress to pass ECPA reform, Texas stepped up and passed privacy protection on its own. And its not the only state to do so. EFF sponsored similar legislation in California, SB 467, that recently passed the California Senate 33-1 and is set to be heard by the Assembly's Public Safety Committee on June 11.
Meanwhile, over in Maine, the legislature just passed LD415, which requires police get a search warrant before tracking a person through their cell phone or other electronic device. We've long argued in court that people have a reasonable expectation of privacy in their public movements, meaning a search warrant is required before police can use cell site tracking, a GPS device or a "Stingray" to follow a person's movements throughout the day. Last year, Supreme Court justices Sotomayor and Alito gave support to this idea in their concurring opinions in United States v. Jones where both believed people have a reasonable expectation of privacy in their public movements. Justice Alito even wrote that "in circumstances involving dramatic technological change, the best solution to privacy concerns may be legislative."
Maine heeded Justice Alito's words, ensuring its residents' locational privacy remains protected by statute. Maine isn't the first state to pass this type of legislation. Last year, the California legislature passed SB 1434, a bill co-sponsored by EFF and the ACLU of Northern California that also would have required police obtain a search warrant before tracking a person's location through an electronic device. Despite broad bipartisan support for the law, Governor Jerry Brown vetoed the law. We hope Maine's bill meets a better fate.
Location privacy legislation has been introduced in Congress, too. Two separate bills introduced by Senator Ron Wyden (S 639) and Representative Zoe Lofgren (HR 983) this year seek to do exactly what Maine and California's laws did: require a warrant for location tracking. But the last time Senator Wyden introduced his GPS Act in 2011, the bill languished for almost a year before even getting a committee hearing and then disappeared for the remainder of the congressional term.
With states getting in on the privacy protection action, Congress should feel pressure to update the law to protect everyone across the country. Now that states as politically diverse as California, Texas, and Maine are taking affirmative steps to bring search warrant requirements to sensitive electronic data, Congress should see that privacy legislation is bipartisan and feasible. Hopefully, that means the legislation currently pending in Congress won't get stuck in the rigors of DC politics but actually have a chance at passing.
|
{
"pile_set_name": "OpenWebText2"
}
|
As the United States enters a new phase of its war in Afghanistan, FDD’s Long War Journal is proud to present a renewed assessment of the Taliban’s strength and disposition, with new interactive features. Our assessment highlights the Taliban’s rural control, a key source of insurgent strength that the US military underestimates. The coalition and Afghan government cannot roll back Taliban gains or ultimately defeat it while ignoring the Taliban’s rural advantage.
“Taliban Control in Afghanistan” is a mapped assessment of districts controlled and contested by the Taliban. FDD’s Long War Journal estimates the Taliban currently controls 41 districts and contests an additional 118. The assessment is developed by regularly evaluating local, open-source reports for each district in Afghanistan. A controlled district is one in which the Taliban is openly administering a district, providing services and security, running the local courts and imposing sharia law.
Overall, LWJ has determined that 45 percent of Afghanistan’s districts are controlled or contested by the Taliban.
In developing this mapped assessment, FDD’s Long War Journal evaluates the Taliban’s claims of control. LWJ consulted local reports and utilized expertise of historical dynamics to validate any Taliban claims. When unable to corroborate the Taliban’s claims, LWJ indicated a district as “un-confirmable Taliban claim of control/contested.” Sometimes, the Taliban chooses not to claim districts one might expect, including districts considered the birthplace of and the traditional heartland of the Taliban in Kandahar province. As such, the Taliban’s self-assessment are regarded with some degree of validity. There are 25 districts where the Taliban claims some measure of control that cannot be independently verified. By and large, most of the Taliban’s claims to control or contest specific districts are rather honest self-assessments.
The Special Inspector General for Afghanistan Reconstruction (SIGAR), the congressionally-mandated oversight body on Afghanistan, reported 11 districts under insurgent control, 34 under insurgent influence, and 119 contested. SIGAR, which obtains its information for the US military and Resolute Support – NATO’s mission in Afghanistan – does not, however, release district-specific assessments. SIGAR’s assessment is dated; its latest report from Aug. 1 is based on information provided in June.
FDD’s Long War Journal assessment aligns closely with those of both the US military and the Taliban itself. The Taliban claims to control or contest 50 percent of the country’s 407 districts. The US military puts the estimate at 40 percent (note that LWJ believes that the US military’s assessment of Taliban controlled and contested districts is flawed).
The Taliban is fighting a rural insurgency
The US military and Afghan security forces tend to emphasize urban control in assessing the Taliban’s strength and downplay the Taliban’s control of rural areas. In recent SIGAR reports, the US military has described these rural regions controlled or contested by the Taliban as “less vital areas” that have “less strategic importance.”
This urban focus underestimates the Taliban and its strategy to leverage control of rural areas to launch attacks against urban centers. Continual attacks against urban centers delegitimize the Afghan government and force the redeployment Afghan National Security Forces. The LWJ classified districts in which the Taliban controls everything except the district center as “contested.” The Taliban self-assessed rural control (all but the district center) in 124 districts.
In addition to safe havens in Pakistan and Pakistani state support, rural areas in Afghanistan are essential to the Taliban’s resilience and ability to consistently undermine Afghan security. The Taliban has a stated strategy of opening interior lines in southern provinces to threaten other areas. This belt of districts, stretching east-west from Farah to Paktia, allows the Taliban to consistently attack urban centers. For example, the Taliban uses these districts to threaten the cities of Lashkar Gah, Kandahar, Farah, and Tarinkot. LWJ‘s mapped assessment clearly shows this southern belt. The Taliban has attempted a similar approach in the north, albeit with less success.
Although the NATO mission in Afghanistan downplays the significance of these rural districts, the Taliban considers them pivotal. For example, the Taliban heralded its capture of Sangin district center as a “strategic victory” Although these districts may be nothing more than “rubble and dirt” to Resolute Support, they represent the lifeblood of the insurgency for the Taliban. The Taliban utilizes rural areas to launch attacks against population centers, as well as to fundraise, resupply, recruit, and train fighters.
The new American strategy for Afghanistan places much needed emphasis on Pakistan. FDD’s Long War Journal has mapped terrorist groups operating openly in Pakistan and continues to track US strikes in the country.
Bill Roggio is a Senior Fellow at the Foundation for Defense of Democracies and the Editor of FDD's Long War Journal. Alexandra Gutowski is a military affairs analyst at the Foundation for Defense of Democracies.
Are you a dedicated reader of FDD's Long War Journal? Has our research benefitted you or your team over the years? Support our independent reporting and analysis today by considering a one-time or monthly donation. Thanks for reading! You can make a tax-deductible donation here.
|
{
"pile_set_name": "OpenWebText2"
}
|
package context
import (
"os"
"strconv"
"time"
"github.com/spf13/viper"
)
// ExternalCalls is the extruct that performs exernal calls.
type ExternalCalls struct{}
// SetConfigFile will set a configfile into a path.
func (eC *ExternalCalls) SetConfigFile(configName, configPath string) error {
viper.SetConfigName(configName)
viper.AddConfigPath(configPath)
return viper.ReadInConfig()
}
// GetEnvironmentVariable will return the value of an env var.
func (eC *ExternalCalls) GetEnvironmentVariable(envName string) string {
return os.Getenv(envName)
}
// ConvertStrToInt converts a string into int.
func (eC *ExternalCalls) ConvertStrToInt(str string) (int, error) {
return strconv.Atoi(str)
}
// GetTimeDurationInSeconds returnin the number of seconds of a duration.
func (eC *ExternalCalls) GetTimeDurationInSeconds(duration int) time.Duration {
return time.Duration(duration) * time.Second
}
// GetStringFromConfigFile returns a string from a config file.
func (eC *ExternalCalls) GetStringFromConfigFile(value string) string {
return viper.GetString(value)
}
// GetBoolFromConfigFile returns a bool from a config file.
func (eC *ExternalCalls) GetBoolFromConfigFile(value string) bool {
return viper.GetBool(value)
}
// GetIntFromConfigFile returns a int from a config file.
func (eC *ExternalCalls) GetIntFromConfigFile(value string) int {
return viper.GetInt(value)
}
// CallerInterface is the interface that stores all external call functions.
type CallerInterface interface {
SetConfigFile(configName, configPath string) error
GetStringFromConfigFile(value string) string
GetBoolFromConfigFile(value string) bool
GetIntFromConfigFile(value string) int
GetEnvironmentVariable(envName string) string
ConvertStrToInt(str string) (int, error)
GetTimeDurationInSeconds(duration int) time.Duration
}
|
{
"pile_set_name": "Github"
}
|
Pilar and Deion Sanders Will Still Be Fighting In 2013
Despite continuous requests for the former couple to let the overweight woman croon, it looks as though Deion Sanders and Pilar Sanders will carry their legal back and forth well into 2013. Pilar Sanders has recently vowed to continue fighting with her ex over custody of their two children. In response to losing the most recent custody battle in court, Pilar says she is a “victim of Deion’s celebrity status.”
At a Dallas court hearing on Wednesday, model and actress Pilar Sanders lost temporary custody of her two boys, who have been living with their NFL Network analyst and Hall of Famer father. The judge also reduced Pilar’s child support from $10,500 to $5,500 a month. She will retain custody of their daughter. Her publicist, Kali Bowyer, said, “Pilar has become a victim of Deion’s celebrity status, which has swayed the courts and blinded justice . . . It has become evident at this point that there is an absolute prejudice against Pilar, and this has become a completely one-sided court circus.” Pilar herself said, “I am sad that Deion has been able to keep my boys away from me since Oct. 26 — no Halloween, no Thanksgiving — and now he is threatening to keep them away from me for Christmas. . . . He is using our innocent children as a pawn in this ugly, ugly divorce.” The warring pair, whose battle began with an April domestic dispute at their home, are due back in court Jan. 9 to discuss child custody issues. Pilar wants their 13-year marriage annulled, and their drama-filled divorce case will go to a jury.
|
{
"pile_set_name": "Pile-CC"
}
|
namespace Microsoft.eShopOnContainers.Services.Ordering.API.Infrastructure.Filters
{
using AspNetCore.Mvc;
using global::Ordering.Domain.Exceptions;
using Microsoft.AspNetCore.Hosting;
using Microsoft.AspNetCore.Mvc.Filters;
using Microsoft.eShopOnContainers.Services.Ordering.API.Infrastructure.ActionResults;
using Microsoft.Extensions.Logging;
using System.Net;
public class HttpGlobalExceptionFilter : IExceptionFilter
{
private readonly IHostingEnvironment env;
private readonly ILogger<HttpGlobalExceptionFilter> logger;
public HttpGlobalExceptionFilter(IHostingEnvironment env, ILogger<HttpGlobalExceptionFilter> logger)
{
this.env = env;
this.logger = logger;
}
public void OnException(ExceptionContext context)
{
logger.LogError(new EventId(context.Exception.HResult),
context.Exception,
context.Exception.Message);
if (context.Exception.GetType() == typeof(OrderingDomainException))
{
var json = new JsonErrorResponse
{
Messages = new[] { context.Exception.Message }
};
// Result asigned to a result object but in destiny the response is empty. This is a known bug of .net core 1.1
//It will be fixed in .net core 1.1.2. See https://github.com/aspnet/Mvc/issues/5594 for more information
context.Result = new BadRequestObjectResult(json);
context.HttpContext.Response.StatusCode = (int)HttpStatusCode.BadRequest;
}
else
{
var json = new JsonErrorResponse
{
Messages = new[] { "An error occur.Try it again." }
};
if (env.IsDevelopment())
{
json.DeveloperMessage = context.Exception;
}
// Result asigned to a result object but in destiny the response is empty. This is a known bug of .net core 1.1
// It will be fixed in .net core 1.1.2. See https://github.com/aspnet/Mvc/issues/5594 for more information
context.Result = new InternalServerErrorObjectResult(json);
context.HttpContext.Response.StatusCode = (int)HttpStatusCode.InternalServerError;
}
context.ExceptionHandled = true;
}
private class JsonErrorResponse
{
public string[] Messages { get; set; }
public object DeveloperMessage { get; set; }
}
}
}
|
{
"pile_set_name": "Github"
}
|
After nearly 13 hours of debate that went late into the night, the Republican-controlled Senate voted early on January 22 to approve rules for the impeachment trial of President Donald Trump, who allegedly abused his power by withholding military aid to pressure Ukraine into opening an investigation of Democratic presidential candidate Joe Biden.
The Senate rejected all 11 amendments Democrats proposed, sparking concerns from them over the plausibility that the trial will be, in effect, rigged to protect and acquit Trump. Among the amendments that failed were subpoenas for key witnesses, such as former national security adviser John Bolton and acting White House chief of staff Mick Mulvaney. Amendments that would have called for additional relevant documents from the Department of Defense and the Office of Management and Budget were also rejected.
Now, right-wing media are using Democratic concerns to downplay the impeachment trial. Some are arguing that Democrats’ complaints about the process prove that they don’t actually have a case, while others are complaining that Trump supposedly didn’t get a fair process in the House (he did). Some are also pointing to Democratic senators’ calls to hear from more witnesses as evidence that the House didn’t properly call witnesses during the impeachment inquiry, despite the fact that the administration prevented key witnesses from testifying.
|
{
"pile_set_name": "OpenWebText2"
}
|
About
Downtown
Once home to a jazz club that broadcast live on local radio in the late 1960s, the hotel is part of downtown Austin history and carries with it a storied legacy that the LINE seeks to foster and continue. The redesign of the 1965 building, a collaboration between Austin architect Michael Hsu and LA-based designer Sean Knibb, showcases art by emerging local artists throughout the property. The LINE hosts events and programs that build on the hotel’s historic cultural contribution and pay tribute to the unique character of Austin.
images15
Gallery
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Gallery
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3
Dining
Led by Executive Chefs Kristen Kish and Justin Ermini, LINE Austin’s many options for eating combine a commitment to the ingredients of Central Texas with the desire to reinvent classic techniques and flavors – bringing entirely new culinary perspectives to downtown.
Serving coffee, signature matcha and easy food to take away in the lobby.
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4
Pool
Enjoy a cocktail and a swim with the best vista in town at the LINE’s lakeside infinity pool. Overlooking the Ann W. Richards Congress Avenue Bridge, Town Lake and the lush Austin skyline, it’s a spot that will make you forget you’re in the heart of the city.
Wellness
Add a dose of fresh air to your work out routine with LINE Austin wellness classes. Open to travelers and locals, join us weekly and choose from Empowered Yoga with Gustavo Padron, kickboxing sessions with studio KNOCKOUT, and dance classes in partnership with local fitness favorite, Outdoor Voices.
Pet-Friendly
We’re dog people, but cats are ok too. All pets stay for free at the LINE. No fees. No weight limits. No hassle. The LINE’s Guest Experience teams make it easy with neighborhood recommendations for walks, parks and pet-friendly bars and restaurants. Check with our front desk for courtesy bags, water bowls and treats.
images15
images15
8
Neighborhood
From an Ellsworth Kelly masterpiece to an iconic Texas blues club, the LINE is centrally located downtown among Austin’s most interesting cultural treasures. Every direction offers something to discover: walk north for a museum day at The Blanton and The Contemporary or ride a bike to the eastside for tacos and drinks on a patio. Stay downtown for a live show at the Paramount Theater, travel across the bridge to the South Congress district or rent a canoe and explore the lake – which also happens to be a river.
|
{
"pile_set_name": "Pile-CC"
}
|
Meta
Month: August 2018
In one of my old blog posts I covered some scripts to update Cloudflare’s DNS system. This is useful if you’re hosting sites at home on a Raspberry PI (like this one still is!), where you might not have a static IP.
In the intervening 3 years, the API has changed, so I’ve revisited the scripts to update them to the new shiny “Cloudflare API V4”. The updated scripts are tested on the current latest image of Raspbian Stretch at the time of writing. The new scripts are available on GitHub here.
The structure of the scripts is still the same:
cf-ddns.sh is the main update script, intended to be setup to run automatically via crontab or similar.
cf-ddns-read.sh is used to read the host id value from the host record that needs updating (while Cloudflare mention some API details and stubs of requests in the API section of the DNS dash page, there still doesn’t seem to be a nice way to get this id. Its just mentioned as “:identifier” in those stubs).
If they break again and I don’t notice, or if there are any problems with the scripts, please raise an issue on the Github Repo.
|
{
"pile_set_name": "Pile-CC"
}
|
Is online trading for firm only?
Debra Perlingiere
Enron North America Corp.
1400 Smith Street, EB 3885
Houston, Texas 77002
dperlin@enron.com
Phone 713-853-7658
Fax 713-646-3490
|
{
"pile_set_name": "Enron Emails"
}
|
Use and toxicity of the colony-stimulating factors.
The colony-stimulating factors (CSFs) have emerged as effective drugs in a variety of clinical situations. These drugs stimulate the production and activity of haematopoietic cells in vitro and in vivo. Two members of this group, granulocyte CSF (G-CSF) and granulocyte-macrophage CSF (GM-CSF), have been approved in the US and Europe for use following cytotoxic chemotherapy and autologous bone marrow transplantation. Other uses of the CSFs include myelodysplastic syndromes, aplastic anaemia, the acquired immunodeficiency syndrome (AIDS) and cyclic and congenital neutropenias. Although CSFs have generally been well tolerated in clinical use there are a number of theoretical concerns, including disease acceleration, biased stem cell commitment and bone marrow exhaustion. New CSFs are currently under development. Combinations of growth factors in the future may maximise effectiveness while minimising toxicity.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
We are still taking orders online. However, due to current Covid-19 issues there may be some delays in processing orders. We will endeavour to dispatch all orders as soon as practically possible. Stay safe and well!
More info
Shimano Baitrunner X-Aero
Baitrunner X-Aero RA
The new Baitrunner X Aero combines the benefits and convenience of a traditional Baitrunner reel with the casting performance rivalling that of a compact Big Pit reel. This outstanding casting performance is achieved by the use of an oversized Aero Concept spool which is noticeably larger in diameter than a normal sized spool. The Baitrunner X Aero also uses Aero Wrap II (Shimano's top line lay system) and 2-speed oscillation for almost perfect spool line management. Another advantage of the large diameter spool is that one turn of the handle retrieves nearly 1 metre of line making retrieving from distance faster. To satisfy modern anglers thinking both the 8000 and 10000 sized reels now have a single handle which generates more winding power than the double handle which is still fitted to the smaller 6000 model. The hybrid body of the Baitrunner X Aero has a black satin finish and the line clip on the XGT-7 rotor is line friendly to prevent line damage. For more than 20 years the Shimano Baitrunner reel has been the most popular specimen reel available, trusted by millions of anglers throughout Europe. Now, with the addition of the Aero Concept spool, a single handle in the larger sizes and a satin black finish, it is set to continue to be the anglers favourite for many years.
|
{
"pile_set_name": "Pile-CC"
}
|
= 0 for i.
-1
Solve 2*k + 30 = 8*k for k.
5
Solve 24*y = 8 - 32 for y.
-1
Solve -45*m = 152 + 118 for m.
-6
Solve 49*p - 62*p = 117 for p.
-9
Solve -12 = -5*f - 27 for f.
-3
Solve 0 = 13*q - 26 - 13 for q.
3
Solve 63*v + 45 = 78*v for v.
3
Solve -74 = 9*c - 29 for c.
-5
Solve 7*c + 24 = -11 for c.
-5
Solve 62*r - 48*r = 56 for r.
4
Solve 0 = -3*j + 436 - 442 for j.
-2
Solve 675*v + 16 = 671*v for v.
-4
Solve 11 = 4*s + 7 for s.
1
Solve 0 = -9*u + 17*u + 32 for u.
-4
Solve 71*t = -63 + 276 for t.
3
Solve 11 = -6*v + 11 for v.
0
Solve -27 = -514*o + 541*o for o.
-1
Solve 177*a = 172*a - 10 for a.
-2
Solve 0 = -2*c + 3 - 1 for c.
1
Solve 43*i - 42*i + 4 = 0 for i.
-4
Solve -17*b = 1 - 154 for b.
9
Solve 1 = 7*a + 8 for a.
-1
Solve -47 - 49 = -24*a for a.
4
Solve 333*d = 316*d + 136 for d.
8
Solve 92 - 67 = -5*a for a.
-5
Solve 0 = 34*r - 18*r - 32 for r.
2
Solve -6*v - 63 + 15 = 0 for v.
-8
Solve 7155*b - 7146*b - 36 = 0 for b.
4
Solve -706 + 762 = -8*l for l.
-7
Solve -6*k + 83 = 71 for k.
2
Solve 0 = 41*b - 349 + 62 for b.
7
Solve -3 = -g - 0 for g.
3
Solve 6*n = 12 - 0 for n.
2
Solve -4 = -25*u + 29*u for u.
-1
Solve 1315 = -7*x + 1378 for x.
9
Solve -7 = -6*j - 1 for j.
1
Solve -6*x = -1 + 7 for x.
-1
Solve 8*f - 3 = -11 for f.
-1
Solve -5*i - 27 = -7 for i.
-4
Solve 5*d - 4 - 16 = 0 for d.
4
Solve -3*a = 722 - 752 for a.
10
Solve -7*w - 176 = -232 for w.
8
Solve 15 - 11 = 4*s for s.
1
Solve 18*i + 5 = 17*i for i.
-5
Solve 0 = 19*m - 21*m - 8 for m.
-4
Solve -13*w + 11 + 41 = 0 for w.
4
Solve 0 = 44*b - 49*b - 40 for b.
-8
Solve 9*d = -16 + 43 for d.
3
Solve -7 + 23 = 4*a for a.
4
Solve 2*f - 65 + 57 = 0 for f.
4
Solve 0 = 9*a + 22 + 68 for a.
-10
Solve 0 = -16*r + 9*r - 7 for r.
-1
Solve -d + 2*d - 1 = 0 for d.
1
Solve 4*b = 20 - 0 for b.
5
Solve -10*s + 17*s = -21 for s.
-3
Solve -71*u + 46 = -25 for u.
1
Solve -9*n + 80 = 17 for n.
7
Solve 13*r - 4 = 15*r for r.
-2
Solve -10*b + b = 0 for b.
0
Solve 16 = 7*q - 5 for q.
3
Solve 425*z - 416*z = -81 for z.
-9
Solve -9*u - 374 + 455 = 0 for u.
9
Solve 17*r - 6 = 14*r for r.
2
Solve 4*y + 56 = 80 for y.
6
Solve -22 = -5*n - 22 for n.
0
Solve -9*z - 15*z = 120 for z.
-5
Solve -8 = -9*r + 10 for r.
2
Solve 2*i + i = -15 for i.
-5
Solve 0 = 209*y - 214*y + 10 for y.
2
Solve -277*c + 349*c + 432 = 0 for c.
-6
Solve 68*l + 94 = 26 for l.
-1
Solve 0 = g + 37 - 34 for g.
-3
Solve -111 = -g - 113 for g.
-2
Solve -34*a - 52 = -8*a for a.
-2
Solve 447*u = 454*u + 7 for u.
-1
Solve 0 = -50*l + 51*l - 2 for l.
2
Solve 441*y - 433*y = 40 for y.
5
Solve -335 = 40*d - 15 for d.
-8
Solve -7*c = 164 - 115 for c.
-7
Solve -33*x - 76 = -10 for x.
-2
Solve -1550 = -13*t - 1472 for t.
6
Solve 15*s = -10 - 5 for s.
-1
Solve -8*t + t = -14 for t.
2
Solve 0 = n + 5 for n.
-5
Solve 52*u - 219 = -21*u for u.
3
Solve -9*h - 14 = -50 for h.
4
Solve 3*a + 20 = -a for a.
-5
Solve 0 = 4*q - 57 + 49 for q.
2
Solve -25*t + 21*t = -20 for t.
5
Solve -47 + 49 = -a for a.
-2
Solve 0 = -22*p + 22 + 44 for p.
3
Solve 0 = -10*m + 21*m - 33 for m.
3
Solve 36 = -a - 8*a for a.
-4
Solve -85*h = -30*h - 220 for h.
4
Solve 9 = -6*p + 33 for p.
4
Solve -6*h = h - 7 for h.
1
Solve 69*p - 67*p - 4 = 0 for p.
2
Solve 0 = -7*n - 124 + 145 for n.
3
Solve 6*n + 9 = -3*n for n.
-1
Solve 0 = -26*k - 52 for k.
-2
Solve 420 = -12*m - 128*m for m.
-3
Solve r + 3 + 1 = 0 for r.
-4
Solve -21*f - 16 = -17*f for f.
-4
Solve 28 = 106*x - 102*x for x.
7
Solve 495*m - 499*m = -12 for m.
3
Solve 0*o = 3*o - 6 for o.
2
Solve 0 = -17*t + 14*t - 12 for t.
-4
Solve 5*y - 9 = -4 for y.
1
Solve 19*g = 4*g + 60 for g.
4
Solve -39 = 7*q - 18 for q.
-3
Solve -2*q + 122 = 130 for q.
-4
Solve 0 = u - 2*u - 4 for u.
-4
Solve 0 = -a + 80 - 82 for a.
-2
Solve 0*y = -y + 5 for y.
5
Solve -143*x + 65 = -130*x for x.
5
Solve 15*g - 114 + 24 = 0 for g.
6
Solve 54 = -5*g + 29 for g.
-5
Solve -14*w - 341 = -411 for w.
5
Solve -x = 20 - 19 for x.
-1
Solve -13*m = -32 - 7 for m.
3
Solve -82*w = -23*w - 118 for w.
2
Solve 9*z + 2 = 8*z for z.
-2
Solve -64 - 36 = -20*s for s.
5
Solve -16*r - 60 = -172 for r.
7
Solve 2*r + 6 = -0*r for r.
-3
Solve 6 = 164*v - 166*v for v.
-3
Solve -4 = 16*q - 15*q for q.
-4
Solve 177 = -d + 175 for d.
-2
Solve -17*i = -25*i for i.
0
Solve -26*k = -33*k + 14 for k.
2
Solve -175*q = -150*q + 225 for q.
-9
Solve 708*k = 707*k + 7 for k.
7
Solve -81 = -3*f - 69 for f.
4
Solve -w = -4*w + 15 for w.
5
Solve 3*q - 14 = -11 for q.
1
Solve 4*c - 4 = 2*c for c.
2
Solve -12*o - 39*o + 16*o = 0 for o.
0
Solve 0 = 35*m + 194 + 51 for m.
-7
Solve -25 = 4*t + t for t.
-5
Solve 7*i + 6 = 9*i for i.
3
Solve 0 = -84*p + 56*p + 168 for p.
6
Solve -2*z + 3*z = -0*z for z.
0
Solve 0 = 18*u - 16*u - 10 for u.
5
Solve -15*n + 188 = 32*n for n.
4
Solve 8*w = 12*w for w.
0
Solve 41*i = 57*i + 32 for i.
-2
Solve 578*o + 25 = 573*o for o.
-5
Solve 4*g - 13 + 9 = 0 for g.
1
Solve -11*s + 15*s = 16 for s.
4
Solve 238 = -35*q + 308 for q.
2
Solve -13*r + 10 = 62 for r.
-4
Solve 4*o + 28 = -3*o for o.
-4
Solve 106 - 74 = 32*t for t.
1
Solve 397*q - 402*q = 15 for q.
-3
Solve 5*u + 19 = -6 for u.
-5
Solve -11*y = 12 - 56 for y.
4
Solve 2*v - 24 + 26 = 0 for v.
-1
Solve -2 = b + 2 for b.
-4
Solve 5*y - 113 = -88 for y.
5
Solve -160 = 16*j - 32 for j.
-8
Solve 0 = -21*f - 4*f + 75 for f.
3
Solve 12*k - 37 + 1 = 0 for k.
3
Solve 2*o + 29 = 35 for o.
3
Solve 21*l + 97 = -8 for l.
-5
Solve -38*b = -236 - 68 for b.
8
Solve -4*q - 30 = -18 for q.
-3
Solve -26*d - 83 = -5 for d.
-3
Solve 8*t + 17 - 57 = 0 for t.
5
Solve -54*w = -46*w + 32 for w.
-4
Solve 0 = j - 17 + 14 for j.
3
Solve 16*g + 107 - 11 = 0 for g.
-6
Solve -1186 = 8*d - 1178 for d.
-1
Solve 14 = 10*q + 4*q for q.
1
Solve 5*v + v = -18 for v.
-3
Solve 21*y - 38 - 4 = 0 for y.
2
Solve -1 = -15*k + 14 for k.
1
Solve -63 = 3*t - 66 for t.
1
Solve -26*q + 68 = -9*q for q.
4
Solve -6*x = 178 - 154 for x.
-4
Solve 4*f + 0*f - 12 = 0 for f.
3
Solve 0 = 19*y - 20*y + 2 for y.
2
Solve 13*k = -10*k for k.
0
Solve 30 = -12*o + 42 for o.
1
Solve -5*q - 8 = 2 for q.
-2
Solve -47 - 1 = -16*i for i.
3
Solve -104*c = -131*c + 27 for c.
1
Solve -6*f + 16 = 10 for f.
1
Solve 17 = 8*v - 23 for v.
5
Solve 19*p = -18 - 39 for p.
-3
Solve -508 + 100 = -51*b for b.
8
Solve 0 = -17*y - 14 - 3 for y.
-1
Solve 0 = 5*a - 12*a - 35 for a.
-5
Solve -579*w + 568*w - 55 = 0 for w.
-5
Solve 2*h + 47 = 51 for h.
2
Solve 0 = -5*u + 31 - 21 for u.
2
Solve -29*l + 104 + 12 = 0 for l.
4
Solve 8 = -4*j + 12*j for j.
1
Solve 4*s = -0*s - 16 for s.
-4
Solve 358 = 4*k + 378 for k.
-5
Solve -7*p - 19 + 5 = 0 for p.
-2
Solve 4 = 5*u + 14 for u.
-2
Solve 0 = 2*y - 3507 + 3505 for y.
1
Solve -34*h + 69 = 35*h for h.
1
Solve f = 4*f - 12 for f.
4
Solve -17*j - 383 = -298 for j.
-5
Solve -465 + 453 = -2*h for h.
6
Solve 0 = 183*h - 202*h - 38 for h.
-2
Solve 19*m - 24*m = 30 for m.
-6
Solve 18*h - 20 = 70 for h.
5
Solve 8*h - 18 = -h for h.
2
Solve -3*j = j - 2*j for j.
0
Solve 0 = 4*v + 11 - 3 for v.
-2
Solve -2*i - 34 = -30 for i.
-2
Solve z + 14*z = -60 for z.
-4
Solve 5*j - 8*j = 6 for j.
-2
Solve 4 = -12*w + 11*w for w.
-4
Solve -16*r + 290 = 242 for r.
3
Solve -4*l = -24*l - 60 for l.
-3
Solve -450*v - 187 = -467*v for v.
11
Solve -42*b = -13*b + 29 for b.
-1
Solve -8*v = -2*v - 18 for v.
3
Solve 0 = 132*v + 180 - 708 for v.
4
Solve 0 = -4*z + 2*z - 6 for z.
-3
Solve 0 = 54*h + 2*h + 336 for h.
-6
Solve 0 = 158*r - 165*r + 7 for r.
1
Solve -19 = -6*l - 1 for l.
3
Solve -158 = -3*f - 176 for f.
-6
Solve 0 = 47*j - 12 + 294 for j.
-6
Solve 188*x + 12 = 191*x for x.
4
Solve 0 = 21*v - 149 + 2 for v.
7
Solve 9*t - 19 = -64 for t.
-5
Solve -6*n = 110 - 98 for n.
-2
Solve 0 = -0*i - 8*i - i for i.
0
Solve -11*f - 32 = 23 for f.
-5
Solve 35*q - 40*q = 25 for q.
-5
Solve 34*y = 10*y - 48 for y.
-2
Solve 215*n = 208*n - 14 for n.
-2
Solve 30 = -q - 14*q for q.
-2
Solve 90 - 140 = 10*c for c.
-5
Solve 264 = -47*d - 65 for d.
-7
Solve 0 = -49*a + 45*a - 12 for a.
-3
Solve 4*f = -6*f for f.
0
Solve -6*t - 73 = -43 for t.
-5
Solve 0 = i - 56*i + 110 for i.
2
Solve -5*i = 19 + 6 for i.
-5
Solve -111*s + 480 = -31*s for s.
6
Solve 36 = -0*s + 6*s for s.
6
Solve -20*v + 68 = -3*v for v.
4
Solve 2 = 7*u - 9*u for u.
-1
Solve 13*x - 1072 = -1137 for x.
-5
Solve -18 = -3*z - 33
|
{
"pile_set_name": "DM Mathematics"
}
|
Q:
How can I identify and count unique pairs at every level in a list of lists in R?
I have a list of lists that looks like this:
> class(cladelist)
[1] "list"
cladelist <- list( `46` = scan(text=' "KbFk2" "PeHa3" "PeHa51" "EeBi27" "EeBi17" "PeHa23" "PeHa44" "EeBi4" "EeBi26" "PeHa8" "PeHa26" "EeBi24" "EeBi3"
"EeBi20" "KbFk5" "PeHa15" "PeHa43" "PeHa11" "PeHa12" "PeHa49" "PeHa67" "PeHa17" "PeHa59" "KbFk4" "PeHa10" "PeHa55"
"PeHa73" "EeBi23" "PeHa78" "PeHa81" "EeBi11" "PeHa45" "EeBi6" "EeBi34" "PeHa25" "PeHa52" "PeHa62" "PeHa31" "PeHa65"
"PeHa47" "PeHa50" "PeHa34" "PeHa54" "PeHa22" "PeHa30"', what=""),
`47`= scan(text='
"KbFk2" "EeBi27" "EeBi17" "EeBi4" "EeBi26" "EeBi3" "EeBi20" "KbFk5" "KbFk4" "EeBi6" "EeBi34"', what=""),
`48`= scan(text=' "PeHa3" "PeHa51" "PeHa23" "PeHa44" "PeHa8" "PeHa26" "EeBi24" "PeHa15" "PeHa43" "PeHa11" "PeHa12" "PeHa49" "PeHa67"
"PeHa17" "PeHa59" "PeHa10" "PeHa55" "PeHa73" "EeBi23" "PeHa78" "PeHa81" "EeBi11" "PeHa45" "PeHa25" "PeHa52" "PeHa62"
"PeHa31" "PeHa65" "PeHa47" "PeHa50" "PeHa34" "PeHa54" "PeHa22" "PeHa30"', what=""),
`49`= scan(text=' "PeHa51" "PeHa23" "PeHa44" "PeHa8" "PeHa26" "EeBi24" "PeHa15" "PeHa43" "PeHa11" "PeHa12" "PeHa49" "PeHa67" "PeHa17"
"PeHa59" "PeHa10" "PeHa55" "PeHa73" "EeBi23" "PeHa78" "PeHa81" "EeBi11" "PeHa45" "PeHa25" "PeHa52" "PeHa62" "PeHa31"
"PeHa65" "PeHa47" "PeHa50" "PeHa34" "PeHa54" "PeHa22" "PeHa30"', what=""),
`50`= scan(text=' "EeBi27" "EeBi17" "EeBi4" "EeBi26" "EeBi3" "EeBi20" "KbFk5" "KbFk4" "EeBi6" "EeBi34"', what="") )
Each of these sublists (ie "46", "47" etc) represents a clade in a dendogram that I've extracted using:
> cladelist <- clade.members.list(VB.phy, tips = FALSE, tip.labels = TRUE, include.nodes=FALSE)
Im trying to find each unique pair found within each sublist, and calculate the sum of times it appears between all sublists (clades).
The ideal output would be a dataframe that looks like this where the count is the number of times this pair was found between all sublists (clades):
Pair Count
Peha1/PeHa2 2
Peha1/PeHa3 4
PeHa1/PeHa4 7
PeHa1/PeHa5 3
What sort of formulas am I looking for?
Background for the question (just for interest, doesnt add that much to question):
The idea is that I have a data set of 121 of these elements (Peha1, KbFk3, etc). They are artifacts (I'm an archaeologist) that I'm evaluating using 3D geometric morphometrics. The problem is that these artifacts are not all complete; they are damaged or degraded and thus provide an inconsistent amount of data. So I've had to reduce what data I use per artifact to have a reasonable, yet still inconsistent, sample size. By selecting certain variables to evaluate, I can get useful information, but it requires that I test every combination of variables. One of my analyses gives me the dendograms using divisive hierarchical clustering.
Counting the frequency of each pair as found between each clade should be the strength of the relationship of each pair of artifacts. That count I will then divide by total number of clades in order to standardize for the following step. Once I've done this for X number of dendograms, I will combine all these values for each pair, and divide them by the number representing whether that pair appeared in a dendogram (if it shows up in 2 dendograms, that I divide by 2), because each pair will not appear in each of my tests and I have to standardize it so that more complete artifacts that appear more often in my tests don't have too much more weight. This should allow me to evaluate which pairs have the strongest relationships.
A:
This falls into a set of association kind of problems for which I find the widyr package to be super useful, since it does pairwise counts and correlations. (The stack() function just converts into a dataframe for the rest to flow).
I couldn't check against your sample output, but for an example like "PeHa23/PeHa51", the output shows they are paired together in 3 different clades.
This currently doesn't include zero counts to exhaust all possible pairs, but that could be shown as well (using complete()).
UPDATE: Made references clearer for packages like dplyr, and filtered so that counts are non-directional (item1-item2 is same as item2-item1 and can be filtered).
library(tidyverse)
library(widyr)
df <- stack(cladelist) %>%
dplyr::rename(clade = "ind", artifact = "values")
df %>%
widyr::pairwise_count(feature = clade, item = artifact) %>%
filter(item1 > item2) %>%
mutate(Pair = paste(item1, item2, sep = "/")) %>%
dplyr::select(Pair, Count = n)
#> # A tibble: 990 x 2
#> Pair Count
#> <chr> <dbl>
#> 1 PeHa3/KbFk2 1
#> 2 PeHa51/KbFk2 1
#> 3 PeHa23/KbFk2 1
#> 4 PeHa44/KbFk2 1
#> 5 PeHa8/KbFk2 1
#> 6 PeHa26/KbFk2 1
#> 7 KbFk5/KbFk2 2
#> 8 PeHa15/KbFk2 1
#> 9 PeHa43/KbFk2 1
#> 10 PeHa11/KbFk2 1
#> # … with 980 more rows
|
{
"pile_set_name": "StackExchange"
}
|
INTRODUCTION {#s1}
============
Lung cancer is the leading cause of cancer-related deaths worldwide, with non-small cell lung cancer (NSCLC) accounting for approximately 85% of all cases \[[@R1]\]. Most NSCLC patients are diagnosed at an advanced stage and have a 5-year survival rate of less than 20% \[[@R1], [@R2]\] because of their advanced stage diagnoses \[[@R3]\]. Lack of early diagnosis markers and high potential for the invasion ability of NSCLC are challenging for NSCLC therapy. Hence, the molecular mechanisms involved in the development and progression of NSCLC must be investigated.
Long noncoding RNAs (lncRNAs), defined as a class of noncoding RNA with a length of more than 200 nucleotides, have critical roles in the gene expression regulation \[[@R4]\], epigenetic control \[[@R5]\], chromatin structure \[[@R6], [@R7]\], development process, genomic imprinting, and pluripotency of embryonic stem cells \[[@R6], [@R8], [@R9]\]. In addition, dysregulation of lncRNAs has been reported to play a vital role in the carcinogenesis, disease progression, and metastasis of human cancers \[[@R6], [@R7], [@R10]--[@R12]\]. Some lncRNAs such as H19, HOTAIR, ANRIL, MALAT1, and SCAL1 \[[@R13]--[@R15]\] have been reported to be associated with the development and progression of lung cancers. However, the roles of lncRNAs in NSCLC development and metastasis remain largely unknown. Hence, the identification of lung cancer-associated lncRNAs and the investigation of their molecular and biological functions in lung cancers are vital.
Myocardial infarction-associated transcript (MIAT) is one of the noncoding RNAs first identified as an lncRNA in 2006 \[[@R16]\]. MIAT is involved in various cellular processes, including myocardial infarction \[[@R16], [@R17]\], microvascular dysfunction \[[@R18]\], paranoid schizophrenia \[[@R19]\], nuclear body formation \[[@R20]\], and neurogenic commitment \[[@R21]\]. Because MIAT physically interacts with SF1 splicing factor, it is supposed to be involved in RNA splicing and regulating gene expression \[[@R22]\]. Recent studies have demonstrated that MIAT constitutes a loop with Oct4 in malignant mature B cells and is essential for cell survival \[[@R23]\]. MIAT is also upregulated and interacts with the polycomb in neuroendocrine prostate cancer to participate in tumorigenesis \[[@R24]\]. However, the expression pattern, biological function, and underlying mechanism of MIAT in NSCLC are still unclear.
In the present study, we investigated the potential mechanisms of MIAT in NSCLC progression. We observed that MIAT was upregulated and played a role in the advanced pathological stage. Moreover, our data revealed that MIAT could interact with MLL and epigenetically activate MMP9 to facilitate cell proliferation, migration, and invasion in NSCLC.
RESULTS {#s2}
=======
MIAT expression was upregulated and correlated with advanced tumor stage {#s2_1}
------------------------------------------------------------------------
To explore whether MIAT played a role in carcinogenesis, we first profiled the expression of MIAT in 60 pairs of NSCLC tissues (30 paired of adenocarcinoma and 30 paired of squamous) and paired adjacent non-tumor tissues. The qPCR data indicated that the expression level of MIAT in tumor tissues was significantly higher than that in the corresponding non-tumor tissues (mean dCT of tumor vs. normal tissue: 2.95 vs. 3.71, *p* = 0.0014; Figure [1A](#F1){ref-type="fig"}). Furthermore, we analysed the association between *MIAT* gene expression and the clinical stage of NSCLC and the state of metastasis. *MIAT* upregulation in the tumor tissues was associated with an advanced stage (stages III, IV, *n* = 24, *p* = 0.001) but not early stage cancer (stages I and II, *n* = 36, *p* = 0.09; Figure [1B](#F1){ref-type="fig"}). Next we tested the MIAT expression in NSCLC cell lines, including A549, H1299, H460, and H520. Among these cell lines, MIAT was relative higher expressed in A549 and H1299 (Figure [1C](#F1){ref-type="fig"}); thus, we chose A549 and H1299 cells to perform the following experiments. Moreover, to investigate the clinical significances of MIAT, we evaluated the correlation between MIAT level and clinicopathological factors. Results revealed that MIAT levels were correlated with tumor size (*p* = 0.0035), TMN stage (*p* = 0.001), and lymph node metastasis (*p* = 0.0185) in NSCLC. Nevertheless, MIAT levels were not associated with age (*p* = 1.000) or gender (*p* = 0.0581) (Table [1](#T1){ref-type="table"}). These results indicated that upregulated expression of MIAT might play a role in NSCLC tumorigenesis.
{#F1}
###### MIAT expression and clinicopathological factors in NSCLC patients (*n* = 60)
Parameter *N* Relative MIAT expression *p*-value
-------------------------------- ----- -------------------------- ----------- --------
Age (year) 1.000
≤ 65 34 20 14
\> 65 26 16 10
Gender
Male 37 26 11 0.0581
Female 23 10 13
Tumor size (maximum diameters)
≤ 3 cm 32 25 7 0.0035
\> 3 cm 28 11 17
Lymph node metastasis
N1 26 11 15 0.0185
N0 34 25 9
TMN stage
I--II 36 28 8 0.0010
III--IV 24 8 16
*P* values when expression levels were compared using Fisher\'s exact test.
Knockdown of MIAT impaired lung cancer cells proliferation and cell cycles arrest *in vitro* {#s2_2}
--------------------------------------------------------------------------------------------
Because the overexpression of MIAT was significantly associated with progression in NSCLC patients, we further modulated MIAT expression to examine whether MIAT regulated the proliferation of A549 and H1299 cells. A cell counting assay revealed that cell growth rate of A549 and H1299 were dose-dependently inhibited with siMIAT compared with the control (Figure [2A](#F2){ref-type="fig"}). Colony formation assay data also revealed that clonogenic survival were inhibited in si-MIAT-treated A549 and H1299 cells (Figure [2B](#F2){ref-type="fig"}). To further examine whether the effect of MIAT on proliferation reflected cell cycle arrest, cell cycle progression was analysed using flow cytometry analysis. The results indicate that MIAT knockdown retarded the G1/S transition in si-MIAT A549 and H1299 cells (Figure [2C](#F2){ref-type="fig"}). We then performed Western blot and found that knockdown of MIAT would decrease the expressions of cyclin D3 and cdk2 in A549 and H1299 cells (Figure [2D](#F2){ref-type="fig"}). These data indicated that MIAT could promote the proliferation phenotype of NSCLC cells.
{#F2}
MIAT silencing impaired cell migration and invasion *in vitro* {#s2_3}
--------------------------------------------------------------
Next, we explored the efficiency of MIAT on migration and invasion in A549 and H1299 cells. The wound healing scratch assay revealed that the ratio of the recovered region were decreased in MIAT knockdown A549 and H1299 cells compared with the control (Figure [3A](#F3){ref-type="fig"}). Furthermore, a matrigel transwell assay demonstrated that decreasing MIAT expression could dose-dependently impede the invasion abilities of A549 and H1299 cells (Figure [3B](#F3){ref-type="fig"}) compared with control. These results indicate that knockdown of MIAT expression retarded cell migration and invasion motility in NSCLC cells.
{#F3}
MIAT silencing impaired A549 cell migration and invasion *in vivo* {#s2_4}
------------------------------------------------------------------
To validate the oncogenic efficiency of MIAT *in vivo*, A549 cells stably transfected with shMIAT or scramble were subcutaneously inoculated into the left flank (stable shMIAT cells) and right flank (scramble cells) of BALB/c athymic male nude mouse, respectively (*n* = 6). After 24 days, the tumors formed in the shMIAT group were substantially smaller than those in the scramble group (Figure [4A](#F4){ref-type="fig"} and [4B](#F4){ref-type="fig"}). Moreover, the tumor weight at the end of the experiment was lower in the shMIAT group (0.466 ± 0.021 g) compared with that in the scramble group (0.333 ± 0.051 g) (Figure [4C](#F4){ref-type="fig"}). QPCR analysis confirmed that the MIAT levels were lower in shMIAT tumor tissues than in scramble tumor tissues (Figure [4D](#F4){ref-type="fig"}). These findings indicate that *MIAT* knockdown would decelerate tumor growth *in vivo* by repressing cell proliferation and migration.
{#F4}
MIAT knockdown suppressed MMPs expression {#s2_5}
-----------------------------------------
Because the MIAT expression level is correlated with advanced stage and affects cell invasion, we further explored whether MIAT regulated epithelial--mesenchymal transition (EMT) or matrix metallopeptidases (MMPs) expression. The qRT-PCR results revealed that MIAT knockdown has no effect on EMT inducers such as TWIST1, SANI1, and ZEB1; however, MIAT knockdown significantly reduced MMP9 expression (*p* = 0.02) and has a trend of decreasing MMP2 (*p* = 0.07; Figure [5A](#F5){ref-type="fig"}) in A549 and H1299 cells. We then detected the activities of MMP2 and MMP9 through gelatin zymography. The data revealed that MIAT knockdown could reduce MMP9 expression but has no effects on MMP2 in A549 and H1299 cells (Figure [5B](#F5){ref-type="fig"}). We also observed that MMP9 but not MMP2 was overexpressed in tumor parts (mean dCT of tumor vs. normal tissue: 1.30 vs. 3.43, *p* \< 0.0001; Figure [5C](#F5){ref-type="fig"}), and that increased MMP9 in early and advanced stages in 60 paired NSCLC tissues was correlated with MIAT (Figure [5D](#F5){ref-type="fig"}). These results indicated that MMP9 might be a downstream gene that was regulated by MIAT to affect NSCLC migration and invasion.
{#F5}
MIAT was associated with MLL and epigenetically regulates MMP9 activity {#s2_6}
-----------------------------------------------------------------------
To investigate the potential mechanism of MIAT in regulating MMP9 in NSCLC cells, we first analysed the distribution of MIAT in cells. The cell fractional data revealed that MIAT was distributed in both the cytoplasm and nucleus; however, the ratio of MIAT in the nucleus was higher than that in the cytoplasm (Figure [6A](#F6){ref-type="fig"}). Previous studies have reported that lncRNAs could function in cooperation with chromatin-modifying enzymes to promote epigenetic activation or silencing of gene expression. Therefore, we performed the RIP assay to examine whether a physical interaction is present between histone modifiers and MIAT. The results revealed that MIAT could interact with H3K4 methyltransferase MLLs (activator complex) but not EZH2 (enhancer of zeste homolog 2 in polycomb group repressive complex) in A549 and H1299 cells (Figure [6B](#F6){ref-type="fig"}). We also performed an immunostaining combined with RNA-FISH experiment and observed that MIAT could colocalize with MLL in the nucleus (Figure [6C](#F6){ref-type="fig"}). To elucidate whether MLL could regulate MMP9 activity, we knockdown MLL expression in A549 and H1299 cells. inthen transfected 50 nM of siMLL into A549 and H1299 to elucidate whether MLL could affect the expression levels of MMP9. The data showed that the expressions of MLL and MMP9 were been silenced (Figure [6D](#F6){ref-type="fig"}). Therefore, to investigate whether MLL is involved in the regulation of MIAT on MMP9, we first designed three sets of primers of the MMP9 promoter region and found that MLL was bound to the sequences within 1634 bp upstream of the transcript start site (Figure [6E](#F6){ref-type="fig"}). To further address whether MIAT regulated MMP9 through MLL enrichment, we performed ChIP in the A549 and H1299 cell lines with MIAT knockdown. The results revealed that MIAT silencing reduced the binding activity of MLL and the status of H3K4me3 with the MMP9 promoters in A549 and H1299 cells (Figure [6F](#F6){ref-type="fig"} and [6G](#F6){ref-type="fig"}). These results indicated that MIAT interacted with MLL in the nucleus and was essential for MLL to regulate MMP9 activity through epigenetic regulation.
{#F6}
DISCUSSION {#s3}
==========
Many studies have reported that lncRNA dysregulation is associated with pathological and physiological processes in different human diseases. The expression levels of lncRNA are also associated with cancer development and progression, including NSCLC \[[@R25]--[@R27]\]. For example, lncRNA BANCR functions as a tumor suppressor in NSCLC \[[@R28]\], whereas HOTAIR and MALAT1 promote oncogenic functions in NSCLC \[[@R29], [@R30]\]. However, the roles of lncRNAs in NSCLC tumorigenesis are still unknown.
MIAT was first identified as a candidate gene for myocardial infarction \[[@R16]\]; it is abundantly expressed in the nervous system \[[@R31]\] and retinal tissue \[[@R32]\]. Recent studies have reported that MIAT participates in chronic lymphocytic leukaemias progression \[[@R23]\] and prostate cancer formation \[[@R24]\]; however, the underlying mechanism of MIAT in tumorigenesis remains unclear. We speculated that MIAT might be involved in NSCLC progression. In the NSCLC cohort, we observed that MIAT was upregulated in lung cancer tissues compared with the non-tumor tissues. In addition, MIAT expression level was significantly different in the advanced tumor stage. Because treatment failure and the poor prognosis of lung cancer are due to high metastasis and invasion, we further identified the biological role of MIAT in tumor progression. A loss-of-function assay demonstrated that MIAT silencing impaired cell proliferation, migration, and invasion *in vitro* and inhibited tumor formation *in vivo*.
To further elucidate the molecular mechanism through which MIAT contributes to invasion and metastasis in NSCLC, we investigated potential target proteins involved in cell motility and matrix invasion. During tumor metastasis, cancer cells lose their polarity and intercellular adhesions and then get invasive characteristics of mesenchymal cells through EMTs \[[@R33]\]. MMPs could degrade the proteins of the extracellular matrix and basement membrane to promote tumor metastasis \[[@R34]\]. Therefore, we determined whether any interaction was present between EMTs, MMPs, and MIAT. MIAT silencing had no effects on EMT transcriptional factors (TWIST1, SNAI1, and ZEB1), but repressed MMP2 and MMP9 expressions in A549 cells. We further determined the expression levels of MMP2 and MMP9 in our NSCLC cohort; the results revealed that the expression level of MMP9 but not MMP2 was correlated with MIAT to express highly in tumor tissue and advanced stage (Figure [1A, 1B](#F1){ref-type="fig"} and Figure [5C, 5D](#F5){ref-type="fig"}). MMP9 is a member of the MMP family. MMP9 is overexpressed in colorectal and lung tumor and is related to metastasis and invasion in the breast, upper urinary tract, and oral squamous cell tumor \[[@R35]--[@R38]\]. Our findings demonstrated that MIAT-mediated NSCLC cell migration, invasion, and metastasis suppression through MMP9.
Although several recent studies have indicated that MMP9 expression could also be regulated by some lncRNAs, such as BCRYN1 and MVIH \[[@R39], [@R40]\], the regulation mechanism remains unclear. Generally, lncRNAs regulate cancer cell phenotypes by interacting with specific RNA binding proteins and resulting in gene activation or repression through chromosome reprogramming, DNA methylation, RNA decay, and histone protein modification \[[@R41], [@R42]\]. Our RNA-IP experiment demonstrated that MIAT could interact with the histone methyltransferase MLL. MLL is a histone methyltransferase that mediates histone H3 lysine 4 and can catalyze H3K4 monomethylation, dimethylation, and trimethylation \[[@R43]\]. Abnormal methylation of H3K4 frequently occurs in cancer progression. A recent study also revealed that decreased H3K4me3 modification at the MMP9 promoter reduces MMP9 expression and inhibits tumor cell proliferation \[[@R44]\]. Moreover, lncRNAs regulated gene expression by mediating histone modifiers to the promoter of target genes \[[@R45]--[@R47]\]. Therefore, we further validated MIAT and MLL on the MMP9 promoter and found that MLL could bind on the MMP9 promoter and that MIAT silencing reduced the binding of MLL and H3K4me3 level with the MMP9 promoter. The hypothesis of the mechanism of MIAT on NSCLC is presented in Figure [7](#F7){ref-type="fig"}. These results indicated that MIAT might play crucial roles in the MLL-mediated activation of oncogenes in NSCLC.
{#F7}
In conclusion, our results clarified that MIAT was upregulated in NSCLC tumor tissues and was correlated with tumor advanced stage. MIAT knockdown inhibited cell proliferation, migration, and invasion in A549 and H1299 cells and inhibited tumorigenesis *in vivo.* Furthermore, MIAT-mediated oncogenic effects are partially due to the epigenetic silencing of MMP9 through the direct binding of MIAT with MLL. These findings indicate a role of MIAT-dependent histone H3K4 methylation in MMP9 transactivation and lung carcinogenesis and reinforce the notion that targeting the lung cancer epigenome may yield novel therapeutic solutions.
MATERIALS AND METHODS {#s4}
=====================
Patients and tissue samples {#s4_1}
---------------------------
Sixty paired NSCLC tissues (30 paired of adenocarcinoma and 30 paired of squamous) and adjacent non-tumor tissues from patients (37 males, 23 females, mean age 63.0, SD ± 12.6) who received surgical resection of NSCLC between 2006 and 2014 were obtained from the Bio-Bank of China Medical University Hospital (CMUH) after approval from CMUH\'s Institutional Research Ethics Committee (CMUH103-REC2-140), according to the Declaration of Helsinki guideline. None of the patients had received chemotherapy or radiotherapy prior to surgery. All surgical specimens were snap-frozen and stored in liquid nitrogen immediately after resection until total RNA extraction. All tumor and paired non-tumor tissues were confirmed by experienced pathologists, and the pathological stage, grade, and nodal status of the tissues were provided. Clinical and pathological characteristics were also collected for each patient. Informed written consent was obtained from all patients in this study.
Cell culture and transfection {#s4_2}
-----------------------------
A549 and H1299 cell lines were respectively cultured in DMEM and RPMI supplemented with 10% fetal bovine serum (10% FBS, Gibco), 100 U/ml penicillin, and 100 mg/ml streptomycin in humidified air at 37°C with 5% CO~2~. A549 and H1299 cells were transfected with various dosages of siRNA or negative control by using RNAimax Lipofectamine (Invitrogen, USA) according to the manufacturer\'s instructions. The siRNA oligonucleotides were synthesized by MDBio, Inc. The siRNA sequences of MIAT were as follows: 5′-ACUUCUUCGUAUGUUCGGCTT-3′ and a negative control (a scrambled matched %GC oligonucleotide). The siRNA sequences of MLL were as follows: 5′-GCUCUUUCCUAUUGGAUAUTT-3′ and a negative control (a scrambled matched %GC oligonucleotide).
Subcellular fractionation, total RNA extraction, and qRT-PCR analysis {#s4_3}
---------------------------------------------------------------------
The separation of the nuclear and cytosolic fractions of the A549 and H1299 cell lines was performed according to the protocol of the PARIS Kit (Life Technologies, Carlsbad, CA, USA) Total RNA was extracted from tissues or cultured cells with TRIzol reagent (Life Technologies, Scotland, UK, USA) according to the supplier\'s instructions. Two micrograms of RNA was reverse-transcribed into cDNA by using a high-capacity cDNA reverse transcriptase kit (Thermo Fisher Scientific-Applied Biosystems, Waltham, MA, USA). Quantitative PCR was performed using the Taqman assay and GAPDH mRNA was employed as an endogenous control for mRNA. Relative expression levels of the target genes were calculated as ratios normalized against GAPDH. The quantification of gene expression was performed by using the 2−ΔΔCt method. All primers were designed and synthesized by Genomics BioSci & Tech, Taipei, Taiwan. The following primer sequences were used: *MMP2*-forward: ccccaaaacggacaaagag, reverse: cttcagcacaaacaggttgc; *MMP9*-forward: cgcagacatcgtcatccagt, reverse: cgcagacatcgtcatccagt; *TWIST1*-forward: ggcatcactatggactttctctatt, reverse: ggccagtttgatcccagtatt; *SANI1-*forward: aggatctccaggctcgaaag, reverse: tcggatgtgcatcttgagg; and *ZEB1-*forward: aactgctgggaggatgacac, reverse: tcctgcttcatctgcctga.
Cell proliferation assay {#s4_4}
------------------------
Cell proliferation was assessed using a trypan blue exclusion assay. Cells were seeded in 60-mm culture dishes at a density of 1 × 10^5^ cells/dish and incubated for 24 h or 48 h. After incubation, cell number was determined using a trypan blue exclusion test with trypan blue (0.4%) purchased from Sigma Chemical Co.
Colony formation assay {#s4_5}
----------------------
A total of 10,000 control and siMIAT cells were placed in a 6-well plate and maintained in media containing 10% FBS; the medium was replaced every 3 days. After 14 days, cells were fixed with methanol and stained with 0.1% crystal violet. Viable colonies were manually counted. For each treatment group, wells were measured in triplicate.
Cell cycle analysis {#s4_6}
-------------------
Transfected A549 and H1299 cells were collected and fixed in 70% ethanol at −20°C overnight. Fixed cells were washed once with PBS and then labelled with propidium iodide (Sigma-Aldrich) in the presence of RNase A (Sigma-Aldrich) and Triton X-100 for 30 min in the dark. Cells were run on a FACSCanto flow cytometer (Becton-Dickinson, FL, NJ, USA). The percentages of the cells within each phase of the cell cycle were analysed using the ModFit LT program.
Western blot {#s4_7}
------------
Whole cell extracts were prepared from A549 and H1299 cells by adding RIPA lysis buffer (150 mM NaCl, 0.1% SDS, 0.5% sodium deoxycholate, 1% NP-40) (Sigma) with complete protease inhibitor cocktails (Sigma). Equal quantities of total protein samples were separated on 10% SDS-PAGE gels and transferred to PVDF membranes. Blots were incubated with primary antibody against Cyclin D3, cdk2 (Abcam) and β-actin (GeneTex) overnight at 4°C. After secondary antibody incubation, the electrochemiluminescence (ECL) kit (EMD Millipore, St. Charles, MO) was used to visualize protein signals. β-actin was used as internal control.
Wound healing scratch and transwell assays *in vitro* {#s4_8}
-----------------------------------------------------
A wound healing assay was used to assess the ability of cell migration, and appropriate A549 and H1299 cells were seeded into 24-well plates at a density that reached 95%--100% confluence as a monolayer. The monolayer was gently scratched across the centre of the well with a 200-μl plastic tip. The rate of closure was assessed through imaging with an inverted microscope (DMi1; Leica, Wetzlar, Germany). The migration movement throughout the wound area was examined and calculated using the free software 'TScratch'. For the invasion assay, 24-well transwell chambers with 8 mM pore size polycarbonate membranes were used. Approximately 1 × 10^5^ control or siMIAT cells were seeded into the upper chamber of the insert. After culturing the cells in the upper chamber for 24 h, they were carefully removed, and cells adhering to the underside of the membrane were stained with 0.1% crystal violet solution. The numbers of cells were counted under an inverted microscope (DMi1; Leica, Wetzlar, Germany). For each experimental group, the assay was performed in triplicate.
*In vivo* tumor formation {#s4_9}
-------------------------
BALB/c athymic nude mice (male, 4--6 weeks old) were purchased from National Laboratory Animal Breeding and Research Center, Taiwan. To establish a lung cancer xenograft model, 1 × 10^7^ scramble or shMIAT-A549 cells were suspended in 100 ml PBS and inoculated subcutaneously into the flanks of six nude mice (left: shMIAT; right: scramble). The following shRNA sequence was used for MIAT knockdown: 5′-GATCCCCGGACA GAGAATGCAAATAATTCAAGAG ATTATTTGCATTC TCTGTCCTTTTTA-3′. The tumor size was calculated by measuring length (L) and width (W) with callipers every 3 days. The tumor volumes were calculated using the formula (L × W^2^)/2. All animal experiments were performed in accordance with the guidelines set by the Institutional Animal Care and Use Committee (IACUC) of China Medical University (CMU). All animals were housed in the Laboratory Animal Center of CMU under a 12 h light/dark (08:00/20:00) cycle with free access to food and water. The
mice were sacrificed using CO~2~, and the tissues were subsequently harvested. All breeding and subsequent use of animals in this study, including sacrifice, was approved by the IACUC of CMU. The IACUC approval number was 102-203-N.
Gelatin zymography assay {#s4_10}
------------------------
Gelatin zymography was performed to determine the activity of MMP2 and MMP9. In brief, the protein in control or siMIAT cell medium were separated in 10% SDS-PAGE containing 3 mg/ml gelatin at 4°C. PAGE was then incubated at 37°C with incubation buffer (50 mM Tris-HCl pH 7.6, 10 mM CaCl~2~.2H~2~O, 50 mM NaCl) for 24 h. Gelatinolytic activities appeared as clear bands after the cells were stained with 0.25% Coomassie brilliant blue R-250.
RNA immunoprecipitation (RIP) {#s4_11}
-----------------------------
RNA immunoprecipitation (RIP) was performed using ChIP-IT (Active Motif, Carlsbad, CA, USA) according to the manufacturer\'s instructions. In brief, endogenous MLL and EZH2 complexes from the whole-cell extract were pulled down using anti-MLL1 (EMD Millipore, St. Charles, MO) and anti-EZH2 (Cell Signaling Technology, Danvers, MA, USA) antibody-coated beads. The beads were washed with wash buffer and eluted with elution buffer. The eluted samples were incubated with 0.5 mg/ml protease K to remove proteins. The isolate from the IP product was further analysed using qRT-PCR. The primers for detecting MIAT expression were as follows: forward: ctggagagggaggcatctaa and reverse: aactcatccccacccacac.
Immunofluorescence combined with RNA-FISH {#s4_12}
-----------------------------------------
Simultaneous protein and mRNA detection using immunofluorescence-combined single-molecule RNA fluorescence *in situ* hybridization (FISH) was performed as described previously \[[@R48]\]. The RNA-FISH probe primer were as follows: forward: tgactccctgaagatctcatcc and reverse: tgctaggaagctgttccagac. The PCR product of MIAT RNA was purified and labelled using Label IT Cy^®^3 nucleic acid labelling kit (Mirus Bio Corp., Madison, WI, USA). In brief, A549 cells were plated on glass coverslips in 6-well culture plates at a density of 10,000 cells/well. Cells were fixed for 10 min in 4% formaldehyde (Thermo Scientific, Rockford, IL, USA) in 1× RNase-free PBS at room temperature. Next, specimens were blocked and permeabilised for 60 min at room temperature in blocking buffer (1× RNase-free PBS, 1% acetylated BSA, 0.3% Triton X-100, and 2 mM vanadyl ribonucleoside complexes). Blocked specimens were incubated with antibodies diluted in blocking buffer. MLL protein was stained with anti-MLL1 (EMD Millipore, St. Charles, MO, USA) and Alexa Fluor 488-conjugated donkey anti-mouse antibody (Jackson ImmunoResearch, West Grove, PA, USA). Incubations with primary antibodies were performed overnight in the dark at 4°C and those with secondary antibodies for 90 min in the dark at room temperature in a humidifying chamber. The RNA-FISH probe were 2192 bps PCR product of MIAT RNA was purified and labelled by Label IT Cy^®^3 nucleic acid labelling kit (Mirus Bio Corp., Madison, WI). After postfixation (10 min in 4% methanol-free formaldehyde in 1× RNase-free PBS at room temperature), the RNA-FISH procedure was performed as described above. Finally, all samples were mounted onto slides in the Vectashield Mounting Medium with DAPI (Vector Laboratories, Burlingame, CA, USA), sealed with nail polish, and imaged using a Leica DMI6000B (AF7000 version) inverted widefield fluorescence microscope (Leica Microsystems, Wetzlar, Germany).
Chromatin immunoprecipitation (ChIP) {#s4_13}
------------------------------------
DNA ChIP assay was performed using ChIP-IT (Active Motif, Carlsbad, CA, USA) according to the manufacturer\'s instructions by using Anti-MLL1 (EMD Millipore, St. Charles, MO, USA), anti-EZH2 (Cell Signaling Technology) antibodies, and IgG. Three sets of primers were designed to amplify the MMP9 promoter region. P1 (−1563 to −1634)-forward: ggagatttggctgcatgg, reverse: gcaggatatgggggaaaataat; P2 (−893 to −966)-forward: cctagcagagcccattcctt, reverse: ccctgacagccttctttgac; and P3 (−207 to −288)-forward: cagtccacccttgtgctctt, reverse: ctaggtgtttgcccacctct.
Statistical analysis {#s4_14}
--------------------
All experimental data from three independent experiments were analyzed by GraphPad Prism version 5 (GraphPad Software Inc., La Jolla, California, USA) and results were expressed as mean ± SD (standard deviation, SD). The association between relative MIAT RNA expression levels and clinical parameters (age, gender, tumor size, lymph node metastasis and TNM stage) was analyzed using Fisher\'s exact test. Student *t*-test was conducted to analyze the *in vitro* and *in vivo* assays. *P* \< 0.05 was considered to indicate a statistically significant difference.
This work was supported by the grant to the Ministry of Science and Technology (NSC 99-2320-B-039-038-MY3, NSC 105-2811-B-039-038, MOST 106-2632-E-468-002, MOST 106-2221-E-468-018), National Health Research Institutes (NHRI-EX103-10326BI), Ministry of Health and Welfare (MOHW106-TDU-B-212-113004), China Medical University Hospital (DMR-104-101) and Asia University (ASIA-104-CMUH-22, ASIA-105-CMUH-15).
**CONFLICTS OF INTEREST**
The authors declare that there are no conflicts of interest.
|
{
"pile_set_name": "PubMed Central"
}
|
Shelf-life extension of semi-dried buckwheat noodles by the combination of aqueous ozone treatment and modified atmosphere packaging.
The present study investigated the combined effects of aqueous ozone treatment and modified atmosphere packaging (MAP) on prolonging the shelf-life of semi-dried buckwheat noodles [SBWN; moisture content (22.5±0.5%)] at 25°C. Firstly, the different concentrations of ozonated water were used to make SBWN. Subsequently, SBWN prepared with ozonated water were packaged under six different conditions and stored for 11days. Changes in microbial, chemical-physical, textural properties and sensorial qualities of SWBN were monitored during storage. Microbiological results indicated that adopting 2.21mg/L of ozonated water resulted in a 1.8 log10 CFU/g reduction of the initial microbial loads in SBWN. In addition, MAP suppressed the microbial growth with a concomitant reduction in the rates of acidification and quality deteriorations of SBWN. Finally, the shelf-life of sample packed under N2:CO2=30:70 was extended to 9days, meanwhile textural and sensorial characteristics were maintained during the whole storage period.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
How can I configure travis-ci such that my project builds with more than one version of a compiler?
Say, I want to build it with gcc-4.8, gcc-4.9, clang-3.4, clang-3.5 and clang-3.6.
I know how to build on both gcc and clang, but not on more than one version of them.
To give a little bit more context, my project is a C++ library and I want to ensure compatibility with those compilers.
|
{
"pile_set_name": "OpenWebText2"
}
|
KF26777 (2-(4-bromophenyl)-7,8-dihydro-4-propyl-1H-imidazo[2,1-i]purin-5(4H)-one dihydrochloride), a new potent and selective adenosine A3 receptor antagonist.
We investigated the biochemical and pharmacological properties of a new adenosine A(3) receptor antagonist, KF26777 (2-(4-bromophenyl)-7,8-dihydro-4-propyl-1H-imidazo[2,1-i]purin-5(4H)-one dihydrochloride). This compound was characterized using N(6)-(4-amino-3-iodobenzyl)adenosine-5'-N-methyluronamide ([125I]AB-MECA) or [35S]guanosine 5'-O-(3-thiotriphosphate) (GTPgammaS) binding to membranes from human embryonic kidney 293 (HEK293) cells expressing human adenosine A(3) receptors. KF26777 showed a K(i) value of 0.20+/-0.038 nM for human adenosine A(3) receptors labeled with [125I]AB-MECA and possessed 9000-, 2350- and 3100-fold selectivity vs. human adenosine A(1), A(2A) and A(2B) receptors, respectively. The inhibitory mode of binding was competitive. KF26777 inhibited the binding of [35S]GTPgammaS stimulated by 1 microM 2-chloro-N(6)-(3-iodobenzyl)adenosine-5'-N-methyluronamide (Cl-IB-MECA). The IC(50) value was 270+/-85 nM; the compound had no effect on basal activity. Dexamethasone treatment for HL-60 cells, human promyelocytic leukemia, up-regulated functional adenosine A(3) receptors expression, and resulted in the enhanced elevation of intracellular Ca(2+) concentration ([Ca(2+)](i)) via the adenosine A(3) receptor. KF26777 antagonized this [Ca(2+)](i) mobilization induced by Cl-IB-MECA, with a K(B) value of 0.42+/-0.14 nM. These results indicate that KF26777 is a highly potent and selective antagonist of the human adenosine A(3) receptor.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
// Copyright 2018 The Chromium Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.
#ifndef COMPONENTS_IMAGE_FETCHER_CORE_CACHE_IMAGE_METADATA_STORE_H_
#define COMPONENTS_IMAGE_FETCHER_CORE_CACHE_IMAGE_METADATA_STORE_H_
#include <string>
#include "base/time/time.h"
#include "components/image_fetcher/core/cache/image_store_types.h"
namespace image_fetcher {
// Interface for an object capable of saving/loading image metadata.
class ImageMetadataStore {
public:
virtual ~ImageMetadataStore() = default;
// Initialize this store. If calls are made to the class before the
// initialization has completed, they are ignored. Ignored requests won't do
// any meaningful work. It's the responsibility of the caller to check for
// initialization before calling.
virtual void Initialize(base::OnceClosure callback) = 0;
// Returns true if initialization has finished successfully, else false.
// While this is false, initialization may have already started.
virtual bool IsInitialized() = 0;
// Loads the image metadata for the |key|.
virtual void LoadImageMetadata(const std::string& key,
ImageMetadataCallback) = 0;
// Adds or updates the image metadata for the |key|. If metadata exists for an
// image and the |needs_transcoding| is still true, we don't need to update
// the existing metadata.
virtual void SaveImageMetadata(const std::string& key,
const size_t data_size,
bool needs_transcoding,
ExpirationInterval expiration_interval) = 0;
// Deletes the image metadata for the |key|.
virtual void DeleteImageMetadata(const std::string& key) = 0;
// Updates |last_used_time| for the given |key| if it exists.
virtual void UpdateImageMetadata(const std::string& key) = 0;
// Returns all the keys this store has.
virtual void GetAllKeys(KeysCallback callback) = 0;
// Returns the total size of what's in metadata for a given cache option,
// possibly incorrect.
virtual int64_t GetEstimatedSize(CacheOption cache_option) = 0;
// Deletes all metadata that's been cached before the boundary given as
// |expiration_time|.
void EvictImageMetadata(base::Time expiration_time, KeysCallback callback) {
EvictImageMetadata(expiration_time, /* Max size_t */ -1,
std::move(callback));
}
// Deletes all metadata that's been cached before the boundary given as
// |expiration_time|. Evicts other metadata until there are |bytes_left|
// in storage.
virtual void EvictImageMetadata(base::Time expiration_time,
const size_t bytes_left,
KeysCallback callback) = 0;
};
} // namespace image_fetcher
#endif // COMPONENTS_IMAGE_FETCHER_CORE_CACHE_IMAGE_METADATA_STORE_H_
|
{
"pile_set_name": "Github"
}
|
---
abstract: |
We consider the two dimensional shrinking target problem in the beta dynamical system for general $\beta>1$ and with the general error of approximations. Let $f, g$ be two positive continuous functions such that $f(x)\geq g(y)$ for all $x,y\in~[0,1]$. For any $x_0,y_0\in[0,1]$, define the shrinking target set $$\begin{aligned}
E(T_\beta, f,g)=\Big\{(x,y)\in [0,1]^2:|T_{\beta}^{n}x-&x_{0}|<e^{-S_nf(x)},\\ |T_{\beta}^{n}y-&y_{0}|< e^{-S_ng(y)}~~~\text{for infinitely many}~n\in \mathbb{N}\},\end{aligned}$$ where $S_nf(x)=\sum_{j=0}^{n-1}f(T_\beta^jx)$. We calculate the Hausdorff dimension of this set and prove that it is the solution to some pressure function. This represents the first result of this kind for the higher dimensional beta dynamical systems.
address:
- 'Mumtaz Hussain, Department of Mathematics and Statistics, La Trobe University, PoBox199, Bendigo 3552, Australia. '
- 'Weiliang Wang, School of Mathematics and Statistics, Huazhong University of Science and Technology, 430074 Wuhan, China'
author:
- Mumtaz Hussain
- Weiliang Wang
title: Higher dimensional shrinking target problem in beta dynamical systems
---
introduction
============
The study of the Diophantine properties of the distribution of orbits for a measure preserving dynamical system has received much attention recently. Let $T:X\to X$ be a measure preserving transformation of the system $(X,\mathcal{B},\mu)$ with a consistent metric $d$. If the transformation $T$ is ergodic with respect to the measure $\mu$, Poincare’s recurrence theorem implies that, for almost every $x\in X$, the orbit $\{T^nx\}_{n=0}^\infty$ returns to $X$ infinitely often. In other words, for any $x_0\in X,$ almost surely $$\liminf\limits_{n\rightarrow\infty} d(T^nx,x_0)=0.$$ Poincare’s recurrence theorem is qualitative in nature but it does motivates the study of the distribution of $T$-orbits of points in $X$ quantitatively. In other words, a natural motivation is to investigate *how fast the above liminf tends to zero?* To this end, the spotlight is on the size of the set $$D(T, \varphi):=\{x\in X: d(T^n x, x_0)<\varphi(n)~~\text{for infinitely many}~n\in \mathbb{N}\},$$ where $\varphi:\N\rightarrow \R_{\geq 0}$ is a positive function such that $\varphi(n)\rightarrow 0$ as $n\rightarrow \infty.$ The set $D(T,\varphi)$ can be viewed as the collection of points in $X$ whose $T$-orbit hits a shrinking target infinitely many times. The set $D(T,\varphi)$ is the dynamical analogue of the classical inhomogeneous well-approximable set $$W(\varphi):=\{x\in [0, 1): |x-p/q-x_0|<\varphi(q)~~\text{for infinitely many}~p/q\in \mathbb Q\}.$$ As one would expect the ‘size’ of both of these sets depend upon the nature of the function $\varphi$ i.e. how fast it is approaching to zero. The typical notion of size is in terms of Lebesgue measure but if the speed of approximation is rapid then, irrespective of the approximating function, the Lebesgue measure of the corresponding sets is zero (null-sets). For instance, if $\varphi(q)=|q|^{-\eta}$ then it follows from Schmidt’s theorem (1964) that the Lebesgue measure of the set $W(\varphi)$ is zero for any $\eta>2$. To distinguish between null-sets the notion of Hausdorff measure and dimension are appropriate tools in this study. Note that both of the sets $D(T, \varphi)$ and $W(\varphi)$ are limsup sets and estimation of the size of such sets, in general, is a difficult task. However, in the last two decades, a lot of work has been done in developing the measure theoretic frameworks to estimate the size of limsup sets, for example, the ubiquity framework [@BDV] and the mass transference principle [@BeresnevichVelani; @WWX; @HussainSimmons2] are two such powerful tools. As a consequence of these tools a complete metrical theory, in all dimensions, has been established for the set $W(\varphi)$. However, not much is known for the higher dimensional version of the set $D(T, \varphi)$.
Following the work of Hill and Velani [@HillVelani1; @HillVelani2], the Hausdorff dimension of the set $D(T, \varphi)$ has been determined for many dynamical systems, from the system of rational expanding maps on their Julia sets to conformal iterated function systems [@Urbanski11]. We refer the reader to [@CHW] for a comprehensive discussion regarding the Hausdorff dimension of various dynamical systems. In this paper, we confine ourself to the two dimensional shrinking target problem in the beta dynamical system with a general error of approximation.
For a real number $\beta>1$, define the transformation $T_\beta:[0,1]\to[0,1]$ by $$T_\beta: x\mapsto \beta x\bmod 1.$$ This map generates the $\beta$-dynamical system $([0,1], T_\beta)$. It is well known that $\beta$-expansion is a typical example of an expanding non-finite Markov system whose properties are reflected by the orbit of some critical point, in other words, it is not a subshift of finite type with mixing properties. This causes difficulties in studying the metrical questions related to $\beta$-expansions. General $\beta$-expansions have been widely studied in the literature, see for instance [@TanWang; @SeuretWang; @LB; @HussainWeiliang] and references therein.
We are interested in the Hausdorff dimension of the following higher dimensional dynamically defined limsup set. For any function $h$, let $S_nh$ denotes the ergodic sum of $h$ defined as $$S_nh(r)=h(r)+h(Tr)+\ldots+h(T^{n-1}r).$$ Let $f,g$ be two positive continuous function on $[0,1]$ with $f(x)\geq g(y)$ for all $x,y\in [0,1]$. Let $x_0, y_0$ be two fixed real numbers in the unit interval $(0, 1]$. Define $$\begin{aligned}
E(T_\beta, f,g)=\Big\{(x,y)\in [0,1]^2:|T_{\beta}^{n}x-&x_{0}|<e^{-S_nf(x)},\\ |T_{\beta}^{n}y-&y_{0}|< e^{-S_ng(y)}
\text{~~~for infinitely many}\ n\in \N\Big\}.\end{aligned}$$
The set $E(T_\beta, f,g)$ is the set of all points $(x, y)$ in the unit square such that the pair $\{T^{n}x, T^{n} y\}$ is in the shrinking ball $B\left ( (x_0, y_0); (e^{-S_nf(x)}, e^{-S_nf(y)}) \right)$ for infinitely many $n$. The rectangular ball shrink to zero at a rate governed by the ergodic sums $e^{-S_nf(x)}, e^{-S_nf(y)}$. The shrinking rates depend upon the points to be approximated and hence naturally provide better approximation properties than the conventional positive error function $\varphi(n)$. Dependence of the error functions on the points to be approximated significantly increases the level of difficulty.
The set $E(T_\beta, f,g)$ is the dynamical analogue of the following two dimensional classical inhomogeneous simultaneous Diophantine approximation set;
$$\begin{aligned}
W(\varphi_1, \varphi_2)=\Big\{(x,y)\in [0,1]^2:|x-&p_1/q-x_0|<\varphi_1(q),|y-p_2/q-y_0|< \varphi_2(q)\\
& \text{~~~for infinitely many}\ (p_1, p_2, q)\in \mathbb Z^2\times\N\Big\}.\end{aligned}$$
Where both $\varphi_1, \varphi_2$ are positive functions tending to zero as $q$ tends to infinity. A complete metric theory for this set has already been established some time ago. In particular, the Lebesgue measure of the set $W(\varphi_1, \varphi_2)$ has been established in [@HussainYusupova2], the Hausdorff measure for $W(\varphi, \varphi)$ in [@Bugeaud_Glasgow] and the Hausdorff measure for $W(\varphi_1, \varphi_2)$ follows from [@HussainYusupova1]. However, hardly anything is known for the set $E(T_\beta, f,g)$. We remedy this situation and prove the following theorem.
\[t2\] Let $f,g$ be two continuous functions on $[0,1]$ with $f(x)\geq g(y)$ for all $x,y\in [0,1]$. Then $${\dim_{\mathrm H}}E(T_\beta, f,g)=\min\{s_1,s_2\},$$ where $$\begin{aligned}
s_1&=\inf\{s\geq 0: P(f-s(\log\beta+f))+P(-g)\leq 0\}, \\ s_2&=\inf\{s\geq 0: P(-s(\log\beta+g))+\log\beta\leq 0\}.\end{aligned}$$
Here the notation $P(\cdot)$ stands for the pressure function for the $\beta$-dynamical system associated to continuous potentials $f$ and $g$. To keep the introductory section short, we formally give the definition of pressure function in section \[pre\]. The reason that the Hausdorff dimension is in terms of the pressure function is because of the dynamical nature of the set $E(T_\beta, f, g)$. For the detailed analysis of the properties of the pressure function, ergodic sums for general dynamical systems we refer the reader to Chapter 9 of the book [@Walterbook].
The proof of this theorem splits into two parts: establishing the upper bound and then the lower bound. Proving the upper bound is reasonably straightforward by simply using the natural cover of the set. However, establishing the lower bound is challenging and the main substance of this paper. Actually, the main obstacle in determining the metrical properties of general $\beta$-expansions lies in the difficulty of estimating the length of a general cylinders and, since we are dealing with two dimensional settings, as a consequence area of the cross product of general cylinders. As far as the Hausdorff dimension is concerned, one does not need to take all points into consideration; instead, one may choose a subset of points with regular properties to approximate the set in question. This argument, in turn require some continuity of the dimensional number, when the system is approximated by its subsystem.
The paper is organised as follows. Section \[pre\] is devoted to recalling some elementary properties of $\beta$-expansions. Short proofs are also given when we could not find any reference. Definitions and some properties of the pressure function are stated in this section as well. In section \[upperbound\], we prove the upper bound of the Theorem \[t2\]. In section \[lowerbound\], we prove the lower bound of Theorem \[t2\] and since this carries the main weightage we subdivide this section into several subsections.
Preliminaries {#pre}
=============
We begin with a brief account on some basic properties of $\beta$-expansions and fixing some notation. We then state and prove two propositions which will give the covering and packing properties.
The $\beta$-expansion of real numbers was first introduced by Rényi [@Renyi], which is given by the following algorithm. For any $\beta>1$, let $$\label{e1}
T_{\beta}(0):=0,~~ T_{\beta}(x)=\beta x-\lfloor\beta x\rfloor, x\in[0,1),$$ where $\lfloor\xi\rfloor$ is the integer part of $\xi\in \mathbb{R}$. By taking $$\epsilon_{n}(x,\beta)=\lfloor\beta T_{\beta}^{n-1}x\rfloor\in \mathbb{N}$$ recursively for each $n\geq 1,$ every $x\in[0,1)$ can be uniquely expanded into a finite or an infinite sequence $$\label{e2}
x=\frac{\epsilon_{1}(x,\beta)}{\beta}+\frac{\epsilon_{2}(x,\beta)}{\beta^2}+\cdots+\frac{\epsilon_{n}(x,\beta)}{\beta^n}+
\frac{T_{\beta}^n x}{\beta^n},$$ which is called the $\beta$-expansion of $x$ and the sequence $\{\epsilon_{n}(x,\beta)\}_{n\geq1}$ is called the digit sequence of $x.$ We also write the $\beta$-expansion of $x$ as $$\epsilon(x,\beta)=\big(\epsilon_{1}(x,\beta),\cdots,\epsilon_{n}(x,\beta),\cdots\big).$$ The system $([0,1],T_{\beta})$ is called the *$\beta$-dynamical system* or just the *$\beta$-system.*
A finite or an infinite sequence $(w_{1},w_{2},\cdots)$ is said to be admissible $(\text{with respect to the base}~\beta),$ if there exists an $x\in[0,1)$ such that the digit sequence of $x$ equals $(w_{1},w_{2},\cdots).$
Denote by $\Sigma_{\beta}^n$ the collection of all admissible sequences of length $n$ and by $\Sigma_{\beta}$ that of all infinite admissible sequences.
Let us now turn to the infinite $\beta$-expansion of $1$, which plays an important role in the study of $\beta$-expansion. Applying algorithm $(\ref{e1})$ to the number $x=1$, then the number $1$ can be expanded into a series, denoted by $$1=\frac{\epsilon_{1}(1,\beta)}{\beta}+\frac{\epsilon_{2}(1,\beta)}{\beta^2}+\cdots+\frac{\epsilon_{n}(1,\beta)}{\beta^n}+
\cdots.$$
If the above series is finite, i.e. there exists $m\geq1$ such that $\epsilon_{m}(1,\beta)\neq 0$ but $\epsilon_{n}(1,\beta)=0$ for $n>m$, then $\beta$ is called a simple Parry number. In this case, we write $$\epsilon^*(1,\beta):=(\epsilon_{1}^{*}(\beta),\epsilon_{2}^{*}(\beta),\cdots)=(\epsilon_{1}(1,\beta),\cdots,\epsilon_{m-1}(1,\beta),
\epsilon_{m}(1,\beta)-1)^{\infty},$$ where $(w)^\infty$ denotes the periodic sequence $(w,w,w,\cdots).$ If $\beta$ is not a simple Parry number, we write $$\epsilon^*(1,\beta):=(\epsilon_{1}^{*}(\beta),\epsilon_{2}^{*}(\beta),\cdots)=(\epsilon_{1}(1,\beta),\epsilon_{2}(1,\beta),
\cdots).$$
In both cases, the sequence $(\epsilon_{1}^{*}(\beta),\epsilon_{2}^{*}(\beta),\cdots)$ is called the infinite $\beta$-expansion of $1$ and we always have that $$\label{e3}
1=\frac{\epsilon_{1}^*(\beta)}{\beta}+\frac{\epsilon_{2}^*(\beta)}{\beta^2}+\cdots+\frac{\epsilon_{n}^*(\beta)}{\beta^n}+
\cdots.$$
The lexicographical order $\prec$ between the infinite sequences is defined as follows: $$w=(w_{1},w_{2},\cdots,w_{n},\cdots)\prec w'=(w_{1}',w_{2}',\cdots,w_{n}',\cdots)$$ if there exists $k\geq1$ such that $w_{j}=w_{j}'$ for $1\leq j<k$, while $w_{k}<w_{k}'.$ The notation $w\preceq w'$ means that $w\prec w'$ or $w=w'.$ This ordering can be extended to finite blocks by identifying a finite block $(w_{1},w_2,\cdots,w_n)$ with the sequence $(w_{1},w_2,\cdots,w_n,0,0,\cdots)$.
The following result due to Parry [@Parry] is a criterion for the admissibility of a sequence.
\[le1\] Let $\beta>1$ be a real number. Then a non-negative integer sequence $\epsilon=(\epsilon_1,\epsilon_2,\cdots)$ is admissible if and only if, for any $k\geq 1$, $$(\epsilon_k,\epsilon_{k+1},\cdots)\prec(\epsilon_1^*(\beta),\epsilon_2^*(\beta),\cdots).$$
The following result of Rényi implies that the dynamical system $([0,1],T_\beta)$ admits $\log\beta$ as its topological entropy.
\[le2\] Let $\beta>1.$ For any $n\geq 1,$ $$\beta^{n}\leq\#\Sigma_{\beta}^n\leq\frac{\beta^{n+1}}{\beta-1},$$ where $\#$ denotes the cardinality of a finite set.
It is clear from this lemma that $$\lim_{n\to\infty}\frac{\log\left(\#\Sigma_{\beta}^n\right)}{n}=\log\beta.$$ For any $(\epsilon_1,\cdots,\epsilon_n)\in \Sigma_{\beta}^n,$ call $$I_{n}(\epsilon_1,\cdots,\epsilon_n):=\{x\in[0,1),\epsilon_j(x,\beta)=\epsilon_j,1\leq j\leq n\}$$ an $n$-th order cylinder $(\text{with respect to the base}~\beta)$. It is a left-closed and right-open interval with the left endpoint $$\frac{\epsilon_1}{\beta}+\frac{\epsilon_2}{\beta^2}+\cdots+\frac{\epsilon_n}{\beta^n}$$ and of length $$|I_n(\epsilon_1,\cdots,\epsilon_n)|\leq\frac{1}{\beta^n}.$$ Here and throughout the paper, we use $|\cdot|$ to denote the length of an interval. Note that the unit interval can be naturally partitioned into a disjoint union of cylinders; that is for any $n\geq 1$, $$\label{e4}[0,1]=\bigcup\limits_{(\epsilon_1,\cdots,\epsilon_n)\in\Sigma_{\beta}^n}
I_{n}(\epsilon_1,\cdots,\epsilon_n).$$ One difficulty in studying the metric properties of $\beta$-expansion is that the length of a cylinder is not regular. It may happen that $|I_n(\epsilon_1,\cdots, \epsilon_n)|\ll \beta^{-n}$. The following notation plays an important role to bypass this difficulty.
A cylinder $I_n(\epsilon_1,\cdots,\epsilon_n)$ is called full if it has maximal length, i.e. if $$|I_n(\epsilon_1,\cdots,\epsilon_n)|=\frac{1}{\beta^n}.$$ Correspondingly, we also call the word $(\epsilon_1,\cdots,\epsilon_n)$, defining the full cylinder $I_n(\epsilon_1,\cdots,\epsilon_n)$, a full word.
Next, we collect some properties about the distribution of full cylinders.
\[le4\] An $n$-th order cylinder $I_{n}(\epsilon_{1}\cdots\epsilon_{n})$ is full, if and only if for any admissible sequence $(\epsilon_{1}',\epsilon_{2}',\cdots,\epsilon_{m}')\in\Sigma_{\beta}^m$ with $m\geq 1$, $$(\epsilon_{1}\cdots\epsilon_{n}, \epsilon_{1}',\epsilon_{2}',\cdots,\epsilon_{m}')\in\Sigma_{\beta}^{n+m}.$$ Moreover $$|I_{n+m}(\epsilon_{1},\cdots,\epsilon_{n},\epsilon_{1}',\cdots,\epsilon_{m}')|=
|I_{n}(\epsilon_{1},\cdots,\epsilon_{n})|\cdot|I_{m}(\epsilon_{1}',\cdots,\epsilon_{m}')|.$$ So, for any two full cylinders $I_{n}(\epsilon_{1}\cdots\epsilon_{n}),~ I_{m}(\epsilon_{1}',\epsilon_{2}',\cdots,\epsilon_{m}')$, the cylinder $$I_{n+m}(\epsilon_{1},\cdots,\epsilon_{n},\epsilon_{1}',\cdots,\epsilon_{m}')$$ is also full.
\[le3\] For $n\geq 1$, among every $n+1$ consecutive cylinders of order $n$, there exists at least one full cylinder.
As a consequence, one has the following relationship between balls and cylinders.
\[p1\]Let $J$ be an interval of length ${\beta}^{-l}$ with $l\geq 1$. Then it can be covered by at most $2(l+1)$ cylinders of order $l$.
By Lemma \[le3\], among any $2(l+1)$ consecutive cylinders of order $l$, there are at least $2$ full cylinders. So the total length of these intervals is larger than $2{\beta}^{-l}$. Thus $J$ can be covered by at most $2(l+1)$ cylinders of order $l$.
The following result may have an independent interest.
\[p2\] Fix $0<\epsilon<1$. Let $~n_0$ be an integer such that $2n^2\beta<{\beta}^{(n-1)\epsilon}$ for all $n\ge n_0$. Let $J\subset [0,1]$ be an interval of length $r$ with $0<r<2n_{0}\beta^{-n_0}$. Then inside $J$, there exists a full cylinder $I_n$ satisfying $$r\geq|I_n|>r^{1+\epsilon}.$$
Let $n>n_0$ be the integer such that $$2n\beta^{-n}\leq r<2(n-1)\beta^{-n+1}.$$ Since every cylinder of order $n$ is of length at most $\beta^{-n}$, the interval $J$ contains at least $2n-2\geq n+1$ consecutive cylinders of order $n$. Thus, by Lemma \[le3\], it contains a full cylinder of order $n$ and we denote such a cylinder by $I_n$. By the choice of $n_0$, we have $$r\geq|I_n|=\beta^{-n}>\Big(2(n-1)(\beta^{-n+1})\Big)^{1+\epsilon}>r^{1+\epsilon}.$$ This completes the proof.
Now we define a sequence of numbers $\beta_N$ approximating $\beta$ from below. For any $N$ with $\epsilon_N^*(\beta)\geq1,$ define $\beta_N$ to be the unique real solution to the algebraic equation $$\label{g1}
1=\frac{\epsilon_{1}^*(\beta)}{\beta_N}+\frac{\epsilon_{2}^*(\beta)}{\beta_N^2}+\cdots+\frac{\epsilon_{N}^*(\beta)}{\beta_N^N}.$$ Then $\beta_N$ approximates $\beta$ frow below and the $\beta_N$-expansion of the unity is $$(\epsilon_{1}^*(\beta),\cdots,\epsilon_{N-1}^*(\beta),\epsilon_{N}^*(\beta)-1)^{\infty}.$$
More importantly, by the criterion of admissible sequence, we have, for any $(\epsilon_1,\cdots,\epsilon_n)\in \Sigma_{\beta_N}^n$ and $(\epsilon_1',\cdots,\epsilon_m')\in \Sigma_{\beta_N}^m$, that $$\label{g2}
(\epsilon_1,\cdots,\epsilon_n,0^N,\epsilon_1',\cdots,\epsilon_m')\in\Sigma_{\beta_N}^{n+N+m},$$ where $0^N$ means a zero word of length $N$.
From the assertion $(\ref{g2})$, we get the following proposition.
For any $(\epsilon_1,\cdots,\epsilon_n)\in \Sigma_{\beta_N}^n$, $I_{n+N}(\epsilon_1,\cdots,\epsilon_n,0^N)$ is a full cylinder. So, $$\frac{1}{\beta^{n+N}}\leq|I_{n}(\epsilon_1,\cdots,\epsilon_n)|\leq\frac{1}{\beta^{n}}.$$
We end this section with a definition of the pressure function for $\beta$-dynamical system associated to some continuous potential $g$. The readers are referred to [@Walters] for more details. $$\label{g3}
P(g, T_\beta):=\lim\limits_{n\rightarrow \infty}\frac{1}{n}\log\sum\limits_{(\epsilon_1,\cdots,\epsilon_n)\in\Sigma_\beta^n}
\sup\limits_{y\in I_n(\epsilon_1,\cdots,\epsilon_n)}e^{S_ng(y)},$$ where $S_ng(y)$ denotes the ergodic sum $\sum_{j=0}^{n-1}g(T^j_\beta y)$. Since $g$ is continuous, hence the limit does not depend upon the choice of $y$. The existence of the limit follows from the subadditivity: $$\log\sum\limits_{(\epsilon_1,\cdots,\epsilon_n, \epsilon_1^\prime,\cdots,\epsilon_m^\prime)\in\Sigma_\beta^{n+m}}
e^{S_{n+m}g(y)}\leq \log\sum\limits_{(\epsilon_1,\cdots,\epsilon_n)\in\Sigma_\beta^{n}}
e^{S_{n}g(y)}+\log\sum\limits_{(\epsilon_1^\prime,\cdots,\epsilon_m^\prime)\in\Sigma_\beta^{m}}
e^{S_{n}g(y)}.$$
Proof of Theorem \[t2\]: the upper bound {#upperbound}
========================================
As is typical in determining the Hausdorff dimension of a set; we split the proof of Theorem $\ref{t2}$ into two parts: the upper bound and the lower bound.
For any $U=(\epsilon_1,\cdots\epsilon_n)\in\Sigma_\beta^n$ and $W=(\omega_1,\cdots,\omega_n)\in\Sigma_\beta^n,$ we always take $$x^*=\frac{\epsilon_{1}}{\beta}+\frac{\epsilon_{2}}{\beta^{2}}+\cdots+\frac{\epsilon_{n}}{\beta^{n}}$$ to be the left endpoint of $I_n(U)$ and $$y^*=\frac{\omega_{1}}{\beta}+\frac{\omega_{2}}{\beta^{2}}+\cdots+\frac{\omega_{n}}{\beta^{n}}$$ to be the left endpoint of $I_n(W)$.
Instead of directly considering the set $E(T_\beta,f,g)$, we will consider a closely related lim sup set $$\overline{E}(T_\beta,f,g)=\bigcap_{N=1}^{\infty}\bigcup_{n=N}^{\infty}\bigcup_{U,W\in \Sigma_{\beta}^{n}}J_n(U)\times J_n(W),$$ where $$\begin{aligned}
J_n(U)&=\{x\in[0,1]:|T_\beta^nx-x_0|<e^{-S_nf(x^*)}\},\\
J_n(W)&=\{y\in[0,1]:|T_\beta^ny-y_0|<e^{-S_ng(y^*)}\}.
\end{aligned}$$ In the sequel it will be clear that the set $\overline{E}(T_\beta,f,g)$ is easier to handle. Since $f$ and $g$ are continuous functions, for any $\delta>0$ and $n$ large enough, we have$$|S_nf(x)-S_nf(x^*)|<n\delta,\quad |S_ng(y)-S_ng(y^*)|<n\delta.$$ Thus we have $$\overline{E}(T_\beta, f+\delta,g+\delta)\subset E(T_\beta,f,g)\subset \overline{E}(T_\beta, f-\delta,g-\delta).$$ Therefore, to calculate the Hausdorff dimension of the set $E(T_\beta,f,g)$, it is sufficient to determine the Hausdorff dimension of $\overline{E}(T_\beta,f,g)$.
The length of $J_n(U)$ satisfies $$|J_n(U)|\leq2\beta^{-n}e^{-S_nf(x^*)},$$ since, for every $x\in J_n(U)$, we have $$|x-(\frac{\epsilon_1}{\beta}+\cdots+\frac{\epsilon_n+x_0}{\beta^n})|=\frac{|T_\beta^nx-x_0|}{\beta^n}<\beta^{-n}e^{-S_nf(x^*)}.$$ Similarly, $$|J_n(W)|\leq2\beta^{-n}e^{-S_nf(y^*)}.$$ So, $\overline{E}(T_\beta,f,g)$ is a $\limsup$ set defined by a collection of rectangles. There are two ways to cover a single rectangle $J_n(U)\times J_n(W)$ as follows.
Covering by shorter side length {#sectionshorter}
-------------------------------
Recall that $f(x)\geq g(y)$ for all $x, y\in [0, 1]$. This implies that the length of $J_n(U)$ is shorter than the length of $J_n(W)$. Then the rectangle $J_n(U)\times J_n(W)$ can be covered by $$\frac{\beta^{-n}e^{-S_ng(y^*)}}{\beta^{-n}e^{-S_nf(x^*)}}=\frac{e^{S_nf(x^*)}}{e^{S_ng(y^*)}}$$ many balls of side length $\beta^{-n}e^{-S_nf(x^*)}.$
Since for each $N$, $$\overline{E}(T_\beta,f,g)\subseteq\bigcup_{n=N}^{\infty}\bigcup_{U,W\in \Sigma_{\beta}^{n}}J_n(U)\times J_n(W),$$ therefore, the $s$-dimensional Hausdorff measure $\H^s$ of $\overline{E}(T_\beta,f,g)$ can be estimated as $$\H^s\Big(\overline{E}(T_\beta,f,g)\Big)\le \liminf_{N\to\infty}\sum_{n=N}^{\infty}\sum_{U,W\in \Sigma_{\beta}^n}
\frac{e^{S_nf(x^*)}}{e^{S_ng(y^*)}}\Big(\frac{1}{\beta^ne^{S_nf(x^*)}}\Big)^s.$$
Define $$s_1=\inf\{s\geq 0: P(f-s(\log\beta+f))+P(-g)\leq 0\}.$$ Then from the definition of the pressure function , it is clear that
$$P(f-s(\log\beta+f))+P(-g)\leq 0 \quad \iff \quad \sum_{n=1}^{\infty} \sum_{U,W\in \Sigma_{\beta}^n}
\frac{e^{S_nf(x^*)}}{e^{S_ng(y^*)}}\Big(\frac{1}{\beta^ne^{S_nf(x^*)}}\Big)^s<\infty.$$
Hence, for any $s>s_1$
$$\H^s\Big(\overline{E}(T_\beta,f,g)\Big)= 0.$$ Hence it follows that ${\dim_{\mathrm H}}(\overline{E}(T_\beta,f,g))\leq s_1.$
Covering by longer side length {#sectionlonger}
------------------------------
From the previous subsection (§\[sectionshorter\]), it is clear that only one ball of side length $\beta^{-n}e^{-S_ng(y^*)}$ is needed to cover the rectangle $J_n(U)\times J_n(W)$. Hence, in this case, the $s$-dimensional Hausdorff measure $\H^s$ of $\overline{E}(T_\beta,f,g)$ can be estimated as
$$\mathcal{H}^s(\overline{E}(T_\beta,f,g))\leq\liminf\limits_{N\rightarrow\infty}\sum_{n=N}^{\infty}\sum_{U,W\in \Sigma_{\beta}^n}\Big(
\frac{1}{\beta^{n}e^{S_ng(y^*)}}\Big)^s.$$ Define $$s_2=\inf\{s\geq 0: P(-s(\log\beta+g))+\log\beta\leq 0\}.$$Then, from the definition of pressure function and Hausdorff measure, it follows that, for any $s>s_2$, $\H^s\Big(\overline{E}(T_\beta,f,g)\Big)= 0.$ Hence, $${\dim_{\mathrm H}}(\overline{E}(T_\beta,f,g))\leq s_2.$$
Completing the upper bound proof
--------------------------------
Finally to complete the proof, we need to show that if $s_0=\min\{s_1,s_2\}$ then we have that $${\dim_{\mathrm H}}\overline{E}(T_\beta,f,g)\leq s_0.$$
One may argue that for different $n$, the most appropriate cover of $J_n(U)\times J_n(W)$ may be different, so it may be better to consider the minimum of the two covers for every $n$. This leads to another $s$-dimension Hausdorff measure of $E$ given as: $$\mathcal{H}^s( \overline{E}(T_\beta,f,g))\leq\liminf\limits_{N\rightarrow\infty}\sum_{n=N}^{\infty}\sum_{U,W\in \Sigma_{\beta}^n}\min\left\{\frac{e^{S_nf(x^*)}}{e^{S_ng(y^*)}}\Big(
\frac{1}{\beta^{n}e^{S_nf(x^*)}}\Big)^s,\Big
(\frac{1}{\beta^{n}e^{S_ng(y^*)}}\Big)^s\right\}.$$ Then an upper bound of the dimension of $ \overline{E}(T_\beta,f,g)$ is related to the convergence of the series $$\label{f7}
\sum_{n=1}^{\infty}\sum_{U,W\in \Sigma_{\beta}^n}\min\left\{\frac{e^{S_nf(x^*)}}{e^{S_ng(y^*)}}\Big(
\frac{1}{\beta^{n}e^{S_nf(x^*)}}\Big)^s,\Big
(\frac{1}{\beta^{n}e^{S_ng(y^*)}}\Big)^s\right\}.$$ So, we can define $$s_0^{'}=\inf\left\{s\geq0:\sum_{n=1}^{\infty}\sum_{U,W\in \Sigma_{\beta}^n}\min\left\{\frac{e^{S_nf(x^*)}}{e^{S_ng(y^*)}}\Big(
\frac{1}{\beta^{n}e^{S_nf(x^*)}}\Big)^s,\Big
(\frac{1}{\beta^{n}e^{S_ng(y^*)}}\Big)^s\right\}<\infty\right\},$$ and it turns out that, actually, $s_0^{'}$ is the same as $s_0$ as the following proposition demonstrates.
$s_0=s_0^{'}$
It can be readily verified that for any $s<s_0^{'}$, both the series
$$\label{sum1}
\sum_{n=N}^{\infty}\sum_{U,W\in \Sigma_{\beta}^n}
\frac{e^{S_nf(x^*)}}{e^{S_ng(y^*)}}\Big(\frac{1}{\beta^ne^{S_nf(x^*)}}\Big)^s,$$
$$\label{sum2}
\sum_{n=1}^{\infty}\sum_{U,W\in \Sigma_{\beta}^n}\Big(
\frac{1}{\beta^{n}e^{S_ng(y^*)}}\Big)^s$$
diverges. Hence $s_0^{'}\leq s_0. $
To prove the reverse inequality, we split the proof into two cases; $s_0^{'}<1$ or $s_0^{'}\geq1.$
If $s_0^{'}<1$ then for any $s_0^{'}<s<1$, the series (\[f7\]) converges. However, in this case, it is clear that $$\min\left\{\frac{e^{S_nf(x^*)}}{e^{S_ng(y^*)}}\Big(
\frac{1}{\beta^{n}e^{S_nf(x^*)}}\Big)^s,\Big
(\frac{1}{\beta^{n}e^{S_ng(y^*)}}\Big)^s\right\}=\Big(\frac{1}{\beta^{n}e^{S_ng(y^*)}}\Big)^s.$$ So, the series (\[sum2\]) converges. Thus $s_2\leq s.$ This shows that $\min\{s_1,s_2\}\leq s_0^{'}.$
Now if $s_0^{'}\geq1$, then for any $s>s_0^{'}\geq1,$ the series (\[f7\]) converges. However, in this case, it is clear that $$\min\left\{\frac{e^{S_nf(x^*)}}{e^{S_ng(y^*)}}\Big(
\frac{1}{\beta^{n}e^{S_nf(x^*)}}\Big)^s,\Big
(\frac{1}{\beta^{n}e^{S_ng(y^*)}}\Big)^s\right\}=\frac{e^{S_nf(x^*)}}{e^{S_ng(y^*)}}\Big(
\frac{1}{\beta^{n}e^{S_nf(x^*)}}\Big)^s.$$ So, the series (\[sum1\]) converges. Thus $s_1\leq s.$ This shows that $\min\{s_1,s_2\}\leq s_0^{'}.$
Theorem \[t2\]: The lower bound {#lowerbound}
================================
It should be clear from the previous section that proving the upper bound requires only a suitable covering of the set $\overline{E}(T_\beta,f,g)$. However, in contrast, proving the lower bound is a challenging task, requiring all possible coverings to be considered and, therefore, represents the main problem in metric Diophantine approximation (in various settings). The following principle commonly known as the Mass Distribution Principle [@Falconer_book] has been used frequently for this purpose.
\[mdp\] Let $E$ be a Borel measurable set in $R^d$ and $\mu$ be a Borel measure with $\mu(E)>0$. Assume that there exist two positive constant $c,\delta$ such that, for any set $U$ with diameter $|U|$ less than $\delta$, $\mu(U)\leq c |U|^s$, then ${\dim_{\mathrm H}}E\geq s$.
Specifically, the mass distribution principle replaces the consideration of all coverings by the construction of a particular measure $\mu$ and it is typically deployed in two steps:
- construct a suitable Cantor subset $\mathcal F_\infty$ of $\overline{E}(T_\beta,f,g)$ and a probability measure $\mu$ supported on $\mathcal F_\infty$,
- show that for any fixed $c>0$, $\mu$ satisfies the condition that for any measurable set $U$ of sufficiently small diameter, $\mu (U)\leq c |U|^s$.
If this can be done, then by the mass distribution principle, it follows that $${\dim_{\mathrm H}}(\overline{E}(T_\beta,f,g))\geq {\dim_{\mathrm H}}(\mathcal F_\infty)\geq s.$$
The main intricate and substantive part of this entire process is the construction of a suitable Cantor type subset $\mathcal F_\infty$ which supports a probability measure $\mu$. In the remainder of this paper, we will construct a suitable Cantor type subset of the set $\overline{E}(T_\beta,f,g)$ and demonstrate that it satisfies the mass distribution principle.
Construction of the Cantor subset. {#construction-of-the-cantor-subset. .unnumbered}
----------------------------------
We construct the Cantor subset $\mathcal F_\infty$ iteratively. Start by fixing an $\epsilon>0$ and assume that $f(x)\geq(1+\epsilon)g(y)\geq g(y)$ for all $x,y\in[0,1].$ We construct a Cantor subset level by level and note that each level depends on its predecessor. Choose a rapidly increasing subsequence $\{m_k\}_{k\geq 1}$ of positive integers with $m_1$ large enough.
Level 1 of the Cantor set.
--------------------------
Let $n_1=m_1.$ For any $U_1,W_1\in \Sigma_\beta^{n_1}$ ending with the zero word of order $N$, i.e. $0^N.$ Let $x_1^*\in I_{n_1}(U_1), ~y_1^*\in I_{n_1}(W_1).$ From Proposition \[p2\], it follows that there are two full cylinders $I_{k_1}(K_1), I_{l_1}(L_1)$ such that $$\begin{aligned}
I_{k_1}(K_1)&\subset B\Big(x_0,e^{-S_{n_1}f(x_1^*)}\Big), \\ I_{l_1}(L_1)& \subset B\Big(y_0,e^{-S_{n_1}g(y_1^*)}\Big), \end{aligned}$$ and $$e^{-S_{n_1}f(x_1^*)}>\beta^{-k_1}>\Big(e^{-S_{n_1}f(x_1^*)}\Big)^{1+\epsilon},$$ $$e^{-S_{n_1}g(y_1^*)}>\beta^{-l_1}>\Big(e^{-S_{n_1}g(y_1^*)}\Big)^{1+\epsilon}=e^{-S_{n_1}(1+\epsilon)g(y_1^*)}.$$
So, we get a subset $I_{n_1+k_1}(U_1,K_1)\times I_{n_1+l_1}(W_1,L_1)$ of $J_{n_1}(U_1)\times J_{n_1}(W_1)$. Since $f(x)\geq (1+\epsilon)g(y)$ for all $x,y\in [0,1],$ then $k_1\geq l_1.$ It should be noted that $K_1$ and $L_1$ depends on $U_1$ and $W_1$ respectively. Consequently, for different $U_1$ and $W_1,$ the choice of $K_1$ and $L_1$ may be different.
The first level of the Cantor set is defined as $$\mathcal{F}_1=\Big\{I_{n_1+k_1}(U_1,K_1)\times I_{n_1+l_1}(W_1,L_1):U_1,W_1\in \Sigma_\beta^{n_1} ~~\text{ending with}~~ 0^N\Big\},$$ which is composed of a collection of rectangles. Next, we cut each rectangle into balls with the radius as the shorter side length of the rectangle: $$\begin{aligned}
I_{n_1+k_1}(U_1,K_1)\times I_{n_1+l_1}(W_1,L_1)\rightarrow\Big\{I_{n_1+k_1}&(U_1,K_1)\\&\times I_{n_1+k_1}(W_1,L_1,H_1):H_1\in \Sigma_\beta^{k_1-l_1}\Big\}.\end{aligned}$$ Then we get a collection of balls $$\begin{aligned}
\mathcal{G}_1=\Big\{I_{n_1+k_1}(U_1,K_1)\times I_{n_1+k_1}(W_1,L_1,H_1):U_1,&W_1\in \Sigma_\beta^{n_1}\\& \text{ending with}~~ 0^N,
H_1\in \Sigma_\beta^{k_1-l_1}\Big\}.\end{aligned}$$
Level 2 of the Cantor set.
--------------------------
Fix a $J_1=I_{n_1+k_1}(\Gamma_1)\times I_{n_1+k_1}(\Upsilon_1)$ in $\mathcal{G}_1$. We define the local sublevel $\mathcal{F}_2(J_1)$ as follows.
Choose a large integer $m_2$ such that $$\frac{\epsilon}{1+\epsilon}\cdot m_2\log\beta\geq\Big(n_1+\sup\{k_1:I_{n_1+k_1}(\Gamma_1)\}\Big)||f||,$$ where $||f||=\sup\Big\{|f(x)|:x\in[0,1]\Big\}.$
Write $n_2=n_1+k_1+m_2.$ Just like the first level of the Cantor set, for any $U_2,W_2\in \Sigma_\beta^{m_2}$ ending with $0^N$, applying Proposition \[p2\] to $J_{n_2}(\Gamma_1,U_2)\times J_{n_2}(\Upsilon_1,W_2)$, we can get two full cylinders $I_{k_2}(K_2)$, $I_{l_2}(L_2)$ such that
$$I_{k_2}(K_2)\subset B\Big(x_0,e^{-S_{n_2}f(x_2^*)}\Big),~ I_{l_2}(L_2)\subset B\Big(y_0,e^{-S_{n_2}g(y_2^*)}\Big)$$ and $$e^{-S_{n_2}f(x_2^*)}>\beta^{-k_2}>\Big(e^{-S_{n_2}f(x_2^*)}\Big)^{1+\epsilon},$$ $$e^{-S_{n_2}g(y_2^*)}>\beta^{-l_2}>\Big(e^{-S_{n_2}g(y_2^*)}\Big)^{1+\epsilon}=e^{-S_{n_2}(1+\epsilon)g(y_2^*)},$$ where $x_2^*\in I_{n_2}(\Gamma_1,U_2),~y_2^*\in I_{n_2}(\Upsilon_1,W_2).$
Obviously, we get a subset $$I_{n_2+k_2}(\Gamma_1,U_2,K_2)\times I_{n_2+l_2}(\Upsilon_1,W_2,L_2)$$ of $$J_{n_2}(\Gamma_1,U_2)\times J_{n_2}(\Upsilon_1,W_2)$$ and $k_2\geq l_2$.
Then, the second level of the Cantor set is defined as
$$\begin{aligned}
\mathcal{F}_2(J_1)=\Big\{I_{n_2+k_2}(\Gamma_1,U_2,K_2)\times &I_{n_2+l_2}(\Upsilon_1,W_2,L_2)\\&:U_2,W_2\in \Sigma_\beta^{m_2} ~~\text{ending with}~~ 0^N\Big\},\end{aligned}$$
which is composed of a collection of rectangles.
Next, we cut each rectangle into balls with the radius as the shorter sidelength of the rectangle: $$\begin{aligned}
I_{n_2+k_2}(\Gamma_1,U_2,K_2)\times &I_{n_2+l_2}(\Upsilon_1,W_2,L_2)\rightarrow\Big\{I_{n_2+k_2}(\Gamma_1,U_2,K_2)\\&\times I_{n_2+k_2}(\Upsilon_1,W_2,L_2,H_2):H_2\in \Sigma_\beta^{k_2-l_2}\Big\}:=\mathcal{G}_2(J_1).\end{aligned}$$
Therefore, the second level is defined as $$\mathcal{F}_2=\bigcup
\limits_{J\in \mathcal{G}_1}\mathcal{F}_2(J),~\mathcal{G}_2=\bigcup\limits_{J\in \mathcal{G}_1}\mathcal{G}_2(J).$$
From Level $(i-1)$ to Level $i$.
--------------------------------
Assume that the $(i-1)$th level of the Cantor set $\mathcal{G}_{i-1}$ has been defined. Let $J_{i-1}=I_{n_{i-1}+k_{i-1}}(\Gamma_{i-1})\times I_{n_{i-1}+k_{i-1}}(\Upsilon_{i-1})$ be a generic element in $\mathcal{G}_{i-1}.$ We define the local sublevel $\mathcal{F}_i(J_{i-1})$ as follows.
Choose a large integer $m_{i}$ such that $$\label{espil}
\frac{\epsilon}{1+\epsilon}\cdot m_i\log\beta\geq\Big(n_{i-1}+\sup\big\{k_{i-1}:I_{n_{i-1}+k_{i-1}}(\Gamma_{i-1})\big\}\Big)||f||.$$
Write $n_i=n_{i-1}+k_{i-1}+m_i.$ For each $U_i,W_i\in \Sigma_\beta^{m_i}$ ending with $0^N$, apply Proposition \[p2\] to $$J_{n_i}(\Gamma_{n_{i-1}+k_{i-1}},U_{i})\times J_{n_i}(\Upsilon_{n_{i-1}+k_{i-1}},W_i),$$ we can get two full cylinders $I_{k_i}(K_i)$, $I_{l_i}(L_i)$ such that
$$I_{k_i}(K_i)\subset B\Big(x_0,e^{-S_{n_i}f(x_i^*)}\Big), I_{l_i}(L_i)\subset B\Big(y_0,e^{-S_{n_i}g(y_i^*)}\Big)$$ and $$e^{-S_{n_i}f(x_i^*)}>\beta^{-k_i}>\Big(e^{-S_{n_i}f(x_i^*)}\Big)^{1+\epsilon},$$ $$e^{-S_{n_i}g(y_i^*)}>\beta^{-l_i}>\Big(e^{-S_{n_i}g(y_i^*)}\Big)^{1+\epsilon}=e^{-S_{n_i}(1+\epsilon)g(y_i^*)},$$ where $x_i^*\in I_{n_i}(\Gamma_{i-1},U_{i}), ~y_i^*\in I_{n_i}(\Upsilon_{i-1},W_{i}).$
Obviously, we get a subset $$I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)\times I_{n_i+l_i}(\Upsilon_{i-1},W_i,L_i)$$ of $$J_{n_i}(\Gamma_{i-1},U_i)\times J_{n_i}(\Upsilon_{i-1},W_i)$$ and $k_i\geq l_i$. Then, the $i$-th level of the Cantor set is defined as
$$\begin{aligned}
\mathcal{F}_i(J_{i-1})=\Big\{I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)\times &I_{n_i+l_i}(\Upsilon_{i-1},W_i,L_i)\\&:U_i,W_i\in \Sigma_\beta^{m_i} ~~\text{ending with}~~ 0^N\Big\},\end{aligned}$$
which is composed of a collection of rectangles. As before, we cut each rectangle into balls with the radius as the shorter sidelength of the rectangle: $$\begin{aligned}
I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)\times I_{n_i+l_i}&(\Upsilon_{i-1},W_i,L_i)\rightarrow\Big\{I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)\times\\ &I_{n_i+k_i}(\Upsilon_{i-1},W_i,L_i,H_i):H_i\in \Sigma_\beta^{k_i-l_i}\Big\}:=\mathcal{G}_i(J_{i-1}).\end{aligned}$$
Therefore, the $i$-th level is defined as $$\mathcal{F}_i=\bigcup
\limits_{J\in \mathcal{G}_{i-1}}\mathcal{F}_i(J),~\mathcal{G}_i=\bigcup\limits_{J\in \mathcal{G}_{i-1}}\mathcal{G}_i(J).$$
Finally, the Cantor set is defined as $$\mathcal{F}_\infty=\bigcap\limits_{i=1}^\infty\bigcup\limits_{J\in \mathcal{F}_i}J=\bigcap\limits_{i=1}^\infty\bigcup\limits_{I\in \mathcal{G}_i}I.$$ It is straightforward to see that $\mathcal{F}_\infty\subset \overline{E}(T_\beta,f,g)$.
\[rem1\]It should be noted that the integer $k_i$ depends upon $\Gamma_{i-1}$ and $U_i$. However,(assume that $f$ is strictly positive, otherwise replace $f$ by $f+\epsilon$ ), since $m_i$ can be chosen such that $m_i\gg n_{i-1}$ for all $n_{i-1}$. So, $$\beta^{-k_i}\approx e^{-S_{n_i}f(x_i^*)}=\Big(e^{-S_{m_i}f(T_\beta^{n_{i-1}+k_{i-1}}x_i^*)}\Big)^{1+\epsilon}.$$ where $x_i^*\in I_{n_{i-1}+k_{i-1}+m_i}(\Gamma_{i-1},U_i).$ In other words, $k_i$ is almost dependent only on $U_i$ and $$\label{eqki}
\beta^{-k_i}\approx e^{-S_{m_i}f(x_i')}, {x_i'}\in I_{m_i}(U_i).$$
The same is true for $l_i$, $$\label{eqli}
\beta^{-l_i}\approx e^{-S_{m_i}f(y_i')}, {y_i'}\in I_{m_i}(W_i).$$
**Supporting measure**
-----------------------
Now we construct a probability measure $\mu$ supported on $\mathcal{F}_\infty$, which is defined by distributing masses among the cylinders with non-empty intersection with $\mathcal{F}_\infty$. The process splits into two cases: when $s_0>1$ and $ 0\leq s_0\leq 1$.
### **Case I: $s_0>1$** {#case-i-s_01 .unnumbered}
In this case, for any $1<s<s_0,$ notice that $$\frac{e^{S_nf(x')}}{e^{S_ng(y')}}\left(\frac{1}{\beta^ne^{S_nf(x')}}\right)^s\leq\left(\frac{1}{\beta^ne^{S_ng(y')}}\right)^s.$$ This means that the covering the rectangle $J_n(U)\times J_n(W)$ by balls of shorter side length preferable and therefore, it reasonable to define the probability measure on smaller balls. To this end, let $s_i$ be the solution to the equation $$\sum\limits_{U,W\in \Sigma_{\beta_N}^{m_i}}
\frac{e^{S_{m_i}f(x_i')}}{e^{S_{m_i}g(y_i')}}\Big(\frac{1}{\beta^{m_i}e^{S_{m_i}f(x_i')}}\Big)^s=1,$$ where $x_i'\in I_{m_i}(U_i),~ y_i'\in I_{m_i}(W_i).$
By the continuity of the pressure function $P(T_\beta,f)$ with respect to $\beta$ [@TanWang Theorem 4.1], it can be shown that $s_i\rightarrow s_0$ when $m_i\rightarrow \infty.$ Thus without loss of generality, we choose that all $m_i$ are large enough such that $s_i>1$ for all $i$ and $|s_i-s_0|=o(1).$
We systematically define the measure $\mu$ on the Cantor set by defining it on the basic cylinders first. Recall that for the level 1 of the Cantor set construction, we assumed that $n_1=m_1.$ For sub-levels of the Cantor set, roughly speaking, the role of $m_1$ and $m_k$ are to denote how many positions where the digits can be chosen (almost) freely. While $n_1$ and $n_k$ denote the length of a word in level $\F_k$ before shrinking.
- Let $I_{n_1+k_1}(U_1,K_1)\times I_{n_1+k_1}(W_1,L_1,H_1)$ be a generic cylinder in $\mathcal{G}_1.$ Then define $$\mu\Big(I_{n_1+k_1}(U_1,K_1)\times I_{n_1+k_1}(W_1,L_1,H_1)\Big)=\Big(\frac{1}{\beta^{m_1}e^{S_{m_1}f(x_1')}}\Big)^{s_1},$$ where $ x_1'\in I_{m_1}(U_1)$.
Assume that the measure on the cylinders of order $(i-1)$ has been well define. To define measure on the $i$th cylinder,
- Let $I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)\times I_{n_i+k_i}(\Upsilon_{i-1},W_i,L_i,H_i)$ be a generic $i$th cylinder in $\mathcal{G}_i$. Define the probability measure $\mu$ as $$\begin{aligned}
\mu\Big(I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)&\times I_{n_i+k_i}(\Upsilon_{i-1},W_i,L_i,H_i)\Big)= \\&\mu\Big(I_{{n_{i-1}+k_{i-1}}}(\Gamma_{i-1})\times I_{{n_{i-1}+k_{i-1}}}(\Upsilon_{i-1})\Big)\times\Big(\frac{1}{\beta^{m_i}e^{S_{m_i}f(x_i')}}\Big)^{s_i},\end{aligned}$$
where $ x_i'\in I_{m_i}(U_i)$.
The measure of a rectangle in $\mathcal{F}_i$ is then given as $$\begin{aligned}
&\mu\Big(I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)\times I_{n_i+l_i}(\Upsilon_{i-1},W_i,L_i)\Big)\\
&=\mu\Big(I_{{n_{i-1}+k_{i-1}}}(\Gamma_{i-1})\times I_{{n_{i-1}+k_{i-1}}}(\Upsilon_{i-1})\Big)\times{\#\Sigma_\beta^{k_i-l_i}}\times\Big(\frac{1}{\beta^{m_i}e^{S_{m_i}f(x_i')}}\Big)^{s_i}\\
&\approx \mu\Big(I_{{n_{i-1}+k_{i-1}}}(\Gamma_{i-1})\times I_{{n_{i-1}+k_{i-1}}}(\Upsilon_{i-1})\Big)\times\frac{e^{S_{m_i}f(x_i')}}{e^{S_{m_i}g(y_i')}}\times\Big(\frac{1}{\beta^{m_i}e^{S_{m_i}f(x_i')}}\Big)^{s_i},\end{aligned}$$ where the last inequality follows from the estimates and .
### Estimation of the $\mu$-measure of cylinders.
For any $i\geq 1$ consider the generic cylinder, $$I:=I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)\times I_{n_i+k_i}(\Upsilon_{i-1},W_i,L_i,H_i).$$ We would like to show by induction that, for any $1<s< s_0$, $$\mu(I)\leq|I|^{s/(1+\epsilon)}.$$
When $i=1$. The length of $I$ is given as $$|I|=\beta^{-m_1-k_1}\geq\beta^{-m_1}\cdot\Big(e^{-S_{n_1}f(x_1^*)}\Big)^{1+\epsilon}=\beta^{-m_1}\cdot\Big(e^{-S_{m_1}f(x_1^*)}\Big)^{1+\epsilon}.$$ But, by the definition of the measure $\mu$, it is clear that $$\mu(I)\leq|I|^{s_1}\leq|I|^{s/(1+\epsilon)}.$$
Now we consider the inductive process. Assume that $$\begin{aligned}
\mu(I_{n_{i-1}+k_{i-1}}(\Gamma_{i-1})\times &I_{n_{i-1}+k_{i-1}}(\Upsilon_{i-1}))\\&
\leq|I_{n_{i-1}+k_{i-1}}(\Gamma_{i-1})\times I_{n_{i-1}+k_{i-1}}(\Upsilon_{i-1})|^{s/(1+\epsilon)}.\end{aligned}$$
Let $$I=I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)\times I_{n_i+k_i}(\Upsilon_{i-1},W_i,L_i,H_i)$$ be a generic cylinder in $\mathcal{G}_i$. One one hand, its length satisfies $$\begin{aligned}
\label{f9}
|I|&=\beta^{-n_i-k_i}=|I_{n_{i-1}+k_{i-1}}(\Gamma_{i-1})\times I_{n_{i-1}+k_{i-1}}(\Upsilon_{i-1})|\times\beta^{-m_i}\times\beta^{-k_i}\nonumber\\
&\geq|I_{n_{i-1}+k_{i-1}}(\Gamma_{i-1})\times I_{n_{i-1}+k_{i-1}}(\Upsilon_{i-1})|\times\beta^{-m_i}\Big(e^{-S_{n_i}f(x_i^*)}\Big)^{1+\epsilon},\end{aligned}$$ where $x_i^*\in I_{n_i}(\Gamma_i,U_i).$
We compare $S_{n_i}f(x_i^*)$ and $S_{m_i}f(x_i')$ , by (\[espil\]) we have $$\begin{aligned}
|S_{n_i}f(x_i^*)-S_{m_i}f(x_i')|&=|S_{n_{i-1}+k_{i-1}}f(x_i^*)|\\ &\leq({n_{i-1}+k_{i-1}})\|f\| \\ &\leq \frac{\epsilon}{1+\epsilon}m_i\log\beta, \end{aligned}$$ where $x_i'\in I_{m_i}(U_i).$ So, we get
$$\label{geq}
|I|\geq|I_{n_{i-1}+k_{i-1}}(\Gamma_{i-1})\times I_{n_{i-1}+k_{i-1}}(\Upsilon_{i-1})|\times\Big(\beta^{-m_i}e^{-S_{m_i}f(x_i')}\Big)^{1+\epsilon}.$$
On the other hand, by the definition of the measure $\mu$ and the induction, we have that $$\begin{aligned}
\mu(I)&=\mu\Big(I_{{n_{i-1}+k_{i-1}}}(\Gamma_{i-1})\times I_{{n_{i-1}+k_{i-1}}}(\Upsilon_{i-1})\Big)\times\Big(\beta^{-m_i}e^{-S_{m_i}f(x_i')}\Big)^{s_i}\\
&\leq|I_{n_{i-1}+k_{i-1}}(\Gamma_{i-1})\times I_{n_{i-1}+k_{i-1}}(\Upsilon_{i-1})|^{s/(1+\epsilon)}
\Big((\beta^{-m_i}e^{-S_{m_i}f(x_i')})^{1+\epsilon}\Big)^{s/(1+\epsilon)}\\
&\leq |I|^{s/(1+\epsilon)}.\end{aligned}$$
In the following steps, for any $(x,y)\in \mathcal{F}_\infty,$ we will estimate the measure of $I_n(x)\times I_n(y)$ compared with its length $\beta^{-n}.$ By the construction of $\mathcal{F}_\infty,$ there exists $\{k_i,l_i\}_{i\geq1}$ such that for all $i\geq 1,$ $$(x,y)\in I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)\times I_{n_i+l_i}(\Upsilon_{i-1},W_i,L_i).$$
We remark that though $\{k_i,l_i\}$ are different for different cylinders composing $\mathcal{F}_\infty$ is given, once $(x,y)\in \mathcal{F}_\infty$ is given, the corresponding integers $\{k_i,l_i\}$ are fixed.
For any $n\geq 1$, Let $i\geq1$ be the integer such that $$n_{i-1}+k_{i-1}<n\leq n_i+k_i=n_{i-1}+k_{i-1}+m_i+k_i.$$
[**Step 1.**]{} When $n_{i-1}+k_{i-1}+m_i+l_i\leq n \leq n_{i}+k_{i}=n_{i-1}+k_{i-1}+m_i+k_i.$
Then the cylinder $I_n(x)\times I_n(y)$ contains $\beta^{n_{i}+k_{i}-n}$ cylinders in $\mathcal{G}_i$ with order $n_{i}+k_{i}$. Note that by the definition of $\{k_j,l_j\}_{1\leq j\leq i}$, the first $i$-pairs $\{k_j,l_j\}_{1\leq j\leq i}$ depends only on the first $n_i$ digits of $(x,y)$. So the measure of the sub-cylinder of order $n_{i}+k_{i}$ are the same. So, its measure of $I_n(x)\times I_n(y)$ can be estimated as $$\begin{aligned}
\mu\Big(I_n(x)\times I_n(y)\Big)
=\mu\Big(I_{{n_{i-1}+k_{i-1}}}(\Gamma_{i-1})&\times I_{{n_{i-1}+k_{i-1}}}(\Upsilon_{i-1})\Big) \\&\times \Big(\beta^{-m_i}e^{-S_{m_i}f(x_i')}\Big)^{s_i}\times \beta^{n_{i}+k_{i}-n}.\end{aligned}$$ Thus by the measure estimation of cylinders of order $n_{i-1}+k_{i-1}$ and the choice of $k_i$, one has that $$\begin{aligned}
\mu\Big(I_n(x)\times I_n(y)\Big)&\leq \Big(\beta^{-n_{i-1}-k_{i-1}}\Big)^{s/(1+\epsilon)}\Big(\beta^{-m_{i}-k_{i}}\Big)^{s/(1+\epsilon)}\times\beta^{n_{i}+k_{i}-n}\\
&=\Big(\beta^{-n_{i}-k_{i}}\Big)^{s/(1+\epsilon)}\times\beta^{n_{i}+k_{i}-n}
\\ &\leq \Big(\beta^{-n}\Big)^{s/(1+\epsilon)},\end{aligned}$$by noting that $n \leq n_{i}+k_{i}$ and ${s/(1+\epsilon)}>1.$
[**Step 2.**]{} When $n_{i-1}+k_{i-1}+m_i\leq n \leq n_{i}+l_{i}=n_{i-1}+k_{i-1}+m_i+l_i.$
Recalling the definition of $n_{i}+k_{i}$, the first $i$-pairs $\{k_j,l_j\}_{1\leq j\leq i}$ depends only on the first $n_i$ digits of $(x,y)$. So the measure of the sub-cylinder in $\mathcal{G}_i$ with order $n_{i}+k_{i}$ are the same. It is clear that the cylinder $I_n(x)\times I_n(y)$ contains $\beta^{k_{i}-l_i}$ cylinders of order $n_{i}+k_{i}$. So, its measure of $I_n(x)\times I_n(y)$ can be estimated as $$\begin{aligned}
\mu\Big(I_n(x)\times I_n(y)\Big)
=\mu\Big(I_{{n_{i-1}+k_{i-1}}}(\Gamma_{i-1})&\times I_{{n_{i-1}+k_{i-1}}}(\Upsilon_{i-1})\Big)\\& \times \Big(\beta^{-m_i}e^{-S_{m_i}f(x_i'^*)}\Big)^{s_i}\times \beta^{k_{i}-l_i}.\end{aligned}$$ Thus by the measure estimation of cylinders of order $n_{i-1}+k_{i-1}$ and the choice of $k_i$, one has that $$\begin{aligned}
\mu\Big(I_n(x)\times I_n(y)\Big)&\leq \Big(\beta^{-n_{i-1}-k_{i-1}}\Big)^{s/(1+\epsilon)}\Big(\beta^{-m_{i}-k_{i}}\Big)^{s/(1+\epsilon)}\times\beta^{k_{i}-l_i}\\
&=\Big(\beta^{-n_{i}-k_{i}}\Big)^{s/(1+\epsilon)}\times\beta^{k_{i}-l_i}\\
&\leq\Big(\beta^{-n_i-l_i}\Big)^{s/(1+\epsilon)}
\\ &\leq \Big(\beta^{-n}\Big)^{s/(1+\epsilon)},\end{aligned}$$ by noting that $n \leq n_{i}+l_{i}$ and ${s/(1+\epsilon)}>1.$
[**Step 3.**]{} When $n_{i-1}+k_{i-1}\leq n \leq n_{i-1}+k_{i-1}+m_i.$
Assume that $U_i=(\epsilon_1,\epsilon_2,\ldots,\epsilon_{m_i}), W_i=(\omega_1,\omega_2,\ldots,\omega_{m_i}).$ Denote $l=n-(n_{i-1}+k_{i-1})$ and $h=m_i-l$. Then $$\begin{aligned}
&\mu\left(I_n(x)\times I_n(y)\right)\\ &=\sum\limits_{\substack{(\epsilon_{l+1},\ldots,\epsilon_{m_i})\in \Sigma_\beta^l\\ (\omega_{l+1},\ldots,\omega_{m_i})\in \Sigma_\beta^h}}
\mu\left(I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)
\times I_{n_i+k_i}(\Upsilon_{i-1},W_i,L_i,H_i)\right)\times\beta^{k_{i}-l_i}\\
&=\mu\left(I_{{n_{i-1}+k_{i-1}}}(\Gamma_{i-1})\times I_{{n_{i-1}+k_{i-1}}}(\Upsilon_{i-1})\right)\times
\sum\limits_{\substack{(\epsilon_{l+1},\ldots,\epsilon_{m_i})\in \Sigma_\beta^l \\ (\omega_{l+1},\ldots,\omega_{m_i})\in \Sigma_\beta^h}}\left(\beta^{-m_i}e^{-S_{m_i}f(x_i')}\right)^{s_i}
\times\beta^{k_{i}-l_i}\\
&=\mu\left(I_{{n_{i-1}+k_{i-1}}}(\Gamma_{i-1})\times I_{{n_{i-1}+k_{i-1}}}(\Upsilon_{i-1})\right)\times
\sum\limits_{\substack{(\epsilon_{l+1},\ldots,\epsilon_{m_i})\in \Sigma_\beta^l\\ (\omega_{l+1},\ldots,\omega_{m_i})\in \Sigma_\beta^h}}\frac{e^{S_{m_i}f(x_i')}}{e^{S_{m_i}g(y_i')}}
\left(\beta^{-m_i}e^{-S_{m_i}f(x_i')}\right)^{s_i}.\end{aligned}$$ Then by the estimation on the measure of cylinders of order $n_{i-1}+k_{i-1}$ and let $(\widetilde{x_i'},\widetilde{y_i'})=(T_\beta^lx_i',T_\beta^ly_i')$, we get $$\begin{aligned}
\mu\left(I_n(x)\times I_n(y)\right)&\leq(\beta^{-n_{i-1}-k_{i-1}})^{s/(1+\epsilon)}\cdot\frac{e^{S_{l}f(x_i')}}{e^{S_{l}g(y_i')}}\cdot
\left(\beta^{-l}e^{-S_{l}f(x_i')}\right)^{s_i}\times\\&
\quad\quad\quad\quad
\sum\limits_{\substack{(\epsilon_{l+1},\ldots,\epsilon_{m_i})\in \Sigma_\beta^l\\ (\omega_{l+1},\ldots,\omega_{m_i})\in \Sigma_\beta^h}}\frac{e^{S_{h}f(\widetilde{x_i'})}}{e^{S_{h}g(\widetilde{y_i'})}}
\cdot\left(\beta^{-h}e^{-S_{h}f(\widetilde{x_i'})}\right)^{s_i}.\end{aligned}$$
The first part can be estimated as $$\begin{aligned}
\left(\beta^{-n_{i-1}-k_{i-1}}\right)^{s/(1+\epsilon)}\cdot\frac{e^{S_{l}f(x_i')}}{e^{S_{l}g(y_i')}}\cdot
\Big(\beta^{-l}e^{-S_{l}f(x_i')}\Big)^{s_i}&\leq\Big(\beta^{-(n_{i-1}+k_{i-1}+l)}\Big)^{s/(1+\epsilon)}\\ &=\Big(\beta^{-n}\Big)^{ s/(1+\epsilon)},\end{aligned}$$
since $$\frac{e^{S_{l}f(x_i')}}{e^{S_{l}g(y_i')}}\cdot\Big(e^{-S_{l}f(x_i')}\Big)^{s_i}\leq 1, \text{~for~} s_i\geq1.$$
To estimate the second part, we first recall that we defined $s_i$ to be the solution of the equation $$\sum\limits_{U,W\in \Sigma_{\beta_N}^{m_i}}
\frac{e^{S_nf(x_i')}}{e^{S_ng(y_i')}}\Big(\frac{1}{\beta^ne^{S_nf(x_i')}}\Big)^s=1.$$ Therefore, $$\begin{aligned}
1=\sum\limits_{U_1,W_1\in \Sigma_{\beta_N}^{l}}
\frac{e^{S_lf(x_i')}}{e^{S_lg(y_i')}}&\Big(\frac{1}{\beta^le^{S_lf(x_i')}}\Big)^{s_i}\times
\sum\limits_{U_2,W_2\in \Sigma_{\beta_N}^{h}}
\frac{e^{S_hf(\widetilde{x_i'})}}{e^{S_hg(\widetilde{y_i'})}}\Big(\frac{1}{\beta^le^{S_hf(\widetilde{x_i'})}}\Big)^{s_i}.\end{aligned}$$ So, with the similar arguments as in the paper [@TanWang pp. 2095-2097] and [@WW pp. 1331-1332], we derive that $$\sum\limits_{U_2,W_2\in \Sigma_{\beta_N}^{h}}
\frac{e^{S_hf(\widetilde{x_i'})}}{e^{S_hg(\widetilde{y_i'})}}
\Big(\frac{1}{\beta^le^{S_hf(\widetilde{x_i'})}}\Big)^{s_i}\leq\beta^{l\epsilon}.$$
Therefore,$$\mu\Big(I_n(x)\times I_n(y)\Big)\leq\beta^{-n\cdot s/(1+\epsilon)}\cdot\beta^{l\epsilon}\leq(\beta^{-n})^{s/(1+\epsilon)-\epsilon}.$$
As far as the measure of a general ball $B(x,r)$ with $\beta^{-n-1}\leq r<\beta^{-n}$ is concerned, we notice that it can intersect at most $3$ cylinders of order $n$. Thus,$$\mu\Big(B(x,r)\Big)\leq3(\beta^{-n})^{s/(1+\epsilon)-\epsilon}\leq3\beta^sr^{s/(1+\epsilon)-\epsilon}\leq3\beta^2r^{s/(1+\epsilon)-\epsilon}.$$
So, finally, an application of the mass distribution principle (Proposition \[mdp\]) yields that $${\dim_{\mathrm H}}\overline{E}(T_\beta, f,g)\geq s_0.$$
### **Case II: $0\leq s_0\leq1$** {#case-ii-0leq-s_0leq1 .unnumbered}
The arguments are similar to Case I but the calculations are different. In this case, for any $s<s_0\leq 1,$ it is trivial that $$\frac{e^{S_nf(x')}}{e^{S_ng(y')}}\Big(\frac{1}{\beta^ne^{S_nf(x')}}\Big)^s\geq\big(\frac{1}{\beta^ne^{S_ng(y')}}\big)^s.$$ This means that the covering of the rectangle $J_n(U)\times J_n(W)$ by balls of larger side length is more preferable and therefore, it reasonable to define the probability measure of the rectangle to be the same measure for the cylinder of order $n_i+l_i$.
Just like Case I, let $s_i$ be the solution to the equation $$\sum\limits_{U,W\in \Sigma_{\beta_N}^{m_i}~~\text{ending with}~ 0^N}
\Big(\frac{1}{\beta^{m_i}e^{S_{m_i}g(y_i')}}\Big)^s=1,$$ where $y_i'\in I_{m_i}(W_i).$ By the continuity of the pressure function $P(T_\beta,f)$ with respect to $\beta$ we can assume that for all $m_i$ large enough we have that $s_i<1$ for all $i$ and $|s_i-s_0|=o(1).$
We first define the measure $\mu$ on the basic cylinders.
- Let $I_{n_1+k_1}(U_1,K_1)\times I_{n_1+l_1}(W_1,L_1)$ be a generic cylinder in $\mathcal{F}_1.$ Then define $$\mu\Big(I_{n_1+k_1}(U_1,K_1)\times I_{n_1+l_1}(W_1,L_1)\Big)=\Big(\frac{1}{\beta^{m_1}e^{S_{m_1}g(y_1')}}\Big)^{s_1},$$ where $ y_1'\in I_{m_1}(W_1)$.
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- Then the measure of it is evenly distributed on its sub-cylinders in $\mathcal{G}_1$. So, for a generic cylinder $I_{n_1+k_1}(U_1,K_1)\times I_{n_1+k_1}(W_1,L_1,H_1)$ in $\mathcal{G}_1$, define
$$\begin{aligned}
\mu\Big(I_{n_1+k_1}(U_1,K_1)\times I_{n_1+k_1}(W_1,L_1,H_1)\Big)&=\frac{1}{\#\Sigma_\beta^{k_1-l_1}}\Big(\frac{1}{\beta^{m_1}e^{S_{m_1}g(y_1')}}\Big)^{s_1}\\
&\approx\frac{1}{\beta^{k_1-l_1}}\Big(\frac{1}{\beta^{m_1}e^{S_{m_1}g(y_1')}}\Big)^{s_1}.\end{aligned}$$
Assume that the measure on the cylinders of order $(i-1)$ has been well defined. Then to define the measure on the $i$th cylinder we proceed as follows.
- Let $I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)\times I_{n_i+l_i}(\Upsilon_{i-1},W_i,L_i)$ be a generic cylinder in $\mathcal{F}_i$.
Then define $$\begin{aligned}
\mu\Big(I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)\times I_{n_i+l_i}(\Upsilon_{i-1},&W_i,L_i)\Big)
= \mu\Big(I_{{n_{i-1}+k_{i-1}}}(\Gamma_{i-1})\\&\times I_{{n_{i-1}+k_{i-1}}}(\Upsilon_{i-1})\Big)\times\Big(\frac{1}{\beta^{m_i}e^{S_{m_i}g(y_i')}}\Big)^{s_i},\end{aligned}$$ where $ y_i'\in I_{m_i}(W_i)$.
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- By the definition of $k_i,l_i$, the measure of a cylinder in $\mathcal{G}_i$ is then given as $$\begin{aligned}
&\mu\Big(I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)\times I_{n_i+k_i}(\Upsilon_{i-1},W_i,L_i,H_i)\Big)\\
&=\mu\Big(I_{{n_{i-1}+k_{i-1}}}(\Gamma_{i-1})\times I_{{n_{i-1}+k_{i-1}}}(\Upsilon_{i-1})\Big)\times\frac{1}{\#\Sigma_\beta^{k_i-l_i}}\times\Big(\frac{1}{\beta^{m_i}e^{S_{m_i}g(y_i')}}\Big)^{s_i}\\
&\approx \mu\Big(I_{{n_{i-1}+k_{i-1}}}(\Gamma_{i-1})\times I_{{n_{i-1}+k_{i-1}}}(\Upsilon_{i-1})\Big)\times\frac{e^{S_{m_i}g(y_i')}}{e^{S_{m_i}f(x_i')}}\times\Big(\frac{1}{\beta^{m_i}e^{S_{m_i}g(y_i')}}\Big)^{s_i}.\end{aligned}$$
### Estimation of the $\mu$-measure of cylinders.
We first show by induction that for any $i\geq 1$ and a generic cylinder $$I:=I_{{n_{i-1}+k_{i-1}}+m_{i}+k_i}(\Gamma_{i-1},U_i,K_i)\times I_{{n_{i-1}+k_{i-1}}+m_{i}+k_i}(\Upsilon_{i-1},W_i,L_i,H_i),$$ we have $$\mu(I)\leq|I|^{s/(1+\epsilon)}.$$
When $i=1$. On the one hand, the length of $I$ is given as $$|I|=\beta^{-m_1-k_1}\geq\beta^{-m_1}\cdot\Big(e^{-S_{n_1}f(x_1')}\Big)^{1+\epsilon}=\beta^{-m_1}\cdot\Big(e^{-S_{m_1}f(x_1')}\Big)^{1+\epsilon}.$$ But on the other hand, by the definition of the measure $\mu$, it is clear that $$\begin{aligned}
\mu(I)&\leq\frac{e^{S_{m_1}g(y_1')}}{e^{S_{m_1}f(x_1')}}\cdot\Big(\frac{1}{\beta^{m_1}e^{S_{m_1}g(y_1')}}\Big)^{s_1}\\
&\leq\Big(\beta^{-m_1}e^{-S_{m_1}f(x_1')}\Big)^{s_1}\\
&\leq|I|^{s/(1+\epsilon)},\end{aligned}$$ by noting that $s_1<1.$
Just like Case I, we consider the inductive process. Assume that $$\begin{aligned}
\mu(I_{n_{i-1}+k_{i-1}}(\Gamma_{i-1})\times &I_{n_{i-1}+k_{i-1}}(\Upsilon_{i-1}))\leq|I_{n_{i-1}+k_{i-1}}(\Gamma_{i-1})\times I_{n_{i-1}+k_{i-1}}(\Upsilon_{i-1})|^{s/(1+\epsilon)}.\end{aligned}$$ Let $$I=I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)\times I_{n_i+k_i}(\Upsilon_{i-1},W_i,L_i,H_i)$$ be a generic cylinder in $\mathcal{G}_i$. By (\[geq\]) we get $$|I|\geq|I_{n_{i-1}+k_{i-1}}(\Gamma_{i-1})\times I_{n_{i-1}+k_{i-1}}(\Upsilon_{i-1})|\times\Big(\beta^{-m_i}e^{-S_{m_i}f(x_i')}\Big)^{1+\epsilon}.$$
From the definition of the measure $\mu$, the induction and that $s_i<1$, it follows that $$\begin{aligned}
\mu(I)&=\mu\Big(I_{{n_{i-1}+k_{i-1}}}(\Gamma_{i-1})\times I_{{n_{i-1}+k_{i-1}}}(\Upsilon_{i-1})\Big)\times\frac{e^{S_{m_i}g(y_i')}}{e^{S_{m_i}f(x_i')}}
\times\Big(\frac{1}{\beta^{m_i}e^{S_{m_i}g(y_i')}}\Big)^{s_i}\\
&\leq|I_{n_{i-1}+k_{i-1}}(\Gamma_{i-1})\times I_{n_{i-1}+k_{i-1}}(\Upsilon_{i-1})|^{s/(1+\epsilon)}
\Big((\beta^{-m_i}e^{-S_{m_i}f(x_i')})^{1+\epsilon}\Big)^{s/(1+\epsilon)}\\
&\leq |I|^{s/(1+\epsilon)}\\ &=\Big(\beta^{-n_i-k_i}\Big)^{s/(1+\epsilon)}\\ &\approx\Big(\beta^{-m_i-k_i}\Big)^{s/(1+\epsilon)}.\end{aligned}$$
So, for a rectangle $$J=I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)\times I_{n_i+l_i}(\Upsilon_{i-1},W_i,L_i)$$ in $\mathcal{F}_i,$ we have that $$\begin{aligned}
\mu(J)&=\mu\Big(I_{{n_{i-1}+k_{i-1}}}(\Gamma_{i-1})\times I_{{n_{i-1}+k_{i-1}}}(\Upsilon_{i-1})\Big)\times\Big(\frac{1}{\beta^{m_i}e^{S_{m_i}g(y_i')}}\Big)^{s_i}\\
&\leq \Big(\beta^{-n_{i-1}-k_{i-1}}\Big)^{s/(1+\epsilon)}\Big(\beta^{-m_i}\beta^{-l_i}\Big)^{s_i}\\
&\leq\Big(\beta^{-n_{i}-l_{i}}\Big)^{s/(1+\epsilon)}.\end{aligned}$$
For any $(x,y)\in \mathcal{F}_\infty,$ we will estimate the measure of $I_n(x)\times I_n(y)$ compared with its length $\beta^{-n}.$ By the construction of $\mathcal{F}_\infty,$ there exists $\{k_i,l_i\}_{i\geq1}$ such that for all $i\geq 1,$ $$(x,y)\in I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)\times I_{n_i+l_i}(\Upsilon_{i-1},W_i,L_i,).$$
For any $n\geq 1$, let $i\geq1$ be the integer such that $$n_{i-1}+k_{i-1}<n\leq n_i+k_i=n_{i-1}+k_{i-1}+m_i+k_i.$$
[**Step I.**]{} When $n_{i-1}+k_{i-1}+m_i+l_i\leq n \leq n_{i}+k_{i}=n_{i-1}+k_{i-1}+m_i+k_i.$
In this case, the cylinder can intersect only one rectangle in $\mathcal{F}_i,$ so $$\begin{aligned}
\mu\Big(I_n(x)\times I_n(y)\Big)
&=\mu\Big(I_{{n_{i}+k_{i}}}(\Gamma_{i-1},U_i,K_i)\times I_{{n_{i}+k_{i}}}(\Upsilon_{i-1},W_i,L_i)\Big)\\
&\leq\Big(\beta^{-n_{i}-l_{i}}\Big)^{s/(1+\epsilon)}
\\ &\leq \Big(\beta^{-n}\Big)^{s/(1+\epsilon)}.\end{aligned}$$
[**Step II.**]{} When $n_{i-1}+k_{i-1}+m_i\leq n \leq n_{i}+l_{i}=n_{i-1}+k_{i-1}+m_i+l_i.$
Then the cylinder $I_n(x)\times I_n(y)$ contains $\beta^{n_{i}+l_{i}-n}$ cylinders in $\mathcal{F}_i$ with order $n_{i}+l_{i}$. Note that by the definition of $\{k_j,l_j\}_{1\leq j\leq i}$, the first $i$-pairs $\{k_j,l_j\}_{1\leq j\leq i}$ depends only on the first $n_i$ digits of $(x,y)$. So the measure of the sub-cylinder of order $n_{i}+k_{i}$ are the same. So, its measure of $I_n(x)\times I_n(y)$ can be estimated as $$\begin{aligned}
\mu\Big(I_n(x)\times I_n(y)\Big)
&=\mu\Big(I_{{n_{i}+k_{i}}}(\Gamma_{i-1},U_i,K_i)\times I_{{n_{i}+k_{i}}}(\Upsilon_{i-1},W_i,L_i)\Big)\times \frac{1}{\beta^{n-n_{i}-l_{i}}}\\
&\leq \Big(\beta^{-n_{i}-l_{i}}\Big)^{s/(1+\epsilon)}\times \frac{1}{\beta^{n-n_{i}-l_{i}}}
\\ &\leq\Big(\beta^{-n}\Big)^{s/(1+\epsilon)}.\end{aligned}$$
[**Step III.**]{} When $n_{i-1}+k_{i-1}\leq n \leq n_{i-1}+k_{i-1}+m_i.$
Assume $U_i=(\epsilon_1,\epsilon_2,\ldots,\epsilon_{m_i}), W_i=(\omega_1,\omega_2,\ldots,\omega_{m_i}).$ Write $l=n-(n_{i-1}+k_{i-1})$ and $h=m_i-l$. Then $$\begin{aligned}
&\mu\Big(I_n(x)\times I_n(y)\Big)\\ &=\sum\limits_{\substack{ (\epsilon_{l+1},\ldots,\epsilon_{m_i})\in \Sigma_\beta^l\\ (\omega_{l+1},\ldots,\omega_{m_i})\in \Sigma_\beta^h}}
\mu\Big(I_{n_i+k_i}(\Gamma_{i-1},U_i,K_i)
\times I_{n_i+l_i}(\Upsilon_{i-1},W_i,L_i)\Big)\\
&=\mu\Big(I_{{n_{i-1}+k_{i-1}}}(\Gamma_{i-1})\times I_{{n_{i-1}+k_{i-1}}}(\Upsilon_{i-1})\Big)\times
\sum\limits_{\substack{(\epsilon_{l+1},\ldots,\epsilon_{m_i})\in \Sigma_\beta^l\\ (\omega_{l+1},\ldots,\omega_{m_i})\in \Sigma_\beta^h}}
\Big(\beta^{-m_i}e^{-S_{m_i}g(y_i')}\Big)^{s_i}.\end{aligned}$$ Then by the estimation on the measure of cylinders of order $n_{i-1}+k_{i-1}$ and let $\widetilde{y_i'}=T_\beta^ly_i'$, we get $$\begin{aligned}
\mu\Big(I_n(x)\times I_n(y)\Big)&\leq\Big(\beta^{-n_{i-1}-k_{i-1}}\Big)^{s/(1+\epsilon)}\cdot\Big(\beta^{-l}e^{-S_{l}g(y_i')}\Big)^{s_i}\times
\sum\limits_{\substack{(\epsilon_{l+1},\ldots,\epsilon_{m_i})\in \Sigma_\beta^l\\ (\omega_{l+1},\ldots,\omega_{m_i})\in \Sigma_\beta^h}}\Big(\beta^{-h}e^{-S_{h}g(\widetilde{y_i'})}\Big)^{s_i}\\
&\leq\Big(\beta^{-n}\Big)^{s/(1+\epsilon)}\cdot\sum\limits_{\substack{(\epsilon_{l+1},\ldots,\epsilon_{m_i})\in \Sigma_\beta^l\\ (\omega_{l+1},\ldots,\omega_{m_i})\in \Sigma_\beta^h}}
\Big(\beta^{-h}e^{-S_{h}g(\widetilde{y_i'})}\Big)^{s_i}.\end{aligned}$$
Recall the definition of $s_i:$ $$\sum\limits_{U,W\in \Sigma_{\beta_N}^{m_i}}
\Big(\frac{1}{\beta^{m_i}e^{S_{m_i}g(y_i')}}\Big)^s=1.$$ Then $$\begin{aligned}
1=\sum\limits_{U_1,W_1\in \Sigma_{\beta_N}^{l}}
\Big(\frac{1}{\beta^le^{S_lg(y_1')}}\Big)^{s_i}\cdot
\sum\limits_{U_2,W_2\in \Sigma_{\beta_N}^{h}}
\Big(\frac{1}{\beta^le^{S_hg(\widetilde{y_1'})}}\Big)^{s_i},\end{aligned}$$ where $y_1'^*\in I_{l}(U_1),\widetilde{y_1'}\in I_{h}(W_2).$\
So, with the similar argument as in the previous section, we have that $$\sum\limits_{U_2,W_2\in \Sigma_{\beta_N}^{l} }
\Big(\frac{1}{\beta^he^{S_hg(\widetilde{y_h'})}}\Big)^{s_i}\leq\beta^{l\epsilon}.$$
Therefore,$$\mu\Big(I_n(x)\times I_n(y)\Big)\leq\Big(\beta^{-n}\Big)^ {s/(1+\epsilon)}\cdot\beta^{l\epsilon}\leq\Big(\beta^{-n}\Big)^{s/(1+\epsilon)-\epsilon}.$$
Notice that a general ball $B(x,r)$ with $\beta^{-n-1}\leq r<\beta^{-n}$ can intersect at most $3$ cylinders of order $n$. Therefore the measure of the general ball can be estimated as, $$\mu\Big(B(x,r)\Big)\leq3\Big(\beta^{-n}\Big)^{s/(1+\epsilon)-\epsilon}\leq3\beta^sr^{s/(1+\epsilon)-\epsilon}\leq3\beta^2r^{s/(1+\epsilon)-\epsilon}.$$
So, finally, by using the mass distribution principle we have the lower bound of the Hausdorff dimension of this case, $${\dim_{\mathrm H}}\overline{E}(T_\beta, f,g)\geq s_0.$$ Hence combining both the case, we have the desired conclusion.\
[**Acknowledgments.**]{} The first-named author was supported by La Trobe University’s Asia Award and the start-up grant. We would like to thank Professor Baowei Wang for useful discussions on this project.
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|
{
"pile_set_name": "ArXiv"
}
|
---
abstract: 'Extended BRS symmetry is used to prove gauge independence of the fermion renormalization constant $Z_2$ in on-shell QED renormalization schemes. A necessary condition for gauge independence of $Z_2$ in on-shell QCD renormalization schemes is formulated. Satisfying this necessary condition appears to be problematic at the three-loop level in QCD.'
author:
- |
S. Alavian and T.G. Steele[^1]\
[*Department of Physics and Engineering Physics* ]{}\
[*University of Saskatchewan*]{}\
[*Saskatoon, Saskatchewan S7N 5E2, Canada.*]{}
title: ' [Extended BRS Symmetry and Gauge Independence in On-Shell Renormalization Schemes]{} '
---
In on-shell schemes, the fermion mass renormalization $Z_m$ and wave function renormalization $Z_2$ have been observed to be gauge parameter independent in explicit two-loop QED and QCD calculations [@bgs]. Gauge parameter independence of $Z_2$ is phenomenologically significant because it implies that the difference between the (fermion) anomalous dimension of heavy quark effective theories [@iw] and QCD is gauge independent.
An extension of BRS symmetry, which allows variations of the gauge parameter to be included as part of the symmetry transformations [@ps], will be applied to the gauge parameter dependence of $Z_2$. This approach results in an extension of Slavnov-Taylor identities, allowing gauge dependence to be formulated algebraically. Previous application of these techniques resulted in a proof of the gauge independence of the mass renormalization $Z_m$ to all orders in on-shell QED and QCD renormalization schemes [@bls]. We will prove the gauge parameter independence of $Z_2$ in on-shell schemes for QED and formulate a necessary condition for gauge independence in QCD which appears problematic beyond the two-loop level. This complements earlier work on gauge independence of $Z_2$ in QED resulting in the (dimensionally-regularized) relation [@z2] $$\frac{\partial Z_2}{\partial \xi}\sim \int d^Dk\frac{1}{k^4}=0
\label{jz}$$ where $\xi$ is the gauge parameter and the massless tadpole is zero in dimensional regularization. Since the QED result (\[jz\]) cannot be extended to QCD, our extended BRS symmetry proof for QED provides a new approach to formulating questions of gauge independence of $Z_2$ in QCD.
The QED Lagrangian in the auxiliary field formalism [@nl] for covariant gauges is $${\cal L}=-\frac{1}{4}F^2+\bar \psi\left(i\dsl{D}-m\right)\psi +\frac{\xi}{2} B^2 +B\partial
\cdot A-\bar c\partial^2 c
\label{l_qed}$$ where $F$ is the field strength and $B$ is the auxiliary gauge field. This Lagrangian is invariant under the BRS symmetry $$\begin{aligned}
& & \delta A_\mu=\epsilon \partial_\mu c\quad ,\quad \delta \bar\psi=i\epsilon g c\bar
\psi\quad ,\quad \delta c=0\nonumber\\
& &\delta B=0\quad ,\quad \delta \psi=-i\epsilon g c\psi \quad ,\quad \delta \bar c=0
\label{qed_brs}\end{aligned}$$ where $\epsilon$ is a global grassmann quantity. The auxiliary field formalism guarantees nilpotence of the BRS transformations without invoking equations of motion.
An extension of BRS symmetry that includes gauge parameter variations introduces a new term in the Lagrangian $${\cal L}\rightarrow {\cal L}+\frac{\chi}{2}\bar c B
\label{ex_l_qed}$$ where $\chi$ is a global grassmann variable. Although $\chi$ will be set to zero after functional differentiation, it is still important to recognize that since $\chi$ is a global Grassmann quantity, it does not change the dynamics of any process with zero ghost number. The modified Lagrangian (\[ex\_l\_qed\]) is invariant under the following extended BRS symmetry [@ps] $$\begin{aligned}
& &\delta^+ A_\mu=\epsilon \partial_\mu c\quad ,\quad \delta^+ \bar\psi=i\epsilon g c\bar
\psi\quad ,\quad \delta^+ c=0\nonumber\\
& &\delta^+ B=0\quad ,\quad \delta^+ \psi=-i\epsilon g c\psi \quad ,\quad \delta^+ \bar c=B
\label{qed_x_brs}\\
& &\delta^+\xi=\epsilon\chi\quad ,\quad \delta^+\chi=0\end{aligned}$$
As for BRS symmetry, the extended BRS symmetry (\[qed\_x\_brs\]) implies the the following relation for the effective action $\Gamma$. $$0=\partial_\mu c \frac{\delta \Gamma}{\delta A_\mu}
+ \frac{\delta\Gamma}{\delta \bar K} \frac{\delta \Gamma}{\delta \psi}
+ \frac{\delta\Gamma}{\delta K}
\frac{\delta \Gamma}{\delta \bar\psi}
+ B\frac{\delta \Gamma}{\delta \bar c}
+\chi\frac{\partial\Gamma}{\partial\xi}
\label{qed_gamma_x_brs}$$ where $K$ is a current coupled to the composite operator $\delta^+\bar \psi$ and $\bar K$ is coupled to $\delta^+ \psi$. Differentiating (\[qed\_gamma\_x\_brs\]) with respect to $\chi$, $\bar\psi(x)$, $\psi(y)$, setting $\chi=0$ and imposing ghost number conservation leads to the following identity for the proper fermion two-point function [@bls]. $$\frac{\partial}{\partial\xi}\frac{\delta^2\Gamma}{\delta\psi(y)\delta
\bar\psi(x)} =
+
\frac{\delta^3\Gamma}{\delta\psi(y)\delta\bar K\delta \chi}
\frac{\delta^2\Gamma}{\delta\bar\psi(x)\delta\psi}
+
\frac{\delta^2\Gamma}{\delta\psi(y)\delta\bar\psi}
\frac{\delta^3\Gamma}{\delta\bar\psi(x)\delta K\delta\chi}
\label{gamma_ident}$$ Transforming to momentum space and defining [^2] $$\begin{aligned}
& &\frac{\delta^2\Gamma}{\delta\chi\delta {\bar K}(w)\delta\psi (y)}
=\int \frac{d^4q}{(2\pi)^4}\frac{d^4\ell}{(2\pi)^4}\,e^{-iq\cdot(y-z)
-i\ell\cdot(w-z)}
F(q,\ell,-q-\ell)\label{F}\\
& &
\frac{\delta^2\Gamma}{\delta\chi\delta K(w)\delta{\bar\psi} (y)}
=\int \frac{d^4q}{(2\pi)^4}\frac{d^4\ell}{(2\pi)^4}\,e^{-iq\cdot(x-z)
-i\ell\cdot(w-z)}
{\bar F}(q,\ell,-q-\ell) \label{Fbar}\end{aligned}$$ results in the final form needed for studying the gauge dependence of the fermion propagator $S_F$ in QED [@bls]. $$\frac{\partial}{\partial\xi}S_F^{-1}(p)=S_F^{-1}(p)\left[ F(p,-p,0)+
\bar F(-p,p,0) \right]
\label{prop_ident}$$ Note that the Green functions $F(p, -p, 0)$ and $\bar F(p, -p, 0)$ cannot have single particle poles.
In on-shell renormalization schemes the bare mass $m_0$ and the renormalized mass $M$ are related through the condition $$\biggl. S_F^{-1}(p)\biggr|_{\dsl{p}=M}=0
\label{mass_shell}$$ This results in the definition of the mass renormalization constant. $$\frac{m_0}{M}=Z_m
\label{Z_m}$$ The wave function renormalization constant $Z_2$ is the residue of $S_F$ at the $\dsl{p}=M$ pole. $$Z_2=\lim_{\dsl{p}=M} \left(\dsl{p} -M\right)S_F(p)
\label{Z_2}$$ Perturbative expansions of $Z_m$ and $Z_2$ have been calculated to two-loop order in a scheme which dimensionally regulates both the infrared and ultraviolet divergences, resulting in explicitly gauge independent expressions for QED and QCD [@bgs].
The mass renormalization $Z_m$, and hence $M$, has been proven to be gauge independent to all orders of perturbation theory [@bls; @kron]. Thus when both sides of (\[prop\_ident\]) are divided by $\dsl{p}-M$ the quantity $\dsl{p}-M$ commutes with the $\xi$ derivative. $$\frac{\partial}{\partial\xi}\left(\frac{S_F^{-1}(p)}{\dsl{p}-M}\right)
=\frac{S_F^{-1}(p)}{\dsl{p}-M}
\left[ F(p,-p,0)+\bar F(-p,p,0) \right]
\label{Z_2F1}$$ Using the property that $$S_F^{-1}(p)=\frac{\dsl{p}-M}{Z_2}+{\cal O}
\left[\,\left(\dsl{p}-M\right)^2\,\right]
\label{S_F_property}$$ along with the gauge independence of $M$ leads to the following result when (\[Z\_2F1\]) is evaluated on-shell. $$\frac{\partial}{\partial\xi}\left(\frac{1}{Z_2}\right)=\frac{1}{Z_2}
\lim_{\dsl{p}=M}
\left[
F(p,-p,0)+\bar F(-p,p,0)\right]
\label{Z_2_rsult}$$ This is our central result for QED: the gauge dependence of the wave function renormalization constant is related to the on-shell properties of the Green function $F(p,-p,0)+\bar F(p,-p,0)$. In particular, if this Green function is zero on-shell, then $Z_2$ is gauge independent.
Before studying the on-shell behaviour of $F(p,-p,0)+\bar F(p,-p,0)$ we review some aspects of the auxiliary field formalism. Since the $B$ field and $\partial\cdot A$ are mixed in the Lagrangian (\[l\_qed\]) the quadratic part of the Lagrangian must be diagonalized, leading to the free field propagators $$\begin{aligned}
& &
\int d^4x\,e^{ip\cdot x}\langle O\vert T\left(B(x) B(0)\right)\vert O\rangle
=0 \label{bb_prop}\\
& &
\int d^4x\,e^{ip\cdot x}\langle O\vert T\left(B(x) A_\mu(0)\right)\vert O
\rangle = \frac{p_\mu}{p^2}\equiv G_\mu(p) \label{ba_prop}\\
& &
\int d^4x\,e^{ip\cdot x}\langle O\vert T\left(A_\mu(x) A_\nu(0)\right)
\vert O
\rangle =
i\left[-\frac{g^{\mu\nu}}{p^2} +(1-\xi)\frac{p^\mu p^\nu}{p^4}\right]
\equiv D^{\mu\nu}(p)
\label{aa_prop}\end{aligned}$$ BRS symmetry implies that (\[bb\_prop\]) and (\[ba\_prop\]) are valid to all orders in perturbation theory [@bls].
As illustrated in Figure \[f\_fig\], the (QED) Green function $F(p,-p,0)$ is easily written in terms of one-particle irreducible Green functions $$F(p, -p, 0)=\int d^Dk \,\Gamma_\mu(k, p) G_\mu(k) S_F(p+k) \tilde D(k^2)
\label{on-shell_F_1}$$ where $\tilde D(k^2)$ is the ghost propagator (which for QED corresponds to the free field result) and the fermion-photon vertex function $\Gamma_\mu$ is defined by $$S_F(p)\Gamma_\nu (p, k) S_F(p+k) D^{\mu \nu}(k)
=\int d^Dx \int d^Dy \,\,e^{i k\cdot x+i p\cdot y}\langle O\vert T\left[
\psi(0) A_\mu(x) \bar \psi (y)
\right]\vert O\rangle
\label{vertex}$$ Substituting (\[ba\_prop\]) and the (free-field) ghost propagator into (\[on-shell\_F\_1\]) and using the Ward identity for the vertex function $$k^\mu \Gamma_\mu(p,k)=S_F^{-1}(p+k)-S_F^{-1}(p)
\label{ward}$$ simplifies the expression for $F(p, -p, 0)$. $$F(p,-p,0)=iS_F^{-1}(p) \int d^Dk \frac{1}{k^4} S_F(p+k)-i\int d^Dk\frac{1}{k^4}
\label{on-shell_F_2}$$ The second term in the above equation is a massless tadpole which is zero in dimensional regularization, leading to the final expression for $F(p, -p, 0)$ in QED. $$F(p,-p,0)=iS_F^{-1}(p) \int d^Dk \frac{1}{k^4} S_F(p+k)
\label{on-shell_F_3}$$ In the on-shell scheme [@bgs] infrared and ultraviolet divergences are dimensionally regulated, so the integral in (\[on-shell\_F\_3\]) is finite on-shell. Thus the $S_F^{-1}(p)$ prefactor in (\[on-shell\_F\_3\]) implies that $F(p, -p, 0)$ is zero at the $\dsl{p}=M$ mass-shell. This argument can be trivially extended to $\bar F(p, -p, 0)$, and we conclude that to all orders in QED $$\biggl. F(p, -p, 0)+\bar F(p, -p, 0) \biggr|_{\dsl{p}=M}=0$$ and hence from the result (\[Z\_2\_rsult\]) we have proven the gauge independence of the QED renormalization constant $Z_2$ in mass-shell schemes.
![Feynman diagram expressing $F(p,-p,0)$ in terms of one-particle irreducible functions represented by the solid circles. Dashed lines represent the ghost field, and the dotted line represents the auxiliary field $B$. Composite operators coupled to the currents are represented by the partially-filled circles.[]{data-label="f_fig"}](z2_f1.eps)
An explicit illustration of the on-shell behaviour of $F(p, -p,0)+\bar F(p, -p, 0)$ in the regularization scheme [@bgs] to one-loop order requires evaluation of the diagram in Figure \[f\_1l\_fig\]. In terms of the integrals (with the convention $D=4+2\epsilon$) $$\begin{aligned}
& &\int \frac{d^Dk}{(2\pi)^D}
\frac{1}{\left[(k-p)^2-m_0^2\right]^\alpha \,k^{2\beta}}
=I\left[\alpha, \beta\right]
\label{I_alpha_beta}\\
& &\int \frac{d^Dk}{(2\pi)^D}
\frac{k^\mu}{\left[(k-p)^2-m_0^2\right]^\alpha \,k^{2\beta}}=p^\mu
J\left[\alpha , \beta\right]
\label{J_alpha_beta}\end{aligned}$$ we find the one-loop expression for $F(p,-p,0)+\bar F(p,-p,0)$. $$F(p, -p, 0)+\bar F(p, -p, 0)=2i g^2\left[ m_0 \left(\dsl{p}-m_0\right)
J(1,2)+\left(p^2+m_0^2\right) J(1,2) -I(1,1)\right]
\label{F+bar_F}$$ and hence the on-shell behavior of $F+\bar F$ to one-loop order is given by $$\lim_{\dsl{p}=M} \left[F(p,-p,0)+\bar F(p,-p,0)\right]=2ig^2
\lim_{\dsl{p}=M=m_0} \left[
2m_0^2 J(1,2)-I(1,1)\right]
\label{on_shell_F}$$ The desired on-shell values for the integals in (\[on\_shell\_F\]) can be reduced to evaluation of a single class of scalar integrals. $$\Lambda\left[\alpha, \beta\right] =
\int \frac{d^Dk}{(2\pi)^D}
\frac{1}{\left[k^2+2 p\cdot k\right]^\alpha \,k^{2\beta}}$$ a particular example being a relation between $J(\alpha, \beta)$ and $\Lambda(\alpha, \beta)$ $$\lim_{\dsl{p}=m_0}J(\alpha, \beta)=\frac{1}{2 m_0^2}\left[
\Lambda(\alpha, \beta-1) -\Lambda(\alpha-1, \beta)\right]$$ The integration by parts technique [@ct] for these on-shell integrals leads to recursion relations among the $\Lambda(\alpha, \beta)$. The identities $$\begin{aligned}
& &0=\int d^Dk \frac{\partial}{\partial k^\mu}\left(
\frac{p^\mu}{\left[k^2+2 p\cdot k\right]^\alpha \,k^{2\beta}}
\right)\label{int_by_parts_1}\\
& &0=\int d^Dk \frac{\partial}{\partial k^\mu}\left(
\frac{k^\mu}{\left[k^2+2 p\cdot k\right]^\alpha \,k^{2\beta}}
\right)\label{int_by_parts_2}\end{aligned}$$ lead to the recursion relations $$\begin{aligned}
& &0= -\beta \Lambda(\alpha-1, \beta+1)+(\beta-\alpha)\Lambda(\alpha, \beta)-2\alpha m_0^2
\Lambda(\alpha+1, \beta)+\alpha \Lambda(\alpha+1, \beta-1)
\label{rec_1}\\
& & 0=(D-2\beta-\alpha)\Lambda(\alpha, \beta)-\alpha\Lambda(\alpha+1, \beta-1 )
\label{rec_2}\end{aligned}$$ The recursion relation (\[rec\_2\]) can also be obtained from dimensional analysis. These recursion relations allow the on-shell behaviour of the one-loop integrals, after setting mass tadpoles to zero, to be reduced to the fundamental dimensional regularization result $$\Lambda(\alpha, 0)=\int\frac{d^D k}{(2\pi)^D} \frac{1}{\left[ k^2-m_0^2\right]^\alpha}
=\frac{i}{(4\pi)^{D/2}}\left(-m_0^2\right)^{2-\alpha} m_0^{2\epsilon}
\frac{\Gamma(\alpha-2-\epsilon)}{\Gamma(\alpha)}
\label{fund_dim_reg}$$ Using the above techniques it is simple to find the on-shell integrals required in (\[on\_shell\_F\]). $$\begin{aligned}
& & J(1,2)=\frac{i}{(4\pi)^{D/2}}m_0^{2\epsilon} \frac{\Gamma(-\epsilon)}{2 m_0^2(D-3)}
\label{J(1,2)}\\
& & I(1,1)=\frac{i}{(4\pi)^{D/2}}m_0^{2\epsilon} \frac{\Gamma(-\epsilon)}{(D-3)}\end{aligned}$$ and hence in the on-shell regularization scheme [@bgs], the Green function $F+\bar F$ is zero on-shell to one-loop order, providing a specific example of our general result.
![Feynman diagram for one-loop contributions to $F(p,-p,0)$. Dashed lines represent the ghost field, and the dotted line represents the auxiliary field $B$. Composite operators coupled to the currents are represented by the partially-filled circles.[]{data-label="f_1l_fig"}](z2_f2.eps)
The gauge dependence of $Z_2$ in QCD can be formulated in a similar fashion. Analogous to (\[ex\_l\_qed\]) the Lagrangian for QCD becomes $${\cal L}=-\frac{1}{4}F^2+\bar \psi\left(i\dsl{D}-m\right)\psi +\frac{\xi}{2} B^2 +B\partial
\cdot A-\bar c\partial^\mu D_\mu c +\frac{\chi}{2}\bar c B
\label{ex_l_qcd}$$ which is invariant under an extended BRS symmetry $$\begin{aligned}
& &\delta^+ A_\mu=\epsilon D_\mu c\quad ,\quad \delta^+ \bar\psi=i\epsilon g c\bar
\psi\quad ,\quad \delta^+ c=-\frac{1}{2} \epsilon g\left[ c,c\right]\nonumber\\
& &\delta^+ B=0\quad ,\quad \delta^+ \psi=-i\epsilon g c\psi \quad ,\quad \delta^+ \bar c=B
\label{qcd_x_brs}\\
& &\delta^+\xi=\epsilon\chi\quad ,\quad \delta^+\chi=0\end{aligned}$$ The extended BRS symmetry (\[qcd\_x\_brs\]) implies the following identity for the effective action nearly identical in form to the QED identity (\[qed\_gamma\_x\_brs\]) $$0=\frac{\delta\Gamma}{\delta K_\mu}\frac{\delta \Gamma}{\delta A_\mu}
+ \frac{\delta\Gamma}{\delta \bar K} \frac{\delta \Gamma}{\delta \psi}
+ \frac{\delta\Gamma}{\delta K}
\frac{\delta \Gamma}{\delta \bar\psi}
+ B\frac{\delta \Gamma}{\delta \bar c}
+\frac{\delta\Gamma}{\delta \bar K_c}
+\chi\frac{\partial\Gamma}{\partial\xi}\frac{\delta \Gamma}{\delta c}
\label{qcd_gamma_x_brs}$$ where $K_\mu$ and $\bar K_c$ are currents coupled to composite operators respectively coupled to the extended BRS variations of $A^\mu$ and $c$. Following the procedure used to develop (\[gamma\_ident\]) leads to a QCD expression in a similar form. $$\frac{\partial}{\partial\xi}\frac{\delta^2\Gamma}{\delta\psi(y)\delta
\bar\psi(x)} =
+
\frac{\delta^3\Gamma}{\delta\psi(y)\delta\bar K\delta \chi}
\frac{\delta^2\Gamma}{\delta\bar\psi(x)\delta\psi}
+
\frac{\delta^2\Gamma}{\delta\psi(y)\delta\bar\psi}
\frac{\delta^3\Gamma}{\delta\bar\psi(x)\delta K\delta\chi}
\label{qcd_gamma_ident}$$ After transforming to momentum space we find a result identical in form to (\[prop\_ident\]). $$\frac{\partial}{\partial\xi}S_F^{-1}(p)=S_F^{-1}(p)\left[ F(p,-p,0)+
\bar F(-p,p,0) \right]
\label{qcd_prop_ident}$$ As in the QED case, we see that the necessary condition for gauge independence of $Z_2$ in QCD is for the Green function $F+\bar F$ to be zero on shell. The distinction between QED and QCD occurs in the interactions, particularly the ghost-gluon interaction, which will contribute to $F(p,-p,0)$. This is particularly evident at three loop level where diagrams (such as those in Figure \[non\_ab\_fig\]) occur that cannot be related to the fundamental two- or three-point Green functions. Thus at three-loop level there is no simple extension of the result (\[on-shell\_F\_1\]) from QED to QCD, and hence gauge independence of $Z_2$ in on-shell schemes seems problematic at the three-loop level and beyond in QCD.
![A three-loop QCD diagram contributing to $F(p,-p,0)$ which cannot be reduced to the the form (\[on-shell\_F\_1\]) composed of fundamental one-particle irreducible Green functions. []{data-label="non_ab_fig"}](z2_f3.eps)
[**Acknowledgements:**]{} TGS is grateful for the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC). TGS thanks Martin Lavelle and Emilio Bagan for discussions at early stages of this work.
[99]{} D.J. Broadhurst, N. Gray, K. Schilcher: Z. Phys. [**C52**]{} (1991) 111.
N. Isgur, M. Wise: Phys. Lett. [**B232**]{} (1989) 113.
O. Piguet, K. Sibold: Nucl. Phys. [**B253**]{} (1985) 517.
J.C. Breckenridge, M.J. Lavelle, T.G. Steele: Z. Phys. [**C65**]{} (1995) 155.
K. Johnson, B. Zumino: Phys. Rev. Lett. [**3**]{} (1959) 351; T. Fukuda, R. Kubo, K. Yokoyama: Prog. Theor. Phys. [**63**]{} (1980) 1384.
N. Nakanishi: Prog. Theor. Phys. [**35**]{} (1966) 1111; B. Lautrup: Mat. Fys. Medd. Dan. Vid. Selsk. [**35**]{} (1967) 29.
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[^1]: email: Tom.Steele@usask.ca
[^2]: An implicit coordinate integration is associated with the $\chi$ derivative.
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Packet-switched networks, such as networks based on the TCP/IP protocol suite, can distribute a rich array of digital content to a variety of client applications. One popular application is a personal computer browser for retrieving documents over the Internet written in the Hypertext Markup Language (HTML). Frequently, these documents include embedded content. Where once the digital content consisted primarily of text and static images, digital content has grown to include audio and video content as well as dynamic content customized for an individual user.
It is often advantageous when distributing digital content across a packet-switched network to divide the duty of answering content requests among a plurality of geographically dispersed servers. For example, popular Web sites on the Internet often provide links to “mirror” sites that replicate original content at a number of geographically dispersed locations. A more recent alternative to mirroring is content distribution networks (CDNs) that dynamically redirect content requests to an edge server situated closer to the client issuing the request. CDNs either co-locate edge servers within Internet Service Providers or deploy them within their own separate networks.
The use of the same reference symbols in different drawings indicates similar or identical items.
|
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Fibrous structures, particularly sanitary tissue products comprising fibrous structures, are known to exhibit different values for particular properties. These differences may translate into one fibrous structure being softer or stronger or more absorbent or more flexible or less flexible or exhibit greater stretch or exhibit less stretch, for example, as compared to another fibrous structure.
One property of fibrous structures that is desirable to consumers is the Dry Burst of the fibrous structure. It has been found that at least some consumers desire fibrous structures that exhibit a Dry Burst of greater than 100 g as measured according to the Dry Burst Test Method.
Accordingly, there exists a need for fibrous structure that exhibit a Dry Burst of greater than 100 g as measured according to the Dry Burst Test Method.
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Bone Thugs-N-Harmony Interview
When Friedrich Nietzsche wrote, “That which does not kill us makes us stronger,” he could easily have been talking about the long and illustrious, but tumultuous career of Bone Thugs-N-Harmony. Though many and varied obstacles, from artistic and financial differences to prison sentences, have divided the Cleveland quintet over the course of their 15-plus years in the game, the Bone brothers have weathered the storms and are now ready to make their comeback with Uni-5: The World’s Enemy, the first LP to feature the full lineup since 2000’s BTNH: Resurrection.
Set to hit stores and online retailers May 4, via BTNH Worldwide/Asylum/Warner Bros, Uni-5 comes complete with official singles “See Me Shine,” “Rebirth” and “Meet Me in the Sky,” as well as leaked tracks “Vegas,” “Gone,” “Pay What You Owe” and the reader-acclaimed “Gangsta’s Glory.” Fans can currently catch four-fifths of BTNH (Layzie, Krayzie, Wish and Flesh) on their ongoing national tour, which began in late March and will run until May 2.
In an exclusive interview with our own DJ “Z,” Layzie, Krayzie, Wish and Flesh step into the Booth to discuss the ways in which their struggles have shaped their musical output, why Bizzy‘s absence from the tour shouldn’t stop fans from purchasing a ticket, and what it will take for Z to finally get all five members on the phone.
Bone Thugs-N-Harmony Interview Transcription
DJ Booth: What’s goin’ on, everybody? It’s your boy, “Z,” doin’ it real big, and joining me inside the DJ Booth is a Grammy Award-winning group who has sold over 30 million albums over the course of their illustrious, 19-year collective career. Gearing up for the release of their brand new album, Uni-5: The World’s Enemy on May the 4th, please welcome Krayzie, Layzie, Wish and Flesh of Bone Thugs-N-Harmony. Guys, how are you doin’?
Bone Thugs: Yeah, yeah! All right! What’s happening?
DJ Booth: The pleasure is all mine. Being able to talk to you guys is always great.
Krayzie: It’s all love, man. Thanks for havin’ us.
DJ Booth: Absolutely. This is actually the fourth Bone Thugs-N-Harmony interview that I’ll have done over the last seven years. But guys, never once have I had the pleasure of speaking with all five of you in one interview. What is it gonna take – some of my grandma’s cookies?
Bone Thugs: [laughter]
Layzie: Cookies… I don’t know [about] your grandma’s cookies, though!
Bone Thugs: Brownies!
DJ Booth: OK, I’ve just gotta tell Grandma to make some of her “special brownies” and we can get all five of you guys on the phone?
Wish: Yep.
DJ Booth: All right – if I had known it was that simple, I would’ve had her make ‘em like seven years ago.
Bone Thugs: [laughter]
DJ Booth: All right. You guys are out on tour right now. You went out on tour at the end of March, going through to the beginning of May. How has it been so far?
Layzie: Man, it’s been an eventful ride, to say the least. But the shows have been sold out, every show we’ve played has been sold out, so it’s just been nonstop rockin’ and rollin’ thug style.
Krayzie: Yeah. There’s been a lot of energy – you know, the crowd has been givin’ us a great response, comin’ out and supportin’ us. To us it seems like the fans never left, so that’s a blessing, and Z, we just wanna say much love to our fans who have been with us this whole ride.
DJ Booth: Guys, obviously, for anyone who has come to see one of your shows, or who is thinking about it, it’s no surprise that Bizzy has not been a part of them. I read Bizzy said, “They asked me not to be a part of it.” And I don’t wanna cause any rifts or start any beef, but is that really what happened, or what is the real reason he is not a part of this tour?
Layzie: To be perfectly honest with you, it wasn’t that we asked him not to be a part of the tour; it was a financial issue with Bizzy, where he felt that we should be makin’ more money. We understood goin’ out on the road as a promotional tour, to promote the album, and it really wasn’t about the money with us. It was more about just building awareness for the album, things like that. So, Bizzy, he made his decision not to come on his own. And I don’t know if he was intoxicated when he said that, or what it was, but we asked Bizzy to come on tour, but he felt we should get more money, and that’s exactly what it was.
DJ Booth: Money always comes between people – I hate that. Hate that.
Flesh: It definitely is a root of evil.
DJ Booth: Guys, what reassurances can you give to your loyal – I mean, really loyal – fans, who were so much looking forward to seeing the whole group perform live as a quintet, that may now be on the fence about coming out to a show, ‘cause they’re not going to get what they originally expected?
Wish: Well, obviously, if they had ever been to a Bone show, there hasn’t been too many of ‘em where they would miss anything, especially a member bein’ gone. Because the show is still gonna be immaculate, there’s gonna be a lot of energy, you’re still gonna be able to hear all the hits and some new music. So, if anybody takes that stand, they’d be a damn fool!
DJ Booth: Very well said. [laughs] The title, as I mentioned in the intro, is Uni-5: The World’s Enemy. Now, Bone Thugs have never played up the whole “bad guy” persona that you see a lot of artists in this industry try to do, so in the title, who are you referring to as the enemy?
Flesh: We’re the world’s enemy: Bone Thugs-N-Harmony ourselves is the world’s enemy. The concept “Uni-5,” that whole ideology of unity, brotherhood, fraternity. And when you’re talking about togetherness, in essence, the world is against unity, period. When you’ve got a strong family foundation, and you’re makin’ noise and building your situation, you’re an enemy against the world in several aspects, a whole lot of aspects in that sense. We’ve been in the game as long as we have, and it’s like a new twist: we’re comin’ with a twist. There are different angles you can look at [it from], why we’re sayin’ we’re the world’s enemy here on this project. Like you say, there’s obstacles – there are four of us here now, sometimes it’s three. There’s a lot of internal situations goin’ on, but nonetheless it’s Bone Thugs-N-Harmony. Throughout all the odds, [we’re] the world’s enemy, and we’re still makin’ it nonetheless, strivin’ to do what we do best, man.
DJ Booth: That’s a great parlay into my next question, because the first featured song of the new album that made its way onto our homepage was the Lyfe Jennings-assisted “See Me Shine.” In a nutshell, really, the song is about overcoming those obstacles, and the people who don’t wanna see you succeed. So, being that you guys have persevered for so long, what have you done to stand up against adversity, and succeed?
Wish: Keep it real, put God first.
Layzie: It’s all about the combination, man. Anything you try to accomplish, you’re gonna have to face some type of adversity, but we just stay persistent at what we do and understand that the key to success is persistence. We just keep on pushin’ and pushin’, man, even when we’ve got that much opposition against us. We just never give up.
DJ Booth: Now, obviously, you guys have seen your fair share of adversity over the course of your collective recording career. Do you ever stop to think: what might our stuff sound like if it was a walk in the park, if things weren’t so difficult, if we didn’t have all these problems?
Layzie: If we didn’t face the things that we faced, we wouldn’t be rappin’ about what we’re rappin’ about, you know what I mean? Like, these obstacles were put in front of us for a reason, and we understand that. So that’s what builds that character, that’s what makes Bone Thugs Bone Thugs-N-Harmony. So, we welcome a challenge at any time. We’re gonna keep welcoming a challenge, and we don’t want it easy, because anything worth havin’ is worth workin’ for. So that’s what it is, man. It builds character within. That’s why Bone Thugs is still strong.
DJ Booth: Just for fun, though, let’s say everything was smooth; everything was goin’ great, you had all five members, all on great terms, no issues whatsoever. What would there be to talk about in the music? Would you have to try to pull back from some of the older stuff?
Layzie: Nah, not really… I guess we’d just be rappin’ happy.
Flesh: We still have fun with it regardless, period, though. We still have a good time with it and have fun with it. We’re kids at heart with it. At the same time we’re adults, grown men, with wives and children and the whole nine yards, and obviously the situation’s gonna be there, and all these adversities, whatever you wanna call it, obstacles, it’s just fuel for the music. We’re sittin’ on a goldmine of topics, based upon our experience and our history.
DJ Booth: Well, let’s talk about an obstacle of a completely different nature, and that’s, when you have five artists and they all need to be heard on a record, and you don’t want the record to be seven, eight, nine minutes long, how do you guys go about divvying up space in terms of the verses on a song, so that everybody is heard, they all have their chance to shine, but it doesn’t become a really long, drawn-out record?
Layzie: Basically, man, we just cut down our verses. Like, even on this album, we wanted to make sure that all five of us was on damn near every song, so what we did was, we came up with the concept of the “uni-verse,” which is all five of us really chain-rapping a 16 – all of us sharin’ a 16 as opposed to havin’ 16’s apiece. So, there’s plenty of ways to get around it: we can shorten the verses – instead of 16 bars it could be eight bars, it could be 12 bars. We don’t really have a problem with that, ‘cause there’s really no egos in Bone Thugs-N-Harmony, so if we all don’t make it on the song sometimes, it’s really not a big deal.
DJ Booth: Does that make the recording process go longer, ‘cause you kinda have to figure it all out before you go into the studio or, at this point you guys have figured it out, and it’s just bing-bang-boom?
Flesh: Yeah, that’s just part of the process. It ain’t a long recording process. Everything is gonna take some amount of time, and we really really are very meticulous about what we do, and perfectionists at what we do, and it really don’t matter how long it takes for us to go in and do what we do. We’re just in there to work and make sure we perfect what we’re doing. Bang-bing-bang!
DJ Booth: [laughs] Bing-bang-boom! Since the quintet, prior to this recording had never previously recorded a complete album together, was chemistry ever an issue during the creation of the project?
Layzie: Not at all, man. Like you said, we’ve been together all our lives. Our chemistry is just there; it’s like, when you play for a team so long, you know the other players on a team, how they feel, what they like, and what they don’t like. So, you know, our chemistry is always clickin’.
DJ Booth: Guys, “Meet Me in the Sky,” one of the newest records that I’ve heard from the forthcoming album, follows a life-after-death theme. Based on the record, can one of you compare and contrast the beginning of your career and now, in terms of how often you might think of or analyze death?
Wish: Damn!
Flesh: Wow… think of and analyze death?
DJ Booth: Yeah. In terms of where you were at at the time when you first started that career, where do you fall on that line now, being that your life is so different than it was in 1991, ‘92?
Krayzie: Well, first of all, that song, “Meet Me in the Sky,” a lot of people misinterpret the song, ‘cause we’re not really actually talkin’ about life after death. What we’re talkin’ about is, again, all the people that’s tried to hold us down, and all the haters that hate on us. We’re tellin’ them that they can never reach us, ‘cause we’re flyin’ in the sky, and they can’t hate us on the ground. Basically just sayin’ we’re on a high that they can never bring us down from.
DJ Booth: I think the video threw me for a loop there.
Layzie: Flyin’ above the haters, man, all our opposition. We’re lookin’ down at the game, we feel like we’re on a whole ‘nother plateau, a whole ‘nother level.
DJ Booth: Are you guys wearin’ jetpacks, or no?
Layzie: No, we got 747 wings, man – we got real rockets, you know?
DJ Booth: Are those expensive? Would I be able to borrow one from time to time, or no?
Wish: [laughs] As long as you fill it back up when you bring it back.
DJ Booth: [laughs] You know, with gas right now, I don’t know about that. We’re gonna take a few reader questions, guys. The first comes from Jonathan from Beijing, China – it’s no surprise; you guys have fans all around the world – and Jonathan wrote, “I’m intrigued at the new approach you guys are taking, appealing to a more mainstream audience with a few of your new records. During the recording, were you concerned at all that fans of your old-school material might be turned off by this new sound.
Layzie: Not, really – not at all, man. ‘Cause we feel like, as we grow, our fans should grow with us. Our music is from the heart, from real-life experiences and really, out of love is where our topics come from, so whoever really don’t dig it, that’s basically on them. We really don’t entertain that.
Wish: We can’t rap about bein’ on the block, and cars, and big-booty women and all that. We rap from the heart – we bring real music. We ain’t on the block anymore. We ain’t sellin’ dope and all that stuff anymore, so how can we rap about it like that? That would be totally fake, and usin’ the gift that we have in the wrong manner.
DJ Booth: I agree. Second question, guys, comes from David of Crown Point, Indiana, and David wrote, “After executive producing your last album, Strength and Loyalty, do you still maintain a relationship with Swizz Beatz and, if so, did he at all contribute material to the new project?
Layzie: We definitely maintain a relationship with Swizz. Swizz looked out for us when nobody didn’t really wanna look out for us, so that brotherly love is always there. We wasn’t really able to bring Swizz in on this particular project, but we do plan on continuing to work with Swizz here and there. We’ve got a hundred songs with him, so that’s a relationship that’s not gonna go nowhere. This album was more of Bone Thugs-N-Harmony, rekindling the flame of how we originally started.
DJ Booth: Absolutely. Now guys, I read two reader questions, but those are two from a whole stack full of them. It’s amazing to me how loyal your fanbase truly is, even on forums and on different websites where I see fans comment about your material; they get really defensive, as if every single fan is almost like a sixth member of the group. Is it amazing to you guys how loyal your fans are?
Flesh: You hit the nail in the coffin right there. That’s a cult following, a solid fanbase, and that’s a real gift, man – not everybody has that. We’ve been blessed to have that, and that’s a real blessing. It is real amazing, and we’re humble and grateful for that.
Wish: It’s something about telling the truth, and how it actually reaches and touches people.
DJ Booth: You know, I jokingly tell people this: when you meet someone, you’re not supposed to talk about three things: sex, politics, and religion. I, a long time ago, added Bone Thugs-N-Harmony into that grouping, ‘cause people get defensive about it. You cannot argue with someone who thinks they know their Bone Thugs.
Layzie: That’s right.
DJ Booth: Well, as always, guys, it’s a pleasure to get you on the phone and do an interview, and does someone wanna give a website or a social network, so they can find out more about you guys and your tour?
Layzie: Yeah. They can check us out at bonethugsnharmony.com, you can go there for all the information you need on Bone.
DJ Booth: Great. Well, thank you guys so much for taking the time to join me inside the DJ Booth for the interview, and as always, nothing but the best of luck, fellas.
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Tag Archives: Turnaround
There are five stages in the turnaround process: management change, situation analysis, emergency action, business restructuring, and return to normality. Look at these individually to understand what should transpire at each stage, and what role each function in the company should play.
There is a process for guiding an entity through corporate renewal. It involves using a transferable set of skills to revitalize the property and restore it to a sale-worthy state. Then, you sell the entity and realize returns.
Investing in under-performers and rebuilding value has become a more acceptable practice. It can be very profitable if you know what to look for and how to execute, as many buyout firms and investors are finding out.
An outside director is a member of the board of directors or advisors who is not part of the executive management team. These individuals are helpful to your company because they rarely have conflicts of interest and they often see the big picture differently than insiders.
There is an abundance of funding available in the marketplace for good deals. The key wording in this statement is of course “good deals.” When a company is in trouble, it is rarely considered a good deal without some fixing.
Too often, companies die unnecessarily because most business leaders haven’t learned to recognize the symptoms of oncoming illness in their business. Leadership hasn’t had to deal with it in the past and is ill equipped when trouble sets in.
When all attempts to save the business have failed, strongly consider liquidating the company — either as a method to withdraw or as a catalyst to help you start over. Most business owners with a large debt burden choose bankruptcy over a workout because it is easier, but a workout might be your best option based on your situation and desired course of action after liquidation.
Business owners willing to invest in realistic incentives that reward employee achievements are likely to reap the proceeds. The key to success is to set realistic goals and time frames, hold managers accountable for performance, and communicate measurement and reward methodology — then step back and let them perform.
President and CEO Paula Kerger has established PBS as a critically acclaimed player in the digital media space, expanded the broadcaster’s service to educators and children, leveraged social media to facilitate thoughtful debates about some of America’s deepest problems, improved relationships and heightened collaboration with member stations, and tapped new sources of funding and resources.
Taking the helm of a newly rebranded bank, Patricia Husic was facing a profound challenge and shouldering a heavy personal risk. A long-time executive with Pennsylvania community banks, Husic had been hired to strengthen the struggling Vartan National Bank in Central Pennsylvania. However, after the bank’s sole owner passed away, his family decided to sell.
|
{
"pile_set_name": "Pile-CC"
}
|
Pat Carroll (basketball)
Pat Carroll (born September 10, 1982) is a retired American professional basketball player. He is a shooting guard who is a three-point specialist.
Carroll is 6'5" is tall and weighs 190 lbs. He played high school basketball at Hatboro-Horsham High School in Horsham, Pennsylvania under coach Walt Ostrowski. He played college basketball at the Saint Joseph's University for Phil Martelli and played with Chris Michaels and future National Basketball Association players Jameer Nelson, Delonte West and Dwayne Jones, being an integral part of Saint Joe's NCAA Elite Eight run in the 2003-2004 season, his junior year.
He, with his brother, Matt, who starred at the University of Notre Dame and played for the NBA's Charlotte Bobcats along with several other teams, and his grandfather, legendary Pennsylvania high school coach Don Graham began Carroll Camps, a basketball camp run by the brothers to teach the fundamentals of basketball, specifically shooting.
Like his brother, Carroll went undrafted out of college. He has been playing in Europe after going unsigned by an NBA team, having unsuccessful tries so far. After injuring his shoulder in a game in Italy in 2005, Carroll returned to the U.S. to undergo surgery and rehabilitate, missing the entire season.
On July 2, 2006, The Philadelphia Inquirer reported that the Houston Rockets had invited Carroll to play on its summer league team in Las Vegas from July 6–14. On August 17, 2006, Carroll signed a contract with the Dallas Mavericks but was waived October 15 before the 2006-07 season started. He would spend that season with France's BCM Gravelines.
Pat also played for the Iowa Energy in the NBA D-League.
Personal
Father John played football at Penn State University.
Grandfather coached basketball at Pittsburgh's North Catholic High School and is the winningest coach in Pennsylvania history.
External links
D-League stats
Spanish League stats
Carroll Camps
Category:1982 births
Category:Living people
Category:American expatriate basketball people in France
Category:American expatriate basketball people in Greece
Category:American expatriate basketball people in Spain
Category:American men's basketball players
Category:Basketball players from Pennsylvania
Category:BCM Gravelines players
Category:CB Lucentum Alicante players
Category:Real Betis Baloncesto players
Category:Greek Basket League players
Category:Ikaros B.C. players
Category:Iowa Energy players
Category:Liga ACB players
Category:Saint Joseph's Hawks men's basketball players
Category:Shooting guards
Category:Sportspeople from Pittsburgh
Category:Tenerife CB players
|
{
"pile_set_name": "Wikipedia (en)"
}
|
Functional expression of CXC chemokine recepter-4 mediates the secretion of matrix metalloproteinases from mouse hepatocarcinoma cell lines with different lymphatic metastasis ability.
CXC chemokine recepter-4 (CXCR4) and its ligand, stromal cell-derived factor-1alpha (SDF-1alpha) have been implicated in the organ-specific metastasis of several malignancies. Hca-F and its syngeneic cell line Hca-P are mouse hepatocarcinoma cell lines with high and low potential of lymphatic metastasis, respectively. Previous studies showed that the secretion of matrix metalloproteinases (MMPs) associated with the metastatic ability of Hca-F and Hca-P cell line depending on the lymph node environment. However, the mechanism of this process has remained unclear. This study investigated the roles of CXCR4 on Hca-F cell and SDF-1alpha of lymph node in lymphatic metastasis. The RT-PCR and Flow cytometry analysis results show that Hca-F cells express higher level CXCR4 mRNA and cell-surface CXCR4 protein, as compared with Hca-P cells. Treatment of recombinant SDF-1alpha proteins induced greater amount of calcium-flux in Hca-F cells than that in Hca-P cells, demonstrating higher functional CXCR4 expression on Hca-F cells than that on Hca-P cells. Furthermore, both the cell-free extratcs of lymph node and recombinant SDF-1alpha proteins induced secretions of active MMP-9 and MMP-2 from Hca-F cells in vitro. But those secretions were significantly reduced by blockade of cell surface CXCR4 with rabbit anti-mouse CXCR4 polyclonal antibody (pAb) and neutralization of SDF-1alpha in lymph node extracts with rabbit anti-mouse SDF-1alpha pAb as well. These results suggest that the CXCR4/SDF-1alpha system mediates active MMP-9 and MMP-2 secretion from Hca-F and Hca-P cells, which facilitates lymphogenous metastasis of those cells consequently.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
//=======================================================================
// Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
// Copyright 2006 The Trustees of Indiana University.
// Copyright (C) 2001 Vladimir Prus <ghost@cs.msu.su>
// Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek, Douglas Gregor
//
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
//=======================================================================
// The mutating functions (add_edge, etc.) were added by Vladimir Prus.
#ifndef BOOST_VECTOR_AS_GRAPH_HPP
#define BOOST_VECTOR_AS_GRAPH_HPP
#include <cassert>
#include <utility>
#include <vector>
#include <cstddef>
#include <iterator>
#include <boost/iterator/counting_iterator.hpp>
#include <boost/range/irange.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/graph/properties.hpp>
#include <algorithm>
/*
This module implements the VertexListGraph concept using a
std::vector as the "back-bone" of the graph (the vector *is* the
graph object). The edge-lists type of the graph is templated, so the
user can choose any STL container, so long as the value_type of the
container is convertible to the size_type of the vector. For now any
graph properties must be stored seperately.
This module requires the C++ compiler to support partial
specialization for the graph_traits class, so this is not portable
to VC++.
*/
namespace boost
{
namespace detail
{
template < class EdgeList > struct val_out_edge_ret;
template < class EdgeList > struct val_out_edge_iter;
template < class EdgeList > struct val_edge;
}
}
namespace boost
{
struct vector_as_graph_traversal_tag : public vertex_list_graph_tag,
public adjacency_graph_tag,
public incidence_graph_tag
{
};
template < class EdgeList > struct graph_traits< std::vector< EdgeList > >
{
typedef typename EdgeList::value_type V;
typedef V vertex_descriptor;
typedef typename detail::val_edge< EdgeList >::type edge_descriptor;
typedef typename EdgeList::const_iterator adjacency_iterator;
typedef
typename detail::val_out_edge_iter< EdgeList >::type out_edge_iterator;
typedef void in_edge_iterator;
typedef void edge_iterator;
typedef counting_iterator< V > vertex_iterator;
typedef directed_tag directed_category;
typedef allow_parallel_edge_tag edge_parallel_category;
typedef vector_as_graph_traversal_tag traversal_category;
typedef typename std::vector< EdgeList >::size_type vertices_size_type;
typedef void edges_size_type;
typedef typename EdgeList::size_type degree_size_type;
static V null_vertex() { return V(-1); }
};
template < class EdgeList > struct edge_property_type< std::vector< EdgeList > >
{
typedef void type;
};
template < class EdgeList >
struct vertex_property_type< std::vector< EdgeList > >
{
typedef void type;
};
template < class EdgeList >
struct graph_property_type< std::vector< EdgeList > >
{
typedef void type;
};
}
namespace boost
{
namespace detail
{
// "val" is short for Vector Adjacency List
template < class EdgeList > struct val_edge
{
typedef typename EdgeList::value_type V;
typedef std::pair< V, V > type;
};
// need rewrite this using boost::iterator_adaptor
template < class V, class Iter > class val_out_edge_iterator
{
typedef val_out_edge_iterator self;
typedef std::pair< V, V > Edge;
public:
typedef std::input_iterator_tag iterator_category;
typedef std::pair< V, V > value_type;
typedef std::ptrdiff_t difference_type;
typedef std::pair< V, V >* pointer;
typedef const std::pair< V, V > reference;
val_out_edge_iterator() {}
val_out_edge_iterator(V s, Iter i) : _source(s), _iter(i) {}
Edge operator*() const { return Edge(_source, *_iter); }
self& operator++()
{
++_iter;
return *this;
}
self operator++(int)
{
self t = *this;
++_iter;
return t;
}
bool operator==(const self& x) const { return _iter == x._iter; }
bool operator!=(const self& x) const { return _iter != x._iter; }
protected:
V _source;
Iter _iter;
};
template < class EdgeList > struct val_out_edge_iter
{
typedef typename EdgeList::value_type V;
typedef typename EdgeList::const_iterator Iter;
typedef val_out_edge_iterator< V, Iter > type;
};
template < class EdgeList > struct val_out_edge_ret
{
typedef typename val_out_edge_iter< EdgeList >::type IncIter;
typedef std::pair< IncIter, IncIter > type;
};
} // namesapce detail
template < class EdgeList, class Alloc >
typename detail::val_out_edge_ret< EdgeList >::type out_edges(
typename EdgeList::value_type v, const std::vector< EdgeList, Alloc >& g)
{
typedef typename detail::val_out_edge_iter< EdgeList >::type Iter;
typedef typename detail::val_out_edge_ret< EdgeList >::type return_type;
return return_type(Iter(v, g[v].begin()), Iter(v, g[v].end()));
}
template < class EdgeList, class Alloc >
typename EdgeList::size_type out_degree(
typename EdgeList::value_type v, const std::vector< EdgeList, Alloc >& g)
{
return g[v].size();
}
template < class EdgeList, class Alloc >
std::pair< typename EdgeList::const_iterator,
typename EdgeList::const_iterator >
adjacent_vertices(
typename EdgeList::value_type v, const std::vector< EdgeList, Alloc >& g)
{
return std::make_pair(g[v].begin(), g[v].end());
}
// source() and target() already provided for pairs in graph_traits.hpp
template < class EdgeList, class Alloc >
std::pair< boost::counting_iterator< typename EdgeList::value_type >,
boost::counting_iterator< typename EdgeList::value_type > >
vertices(const std::vector< EdgeList, Alloc >& v)
{
typedef boost::counting_iterator< typename EdgeList::value_type > Iter;
return std::make_pair(Iter(0), Iter(v.size()));
}
template < class EdgeList, class Alloc >
typename std::vector< EdgeList, Alloc >::size_type num_vertices(
const std::vector< EdgeList, Alloc >& v)
{
return v.size();
}
template < class EdgeList, class Allocator >
typename std::pair< typename detail::val_edge< EdgeList >::type, bool >
add_edge(typename EdgeList::value_type u, typename EdgeList::value_type v,
std::vector< EdgeList, Allocator >& g)
{
typedef typename detail::val_edge< EdgeList >::type edge_type;
g[u].insert(g[u].end(), v);
return std::make_pair(edge_type(u, v), true);
}
template < class EdgeList, class Allocator >
typename std::pair< typename detail::val_edge< EdgeList >::type, bool > edge(
typename EdgeList::value_type u, typename EdgeList::value_type v,
std::vector< EdgeList, Allocator >& g)
{
typedef typename detail::val_edge< EdgeList >::type edge_type;
typename EdgeList::iterator i = g[u].begin(), end = g[u].end();
for (; i != end; ++i)
if (*i == v)
return std::make_pair(edge_type(u, v), true);
return std::make_pair(edge_type(), false);
}
template < class EdgeList, class Allocator >
void remove_edge(typename EdgeList::value_type u,
typename EdgeList::value_type v, std::vector< EdgeList, Allocator >& g)
{
typename EdgeList::iterator i = std::remove(g[u].begin(), g[u].end(), v);
if (i != g[u].end())
g[u].erase(i, g[u].end());
}
template < class EdgeList, class Allocator >
void remove_edge(typename detail::val_edge< EdgeList >::type e,
std::vector< EdgeList, Allocator >& g)
{
typename EdgeList::value_type u, v;
u = e.first;
v = e.second;
// FIXME: edge type does not fully specify the edge to be deleted
typename EdgeList::iterator i = std::remove(g[u].begin(), g[u].end(), v);
if (i != g[u].end())
g[u].erase(i, g[u].end());
}
template < class EdgeList, class Allocator, class Predicate >
void remove_edge_if(Predicate p, std::vector< EdgeList, Allocator >& g)
{
for (std::size_t u = 0; u < g.size(); ++u)
{
// Oops! gcc gets internal compiler error on compose_.......
typedef typename EdgeList::iterator iterator;
iterator b = g[u].begin(), e = g[u].end();
if (!g[u].empty())
{
for (; b != e;)
{
if (p(std::make_pair(u, *b)))
{
--e;
if (b == e)
break;
else
iter_swap(b, e);
}
else
{
++b;
}
}
}
if (e != g[u].end())
g[u].erase(e, g[u].end());
}
}
template < class EdgeList, class Allocator >
typename EdgeList::value_type add_vertex(std::vector< EdgeList, Allocator >& g)
{
g.resize(g.size() + 1);
return g.size() - 1;
}
template < class EdgeList, class Allocator >
void clear_vertex(
typename EdgeList::value_type u, std::vector< EdgeList, Allocator >& g)
{
g[u].clear();
for (std::size_t i = 0; i < g.size(); ++i)
remove_edge(i, u, g);
}
template < class EdgeList, class Allocator >
void remove_vertex(
typename EdgeList::value_type u, std::vector< EdgeList, Allocator >& g)
{
typedef typename EdgeList::iterator iterator;
clear_vertex(u, g);
g.erase(g.begin() + u);
for (std::size_t i = 0; i < g.size(); ++i)
for (iterator it = g[i].begin(); it != g[i].end(); ++it)
// after clear_vertex *it is never equal to u
if (*it > u)
--*it;
}
template < typename EdgeList, typename Allocator >
struct property_map< std::vector< EdgeList, Allocator >, vertex_index_t >
{
typedef identity_property_map type;
typedef type const_type;
};
template < typename EdgeList, typename Allocator >
identity_property_map get(
vertex_index_t, const std::vector< EdgeList, Allocator >&)
{
return identity_property_map();
}
template < typename EdgeList, typename Allocator >
identity_property_map get(vertex_index_t, std::vector< EdgeList, Allocator >&)
{
return identity_property_map();
}
} // namespace boost
#endif // BOOST_VECTOR_AS_GRAPH_HPP
|
{
"pile_set_name": "Github"
}
|
Comfort Keepers San Marcos
San Marcos, TX
Home Health Care
Comfort Keepers San Marcos
109 E Hopkins St, Ste 203San Marcos, TX78666
(830) 302-3684
Comfort Keepers is a leading provider of in-home and in-facility care services. We help seniors and other adults live independent, quality lives in the comfort of their own homes. Our unique, interactive care services include companion and personal care, transportation, transitioning home, and respite care, and our passion for providing loving, experienced care and support is expressed in everything we do. We offer 24/7 care and available for emergencies 24/7.Contact us today for more information!
4.7 stars based on 14 responses
Coming soon!
Comfort Keepers San Marcos
109 E Hopkins St, Ste 203San Marcos, TX78666
(830) 302-3684
Comfort Keepers is a leading provider of in-home and in-facility care services. We help seniors and other adults live independent, quality lives in the comfort of their own homes. Our unique, interactive care services include companion and personal care, transportation, transitioning home, and respite care, and our passion for providing loving, experienced care and support is expressed in everything we do. We offer 24/7 care and available for emergencies 24/7.Contact us today for more information!
|
{
"pile_set_name": "Pile-CC"
}
|
[Influence of endogenous factors on the ash, calciu, magnesium, potassium, sodium, phosphorus, zinc, iron, copper and manganese contents in the bristles of pigs. 4. Effect of time of cutting and heredity on the inorganic components in the hair of the pigs (bristles of sows and piglets, newly grown hair)].
Samples of sow bristles were examined every 3 months. The results obtained confirmed the monthly gathered experimental data on the ash content and the Ca, Mg, K, and Na content (P less than 0.05-0.001) of Boar Bristles. Similarly, investigations made every 3 months showed a significant seasonal influence on the concentration of these mineral components in the bristles of the pigs (P less than 0.05-0.001). A comparison was made between newly grown hair and original bristles showing the presence of other yet unknown factors that had a controlling influence on the mineral composition of the hair. The inorganic components in the short newly grown hair were not different from those found in analogous long hair.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
Authorities in Missouri said Sunday that four teens robbed victims after luring them to a specific location using the “Pokemon Go” smartphone game.
O’Fallon police said that four teens used the game to draw victims to a certain spot in the town and then robbed them. The new mobile game sends players to locations to collect “Pokemon” characters. Police said the robbers used the game to lure victims by putting a “beacon” at a location to draw in players.
O’Fallon Sgt. Phil Hardin joked to reporters that some of the younger officers had to let their colleagues in on the intricacies of the game so they could understand what the victim was talking about.
“All of the elements of a robbery were all there, so that part was easy, but the more in-depth discussion that followed was like, ‘What?’” Hardin said. “You really can’t make this stuff up.”
According to the St. Louis Post-Dispatch, police arrested the group of teens after responding to a report of a robbery near a gas station. The suspects are between the ages of 16 and 18.
Police said the suspects may have been involved in in nearly a dozen robberies around St. Louis.
The Associated Press contributed to this report.
|
{
"pile_set_name": "OpenWebText2"
}
|
---
abstract: |
This paper describes SEPIA, a tool for automated proof generation in Coq. SEPIA combines model inference with interactive theorem proving. Existing proof corpora are modelled using state-based models inferred from tactic sequences. These can then be traversed automatically to identify proofs. The SEPIA system is described and its performance evaluated on three Coq datasets. Our results show that SEPIA provides a useful complement to existing automated tactics in Coq.
Interactive Theorem Proving; Model Inference; Proof Automation
author:
- 'Thomas Gransden, Neil Walkinshaw and Rajeev Raman'
bibliography:
- 'cade-bib.bib'
title: 'SEPIA: Search for Proofs Using Inferred Automata[^1]'
---
Introduction
============
Interactive theorem provers (ITPs) such as Coq [@Coq:manual] and Isabelle [@Isabelle02] are systems that enable the manual development of proofs for a variety of domains. These range from mathematics through to complex software and hardware verification. Thanks to the expressive logics that are used, they provide a very rich programming environment.
Nevertheless, constructing proofs can be a challenging and time-consuming process. A proof development will typically contain many routine lemmas, as well as more complex ones. The ITP system will take care of the bookkeeping and perform simple reasoning steps; however much time is spent manually entering the requisite tactics (even for the most trivial lemmas). In 2008, Wiedijk stated that it takes up to one week to formalize a page of an undergraduate mathematics textbook [@Freek08].
To help combat this problem, we present SEPIA (Search for Proofs Using Inferred Automata) – an automated approach designed to assist users of Coq. SEPIA automatically generates proofs by inferring state-based models from previously compiled libraries of successful proofs, and using the inferred models as a basis for automated proof search.
Background {#sec:background}
==========
This section presents the necessary background required for this paper. We briefly introduce the underlying model inference technique (called MINT), followed by a motivating example.
Inferring EFSMs with MINT {#sub:inferringEfsms}
-------------------------
MINT [@WalkinshawWCRE] is an technique designed to infer state machine models from sequences, where the sequencing of events may depend on some underlying data state. Such systems are modelled as extended finite state machines (see Definition \[def:efsm\]). EFSMs can be conceptually thought of as conventional finite state machines with an added memory. The transitions in an EFSM not only contain a label, but may also contain guards that must hold with respect to variables contained in the memory.
***Extended Finite State Machine*** \[def:efsm\] An Extended Finite State Machine (EFSM) $M$ is a tuple $(S,s_0,F,L,V,\Delta,T)$. $S$ is a set of states, $s_0 \in S$ is the initial state, and $F \subseteq S$ is the set of final states. $L$ is defined as the set of labels. $V$ represents the set of data states, where a single instance $v$ represents a set of concrete variable assignments. $\Delta:V \rightarrow \{True,False\}$ is the set of *data guards*. Transitions $t \in T$ take the form $(a,l,\delta,b)$, where $a,b \in S$, $l \in L$, and $\delta \in \Delta$.
MINT infers EFSMs from sets of *traces*. These can be defined formally as follows:
\[def:traces\] A *trace* $T=\langle e_0,\ldots,e_n\rangle$ is a sequence of $n$ trace elements. Each element $e$ is a tuple $(l,v)$, where $l$ is a label representing the names of function calls or input / output events, and $v$ is a string containing the parameters (this may be empty).
The inference approach adopted by MINT [@WalkinshawWCRE] is an extension of a traditional state-merging approach [@Lang1998] that has been proven to be successful for conventional (non-extended) finite state machines [@WalkinshawStamina]. Briefly, the model inference starts by arranging the traces into a *prefix-tree*, a tree-shaped state machine that exactly represents the set of given traces. The inference then proceeds by a process of *state-merging*; pairs of states in the tree that are roughly deemed to be equivalent (based on their outgoing sequences) are merged. This merging process yields an EFSM that can accept a broader range of sequences than the initial given set.
The transitions in an EFSM not only imply the sequence in which events can occur, but also place constraints on which parameters are valid. This is done by inferring data-classifiers from the training data – each data guard takes the following form $(l,v,possible)$ where $l \in L$, $v \in V$ and $possible \in$ {$true, false$}. When states are merged, the resulting machine is checked to make sure it remains consistent with the data guards.
Motivating Example
------------------
To motivate this work, we consider a typical scenario that arises during interactive proof. Suppose that we are trying to prove the following conjecture: `forall n m p:nat, p + n <= p + m -> n <= m`. The automated Coq tactics [@BC04] have only been able to perform routine reasoning (namely calling the `intros` tactic) to advance the proof to the following:
n : nat
m : nat
p : nat
H : p + n <= p + m
============================
n <= m
There are 2 theories from the Coq Standard Library called `Le.v` and `Lt.v`, that contain proofs about similar properties. The built-in tactics fail to prove the goal. The question we are faced with is this: Given the examples of successful proofs, can we use these to automatically find a proof for the above conjecture?
In previous work [@GransdenCICM] we showed how to use MINT to infer EFSM models of Coq proofs. The resulting EFSMs were simply presented and used manually to derive proofs. This work extends our previous approach by automating the search process, allowing proofs to be completed automatically.
SEPIA System Description {#sec:implementation}
========================
In this section we describe the SEPIA approach. We present the key stages of the technique. It is available[^2] as a ProofGeneral extension that works with Coq. An overview of SEPIA is shown in Figure \[fig:system\]. It contains three main stages:
1. [Generate proof traces from a selection of existing Coq theories.]{}
2. [Use MINT to infer a model from these proof traces.]{}
3. [Systematically search the model, formulating and attempting possible proofs from paths through the model.]{}
![SEPIA overview[]{data-label="fig:system"}](System)
Before describing these three steps in more detail, we look at three properties of the approach that are particularly appealing:
#### Adaptivity
For every iteration, as more valid proofs are discovered they can be incorporated into future cycles to infer more accurate models, forming a ‘virtuous loop’. This is a major benefit over the existing built-in automated tactics, which are typically limited to attempting a fixed set of tactics.
#### Automation
Aside from providing the initial set of theories from which to infer a model, the user is not prompted for any other input. In addition, as will be elaborated later, the overall process typically completes in less than a minute (at least in the context of our experiments).
#### Ability to identify new proofs
The state-merging process [@WalkinshawWCRE] can result in models that accept sequences of tactics which aren’t present in the initial set of proofs. These wouldn’t necessarily be intuitive, or be spotted from manual scrutiny of the proof library. These can however contain valuable steps that lead to a successful proof.
Generating traces from existing proofs
--------------------------------------
To begin a proof attempt we must provide one or more Coq theories from which we wish to generate a model. The proofs within the theories must be converted into their corresponding *proof traces* (see Definition \[def:traces\]). This step is identical to the process used in our previous work [@GransdenCICM].
Figure \[fig:traces\] shows the proof script from the lemma `le_antisym` from `Le.v` and the corresponding proof trace. An important concept in Coq proofs is the semicolon operator. If two (or more) tactics are separated by a semicolon, for example `t1;t2`, this means apply `t1` to the current goal and then apply `t2` to *all* generated subgoals. We record the usage of the semicolon in our traces, so that this information can be reused during proof search.
+:---------------------------------:+:---------------------------------:+
| \(a) Proof Script | \(b) Trace |
+-----------------------------------+-----------------------------------+
| | |
+-----------------------------------+-----------------------------------+
| intros n m H; | ------------------------------- |
| destruct H as [|m' H]; | ------------------------------- |
| auto with arith. | Event $e$ Label $l$ Params |
| intros H1. | $v$ |
| absurd (S m' <= m'); | ----------- ----------- ------- |
| auto with arith. | ------------------------------- |
| apply le_trans with n; | $e_0$ intros “n m H; |
| auto with arith. | "\ |
| | $e_1$ & |
| | destruct&“H as \[$|$m’ H\];"\ |
| | $e_2$ & |
| | auto&“with arith"\ |
| | $e_3$ & |
| | intros&“H1"\ |
| | $e_4$ & |
| | absurd&“(S m’ $<=$ m’);"\ |
| | $e_5$ & |
| | auto&“with arith"\ |
| | $e_6$ & |
| | apply&“le\_trans with n;"\ |
| | $e_7$ & |
| | auto&“with arith" |
| | ------------------------------- |
| | ------------------------------- |
+-----------------------------------+-----------------------------------+
Inferring the model
-------------------
Once the proof traces have been generated, MINT is invoked to infer a model. There are two main parameters associated with MINT. The inference strategy dictates how states are merged during the inference process. A value called $k$ represents the minimum score before a pair of states can be deemed to be equivalent. An in-depth discussion of these variables is outside the scope of this paper.
A preliminary study (with results online) found that using the state merging strategy `redblue` and $k=1$ performed reasonably well for the task of interactive proving. These settings are based on the number of proofs discovered, the time taken and the presence of shorter/novel proofs. For the rest of this paper we refer to these as the default settings for MINT. A portion of the EFSM inferred from [Le.v]{} and [Lt.v]{} is shown in Figure \[fig:efsmexample\].
![Portion of inferred EFSM from [Le.v]{} and [Lt.v]{}[]{data-label="fig:efsmexample"}](model-initial)
Searching for a proof
---------------------
Once a model has been inferred it can be used to search for candidate proofs. We adopt a breadth-first search as this ensures that if a proof is contained in the model, the shortest one will be returned. An instance of Coq is loaded, and the lemma is stated. The proof search moves through the model and applies the tactics and arguments suggested on each transition.
A timeout or a limit on the number of tactics applied can be provided to control the search. If we reach a point where a proof is found, SEPIA outputs the proof (and some proof search statistics). When running SEPIA on our motivating example we obtain the following result:
Proof was: intros m n diff. elim diff; auto with arith.
5611 tactics evaluated.
Inference and search took 0 min, 1 sec
The above proof is particularly interesting for two reasons. Firstly, we have managed to prove something completely automatically that Coq’s automated tools could not. Secondly, the sequence of tactics (and parameters) was not found anywhere else within `Le.v` or `Lt.v`.
Evaluation {#sec:eval}
==========
In this section we provide an experimental evaluation of our approach. We consider the following research questions:
- [[**RQ1:** ]{}Can proofs be derived automatically using our approach?]{}
- (a): How many proofs can be found?
- (b): How long does it take to find a proof?
- [[**RQ2:** ]{}Are there “interesting" characteristics of the proofs?]{}
- (a): Do the proofs contain new sequences of tactics?
- (b): Are the proofs shorter?
- [[**RQ3:** ]{}How does our results compare to Coq’s built-in automated tactics?]{}
Methodology
-----------
The aim of this evaluation is to assess the practicalities of using our approach in real proof developments. We evaluate SEPIA on three distinct Coq contributions as our datasets. We use a method inspired by $k$-folds cross-validation [@KohaviIJCAI] in order to study proof attempts made by our approach.
### Datasets
The datasets used in this evaluation consist of theories selected from three Coq proof developments. The datasets were chosen mainly for their domain, complexity and size. All theories were selected before the experiments took place. SSreflect[^3] contains seven core theories. We select all of these theories as our first dataset. Secondly, MSets[^4] is an implementation of finite sets using lists/trees. All eleven theories are selected to form our second dataset. Finally, we use some theories from CompCert[^5]. Owing to the size of the development, we select a four theories containing both general purpose proofs along with some more specialized ones. Due to the exploratory nature of this evaluation, there are some threats to validity associated with the selection of data. We have only used three Coq datasets, so any results cannot be interpreted to represent performance on all Coq proofs.
### Evaluating Proof Attempts
To provide some answers to RQ1, we want to model the following situation: given some existing proofs, can we use these to prove new properties that are not part of the initial collection. To do this, we use an approach inspired by *k*-folds cross-validation [@KohaviIJCAI].
Each Coq theory file is taken individually and the proofs are randomly partitioned into $k$ non-overlapping sets. We then infer a model from $k-1$ of the sets, and try and prove the lemmas in the remaining set. This process repeats until each set has been used exactly once as the collection of lemmas to be proved.
For each proof attempt, we allow 10,000 tactics to be applied before reporting a failure. The results presented in this paper are from using $k=10$, a standard value for $k$-folds cross-validation [@KohaviIJCAI]. Other values of $k$ have been investigated and the full set of results are online.
As well as capturing whether a proof attempt was successful or not, when a proof is found we analyse how “interesting" the proof is. First, we check and see whether a proof is shorter than the corresponding hand-curated proof. We also check whether the sequence of tactics was new (i.e. not present in the examples the model was inferred from). These provide us with answers to RQ2.
To investigate RQ3 we also run the Coq automated tools to try and prove each lemma. The following command is issued to Coq: `auto with * || eauto with * || tauto || firstorder || trivial`. This simply attempts to prove a goal by trying all of the automated tactics. The default search depth is used in all cases. Where we can specify lemma databases, we allow any available database to be used during proof search.
Results
-------
The full results from our experiments are shown in Table \[tab:res\]. The results are presented for each theory, grouped by library. The remainder of this section provides some answers to the research questions defined earlier.
------------------------ -------------- ---------- ----------- --------- ------------- --------------
(r)[4-6]{} **Library** **Theory** **Size** **Total** **New** **Shorter** **Coq-Tacs**
ssrnat 341 135 (39%) 14 9 59 (17%)
ssrbool 240 120 (50%) 17 10 60 (25%)
seq 394 94 (24%) 14 6 18 (4%)
fintype 243 42 (17%) 15 1 0 (0%)
eqtype 82 36 (44%) 18 2 10 (12%)
choice 30 6 (20%) 0 0 1 (3%)
ssrfun 30 5 (16%) 1 0 7 (23%)
avl 26 0 (0%) 0 0 0 (0%)
decide 22 18 (81%) 0 3 4 (18%)
eqproperties 106 43 (40%) 1 5 47 (44%)
facts 65 17 (26%) 4 8 10 (15%)
gentree 61 9 (15%) 3 3 3 (5%)
list 42 8 (19%) 3 3 3 (7%)
positive 67 13 (19%) 5 4 1 (1%)
properties 137 78 (57%) 9 3 15 (11%)
rbt 89 12 (13%) 10 6 2 (2%)
tofiniteset 14 5 (35%) 2 2 4 (28%)
weaklist 27 8 (30%) 4 5 6 (22%)
cshmgenproof 65 15 (23%) 14 14 0 (0%)
amsgenproof0 57 12 (21%) 9 9 6 (10%)
coqlib 114 36 (31%) 24 23 16 (14%)
values 99 20 (20%) 17 13 5 (5%)
------------------------ -------------- ---------- ----------- --------- ------------- --------------
: Results Summary[]{data-label="tab:res"}
### RQ1(a): A significant proportion of the lemmas were proved automatically using our approach
In Table \[tab:res\], the column headed SEPIA shows the total number of lemmas proved in each theory using our approach. The results suggest that EFSM-based methods are useful at finding proofs automatically. Looking at each dataset as a whole, 32% (438 out of 1360) of the SSreflect dataset were proved. In MSets, 30% (211 out of 687) were successfully proved using our approach. In our selection of CompCert theories, there were 25% (83 out of 335) proved.
### RQ1(b): Many proofs were discovered in under 30 seconds
We measured the time required to derive a proof using our approach. These times take into account both the time required to infer the model and the search time. Over 90% of the proofs were found within 30 seconds. These results show that when a user invokes the process, a proof will usually be delivered quickly. Overall, a proof can be discovered in a relatively small period of time. Of course, this is encouraging for the user involved in the proof development.
### RQ2(a): A quarter of the proofs found were new sequences of tactics
The number of new proofs discovered using our approach are listed under the ‘New’ column in Table \[tab:res\]. We compare the discovered proof with the ones used to infer the model If the sequence is not contained in an existing proof, then it is considered new and only found as a result of inferring an EFSM. Our results show a significant number of new proofs were discovered, backing up further that EFSMs can be useful for automated proof generation. In SSreflect, a total of 79 proofs were new. In the MSets theories, 41 new proofs were found, and 64 were discovered in CompCert.
### RQ2(b): Many proofs discovered were shorter than their original ones
We have listed the number of shorter proofs found in Table \[tab:res\] under the Shorter column. When a proof is found, we compare the discovered proof with the original hand-curated one. The length (in terms of tactics used) of both proofs are then compared, to see if we managed to derive a shorter one. In SSreflect, 28 of the proofs found were shorter than their original counterparts. For MSets, 42 of the proofs were shorter, whilst in CompCert 59 of proofs were shorter. The combination of the state merging algorithms and a breadth-first search means we were able to identify these shorter proofs.
### RQ3: SEPIA provides an alternative to existing Coq tactics
The column headed Coq-Tacs in Table \[tab:res\] provides the number of lemmas that were proved using Coq’s automated tactics. Despite being relatively limited in the steps that they try, they manage to prove 155 SSreflect lemmas, 95 MSets lemmas and 27 of the CompCert lemmas. On the whole, we see that our approach significantly outperforms the automated tactics in terms of number of lemmas proved. This is to be expected, as they only provide modest automation. Nevertheless, there are occasions where the automated tactics prove more lemmas (in `msetproperties` and `ssrfun` for instance).
Related Work {#sec:related}
============
There have been many projects aimed at improving the automation of proofs in ITPs. As we have shown in this work, machine learning can be applied in the context of interactive theorem proving. Specifically, we have shown that the tactics used in proofs can serve as useful features for machine learning algorithms. This is an area that has received moderate attention previously.
Jamnik *et al.* have previously applied an Inductive Logic Programming technique to examples of proofs in the $\Omega$mega system [@Jamnik03]. Given a collection of well chosen proof method sequences, Jamnik *et al.* perform a method of least generalisation to infer what are ultimately regular grammars. The value of even basic models is intuitive. Proofs could be derived automatically using the technique. However, the proof steps learned do not contain any parameters. The parameters required are reconstructed after running the learning technique.
Another approach that concentrated on Isabelle proofs was implemented by Duncan [@Duncan07]. Duncan’s approach was to identify commonly occurring sequences of tactics from a given corpora. After eliciting these tactic sequences, evolutionary algorithms were used to automatically formulate new tactics. The evaluation showed that simple properties could be derived automatically using the technique; however the parameter information was left out of the learning approach.
Conclusion and Future Work {#sec:conclusion}
==========================
This paper has presented SEPIA, an approach to automatically generate proofs in Coq. This has been achieved by applying model inference techniques to interactive proof scripts. We have shown that even learning from tactic sequences, which is admittedly a simplistic view of interactive proofs, can provide effective proof automation. It would be interesting to see what can be achieved by using more sophisticated views such as the proof goal view [@Grov12].
The overall process is fully automated our evaluation shows SEPIA performs well on a range of proofs from three varied Coq datasets. It succeeds in proving a number of lemmas that were out of reach for Coq’s automated tactics. Additionally, when SEPIA finds a proof it usually does so in seconds.
As well as reusing existing proofs, SEPIA can construct proofs using new tactic sequences. These new sequences might not have been identified if manually analysing proof libraries. In our evaluation, we also identified a number of shorter proofs (by comparing the proofs found using SEPIA to original proofs). This follows the trend of other comparisons of automated and human proofs [@Alama12].
We plan to investigate automatic identification of appropriate theories or lemmas that could be used to infer models. Currently, we use whole theories; however it may be the case that only a handful of these proofs are actually useful. By using methods such as ML4PG [@ML4PG13] it may be possible to discover the most useful lemmas from a large collection of theories.
[^1]: The final publication is available at http://link.springer.com.
[^2]: https://bitbucket.org/tomgransden/efsminferencetool
[^3]: http://ssr.msr-inria.inria.fr/doc/ssreflect-1.4/
[^4]: https://coq.inria.fr/library/
[^5]: http://compcert.inria.fr/doc/index.html
|
{
"pile_set_name": "ArXiv"
}
|
Q:
Form created with React doesn't update the backing state object
I am trying to automate the login form of Instagram web app:
https://instagram.com/accounts/login/
With the following code (you can run it on Chrome console):
var frm = window.frames[1].document.forms[0];
frm.elements[0].value = 'qacitester';
frm.elements[1].value = 'qatester';
frm.elements[2].click();
Even though the inputs are populated, when I monitor the XHR request, I see this is posted:
username=&password=&intent=
rather than this:
username=qacitester&password=qatester&intent=
And causes web app to not authenticate. Do you have any idea why the input values are not transferred to the backing state (model?) object of React?
A:
Instagram is using the linkState method from ReactLink:
http://facebook.github.io/react/docs/two-way-binding-helpers.html
The login page links to a bundles/Login.js that contains compressed code like this:
o.createElement("input", {
className:"lfFieldInput",
type:"text",
name:"username",
maxLength:30,
autoCapitalize:!1,
autoCorrect:!1,
valueLink:this.linkState("username")
}))
If you look at the documentation for ReactLink, this means that the input field value only gets sent back to state when the change event fires on the input fields. However, it's not as simple as just firing the change event on the node in question - I think due to the way that React normalises browser events. The React docs specifically say that onChange in React isn't exactly the same as onChange in the browser for various reasons:
http://facebook.github.io/react/docs/dom-differences.html
Fortunately in your case Instagram are using React with Addons included which gives you access to React TestUtils, so you can do:
var frm = window.frames[1].document.forms[0];
var fReact = window.frames[1].React;
fReact.addons.TestUtils.Simulate.change(frm.elements[0], {target: {value: 'qacitester' }});
fReact.addons.TestUtils.Simulate.change(frm.elements[1], {target: {value: 'qatester' }});
frm.elements[2].click();
More documentation here:
http://facebook.github.io/react/docs/test-utils.html
Notice that since the login form itself is in an iframe, you must use the instance of React from that iframe otherwise the TestUtils won't be able to find the nodes correctly.
This will only work in situations where React Addons are included on the page. The normal non-Addons build of React will require another solution. However, if you're specifically talking about ReactLink then that's an addon anyway, so it's not an issue.
A:
Answering my own question, the required event is input event it seems and this code works:
var doc = window.frames[1].document;
var frm = doc.forms[0];
frm.elements[0].value = 'qacitester';
var evt = doc.createEvent('UIEvent');
evt.initUIEvent('input', true, false);
frm.elements[0].dispatchEvent(evt);
frm.elements[1].value = 'qatester';
frm.elements[1].dispatchEvent(evt);
frm.elements[2].click();
|
{
"pile_set_name": "StackExchange"
}
|
Posttraumatic stress symptoms in adolescent survivors of childhood cancer and their mothers.
We examined symptoms of posttraumatic stress disorder (PTSD) in adolescent survivors of childhood cancer and their mothers and the contribution of family functioning, including perceived emotional support and familial conflict, and individual factors including life stress and severity of disease to PTSD symptoms. Participants were 52 adolescent cancer survivors and their mothers and 42 healthy adolescent counterparts and their mothers. Findings revealed that mothers of cancer survivors endorsed more PTSD symptoms than did their healthy counterparts and that survivors and mothers also reported greater recent and past stressful life events. Although no survivors met clinical criteria for a PTSD diagnosis, over 36% endorsed mild subthreshold symptomatology. Findings are discussed in the context of understanding PTSD symptoms within a family systems framework.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
Figure 8 in East Austin doesn't have the serious atmosphere that many Austin coffee shops give off, but the coffee is nothing to joke about. For example, the La Marzocco Italian espresso machine practically lights up the place. The coffee shop features roasters from Portland and San Francisco in addition to local roasters such as Tweed and Wild Gift. The friendly service attracts musicians, DJs and anyone wanting a great cup of coffee. Pastries are the only food option on the menu, but there's plenty of alcohol options.
Figure 8 Coffee Purveyors
Figure 8 in East Austin doesn't have the serious atmosphere that many Austin coffee shops give off, but the coffee is nothing to joke about. For example, the La Marzocco Italian espresso machine practically lights up the place. The coffee shop features roasters from Portland and San Francisco in addition to local roasters such as Tweed and Wild Gift. The friendly service attracts musicians, DJs and anyone wanting a great cup of coffee. Pastries are the only food option on the menu, but there's plenty of alcohol options.
|
{
"pile_set_name": "Pile-CC"
}
|
What if?
Finish watching Silence. My second time – never thought I would rewatched this series. Too bored. For those who don’t know, Silence is a drama featuring a guy with terminal stage cancer and has only 3 more months to live. While it is not anywhere near as sad as One Litre of Tears – it never fails to sadden me, knowing all too well that this portrayal can very well be related to someone in reality. And it’s even sadder to note the ‘anticipation’ of death’s arrival and how their days are numbered without truly knowing when they’re leaving. My only console is that at least they know they are leaving.
Someone once asked me, would I rather die suddenly or would I rather find out that I am dying? My answer was clear – to know when I’ll die. Even though that means I’ll be freaking out, counting frantically for the remaining days I have. Even though that means I’ll be in tears knowing that death is upon me. Because I want to be prepared. I want people around me to be prepared. I don’t want to leave without saying goodbye. Without telling my family how much I love them and I’ll trade in whatever I have just to be with them again in next life (if there is next life). And certainly not without having ‘completed’ my life and purpose on earth.
The character in the drama asked, “If tomorrow is Judgement Day, what will you want to do most?” I thought to myself and came into the conclusion that I’ll probably just continue living like normal because all of us will die together anyway so it doesn’t really matter. But what if tomorrow is the last day of your life? The one thing I want to do the most is to be with my family. I guess it’s kind of true that they say Cancerians are homies. Will I want to tick off the ’10 things you must do before you die’ list? Of course yes. But it doesn’t matter. Right upto this point of my life, while I haven’t been given all I wanted, I really have had what I needed. I am extra grateful for what I have achieved in life so far and if this is the end, then so be it – it’s entirely up to my destiny. I have been leading a very happy and fulfilling life – there’s small bumps here and there but definitely no regrets.
I’m the kind of person who will never commit suicide (unless under very very unusual circumstances) because what else can be worst than not being able to open your eyes and breath life tomorrow? Yes, tomorrow can be painful but if only you know how many people in the world would be willing to trade that one chance with you. If only.
Anyway, this post is directed towards nobody but myself, so don’t panic. And wtf, please don’t think that something has happened to me ok *touch WOOD* – I’m very well thank you. Was just thinking a lot. If you still haven’t get the vibe, I love me life very very much and I sincerely hope you do too ^^,
|
{
"pile_set_name": "Pile-CC"
}
|
Q:
ASP.NET Website Administration Tool: Unable to connect to SQL Server database
I am trying to get authentication and authorization working with my ASP MVC project. I've run the aspnet_regsql.exe tool without any problem and see the aspnetdb database on my server (using the Management Studio tool).
my connection string in my web.config is:
<connectionStrings>
<add name="ApplicationServices"
connectionString="data source=MYSERVERNAME;Integrated Security=SSPI;AttachDBFilename=|DataDirectory|aspnetdb.mdf;User Instance=true"
providerName="System.Data.SqlClient" />
</connectionStrings>
The error I get is:
There is a problem with your selected data store. This can be caused by an invalid server name or credentials, or by insufficient permission. It can also be caused by the role manager feature not being enabled. Click the button below to be redirected to a page where you can choose a new data store.
The following message may help in diagnosing the problem: Unable to connect to SQL Server database.
In the past, I have had trouble connecting to my database because I've needed to add users. Do I have to do something similar here?
Edit
Changing the connection string ultimately solved the problem.
For the records I am using VS2010, ASP MVC2, SServer 2008
<connectionStrings>
<add name="ApplicationServices"
connectionString="data source=MYSERVERNAME;Integrated Security=True;Initial Catalog=aspnetdb"
providerName="System.Data.SqlClient" />
</connectionStrings>
A:
You are using a server name, "MYSERVER" as if this is a full SQl Server Default instance, not Sql Express. I don't think you can use the AttachDbFilename with a full blown sql server. Either add "\SQLEXPRESS" (instance name) to your server name or get rid of the AttachDbFileName and use Database="NAMEOFDATABASE"
|
{
"pile_set_name": "StackExchange"
}
|
Peter Panzerfaust #2
With Calais in the early stages of occupation, Peter and the boys discover a squad of captured British soldiers. Seeing an opportunity to get a ticket to London by saving them, they engage in a dangerous game of espionage that ends with a deadly showdown.
|
{
"pile_set_name": "Pile-CC"
}
|
Recommended Posts
Agree its purpose is not to attack people south of the wall, maybe it wasn't meant to attack people north of the wall either, but let's leave that for now. We don't know what the exact terms of engagement are if it's the watch itself that's threatened by 'people'.
We probably all agree that its true purpose is to guard the realms of men. Legend tells of a particular kind of supernatural enemy.
A supernatural enemy matching the description of the one from legend has now re-appeared and actually wiped out the majority of the watch's fighting men. This enemy grows stronger if allowed to kill any humans still left north of the wall. The logical thing to do is bring these humans south, so you can keep your oath.
Now for another point: Long before there were seven kingdoms there were a hundred, the exact number varied as kings rose and fell and some kingdoms conquered and annexed others. The watch seems to have received enough support from these multiple kings to sustain itself until the current usurper dynasty in place for the last couple of decades starved it of quality recruits. There was no central authority like the Iron Throne for most of the watch's 5000+ years of existence. The only constant in the time of the watch's existence have been the Starks in Winterfell whose help has been sought from time to time, and who according to legend had to cast down one LC of the watch who forgot his oaths.
However, what is different in the timeline where the current story is taking place is that there are multiple claimants for one throne, rather than multiple kings in adjourning kingdoms as was the case before Aegon's conquest. That means there is no central authority the watch answers to. Jon did not seek out Stannis, Stannis answered the call for help while the regency of Tommen did not. It's not for the watch to say if Stannis or Tommen or fAegon or Daenerys has the better claim, but it's to be noted that Jofferey and Tommen's claims were widely opposed by the land, including by two successive Starks of Winterfell, the North, the River lands, most of the Stormlands and the Reach (i.e everybody who declared for either Stannis or Renly or Robb). The Baratheon-Lannisters of King's Landing were able to secure their throne only after getting their allies to break guest rights, considered a huge sin.
Even then Jon has not provided Stannis with any soldiers to fight the illegitimate heir of an usurper, whose regime needed to break guest rights and unleash Qohori sellswords and other sadistic rabble on the civilians of the riverlands to stay in power.
No, he was threatened by one of the guest-right breakers to in turn break guest rights again, asking Jon to give up women and children under his protection. There is also a serious threat that this psychopathic self-proclaimed flayer of women is going to come riding to the wall, with a chance he harms the Free Folk now helping to guard the wall from the true enemy.
Sure, Jon had some personal motives mixed in this as well, but that does not change any of the above reasoning.
By being seen as defending Stannis' heir, Jon has put himself in a position where you can argue he has allowed himself to take sides in politics, but it can also be argued that he is merely protecting his guests from a deranged homicidal maniac. So, technically, there is a chance he might have been about to break his oath, but it was not for the dim-witted execution squad to make that call. By precedent, it should be the Stark of Winterfell who has dealt with oath-breaking LCs. And there is no Stark in Winterfell at the moment.
Since I'm sure this is going to come up as well: The warden of the North is a recent (in the context of the watch's history) term introduced by the Targaryens. So, Roose Bolton is Tommen's 'warden', great, but as long as there are multiple claimants to a central throne, it does not follow that he has some kind of authority over the watch. What was he and his son doing when the watch needed swords?
It's quite laughable if Bowen Marsh and co thought they had some kind of legal authority to act. They were doing it purely out of a sense of what they thought was self-preservation (by currying favour with the Lannisters) but being a set of prize nincompoops, they are not really ending up preserving their sorry little selves either - and are likely going to end up being torn limb from limb by Wun Wun/Free Folk/Queen's Knights who finally had the time to put 2 and 2 together.
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Bowen Marsh is another puppet of the throne and was convinced that he needed to carry out Jon's assassination for the good of the Watch. He was just waiting for the right time and circumstances. He uses similar logic that Walder Frey did to carry out the Red Wedding, all will be forgiven and things will be better if you murder for the throne.
Jon's biggest fault is that he tries to rule alone. He does not seem to do a good job convincing his "commanders" that his actions are not only in the Watch's best interests, but the best interest to the realm, no matter who is king. Instead he works with Tormund on his plan, and then springs it on a room full of people who he can rally around his cause, so it does appear to be self motivating.
He did try to explain his rational for letting the wildings through the wall, but obviously not well enough.
As for helping Stannis, this is a catch 22. The Watch is supposed to stay neutral in the wars between the kingdoms, but if they reject Stannis then they are no longer neutral. Feeding and sheltering the king who saved you is the only thing he could do.
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Sure, Jon had some personal motives mixed in this as well, but that does not change any of the above reasoning.
I agree, it doesn’t change anything. In fact, it only makes Jon’s decisions even more right and righteous imo. Any half-decent human being is not going to sit on their arse knowing a beloved family member is the plaything of someone like Ramsay Bolton. And hiding behind vows and oaths is despicable, just as it was/is in many rw scenarios, “I didn’t do anything, I was just following orders!”. It’s one's actions that matter, not fucking words. No wonder we have so many “words are wind” in Dance. To the point that one of Martin’s editors suggestedcuttingsome and he said no. Blimey, it’s like the author is really, really trying to get the message across, innit.
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Bowen Marsh is another puppet of the throne and was convinced that he needed to carry out Jon's assassination for the good of the Watch. He was just waiting for the right time and circumstances. He uses similar logic that Walder Frey did to carry out the Red Wedding, all will be forgiven and things will be better if you murder for the throne.
Jon's biggest fault is that he tries to rule alone. He does not seem to do a good job convincing his "commanders" that his actions are not only in the Watch's best interests, but the best interest to the realm, no matter who is king. Instead he works with Tormund on his plan, and then springs it on a room full of people who he can rally around his cause, so it does appear to be self motivating.
He did try to explain his rational for letting the wildings through the wall, but obviously not well enough.
As for helping Stannis, this is a catch 22. The Watch is supposed to stay neutral in the wars between the kingdoms, but if they reject Stannis then they are no longer neutral. Feeding and sheltering the king who saved you is the only thing he could do.
I get this, but Jon also isn't dealing with rational and competent people in Bowen Marsh, Othell Yarwyck and co. These people are representative of the decline in the NW, and from the beginning of the story they are made fun of by Mormont, Tyrion, even Mance. Jon truly does try to convince these guys he is right and he attempts to reason with them. They just simply aren't reasonable and Jon finally gives up on them right before they attempt to kill him. That last meeting you see Jon think to himself he knows exactly what they are gonna say before they say it and how it won't be remotely helpful.
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Jon is stabbed because Bowen Marsh and his co-conspirators are moral cowards.
Jon got stabbed because he is guilty of treason, injustice, and hiding the truth about Mance Rayder. Jon executed a man who disrespected him but then he lets the biggest offender of the night's watch get away without punishment. Jon is required to execute Mance Rayder just as Ned Stark was required to execute Gared. The difference is Jon hated Slynt but he liked Mance. Jon also had a personal use for Mance. Jon's lack of ethics compromised the way these two men were judged. He sends Mance Rayder to get Arya. If it's illegal for Jon to do this himself and it is, then it is absolutely also illegal for Mance. They are both sworn to the night's watch. There is no escaping those vows. By ordering Mance to do something illegal Jon committed an act of treason. Bowen Marsh and his co-conspirators are not cowards. They were brave to take a stand against a lord commander who has lost his mind.
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Agree its purpose is not to attack people south of the wall, maybe it wasn't meant to attack people north of the wall either, but let's leave that for now. We don't know what the exact terms of engagement are if it's the watch itself that's threatened by 'people'.
Ramsay threatened the watch because Jon sent Mance to take his wife. Any nobleman would be pissed off at what Jon did. Jon started this fight. Blame him.
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Ramsay threatened the watch because Jon sent Mance to take his wife. Any nobleman would be pissed off at what Jon did. Jon started this fight. Blame him.
A 'wife' given away by the man believed to have killed two of her brothers and betrayed her older brother, hastening her family's downfall after losing their ancestral seat. The fact that the Boltons could not find anyone else to give her away just emphasizes what a shot gun wedding that was.
GRRM set the scenario up to be as provocative as possible. FWIW, Jon did nothing after receiving the wedding invitation, but admittedly does not stop Mel after she predicts a fleeing bride on a dying horse and sends Mance and the SWs down to meet her.
But let's leave that aside, we don't even need the moral argument, the Watch takes no part etc, this is a hard world, tough luck, this is how marriages are made etc
To get back to Bowen, how does he know any of what is in the PL is true? In the private meeting with Tormund, Jon does not confirm on page that Mance is still alive. It does not appear he does it in his Shield hall speech either. All he says is that he means to make this creature who makes cloaks from the skins of women and threatened to cut Jon's heart out answer for his words. Jon also makes clear he's not giving an order to any brother to break their oath.
Is that enough for the steward of the Night's Watch to assasinate the LC? Because the LC said he would ride south to confront a bastard recently legitimized by one of the rival claimants to the throne who demands Jon break guest rights or would otherwise kill him? Based on some claims in a letter? No, Bowen went off the reservation.
Even if Bowen truly believed Tommen was the true king and had authority over the NW (which can be disputed), and had half a brain he would have let Jon and the Wildlings ride out of CB and sent ravens to WF and King's Landing that the watch had no part in this and he and his brothers would deal with Jon if he ever attempted to return. Presumably the senior leadership of the watch should have then met if and when Cotter Pyke returned and held another election.
It's like you are in the army and your superior officer says he is going AWOL, but you have clear information there is no danger to anyone for several weeks from his actions. He's not giving anyone in the unit any orders that would conflict with their standing orders/duties.
Do you:
1. Try to speak to him quickly to dissuade him and if it fails, radio your superiors and the MPs that he's gone AWOL heading south, likely destination WF, in that weather going to be stuck in snow for weeks anyway, taking over the unit to carry on with the mission.
(This is even assuming the Iron Throne and the Boltons have authority over the watch, which is disputable)
2. Try to shoot him without warning, starting a firefight that might actually wipe out your unit, achieving nothing.
Clearly Bowen is dumb as a doormat and daft as a brush, so he goes with option 2.
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I might also mention that NW Brother Mance Rayder murdered Roose Bolton's service people while on this mission from Jon.
??????????? If you are talking about the men who died, then the only one they "confessed" to was Yellow Dick (at least I think that was his name). The other deaths, besides Little Walder, were probably accidents.
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Ramsay threatened the watch because Jon sent Mance to take his wife. Any nobleman would be pissed off at what Jon did. Jon started this fight. Blame him.
Yes, take the 13 year old who was being raped, beaten, and who might have had to be fucked by dogs had she stayed around Ramsay, or lose skin and body parts in the same way Theon did.
How dare anyone try to save that girl from her sadist false husband?
8 hours ago, Allardyce said:
Jon got stabbed because he is guilty of treason, injustice, and hiding the truth about Mance Rayder. Jon executed a man who disrespected him but then he lets the biggest offender of the night's watch get away without punishment. Jon is required to execute Mance Rayder just as Ned Stark was required to execute Gared. The difference is Jon hated Slynt but he liked Mance. Jon also had a personal use for Mance. Jon's lack of ethics compromised the way these two men were judged. He sends Mance Rayder to get Arya. If it's illegal for Jon to do this himself and it is, then it is absolutely also illegal for Mance. They are both sworn to the night's watch. There is no escaping those vows. By ordering Mance to do something illegal Jon committed an act of treason. Bowen Marsh and his co-conspirators are not cowards. They were brave to take a stand against a lord commander who has lost his mind.
I don't know what the injustice you're talking about is. If there's injustice and treason in wanting to save the wildlings from the Others, then bring on the injustice. It's so unfair that Jon has decided that he would take as many wildlings as he possibly could away from the Others.
And when Mance left the Wall, no one knew Roose was going to change the place of the wedding from Barrowton to Winterfell. So we don't know what happened there.
Jeyne Poole (who should have been left to cower in the corner of the bedroom) and Theon are not at the Wall when the letter arrives. Bowen Marsh knows that and he thinks like everyone who was there that Mance is dead. But the letter demands that Jon hands over Melisandre, Shireen, Val, Selyse and a small baby, and this is something Jon is not going to do.
With Jon out of the way, it wouldn't be socking if the first thing brave and strong and wonderful Bowen who is all about saving the realm does is round up women and children and hand them over to Ramsay. And that would make him even worse than a coward.
The next book will suck for you when Bowen Marsh and his ilk are dealt with and Jon comes out of hibernation.
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With Jon out of the way, it wouldn't be socking if the first thing brave and strong and wonderful Bowen who is all about saving the realm does is round up women and children and hand them over to Ramsay. And that would make him even worse than a coward.
I think that's exactly what Bowen the Brave would like to do. Good thing we have Tormund Giantsbane & co there, ready to deal w/ the cowardly xenophobic bigots. It's gonna be a bloodbath.
9 minutes ago, Alexis-something-Rose said:
The next book will suck for you when Bowen Marsh and his ilk are dealt with and Jon comes out of hibernation.
Yup. Been saying it for a while now, there's a group of readers that will hate Winds.
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Jon got stabbed because he is guilty of treason, injustice, and hiding the truth about Mance Rayder. Jon executed a man who disrespected him but then he lets the biggest offender of the night's watch get away without punishment. Jon is required to execute Mance Rayder just as Ned Stark was required to execute Gared. The difference is Jon hated Slynt but he liked Mance. Jon also had a personal use for Mance. Jon's lack of ethics compromised the way these two men were judged. He sends Mance Rayder to get Arya. If it's illegal for Jon to do this himself and it is, then it is absolutely also illegal for Mance. They are both sworn to the night's watch. There is no escaping those vows. By ordering Mance to do something illegal Jon committed an act of treason. Bowen Marsh and his co-conspirators are not cowards. They were brave to take a stand against a lord commander who has lost his mind.
6 hours ago, Nowy Tends said:
Are you serious or trolling? Marsh's fear literally drips from the pages of the book…
There's nothing wrong with fear. It's how you handle it and how it affects your decision that matter. Jon allowed his fear for what might happen to "Arya" drive him to betray the Night's Watch. I am reminded of Anakin's fear for his mother and what it drove him to do.
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Marsh’s concern-trolling about neutrality vis-à-vis Stannis is transparently hypocritical. But, to be fair, he is far from the only character on the Wall who misleads the reader with delusions about the political position of the Watch. We hear from NW members who desperately want to believe they have some small amount of control over how they are perceived, who are baselessly convinced that if only they play by The Rules they will be rewarded and saved. The harsh truth is that public perception of the NW’s neutrality was shot to hell the moment Stannis showed up.
“The father would have handed the realm to Stannis. The son has given him lands and castles.”
“The Night’s Watch is sworn to take no part in the wars of the Seven Kingdoms,” Pycelle reminded them. “For thousands of years the black brothers have upheld that tradition.”
“Until now,” said Cersei. “The bastard boy has written us to avow that the Night’s Watch takes no side, but his actions give the lie to his words. He has given Stannis food and shelter, yet has the insolence to plead with us for arms and men.”
Grand Maester Pycelle nodded ponderously. “I propose that we inform Castle Black that no more men will be sent to them until such time as Snow is gone.”
(Cersei, AFFC)
“More” men. They haven’t even sent criminals since Tyrion was Hand of the King. The farce of neutrality was shot throughout the year before, when the Watch sent out dozens of ravens begging for help with the situation, and the only response they got was Tywin Lannister’s attempt to blackmail them. The realm – and specifically Roose Bolton, who committed a wretched breach of his duty as Warden of the North when he failed to respond to the wildling attack on the Wall – broke faith with the Watch long before the Pink Letter.
This.
The moment Stannis showed up to answer the call, the NW in the perception of the wobbly regime clinging on to power in KL had already 'chosen' sides. There is no point in trying to please the now-defunct Iron Throne. Even when Tywin was around, there was no help coming and at the time of the PL, you have Tywin stinking in his grave and the Lannisters, the Tyrells and the faith in a 3-way tussle. A minor in the throne, Queen Mother (and until recently the Queen) in jail, a Tyrell army effectively besieging the faith - it's utter chaos. You are not getting any help from them ever. They only care you helped Stannis to the extent they can bring themselves to focus on anything other than destroying each other.
The next point that somebody will make is that Roose is the rightful appointee of this rightful central authority blah blah, so the watch is answerable to him. Well he's the nearby appointee of a far away regime on its last legs Vs a nearby claimant to the far away throne. With the latter camped on your doorstep, you were never going to engage with the former.
If Bowen was such a virtuous soul and the Iron Throne is this rightful authority of the land, why didn't he ride out to Roose as soon as Stannis showed up at CB. "My Lord, you are the rightful Warden of the rightful king, His Grace Tommen, <add all the bloody titles here>. The watch has been taken under the control of the usurper Stannis. I can't abide it, I have come to you". No, Bowen waits until he hears Stannis is dead as the OP astutely points out before making his move. Hardly very virtuous, more like covering your arse. And because he is an inept moron, he will not have done that properly either :-D
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They just simply aren't reasonable and Jon finally gives up on them right before they attempt to kill him. That last meeting you see Jon think to himself he knows exactly what they are gonna say before they say it and how it won't be remotely helpful.
This is what I was referring to. How much effort do you put into trying to convince someone if you have already concluded how they will respond. Jon needed to either act diplomatically and accept the advice of his commanders or act like the Lord Commander and just order them to do what he wants.
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This is what I was referring to. How much effort do you put into trying to convince someone if you have already concluded how they will respond.
You put some effort into it, as Jon did, but at some point you have to give up.
5 hours ago, Chris Mormont said:
Jon needed to either act diplomatically and accept the advice of his commanders or act like the Lord Commander and just order them to do what he wants.
Exactly. And let's not forget that this is not your regular dispute over some meaningless minor issue. The threat [to humanity] is real, Jon knows this, regardless of Bowen & co believing in or not. So, you try, then you try again, and you try a third time... but at some point you just have to give up and either "act diplomatically" or just move on. Jon moved on, and that was the right call. Bowen's prejudices, biases, narrow-mindedness, bigotry and xenophobia weren't going to change any time soon. So you put your foot down and move on. The mountain clan chiefs weren't too happy, but accepted Jon's explanations and reasoning. So, it's not like Jon's ideas were that outrageous given the circumstances. But Bowen is a bean-counter who lacks intelligence and is not open-minded, so he went back to the plan of getting rid of Jon in an attempt to ingratiate himself w/ the IT. And now he's as good as dead, and good riddance.
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Jon got stabbed because he is guilty of treason, injustice, and hiding the truth about Mance Rayder.
He didn't actually - no-one who stabbed him knew about Mance. They obviously stabbed him because they felt his decisions were going to bring the Watch to ruin. A debatable point, but it had nothing to do with him hiding the truth about Mance.
I’ve said this a hundred times, but I’m constantly shocked at how people who are avid fans of these books consistently overlook one of its central themes, and make sweeping and strident moral judgments. One of the main points these books consistently make is that it's never black and white. There are shades of grey. Sometimes bad decisions are made for good reasons, and sometimes there is no clear and obvious "good" decision. You can, of course, make the case that Jon shouldn’t have made the decisions he did; but the idea that there is some sort of clear-cut answer to the complex issues he was facing is ridiculous.
Jon’s primary consideration, one that he has consistently grappled with throughout the books, is how to remain true to his vows while also fulfilling the obligations the vows are designed for. He needs to ensure, to the best of his ability, that the 7K are defended against the Others.
The difficulties arise when keeping the letter of those vows comes into conflict with that overriding obligation. Preserving the 7K required him to ride with the Wildlings and sleep with Ygritte. Should he have stood by the letter of his vows, refused to do so, and got killed by the Wildlings?
One strict interpretation of his vows would have meant his refusal to cooperate with Stannis at all. Stannis would have simply had him killed, and either wiped out the NW entirely, or replaced Jon with someone who would have done what he required. Would that have been a better outcome?
Throughout ADWD, we see Jon try to navigate a difficult situation, where he tries to preserve the NW’s independence, fulfil its central obligations, while not blindly leading it to ruin.
As to the issue with the Pink Letter. Yes, there’s a clear case to be made that he crossed a line there by deciding to go into armed conflict with the Boltons But I fail to see how that could have been avoided anyway, if he didn’t march on them, they would march on him. The letter said they would. What alternative actions do people suggest?
On the decision to send Mance south – he did so on the assumption Arya was already riding North. As others have said, he never sent Mance to steal her from Winterfell. Furthermore, would anyone really do any differently? Not just if it were their own sister, but any child under threat of rape and torture? Even if you would (or would like to pretend you would for weird argumentative reasons), do you really so stridently condemn others who wouldn’t? Frankly, I find that a bit creepy.
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Jon got stabbed because he is guilty of treason, injustice, and hiding the truth about Mance Rayder. Jon executed a man who disrespected him but then he lets the biggest offender of the night's watch get away without punishment. Jon is required to execute Mance Rayder just as Ned Stark was required to execute Gared. The difference is Jon hated Slynt but he liked Mance. Jon also had a personal use for Mance. Jon's lack of ethics compromised the way these two men were judged. He sends Mance Rayder to get Arya. If it's illegal for Jon to do this himself and it is, then it is absolutely also illegal for Mance. They are both sworn to the night's watch. There is no escaping those vows. By ordering Mance to do something illegal Jon committed an act of treason. Bowen Marsh and his co-conspirators are not cowards. They were brave to take a stand against a lord commander who has lost his mind.
Slynt was a detriment to the Watch's ability to stand against the Others by constantly undermining its Commander, Mance was not (and since he knew the threat was real, he would be an asset working to support the Watch in this). Exposing Mel's farce which allowed Mance live would damage the Watch's alliance with the single person who was willing to support it in the fight against the Others. If no such circumstances existed, Mance would most likely got the block. Unfortunately, the Watch was under the circumstances when sticking to the letter of the law would be a wrong decision; it was the spirit that mattered and the word... well, the words are wind. If breaking the word to keep the spirit is what it takes, then this is what needs to be done. Just like when Jon had to kill Qhorin and sleep with Ygritte.
On 4/2/2019 at 4:31 AM, Allardyce said:
Ramsay threatened the watch because Jon sent Mance to take his wife. Any nobleman would be pissed off at what Jon did. Jon started this fight. Blame him.
Any noblemen who wasn't making his wife have sex with dogs and who wasn't flaying people alive would be perfectly justified to be pissed off.
9 hours ago, Shouldve Taken The Black said:
On the decision to send Mance south – he did so on the assumption Arya was already riding North. As others have said, he never sent Mance to steal her from Winterfell.
100% true. But curiously, it keeps getting ignored.
9 hours ago, Shouldve Taken The Black said:
Furthermore, would anyone really do any differently? Not just if it were their own sister, but any child under threat of rape and torture? Even if you would (or would like to pretend you would for weird argumentative reasons), do you really so stridently condemn others who wouldn’t? Frankly, I find that a bit creepy.
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Ramsay threatened the watch because Jon sent Mance to take his wife. Any nobleman would be pissed off at what Jon did. Jon started this fight. Blame him.
So quoting this, but also wanting to comment on your double post. He executed Slynt because Slynt disobeyed an order, not because Slynt insulted him. Summary execution for disobedience is something that has existed for thousands of years.There were men executed for less at D-Day.
As was mentioned above, Ramsay SNOW loss his right to have a grievance at some point between kidnapping, raping, and murdering Lady Hornwood and forcing a fourteen year old girl to have sex with dogs. He was never pardoned for the first crime, mind you.
|
{
"pile_set_name": "Pile-CC"
}
|
---
abstract: 'The dissipative dynamics of a two-qubit system is studied theoretically. We make use of the Bloch-Redfield formalism which explicitly includes the parameter-dependent relaxation rates. We consider the case of two flux qubits, when the controlling parameters are the partial magnetic fluxes through the qubits’ loops. The strong dependence of the inter-level relaxation rates on the controlling magnetic fluxes is demonstrated for the realistic system. This allows us to propose several mechanisms for lasing in this four-level system.'
author:
- 'E. A. Temchenko'
- 'S. N. Shevchenko'
- 'A. N. Omelyanchouk'
title: 'Dissipative dynamics of two-qubit system: four-level lasing'
---
Introduction
============
Recently considerable progress has been made in studying Josephson-junctions-based superconducting circuits, which can behave as effectively few-level quantum systems. [@Korotkov] When the dynamics of the system can be described in terms of two levels only, this circuit is called a qubit. Demonstrations of the energy level quantization and the quantum coherence provide the basis for both possible practical applications and for studying fundamental quantum phenomena in systems involving qubits. Important distinctions of these multi-level artificial quantum systems from their microscopic counterparts are high level of controllability and unavoidable coupling to the dissipative environment.
Multi-level systems with solid-state qubits may be realized in different ways. First, the devices used for qubits in reality are themselves multi-level systems with the lowest two levels used to form a qubit. For some recent study of multi-level superconducting devices see Ref. . Then, a qubit can be coupled to another quantum system, e.g. a quantum resonator.[@qb-oscillator] Such a composite system is also described by a multi-level structure. As a particular case of coupling with other systems, the multi-qubit system is of particular interest (see e.g. Ref. ).
Operations with the multi-level systems can be described with level-population dynamics. In particular, population inversion was proposed for cooling and lasing with superconducting qubits.[@Astafiev07; @Grajcar08-i-drugie] However, most of the previous propositions were related to three-level systems, while for practical purposes four-level systems are often more advantageous.[@Svelto]
The natural candidate for the solid-state four-level system is the system of two coupled qubits. The purpose of this paper is the theoretical study of mechanisms of population inversion and lasing, as a result of the pumping and relaxation processes in the system. We will start in the next Section by demonstrating the controllable energy level structure of the system. Our calculations are done for the parameters of the realistic two-flux-qubit system studied in Ref. . To describe the dynamics of the system we will present the Bloch-Redfield formalism in Sec. III. The key feature of the system is the strong dependence of the relaxation rates on the controlling parameters. Then solving the master equation in Sec. IV we will demonstrate several mechanisms for creating the population inversion in our four-level system. We will demonstrate further that applying additional driving induces transitions between the operating states resulting in stimulated emission. We summarize our theoretical results in Sec. V. and, based on our calculations, we then discuss the experimental feasibility of the two-qubit lasing.
Model Hamiltonian and Eigenstates of the two-qubit system
=========================================================
The main object of our study is a system of two coupled qubits. And altough our analysis bears general character, for concreteness we consider superconducting flux qubits, see Fig. \[Fig:scheme\]. A flux qubit, which is a superconducting ring with three Josephson junctions, can be controlled by constant ($\Phi _{\mathrm{dc}}$) and alternating ($\Phi _{\mathrm{ac}}\sin \omega t$) external magnetic fluxes. Each of the two qubits can be considered as a two-level system with the Hamiltonian in the pseudospin notation [@vanderWal03; @Korotkov] $$\widehat{H}_{\mathrm{1q}}^{(i)}=-\frac{1}{2}\epsilon _{i}(t)\widehat{\sigma }_{z}^{(i)}-\frac{1}{2}\Delta _{i}\widehat{\sigma }_{x}^{(i)}, \label{H1q}$$where $\Delta _{i}$ is the tunnelling amplitude, $\widehat{\sigma }_{x,z}^{(i)}$ are the Pauli matrices in the basis $\left\{ \lvert {\downarrow }\rangle ,\lvert {\uparrow }\rangle \right\} $ of the current operator in the $i$-th qubit: $\widehat{I}_{i}=-I_{\mathrm{p}}^{(i)}\widehat{\sigma }_{z}^{(i)},$ with $I_{\mathrm{p}}^{(i)}$ being the absolute value of the persistent current in the $i$-th qubit; then the eigenstates of $\widehat{\sigma }_{z}$ correspond to the clockwise ($\widehat{\sigma }_{z}\left\vert \downarrow \right\rangle =-\left\vert \downarrow
\right\rangle $) and counterclockwise ($\widehat{\sigma }_{z}\left\vert
\uparrow \right\rangle =\left\vert \uparrow \right\rangle $) current in the $i$-th qubit. The energy bias $\epsilon _{i}(t)$ is controlled by constant and alternating magnetic fluxes
\[epsilon\] $$\begin{aligned}
\epsilon _{i}(t) &=&2I_{\mathrm{p}}^{(i)}\left( \Phi _{i}(t)-\frac{1}{2}\Phi
_{0}\right) =\epsilon _{i}^{(0)}+\tilde{\epsilon}_{i}(t), \\
\epsilon _{i}^{(0)} &=&2I_{\mathrm{p}}^{(i)}\Phi _{0}f_{i}\text{, \ \ }f_{i}=\frac{\Phi _{\mathrm{dc}}^{(i)}}{\Phi _{0}}-\frac{1}{2}, \\
\tilde{\epsilon}_{i}(t) &=&2I_{\mathrm{p}}^{(i)}\Phi _{0}f_{\mathrm{ac}}\sin
\omega t\text{, \ \ }f_{\mathrm{ac}}=\frac{\Phi _{\mathrm{ac}}}{\Phi _{0}}.\end{aligned}$$
![(Color online). **Schematic diagram of the two-qubit system**. Two different flux qubits are biased by independent constant magnetic fluxes, $\Phi _{\mathrm{dc}}^{(1)}$ and $\Phi _{\mathrm{dc}}^{(2)}$, and by the same alternating magnetic flux $\Phi _{\mathrm{ac}}\sin \protect\omega t$. The former controls the energy levels structure, while the latter changes the populations of the levels. The dissipation processes are described by coupling the system to the bath of harmonic oscillators.[]{data-label="Fig:scheme"}](Fig1.eps){width="8.6cm"}
The basis state vectors for the two-qubit system $\left\{ \lvert {\downarrow
\downarrow }\rangle ,\lvert {\downarrow \uparrow }\rangle ,\lvert {\uparrow
\downarrow }\rangle ,\lvert {\uparrow \uparrow }\rangle \right\} $ are composed from the single-qubit states: $\lvert {\downarrow \uparrow }\rangle
=\lvert {\downarrow }\rangle _{(1)}\lvert {\uparrow }\rangle _{(2)}$, etc. For identification of the level structure and understanding different transition rates, we will start the consideration from the case of two non-interacting qubits. Then, the energy levels of two qubits consist of the pair-wise summation of single-qubit levels,
$$E_{i}^{\pm }=\pm \frac{\Delta E_{i}}{2}=\pm \frac{1}{2}\sqrt{\epsilon
_{i}^{(0)2}+\Delta _{i}^{2}}, \label{DE}$$
which are the eigenstates of the single-qubit time-independent Hamiltonian (\[H1q\]) at $f_{\mathrm{ac}}=0$. We demonstrate this in Fig. [Fig:levels]{}(a), where we plot the energy levels, fixing the bias in the first qubit $f_{1}$, as a function of the partial bias in the second qubit $f_{2}$. Then the single-qubit energy levels appear as (dashed) horizontal lines at $E_{1}^{\pm }=\pm \frac{1}{2}\sqrt{\epsilon _{1}^{(0)2}+\Delta
_{1}^{2}}$ for the first qubit and as the parabolas at $E_{2}^{\pm
}(f_{2})=\pm \frac{1}{2}\sqrt{\epsilon _{2}^{(0)}(f_{2})^{2}+\Delta _{2}^{2}}
$.
After showing the two-qubit energy levels in Fig. \[Fig:levels\](a), we assume that the relaxation in the first qubit is much faster than in the second (this will be studied in the next Section), which is shown with the arrows in the figure. And now our problem, with four levels and with fast relaxation between certain levels, becomes similar to the one with lasers. [@Svelto] This allows us to propose three- and four-level lasing schemes in Fig. \[Fig:levels\](b,c). This is the subject of our further detailed study.
![(Color online). **Energy level structure of two uncoupled qubits** ($J=0$). (a) One-qubit and two-qubits energy levels are shown by dashed and solid lines as a function of partial flux $f_{\mathrm{2}}$ at fixed flux $f_{\mathrm{1}}$. We mark the energy levels by the current operator eigenstates, $\lvert {\downarrow \downarrow }\rangle $ *etc.* Particularly, we will consider the energy levels and dynamical behaviour of the system for the flux biases $f_{\mathrm{2}}=f_{2\mathrm{L}}$ (marked by the square) and $f_{\mathrm{2}}=f_{2\mathrm{R}}$ (marked by the circle). By the arrows we show the fastest relaxation - for qubit $1$. (b) Scheme for *three-level lasing* at $f_{\mathrm{2}}=f_{2\mathrm{L}}$. The driving magnetic flux pumps (P) the upper level $\left\vert 3\right\rangle $. Fast relaxation (R) creates the population inversion of the first excited level $\left\vert 1\right\rangle $ in respect to the ground state $\left\vert
0\right\rangle $; these two operating levels can be used for lasing (L). (c) Scheme for *four-level lasing* at $f_{\mathrm{2}}=f_{2\mathrm{R}}$. Pumping (P) and fast relaxations (R$_{1}$ and R$_{2}$) create the population inversion of the level $\left\vert 2\right\rangle $ with respect to level $\left\vert 1\right\rangle $.[]{data-label="Fig:levels"}](Fig2){width="8.6cm"}
We have analyzed the relaxation in the system of two uncoupled qubits. However this system can not be used for lasing, since this requires pumping from the ground state to the upper excited state (see Fig. \[Fig:levels\](b,c)). Such excitation of the two-qubit system requires simultaneously changing the state of both qubits and can be done provided the two qubits are interacting. That is why in what follows we consider in detail the system of two *coupled* qubits. The coupling between the two qubits we assume to be determined by an Ising-type (inductive interaction) term $\frac{J}{2}\widehat{\sigma }_{z}^{(1)}\widehat{\sigma }_{z}^{(2)}$, where $J$ is the coupling energy between the qubits. Then the Hamiltonian of the two driven flux qubits can be represented as the sum of time-independent and perturbation Hamiltonians $$\begin{gathered}
\widehat{H}_{\mathrm{2q}}=\widehat{H}_{0}+\widehat{V}(t), \label{H2q} \\
\widehat{H}_{0}=\sum_{i=1,2}\left( -\frac{1}{2}\Delta _{i}\widehat{\sigma }_{x}^{(i)}-\frac{1}{2}\epsilon _{i}^{(0)}\widehat{\sigma }_{z}^{(i)}\right) +\frac{J}{2}\widehat{\sigma }_{z}^{(1)}\widehat{\sigma }_{z}^{(2)},
\label{H0} \\
\widehat{V}(t)=\sum_{i=1,2}-\frac{1}{2}\tilde{\epsilon}_{i}(t)\widehat{\sigma }_{z}^{(i)},\end{gathered}$$where $\widehat{\sigma }_{x,z}^{(1)}=\widehat{\sigma }_{x,z}\otimes \widehat{\sigma }_{0}$, $\widehat{\sigma }_{x,z}^{(2)}=\widehat{\sigma }_{0}\otimes
\widehat{\sigma }_{x,z}$, and $\widehat{\sigma }_{0}$ is the unit matrix. When presenting concrete results we will use the parameters of Ref. : $\Delta _{\mathrm{1}}/h=15.8$ GHz, $\Delta _{\mathrm{2}}/h=3.5$ GHz, $I_{\mathrm{p}}^{(\mathrm{1})}\Phi _{0}/h=375$ GHz, $I_{\mathrm{p}}^{(\mathrm{2})}\Phi _{0}/h=700$ GHz, $J/h=3.8$ GHz.
For further analysis of the system, we have to convert to the basis of eigenstates of the unperturbed Hamiltonian . Eigenstates $\left\{
\lvert {0}\rangle ,\lvert {1}\rangle ,\lvert {2}\rangle ,\lvert {3}\rangle
\right\} $ of the unperturbed Hamiltonian are connected with the initial basis $$\left[
\begin{matrix}
\lvert {0}\rangle \\
\lvert {1}\rangle \\
\lvert {2}\rangle \\
\lvert {3}\rangle\end{matrix}\right] =\widehat{S}\left[
\begin{matrix}
\lvert {\downarrow \downarrow }\rangle \\
\lvert {\downarrow \uparrow }\rangle \\
\lvert {\uparrow \downarrow }\rangle \\
\lvert {\uparrow \uparrow }\rangle\end{matrix}\right] , \label{conversion}$$where $\widehat{S}$ is the unitary matrix consisting of eigenvectors of the unperturbed Hamiltonian . Making use of the transformation $\widehat{H}_{0}^{\prime }=\widehat{S}^{-1}\widehat{H}_{0}\widehat{S}$, we obtain the Hamiltonian $\widehat{H}_{0}^{\prime }$ in the energy representation: $\widehat{H}_{0}^{\prime }=$diag$(E_{0},E_{1},E_{2},E_{3})$. These eigenvalues of the Hamiltonian $H_{0}$ are computed numerically and plotted in Fig. \[Fig:W1\](a) as functions of the bias flux in the second qubit $f_{2}$. The distinction from Fig. \[Fig:levels\](a), calculated with $J=0$, is in that, first, the crossing at $f_{2}=f_{2}^{\ast }$ becomes an avoided crossing, and second, the distance between the \[previously single-qubit\] energy levels is not equal, e.g. now $E_{3}-E_{2}\neq
E_{1}-E_{0}$.
![(Color online). (a) **Energy levels** of the system of two coupled qubits. Arrows show the pumping and dominant relaxation, as in Fig. \[Fig:levels\]. (b) **The relaxation rates** $W_{mn}$, which give the probability of the transition from level $n$ to level $m$, induced by the interaction with the dissipative bath. Dominant relaxations are $W_{13}$ and $W_{02}$ to the left from the avoided crossing at $f_{\mathrm{2}}=f_{\mathrm{2}}^{\ast }$ and $W_{23}$ and $W_{01}$ to the right. (The small relaxation rates $W_{03}$ and $W_{12}$ are not shown.)[]{data-label="Fig:W1"}](Fig3){width="8.6cm"}
Likewise, we could also convert the excitation operator $\widehat{V}(t)$ to the energy representation $$\widehat{V}^{\prime }(t)=\widehat{S}^{-1}\widehat{V}(t)\widehat{S}=\sum_{i=1,2}-\frac{1}{2}\tilde{\epsilon}_{i}(t)\widehat{\tau }_{z}^{(i)},
\label{V'}$$$$\widehat{\tau }_{z}^{(i)}=\widehat{S}^{-1}\widehat{\sigma }_{z}^{(i)}\widehat{S}.$$
Master equation and relaxation
==============================
Bloch-Redfield formalism
------------------------
Following Ref. , we will describe the dissipation in the open system of two qubits, assuming that it is interacting with the thermostat (bath), see Fig. \[Fig:scheme\]. Within the Bloch-Redfield formalism, the Liouville equation for the quantum system interacting with the bath is transformed into the master equation for the reduced system’s density matrix. This transformation is made with several reasonable assumptions: the interaction with the bath is weak (Born approximation); the bath is so large that the effect of the system on its state is ignored; the dynamics of the system depends on its state only at present (Markov approximation). Then the master equation for the reduced density matrix $\rho (t)$ of our driven system in the energy representation can be written in the form of the following differential equations [@MasterEqn] $$\dot{\rho}_{ij}=-i\omega _{ij}\rho _{ij}-\frac{i}{\hbar }\left[ \widehat{V}^{\prime },\widehat{\rho }\right] _{ij}+\delta _{ij}\sum_{n\neq j}\rho
_{nn}W_{jn}-\gamma _{ij}\rho _{ij}. \label{M_eqn}$$Here $\omega _{ij}=(E_{i}-E_{j})/\hbar $, and the relaxation rates $$W_{mn}=2\text{Re}\Gamma _{nmmn}, \label{Ws}$$$$\gamma _{mn}=\sum_{r}\left( \Gamma _{mrrm}+\Gamma _{nrrn}^{\ast }\right)
-\Gamma _{nnmm}-\Gamma _{mmnn}^{\ast } \label{gmn}$$are defined by the relaxation tensor $\Gamma _{lmnk}$, which is given by the Golden Rule$$\Gamma _{lmnk}=\frac{1}{\hbar ^{2}}\int\limits_{0}^{\infty }dte^{-i\omega
_{nk}t}\left\langle H_{\mathrm{I},lm}(t)H_{\mathrm{I},nk}(0)\right\rangle .$$Here $\widehat{H}_{\mathrm{I}}(t)$ is the Hamiltonian of the interaction of our system with the bath in the interaction representation; the angular brackets denote the thermal averaging of the bath degrees of freedom.
It was shown [@vanderWal03; @Governale01-i-drugie] that the noise from the electromagnetic circuitry can be described in terms of the impedance $Z(\omega )$ from a bath of $LC$ oscillators. For simplicity one assumes that both qubits are coupled to a common bath of oscillators, then the Hamiltonian of interaction is written as$$\widehat{H}_{\mathrm{I}}=\frac{1}{2}\left( \widehat{\sigma }_{z}^{(1)}+\widehat{\sigma }_{z}^{(2)}\right) \widehat{X} \label{HI}$$in terms of the collective bath coordinate $\widehat{X}=\sum\nolimits_{k}c_{k}\widehat{\Phi }_{k}$. Here $\widehat{\Phi }_{k}$ stands for the magnetic flux (generalized coordinate) in the $k$-th oscillator, which is coupled with the strength $c_{k}$ to the qubits. We note that the coupling to the environment in the form of Eq. (\[HI\]) applies only to correlated noise, or both qubits interacting with the same environment. One could argue that it would be more realistic to use two separate terms, one for each qubit coupled to its own environment. However, since this term leads to different relaxation rates in our qubits $1$ and $2$ (see below), then the form in Eq. (\[HI\]) should give essentially the same results as two separate coupling terms.
Then it follows that the relaxation tensor $\Gamma _{lmnk}$ is defined by the noise correlation function $S(\omega )$$$\Gamma _{lmnk}=\frac{1}{\hbar ^{2}}\Lambda _{lmnk}S(\omega _{nk}),$$$$\Lambda _{lmnk}=\left( \widehat{\tau }_{z}^{(1)}+\widehat{\tau }_{z}^{(2)}\right) _{lm}\left( \widehat{\tau }_{z}^{(1)}+\widehat{\tau }_{z}^{(2)}\right) _{nk},$$$$S(\omega )=\int\limits_{0}^{\infty }dte^{-i\omega t}\left\langle
X(t)X(0)\right\rangle .$$The noise correlator $S(\omega )$ was calculated in Ref. within the spin-boson model and it was shown that its imaginary part results only in a small renormalization of the energy levels and can be neglected. The relevant real part of the relaxation tensor [@Governale01-i-drugie] $$\text{Re}\Gamma _{lmnk}=\frac{1}{8\hbar }\Lambda _{lmnk}J(\omega _{nk})\left[
\coth \frac{\hbar \omega _{nk}}{2T}-1\right] \label{ReG}$$is defined by the environmental spectral density $J(\omega )$. Here $T$ is the bath temperature ($k_{B}$ is assumed $1$); for the numerical calculations we take $T/h=1$ GHz ($T=50$ mK). The electromagnetic environment can be described as an Ohmic resistive shunt across the junctions of the qubits, $Z(\omega )=R$.[@vanderWal03] Then the low frequency spectral density is linear $J(\omega )\propto \omega Z(\omega
)\propto $ $\omega $ and should be cut off at some large value $\omega _{\mathrm{c}}$; the realistic experimental situation is described by [Governale01-i-drugie]{} $$J(\omega )=\alpha \frac{\hbar \omega }{1+\omega ^{2}/\omega _{\mathrm{c}}^{2}}, \label{J(w)}$$where $\alpha $ is a dimensionless parameter that describes the strength of the dissipative effects; in numerical calculations we take $\alpha =0.01$ and $\omega _{\mathrm{c}}/2\pi =10^{4}$ GHz (the cut-off frequency $\omega _{\mathrm{c}}$ is taken much larger than other characteristic frequencies, so that for relevant values $\omega :$ $J(\omega )\approx \alpha \hbar \omega $).
Relaxation rates
----------------
From the above equations the expression for the relaxation rates from level $\left\vert n\right\rangle $ to level $\left\vert m\right\rangle $ follows$$W_{mn}=\frac{1}{4\hbar }\Lambda _{nmmn}J(\omega _{mn})\left[ \coth \frac{\hbar \omega _{mn}}{2T}-1\right] . \label{Wmn}$$These relaxation rates are plotted in Fig. \[Fig:W1\](b) as functions of the partial flux bias $f_{2}$. This figure demonstrates that the fastest transitions are those between the energy levels corresponding to changing the state of the first qubit and leaving the same state of the second qubit, cf. Fig. \[Fig:W1\](a). Namely, the fastest transitions are those with the rates $W_{13}$ and $W_{02}$ to the left from the avoided crossing and $W_{23} $ and $W_{01}$ to the right, which correspond to the transitions $\lvert {\uparrow \uparrow }\rangle \rightarrow \lvert {\downarrow \uparrow }\rangle $ and $\lvert {\uparrow \downarrow }\rangle \rightarrow \lvert {\downarrow \downarrow }\rangle $. Note that we do not show in the figure the rates $W_{03}$ and $W_{12}$; they correspond to the transitions with simultaneously changing the states of the two qubits and they are much smaller than the rates shown.
The relaxation rates $W_{ij}$ are shown in Fig. \[Fig:W2\] as functions of the two partial bias fluxes, $f_{1}$ and $f_{2}$. Again, one can see the regions where certain relaxation rates are dominant. Such a difference in the relaxation rates creates a sort of artificial selection rules for the transitions similar to the selection rules studied in Refs. . In our case the transitions are induced by the interaction with the environment and the difference is due to the different parameters of the two qubits.[@Paladino09] To further understand this issue, we consider the single-qubit relaxation rates.
![(Color online). **Relaxation rates** $W_{mn}$ versus partial biases of the two qubits, $f_{\mathrm{1}}$ and $f_{\mathrm{2}}$. The square and the circle show the parameters $f_{\mathrm{1}}$ and $f_{\mathrm{2}}=f_{\mathrm{2L(R)}}$, at which the calculations of other figures are done.[]{data-label="Fig:W2"}](Fig4){width="8.6cm"}
From the above equations we can obtain the energy relaxation time $T_{1}$ and the decoherence time $T_{2}$ for single qubit. For the two-level system with two states $\lvert {0}\rangle $ and $\lvert {1}\rangle $ the relaxation time is given by [@MasterEqn] $T_{1}^{-1}=W_{01}+W_{10}$. The Boltzmann distribution, $W_{10}/W_{01}=\exp (-\Delta E/T)$, means that at low temperature the major effect of the bath is the relaxation from the upper level to the lower one. Now, from Eq. (\[Wmn\]) it follows that$$T_{1}^{-1}=\frac{\alpha \Delta ^{2}}{2\hbar \Delta E}\coth \frac{\Delta E}{2T}. \label{T1}$$Also from Eq. (\[gmn\]) we obtain the dephasing rate [@MasterEqn]$$T_{2}^{-1}=\text{Re}\gamma _{01}=\frac{1}{2}T_{1}^{-1}+\frac{\alpha T}{\hbar
}\frac{\epsilon ^{(0)2}}{\Delta E^{2}}. \label{T2}$$For the calculation presented in Fig. \[Fig:levels\](a) for two qubits with $J=0$ in the vicinity of the point $f_{2}=f_{2}^{\ast }$, where $\Delta
E^{(1)}=\Delta E^{(2)}$, we obtain$$\frac{T_{1}^{(1)}}{T_{1}^{(2)}}\simeq \left( \frac{\Delta _{2}}{\Delta _{1}}\right) ^{2}. \label{relation}$$
As we explained above, the lasing in the four-level system requires the hierarchy of the relaxation times. In particular, we assumed $T_{1}^{(1)}\ll
T_{1}^{(2)}$. So, in our calculations we have taken $\Delta _{1}\gg \Delta
_{2}$ and consequently the first qubit relaxed faster. This qualitatively explains the dominant relaxations in Fig. \[Fig:W1\](b).
Equations for numerical calculations
------------------------------------
If we use the Hermiticity and normalization of the density matrix, then the $16$ complex equations can be reduced to $15$ real equations. After the straightforward parametrization of the density matrix, $\rho
_{ij}=x_{ij}+iy_{ij}$, we get [@ShT08]
\[Eqs\] $$\begin{gathered}
\dot{x}_{ii}=-\frac{1}{\hbar }\left[ V^{\prime },y\right] _{ii}+\sum_{r\neq
i}W_{ir}x_{rr}-x_{ii}\sum_{r\neq i}W_{ii},\text{ }i=1,2,3; \\
\dot{x}_{ij}=\omega _{ij}y_{ij}-\frac{1}{\hbar }\left[ V^{\prime },y\right]
_{ij}-\gamma _{ij}x_{ij},\text{ }i>j; \\
\dot{y}_{ij}=-\omega _{ij}x_{ij}+\frac{1}{\hbar }\left[ V^{\prime },y\right]
_{ij}-\gamma _{ij}y_{ij},\text{ }i>j;\end{gathered}$$$y_{ii}=0$, $x_{00}=1-(x_{11}+x_{22}+x_{33})$; $x_{ji}=x_{ij}$, $y_{ji}=-y_{ij}$.
This system of equations can be simplified if the relaxation rates are taken at zero temperature, $T=0$, and neglecting the impact of the inter-qubit interaction on relaxation, $J=0$. Then among all the $W_{ij}$ and $\gamma
_{ij}$ non-trivial are only the elements corresponding to single-qubit relaxations (see Eqs. (\[T1\]-\[T2\])). For example consider $f_{2}<f_{2}^{\ast }$ (see Fig. \[Fig:levels\](a) for the notation of the levels), then non-trivial elements are
$$\begin{aligned}
W_{13} &=&W_{02}=\left( T_{1}^{(1)}\right) ^{-1}=\frac{\alpha \Delta _{1}^{2}}{2\hbar \Delta E_{1}}, \\
W_{23} &=&W_{01}=\left( T_{1}^{(2)}\right) ^{-1}=\frac{\alpha \Delta _{2}^{2}}{2\hbar \Delta E_{2}},\end{aligned}$$
$$\begin{aligned}
\gamma _{13} &=&\gamma _{31}=\gamma _{02}=\gamma _{20}=(T_{2}^{(1)})^{-1}=\frac{1}{2}(T_{1}^{(1)})^{-1}, \\
\gamma _{23} &=&\gamma _{32}=\gamma _{01}=\gamma _{10}=(T_{2}^{(2)})^{-1}=\frac{1}{2}(T_{1}^{(2)})^{-1}.\end{aligned}$$
In our numerical calculations we did not ignore the influence of the coupling on relaxation, i.e. we did not assume $J=0$. However, we have numerically checked that such simplification, $J=0$, resulting in the relaxation rates (25-26), sometimes allows to describe qualitatively dynamics of the system.
Several schemes for lasing
==========================
In Sec. II and in Fig. \[Fig:levels\] we pointed out that in the system of two coupled qubits there are two ways to realize lasing, making use of the three or four levels to create the population inversion between the operating levels. In this Section we will demonstrate the lasing in the two-qubit system solving numerically the Bloch-type equations (\[Eqs\]) with the relaxation rates given by Eqs. (\[Ws\], \[gmn\], \[ReG\]). Besides demonstrating the population inversion between the operating levels, we apply an additional signal with the frequency matching the distance between the operating levels, to stimulate the transition from the upper operating level to the lower one. So, we will first consider the system driven by one monochromatic signal $f(t)=f_{\mathrm{ac}}\sin \omega t$ to pump the system to the upper level and to demonstrate the population inversion. Then we will apply another signal stimulating transitions between the operating laser levels:
$$f(t)=f_{\mathrm{ac}}\sin \omega t+f_{\mathrm{L}}\sin \omega _{\mathrm{L}}t.$$
Solving the system of equations (\[Eqs\]), we obtain the population of $i$-th level of our two-qubit system, $P_{i}=x_{ii}$. The results of the calculations are plotted in Figs. \[Fig:creation\] and \[Fig:stimulated\], where the temporal dynamics of the level populations is presented for different situations.
![(Color online). **Three-level lasing and stimulated transition**. Time evolution of the numerically calculated occupation probabilities at biases $f_{1}=14\times 10^{-3}$ and $f_{2}=11\times 10^{-3}$ is plotted for (a) one-photon driving and (b) two-photon driving. As shown in the inset schemes, the driving and fast relaxation create the inverse population between the levels $\lvert {1}\rangle $ and $\lvert {0}\rangle $. So, these levels can be used for lasing, which we schematically mark by the double arrow. After some time delay (when the population inversion is reached) an additional periodic signal (S) $f_{\mathrm{L}}\cos \protect\omega _{\mathrm{L}}t$ is turned on matching the operating levels, $\hbar \protect\omega _{\mathrm{L}}=E_{1}-E_{0}$. This leads to the stimulated transition $\lvert {1}\rangle \rightarrow \lvert {0}\rangle $.[]{data-label="Fig:creation"}](Fig5){width="8.6cm"}
![(Color online). **Four-level lasing and stimulated transition**. Time evolution of the occupation probabilities at biases $f_{1}=14\times
10^{-3}$ and $f_{2}=20\times 10^{-3}$ is plotted for (a) one-photon driving and (b) two-photon driving. The driving and fast relaxation create the inverse population between the levels $\lvert {2}\rangle $ and $\lvert {1}\rangle $. After a time delay an additional periodic signal $f_{\mathrm{L}}\cos \protect\omega _{\mathrm{L}}t$ is turned on matching the operating levels, $\hbar \protect\omega _{\mathrm{L}}=E_{2}-E_{1}$. This leads to the stimulated transition $\lvert {2}\rangle \rightarrow \lvert {1}\rangle $.[]{data-label="Fig:stimulated"}](Fig6){width="8.6cm"}
In Fig. \[Fig:creation\] we consider the situation where the relevant dynamics includes three levels (for definiteness, we take $f_{1}=14\times
10^{-3}$, $f_{2}=11\times 10^{-3}$, which is marked as the square in Fig. \[Fig:W2\]). Pumping ($\lvert {0}\rangle \rightarrow \lvert {3}\rangle $) and relaxation ($\lvert {3}\rangle \rightarrow \lvert {1}\rangle $) create the population inversion between the levels $\lvert {1}\rangle \ $and $\lvert {0}\rangle $. For pumping we consider two possibilities: one-photon driving, Fig. \[Fig:creation\](a), when $\hbar \omega =E_{3}-E_{0}$, and two-photon driving, Fig. \[Fig:creation\](b), when $2\hbar \omega
=E_{3}-E_{0}$. In the latter case we have chosen the parameters (namely $f_{1}$ and $f_{2}$) so, that the two-photon excitation goes via an intermediate level $\lvert {2}\rangle $. We note here that, as was demonstrated in Ref. , the multi-photon excitation in our multi-level system can be direct, as below in Fig. \[Fig:stimulated\](b), or ladder-type, via an intermediate level, as in Fig. \[Fig:creation\](b). Figure \[Fig:creation\] was calculated for the following parameters: $\omega _{\mathrm{L}}/2\pi =13.7$ GHz ($\hbar \omega _{\mathrm{L}}=E_{1}-E_{0} $) and also (a) $\omega /2\pi =35.2$ GHz, $f_{\mathrm{ac}}=7\times 10^{-3}$, $f_{\mathrm{L}}=5\times 10^{-3}$; (b) $\omega /2\pi
=17.6 $ GHz, $f_{\mathrm{ac}}=2\times 10^{-3}$, $f_{\mathrm{L}}=5\times
10^{-3}$.
Next, we consider the scheme for the four-level lasing, which occurs in a similar scenario, except the changing of the levels. Then, the main relaxation transitions are $\lvert {3}\rangle \rightarrow \lvert {2}\rangle $ and $\lvert {1}\rangle \rightarrow \lvert {0}\rangle $, and now the population inversion should be created between levels $\lvert {2}\rangle $ and $\lvert {1}\rangle $. For this we take the partial biases $f_{1}=14\times 10^{-3}$, $f_{2}=20\times 10^{-3}$ (marked by the circle in Fig. \[Fig:W2\]). First, the system is pumped only with one signal either with $\hbar \omega =E_{3}-E_{0}$, Fig. \[Fig:stimulated\](a), or with $2\hbar \omega =E_{3}-E_{0}$, Fig. \[Fig:stimulated\](b). Such pumping together with fast relaxation ($\lvert {3}\rangle \rightarrow \lvert {2}\rangle $) creates the population inversion between the levels $\lvert {2}\rangle \ $and $\lvert {1}\rangle $. Fast relaxation from lower laser level $\lvert {1}\rangle $ into the ground state $\lvert {0}\rangle $ helps creating the population inversion between the laser levels $\lvert {2}\rangle \ $and $\lvert {1}\rangle $, which is the advantage of the four-level scheme.[@Svelto] Then the second signal is applied with a frequency matching the laser operating levels ($\hbar \omega _{\mathrm{L}}=E_{2}-E_{1}$). This stimulates the transition $\lvert {2}\rangle
\rightarrow \lvert {1}\rangle $, which provides the scheme for the four-level lasing. Figure \[Fig:stimulated\] was calculated for the following parameters: $\omega _{\mathrm{L}}/2\pi =9$ GHz ($\hbar \omega _{\mathrm{L}}=E_{2}-E_{1}$) and also (a) $\omega /2\pi =47.4$ GHz, $f_{\mathrm{ac}}=5\times 10^{-3}$, $f_{\mathrm{L}}=3\times 10^{-3}$; (b) $\omega /2\pi
=23.7$ GHz, $f_{\mathrm{ac}}=5\times 10^{-3}$, $f_{\mathrm{L}}=5\times
10^{-3}$.
In the experimental realization of the lasing schemes proposed here, the system of two qubits should be put in a quantum resonator, e.g. by coupling to a transmission line resonator, as in Ref. . Then the stimulated transition between the operating states, which we have demonstrated here, will result in transmitting the energy from the qubits to the resonator as photons. For this, the energy difference between the operating levels should be adjusted to the resonator’s frequency.
Conclusions and Discussion
==========================
We have considered the dissipative dynamics of a system of two qubits. Assuming *different* qubits makes some of the relaxation rates dominant. With these fast relaxation rates, population inversion can be created involving three or four levels. The four-level situation is more advantageous for lasing since the population inversion between the operating levels can be created more easily. We demonstrated that the upper level can be pumped by one- or multi-photon excitations. We also have shown that after applying additional driving, the transition between the operating levels is stimulated.
When presenting concrete results, we have considered the system of two flux superconducting qubits with the realistic parameters of Ref. . For lasing in a generic two-qubit (four-level) system, our recipe is the following. The hierarchy of the relaxation times in the system is obtained by making it asymmetric, with different parameters for individual qubits. This makes transitions between the levels corresponding to a qubit with smaller tunneling amplitude $\Delta $ negligible, which creates a sort of the artificial selection rule. Based on our numerical analysis, we conclude that the optimal combination of pumping and relaxation is realized for $\Delta _{1}\gg \Delta _{2}\sim J$.
Creation of *the population inversion* and* the stimulated transitions* between the laser operating levels, demonstrated here theoretically, can be the basis for the respective experiments similar to Ref. . In that work, a three-level qubit (artificial atom) was coupled to a quantum (transmission line) resonator. First, spontaneous emission from the upper operating level was demonstrated. In this way the qubit system can be used as a microwave photon source.[Houck09]{} Then, the operating levels were driven with an additional frequency and the microwave amplification due to the stimulated emission was demonstrated. We believe that similar experiments can be done with the two-qubit system (which forms an *artificial four-level molecule* from two atoms/qubits). To summarize, we propose to put the two-qubit system in a quantum resonator with the frequency adjusted with the operating levels and to measure the spontaneous and stimulated emission as the increase of the transmission coefficient. Such lasing in a two-qubit system may become a new useful tool in the qubit toolbox.
We thank E. Il’ichev for fruitful discussions and S. Ashhab for critically reading the manuscript. This work was partly supported by Fundamental Researches State Fund (grant F28.2/019) and NAS of Ukraine (project 04/10-N).
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1. Field of the Invention
The present invention relates to a distributed element filter used in the RF (radio frequency) stage, etc. of mobile communication equipment as a bandpass filter or the like to suppress noise and interfering signals, and more particularly to a distributed element filter which has a flat amplitude characteristic and a flat group delay characteristic in the passband, and transmission zeros in the stopbands, and is simplified in configuration in order to minimize losses for the purpose of improvement in performance.
2. Description of the Related Art
In high frequency circuit sections such as the RF stage of transmitter and receiver circuits for mobile communication equipment represented by analog or digital portable telephones or wireless telephones are often used bandpass filters (BPFs), for example, to attenuate harmonics which are caused by the nonlinearity of amplifier circuits, or to remove undesired signal waves such as interfering waves, sidebands, etc. from the desired signal waves, or when using the same antenna for both the transmitter and receiver circuits, to separate out the transmitter frequency band and the receiver frequency band.
Such bandpass filters for use in communication apparatuses are generally realized and constructed as filter circuits with desired bandpass characteristics by connecting series or parallel resonant circuits constructed with various circuit elements in a plurality of stages. Since the filter circuit blocks can be made smaller in size and have good electrical characteristics as high frequency circuits, in many cases circuit blocks are constructed using unbalanced distributed element transmission lines such as microstrip transmission lines or strip transmission lines. Generally, in a bandpass filter, as shown in FIGS. 24A, 24B, is required a complex circuit design to realize both a flat amplitude characteristic and a flat group delay characteristic, and at the same time, provide transmission zeros in the stopbands.
Procedures for directly synthesizing a bandpass filter having such characteristics based on a clear design theory have not been known as yet, and it has been practiced to construct filters empirically by using various known procedures. For example, as shown in a block diagram of FIG. 25, focusing first only on amplitude characteristics, such a filter 1 is designed from a filter of a known configuration, as has desired amplitude characteristics, namely, a flat amplitude characteristic throughout the passband and transmission zeros in the stopbands, but does not take the group delay characteristic into account yet. Next, in order that the filter 1 has a desired group delay characteristic as a whole, the filter 1 is provided with a phase equalizer 2 with all-pass characteristics, which has an effect of flattening the group delay characteristic in the passband. According to this procedure, the phase or group delay characteristic is improved by adding the phase equalizer 2 to the filter 1.
Such approach, however, has a disadvantage that the phase equalization or correction as shown in FIG. 25 has a limited effect and can not provide a sufficient equalization effect. Additionally, since the circuit design is wasteful requiring more circuit elements than would otherwise be required, the approach involves more difficulties than it solves, such as an adverse effect on the amplitude characteristic produced by the imperfect all-pass characteristics of the phase equalizer 2 and the increased loss produced by the increased complexity of the circuit.
Two procedures are well known in the art to realize transmission zeros in a filter's stopband. One is to realize transmission zeros by inserting a parallel resonator or series resonator in parallel or series in the filter or by combining these resonators. For example, as shown in the circuit diagram of FIG. 26, transmission zeros are formed on both sides of the passband by adding a combination 5 of a parallel resonator 5a and a series resonator 5b to a bandpass filter realized by resonators 3, 4.
The other procedure is to realize transmission zeros by splitting the transmission line into two paths which have the same output amplitude and differs from each other by 180.degree. in phase, and combining the two paths together. For example, as shown in the block diagram of FIG. 27, the circuit is split into two paths which are led to a two-port 6 and a two-port 7, respectively, which provide at a certain frequency the same amplitude output and differ from each other by 180.degree. in phase, and their outputs are combined to obtain an output which provides a transmission zero at that frequency.
Generally, the procedure of FIG. 27 can realize a filter with a circuit configuration easier to implement and smaller in loss than the procedure of FIG. 26 can.
Further, as a modification of FIG. 27, a procedure is known which uses a simple reactance feedback path. For this procedure, an accurate design theory or method for synthesizing the filter from the target circuit network function is not known, and an approximation or an empirical method is used. For example, as shown in the circuit diagram of FIG. 28, transmission zeros are formed by combining a filter block 8 as a conventional filter with a coupling element 9 corresponding to a branch circuit or feedback path. Because of circuit simplicity, this procedure has the effect of reducing the loss, but since no accurate design procedures are known for synthesizing the filter, the design relies on an approximation, which, therefore, has the problem that only approximate characteristics can be obtained and the obtained characteristics are not sufficient.
Another procedure known in the art is to combine a circuit of ladder structure with one of the above-described transmission zero forming procedures, and to thereafter adjust the group delay using a phase equalizer. According to this procedure, it is claimed that a filter with conventional bandpass characteristics can be obtained which has both a flat amplitude characteristic and a flat group delay characteristic throughout the passband and also has transmission zeros in the stopbands.
However, this procedure also has the problem that accurate characteristics cannot be obtained because the design relies on an approximation; furthermore, the circuit configuration becomes complex. Moreover, such filters have the problem that the transmission loss increases or only approximate and insufficient characteristics can be obtained. The problem of transmission loss is particularly pronounced when the filter is constructed of a distributed element filter such as a microstrip line circuit.
|
{
"pile_set_name": "USPTO Backgrounds"
}
|
The synthesis of 7 alpha-methyl-substituted estrogens labeled with fluorine-18: potential breast tumor imaging agents.
The 7 alpha-methyl substituent is reported to increase the binding affinity of estradiol for the estrogen receptor (ER). In order to evaluate whether this substituent would improve the in vitro binding characteristics and the in vivo tissue distribution of 18F labeled estrogens that we are developing as positron emission tomographic (PET) imaging agents for ER-positive breast tumors, we have prepared four 18F labeled analogs of 7 alpha-methylestradiol. These ligands were labeled in the 16 alpha or 16 beta position with 18F by nucleophilic displacement of the corresponding epimeric estrone trifluoromethanesulfonates with 18F fluoride ion. Lithium aluminum hydride reduction afforded the estradiol (E2) series, while lithium trimethylsilylacetylide addition provided the 17 alpha-ethynylestradiol (EE2) series. The decay-corrected yields were 2-35% for a synthesis time of 85 minutes for the E2 series, and 120 minutes for the EE2 series, and the effective specific activities were 158-1213 Ci/mmol. In nearly every case, the 7 alpha-methyl substituent increases ER binding affinity (measured at 25 C) and decreases binding to high affinity serum steroid binding proteins, alphafetoprotein, and sex steroid binding protein; this substituent, however, increases the lipophilicity and the predicted non-specific binding (estimated from octanol-water partition coefficients determined by reverse-phase high-pressure liquid chromatography/[HPLC]), with the result that the ratio of ER binding to non-specific binding is nearly the same for the 7 alpha-methyl substituted analogs as for the corresponding unsubstituted analogs. In vivo distribution studies demonstrated a high level of receptor-mediated uptake in receptor-rich target tissues (uterus, ovaries), and in some cases, other tissues with low ER titers (secondary target tissues, e.g., muscle, thymus) showed significant displaceable uptake, presumed to be receptor-mediated.(ABSTRACT TRUNCATED AT 250 WORDS)
|
{
"pile_set_name": "PubMed Abstracts"
}
|
package com.huawei.security.conscrypt;
import android.util.Log;
import com.huawei.security.HwKeystoreManager;
import com.huawei.security.keymaster.HwKeymasterCertificateChain;
import java.io.ByteArrayInputStream;
import java.security.InvalidKeyException;
import java.security.NoSuchAlgorithmException;
import java.security.NoSuchProviderException;
import java.security.SignatureException;
import java.security.cert.CertificateException;
import java.security.cert.CertificateFactory;
import java.security.cert.X509Certificate;
import java.util.List;
import javax.security.auth.x500.X500Principal;
public class HwTrustCertificateStore {
private static final String TAG = "HwTrustCertificateStore";
private HwKeystoreManager mKeyStore = HwKeystoreManager.getInstance();
/* access modifiers changed from: private */
public interface CertSelector {
boolean match(X509Certificate x509Certificate, X509Certificate x509Certificate2);
}
public HwTrustCertificateStore(HwKeystoreManager keystore) {
this.mKeyStore = keystore;
}
private static X509Certificate[] toCertificates(List<byte[]> bytes) {
if (bytes == null || bytes.size() == 0) {
Log.e(TAG, "Invalid param.");
return null;
}
try {
Log.d(TAG, "toCertificates bytes.size:" + bytes.size());
CertificateFactory certFactory = CertificateFactory.getInstance("X.509");
X509Certificate[] certs = new X509Certificate[bytes.size()];
int i = 0;
do {
byte[] data = bytes.get(i);
if (data != null) {
if (data.length != 0) {
certs[i] = (X509Certificate) certFactory.generateCertificate(new ByteArrayInputStream(data));
i++;
}
}
Log.e(TAG, "data is null");
return null;
} while (i < bytes.size());
return certs;
} catch (CertificateException e) {
Log.w(TAG, "Couldn't parse certificates in keystore CertificateException", e);
return null;
}
}
public X509Certificate getTrustAnchor(X509Certificate c) {
X509Certificate trustCert = (X509Certificate) findCert(c, c.getSubjectX500Principal(), new GetTrustAnchorCertSelector(), X509Certificate.class);
if (trustCert != null) {
return trustCert;
}
return null;
}
public X509Certificate findIssuer(X509Certificate c) {
X509Certificate cert = (X509Certificate) findCert(c, c.getIssuerX500Principal(), new FindIssuerCertSelector(), X509Certificate.class);
if (cert != null) {
return cert;
}
return null;
}
private <T> T findCert(X509Certificate c, X500Principal subject, CertSelector selector, Class<T> desiredReturnType) {
if (this.mKeyStore == null) {
Log.e(TAG, "mKeyStore is null!");
return null;
}
HwKeymasterCertificateChain outChain = new HwKeymasterCertificateChain();
if (this.mKeyStore.exportTrustCert(outChain) != 1) {
Log.e(TAG, "exportTrustCert failed!");
return null;
}
List<byte[]> certsByte = outChain.getCertificates();
if (certsByte == null) {
Log.e(TAG, "findCert failed!");
return null;
}
X509Certificate[] certList = toCertificates(certsByte);
if (certList == null) {
Log.e(TAG, "findCert toCertificates failed!");
return null;
}
for (X509Certificate x509Certificate : certList) {
T t = (T) x509Certificate;
boolean match = selector.match(t, c);
boolean equals = subject != null ? subject.getName().equals(t.getSubjectX500Principal().getName()) : false;
if (!match || !equals) {
Log.d(TAG, "exportTrustCert match:" + match + " equals:" + equals);
}
if (match && equals) {
Log.d(TAG, "findCert find the trust cert!");
if (desiredReturnType == X509Certificate.class) {
return t;
}
if (desiredReturnType == Boolean.class) {
return (T) Boolean.TRUE;
}
throw new AssertionError();
}
}
return null;
}
static class GetTrustAnchorCertSelector implements CertSelector {
GetTrustAnchorCertSelector() {
}
@Override // com.huawei.security.conscrypt.HwTrustCertificateStore.CertSelector
public boolean match(X509Certificate ca, X509Certificate c) {
return ca.getPublicKey().equals(c.getPublicKey());
}
}
static class FindIssuerCertSelector implements CertSelector {
FindIssuerCertSelector() {
}
@Override // com.huawei.security.conscrypt.HwTrustCertificateStore.CertSelector
public boolean match(X509Certificate ca, X509Certificate c) {
try {
c.verify(ca.getPublicKey());
return true;
} catch (CertificateException e) {
Log.e(HwTrustCertificateStore.TAG, "FindIssuerCertSelector match fail CertificateException!");
return false;
} catch (NoSuchAlgorithmException e2) {
Log.e(HwTrustCertificateStore.TAG, "FindIssuerCertSelector match fail NoSuchAlgorithmException!");
return false;
} catch (InvalidKeyException e3) {
Log.e(HwTrustCertificateStore.TAG, "FindIssuerCertSelector match fail InvalidKeyException!");
return false;
} catch (NoSuchProviderException e4) {
Log.e(HwTrustCertificateStore.TAG, "FindIssuerCertSelector match fail NoSuchProviderException!");
return false;
} catch (SignatureException e5) {
Log.e(HwTrustCertificateStore.TAG, "FindIssuerCertSelector match fail SignatureException!");
return false;
}
}
}
}
|
{
"pile_set_name": "Github"
}
|
PKIX1Algorithms88 { iso(1) identified-organization(3) dod(6)
internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-pkix1-algorithms(17) }
DEFINITIONS EXPLICIT TAGS ::= BEGIN
-- EXPORTS All;
-- IMPORTS NONE;
--
-- One-way Hash Functions
--
md2 OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) rsadsi(113549)
digestAlgorithm(2) 2 }
md5 OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) rsadsi(113549)
digestAlgorithm(2) 5 }
id-sha1 OBJECT IDENTIFIER ::= {
iso(1) identified-organization(3) oiw(14) secsig(3)
algorithms(2) 26 }
--
-- DSA Keys and Signatures
--
-- OID for DSA public key
id-dsa OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) x9-57(10040) x9algorithm(4) 1 }
-- encoding for DSA public key
DSAPublicKey ::= INTEGER -- public key, y
Dss-Parms ::= SEQUENCE {
p INTEGER,
q INTEGER,
g INTEGER }
-- OID for DSA signature generated with SHA-1 hash
id-dsa-with-sha1 OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) x9-57 (10040) x9algorithm(4) 3 }
-- encoding for DSA signature generated with SHA-1 hash
Dss-Sig-Value ::= SEQUENCE {
r INTEGER,
s INTEGER }
--
-- RSA Keys and Signatures
--
-- arc for RSA public key and RSA signature OIDs
pkcs-1 OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) 1 }
-- OID for RSA public keys
rsaEncryption OBJECT IDENTIFIER ::= { pkcs-1 1 }
-- OID for RSA signature generated with MD2 hash
md2WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 2 }
-- OID for RSA signature generated with MD5 hash
md5WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 4 }
-- OID for RSA signature generated with SHA-1 hash
sha1WithRSAEncryption OBJECT IDENTIFIER ::= { pkcs-1 5 }
-- encoding for RSA public key
RSAPublicKey ::= SEQUENCE {
modulus INTEGER, -- n
publicExponent INTEGER } -- e
--
-- Diffie-Hellman Keys
--
dhpublicnumber OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) ansi-x942(10046)
number-type(2) 1 }
-- encoding for DSA public key
DHPublicKey ::= INTEGER -- public key, y = g^x mod p
DomainParameters ::= SEQUENCE {
p INTEGER, -- odd prime, p=jq +1
g INTEGER, -- generator, g
q INTEGER, -- factor of p-1
j INTEGER OPTIONAL, -- subgroup factor, j>= 2
validationParms ValidationParms OPTIONAL }
ValidationParms ::= SEQUENCE {
seed BIT STRING,
pgenCounter INTEGER }
--
-- KEA Keys
--
id-keyExchangeAlgorithm OBJECT IDENTIFIER ::=
{ 2 16 840 1 101 2 1 1 22 }
KEA-Parms-Id ::= OCTET STRING
--
-- Elliptic Curve Keys, Signatures, and Curves
--
ansi-X9-62 OBJECT IDENTIFIER ::= {
iso(1) member-body(2) us(840) 10045 }
FieldID ::= SEQUENCE { -- Finite field
fieldType OBJECT IDENTIFIER,
parameters ANY DEFINED BY fieldType }
-- Arc for ECDSA signature OIDS
id-ecSigType OBJECT IDENTIFIER ::= { ansi-X9-62 signatures(4) }
-- OID for ECDSA signatures with SHA-1
ecdsa-with-SHA1 OBJECT IDENTIFIER ::= { id-ecSigType 1 }
-- OID for an elliptic curve signature
-- format for the value of an ECDSA signature value
ECDSA-Sig-Value ::= SEQUENCE {
r INTEGER,
s INTEGER }
-- recognized field type OIDs are defined in the following arc
id-fieldType OBJECT IDENTIFIER ::= { ansi-X9-62 fieldType(1) }
-- where fieldType is prime-field, the parameters are of type Prime-p
prime-field OBJECT IDENTIFIER ::= { id-fieldType 1 }
Prime-p ::= INTEGER -- Finite field F(p), where p is an odd prime
-- where fieldType is characteristic-two-field, the parameters are
-- of type Characteristic-two
characteristic-two-field OBJECT IDENTIFIER ::= { id-fieldType 2 }
Characteristic-two ::= SEQUENCE {
m INTEGER, -- Field size 2^m
basis OBJECT IDENTIFIER,
parameters ANY DEFINED BY basis }
-- recognized basis type OIDs are defined in the following arc
id-characteristic-two-basis OBJECT IDENTIFIER ::= {
characteristic-two-field basisType(3) }
-- gnbasis is identified by OID gnBasis and indicates
-- parameters are NULL
gnBasis OBJECT IDENTIFIER ::= { id-characteristic-two-basis 1 }
-- parameters for this basis are NULL
-- trinomial basis is identified by OID tpBasis and indicates
-- parameters of type Pentanomial
tpBasis OBJECT IDENTIFIER ::= { id-characteristic-two-basis 2 }
-- Trinomial basis representation of F2^m
-- Integer k for reduction polynomial xm + xk + 1
Trinomial ::= INTEGER
-- for pentanomial basis is identified by OID ppBasis and indicates
-- parameters of type Pentanomial
ppBasis OBJECT IDENTIFIER ::= { id-characteristic-two-basis 3 }
-- Pentanomial basis representation of F2^m
-- reduction polynomial integers k1, k2, k3
-- f(x) = x**m + x**k3 + x**k2 + x**k1 + 1
Pentanomial ::= SEQUENCE {
k1 INTEGER,
k2 INTEGER,
k3 INTEGER }
-- The object identifiers gnBasis, tpBasis and ppBasis name
-- three kinds of basis for characteristic-two finite fields
FieldElement ::= OCTET STRING -- Finite field element
ECPoint ::= OCTET STRING -- Elliptic curve point
-- Elliptic Curve parameters may be specified explicitly,
-- specified implicitly through a "named curve", or
-- inherited from the CA
EcpkParameters ::= CHOICE {
ecParameters ECParameters,
namedCurve OBJECT IDENTIFIER,
implicitlyCA NULL }
ECParameters ::= SEQUENCE { -- Elliptic curve parameters
version ECPVer,
fieldID FieldID,
curve Curve,
base ECPoint, -- Base point G
order INTEGER, -- Order n of the base point
cofactor INTEGER OPTIONAL } -- The integer h = #E(Fq)/n
ECPVer ::= INTEGER {ecpVer1(1)}
Curve ::= SEQUENCE {
a FieldElement, -- Elliptic curve coefficient a
b FieldElement, -- Elliptic curve coefficient b
seed BIT STRING OPTIONAL }
id-publicKeyType OBJECT IDENTIFIER ::= { ansi-X9-62 keyType(2) }
id-ecPublicKey OBJECT IDENTIFIER ::= { id-publicKeyType 1 }
-- Named Elliptic Curves in ANSI X9.62.
ellipticCurve OBJECT IDENTIFIER ::= { ansi-X9-62 curves(3) }
c-TwoCurve OBJECT IDENTIFIER ::= {
ellipticCurve characteristicTwo(0) }
c2pnb163v1 OBJECT IDENTIFIER ::= { c-TwoCurve 1 }
c2pnb163v2 OBJECT IDENTIFIER ::= { c-TwoCurve 2 }
c2pnb163v3 OBJECT IDENTIFIER ::= { c-TwoCurve 3 }
c2pnb176w1 OBJECT IDENTIFIER ::= { c-TwoCurve 4 }
c2tnb191v1 OBJECT IDENTIFIER ::= { c-TwoCurve 5 }
c2tnb191v2 OBJECT IDENTIFIER ::= { c-TwoCurve 6 }
c2tnb191v3 OBJECT IDENTIFIER ::= { c-TwoCurve 7 }
c2onb191v4 OBJECT IDENTIFIER ::= { c-TwoCurve 8 }
c2onb191v5 OBJECT IDENTIFIER ::= { c-TwoCurve 9 }
c2pnb208w1 OBJECT IDENTIFIER ::= { c-TwoCurve 10 }
c2tnb239v1 OBJECT IDENTIFIER ::= { c-TwoCurve 11 }
c2tnb239v2 OBJECT IDENTIFIER ::= { c-TwoCurve 12 }
c2tnb239v3 OBJECT IDENTIFIER ::= { c-TwoCurve 13 }
c2onb239v4 OBJECT IDENTIFIER ::= { c-TwoCurve 14 }
c2onb239v5 OBJECT IDENTIFIER ::= { c-TwoCurve 15 }
c2pnb272w1 OBJECT IDENTIFIER ::= { c-TwoCurve 16 }
c2pnb304w1 OBJECT IDENTIFIER ::= { c-TwoCurve 17 }
c2tnb359v1 OBJECT IDENTIFIER ::= { c-TwoCurve 18 }
c2pnb368w1 OBJECT IDENTIFIER ::= { c-TwoCurve 19 }
c2tnb431r1 OBJECT IDENTIFIER ::= { c-TwoCurve 20 }
primeCurve OBJECT IDENTIFIER ::= { ellipticCurve prime(1) }
prime192v1 OBJECT IDENTIFIER ::= { primeCurve 1 }
prime192v2 OBJECT IDENTIFIER ::= { primeCurve 2 }
prime192v3 OBJECT IDENTIFIER ::= { primeCurve 3 }
prime239v1 OBJECT IDENTIFIER ::= { primeCurve 4 }
prime239v2 OBJECT IDENTIFIER ::= { primeCurve 5 }
prime239v3 OBJECT IDENTIFIER ::= { primeCurve 6 }
prime256v1 OBJECT IDENTIFIER ::= { primeCurve 7 }
END
|
{
"pile_set_name": "Github"
}
|
58 B.R. 38 (1986)
In the Matter of GLAUBINGER MACHINERY CO., INC., Debtor.
Bankruptcy No. 84-02971.
United States Bankruptcy Court, D. New Jersey.
January 23, 1986.
Ravin, Greenberg & Zackin, P.A. by Gary N. Marks, Roseland, N.J., for debtor.
Tai Cho, New York City, for Daewoo Intern.
OPINION
DeVITO, Bankruptcy Judge.
The above captioned debtor moves to reclassify a secured claim filed by Daewoo International (America) Corporation ("Daewoo") to the status of a general unsecured claim. For the reasons set forth below, this Court grants the within motion.
The facts of the case are relatively straightforward. Daewoo possessed a perfected security interest in certain milling machines held by the debtor on consignment. One machine, identified as Number *39 180014, was sold to the Southern California Edison Company in or about January of 1983. The debtor was obligated to remit net proceeds of $29,000 to Daewoo. Upon receipt by the debtor of the total payment ($29,000) from Southern California Edison, the debtor actually transmitted $7,500 of the proceeds to Daewoo. The remaining $21,500 due to Daewoo was deposited in the debtor's general operating account. The debtor filed its petition for reorganization under the Bankruptcy Code on June 1, 1984. Daewoo filed a proof of claim in the sum of $21,500, said sum being the balance of the final payment due on the purchase of the machine noted above, and presently held by the debtor.
It is important to note here that the above recitation of facts is based upon the statements contained in the brief filed by debtor's counsel in support of debtor's motion, at 1-2. In re Glaubinger Machinery Co., Inc., (Bankr.D.N.J. Oct. 2, 1985). Daewoo admits that the debtor's version of the facts is correct, subject only to two exceptions. Daewoo takes exception to the statements that the debtor deposited the funds in question in its general operating account and debtor's stated allegation that Daewoo does not have a secured interest in the proceeds. Affidavit in Opposition by K.J. Chea at 1-2, In re Glaubinger Machinery Co., Inc., (Bankr.D.N.J. Nov. 27, 1985). However, the affidavit fails to explain why Daewoo takes the exceptions as noted above, nor does it offer its own version of the disputed statements.
The debtor relies upon the Uniform Commercial Code, as adopted in this jurisdiction; specifically, that Daewoo lost its secured claim when the monies resulting from the sale of the milling machine were commingled with other funds of the debtor, the effect of which reduced Daewoo's claim to that of a general unsecured claim; thus the instant motion to reclassify the claim filed. Daewoo essentially argues that the debtor's motion is misdirected and that the Uniform Commercial Code is still supportive of Daewoo's secured position.
The instant matter concerns the administration of the debtor's estate and is unquestionably a core proceeding. 28 U.S.C. § 157[b][2][A]. This Court is thus empowered to hear and determine the issues at hand. 28 U.S.C. § 157[b][1]. The issue here is one requiring an interpretation of state law. Following the longstanding doctrine of Erie R.R. Co. v. Tompkins, 304 U.S. 64, 58 S.Ct. 817, 82 L.Ed. 1188 (1938), this Court shall apply the law controlling in the forum state of New Jersey.
The specific state statutory provision in question is § 9-306[4] of the Uniform Commercial Code, codified in chapter 12A of the New Jersey Statutes Annotated, which provides:
In the event of insolvency proceedings instituted by or against a Debtor, a secured party with a perfected security interest in proceeds has a perfected security interest only in the following proceeds:
. . . . .
[b] In identifiable cash proceeds in the form of money which is neither commingled with other money nor deposited in a deposit account prior to the insolvency proceedings;
[c] In identifiable cash proceeds in the form of checks and the like which are not deposited in a deposit account prior to the insolvency proceedings; and
[d] In all cash and deposit accounts of the Debtor in which proceeds have been commingled with other funds, but the perfected security interest under this paragraph [d] is:
[i] Subject to any right of set-off; and
[ii] Limited to an amount not greater than the amount of any cash proceeds received by the Debtor within ten days before the institution of the insolvency
. . .
N.J.Stat.Ann. 12A:9-306[4] (West Pocket Part 1985) (subsection [a] omitted as it addresses only non -cash proceeds and is, therefore, irrelevant herein). The impact of this statute is clear. Even for a holder of a perfected security interest in proceeds, the intervention of a bankruptcy filing acts *40 to limit the secured interest only to proceeds which meet the conditions as enumerated above. Id. If it can be demonstrated that the proceeds in question do not meet the conditions set forth above, the secured status of the creditor is lost and, ergo, the claim is a general unsecured one.
Assuming arguendo that Daewoo held a perfected security interest in the proceeds, the instant matter meets the requirements of subparagraph [4] and is within the ambit of § 9-306[4]. Proceeding with a step-by-step analysis, both subsections [b] and [c] are of no help to Daewoo, since the proceeds received by the debtor were deposited in a deposit account prior to the bankruptcy. The Court takes note of the general rule that "proceeds will have been rendered unidentifiable by having been commingled with other funds in a single bank account." Morrison Steel Co. v. Gurtman, 113 N.J.Super. 474, 481, 274 A.2d 306 (App.Div.1974). Returning to the facts presented here, the Court is reminded of the debtor's assertion that it did indeed commingle these proceeds with other funds in its general operating account. While it is true Daewoo took exception to that statement, the Court does not find the opposition to be credible. Daewoo's exception is bereft of any explanation of why Daewoo objects to the allegation. Moreover, Daewoo failed to offer any evidence sufficient to demonstrate what the debtor did with the proceeds, if it indeed did not deposit them in its general fund as claimed. The Court shall accept the debtor's factual allegations on that point as true, and thus, by necessity, determines that Daewoo has no secured interest in proceeds that have been deposited and commingled with other monies, pursuant to the rule of § 9-306[4][b] and [c].
Turning to the final subsection, subsection [d], the Court finds that this portion of the statute does not terminate the secured interest where proceeds have been commingled. However, it is strictly limited to instances where the cash proceeds were received by the debtor within the ten days preceding the bankruptcy. § 9-306[4][d][ii]. It is undisputed that the proceeds were received by the debtor on July 12, 1983, almost a year before the petition in bankruptcy was filed. This being the case, Daewoo loses its secured claim to the proceeds under this subsection as well.
In conclusion, based upon the credible evidence proffered and the law of the Uniform Commercial Code as adopted in New Jersey, Daewoo does not hold a secured claim in the cash proceeds ($21,500) held by the debtor. The claim is properly classified as a general unsecured claim. The Court grants the debtor's motion to reclassify it as such.
Submit an order in accordance with the above.
|
{
"pile_set_name": "FreeLaw"
}
|
Q:
A linear transformation that fixes a subspace
I am struggling with the problem below:
Let $V$ be a finite-dimensional vector space over a field $F$, and $L: V \longrightarrow V$ a linear transformation over $F$. Define a sequence of subspaces $V_0, V_1, V_2, ...$ of $V$ inductively by $V_0 = V$, and $V_{n+1} = L(V_n)$ for $n \geq 1$. Prove that there exists a positive integer $N$ such that $V_{N + 1} = V_N$.
I observed that $V_0 = V$, $V_1 = L(V)$, $V_2 = L^2(V)$, ... That is, $V_K = L^K(V)$. Thus, to show $V_{N + 1} = V_N$, we need to show that $L^{N+1}(V) = L^N(V)$, which occurs if and only if $L^N(V) \cdot (L(V) -1) = 0$, which is true if and only if $L(V)$ is the identity operator or $L$ is nilpotent.
Thus, I've reduced the question down to proving that $L$ is either the identity transformation or nilpotent. How can I proceed with the proof? I'm not sure where to go from here.
Thanks!
A:
Your last claim is false. $L^N(V) \cdot (L(V) - 1) = 0$ does not imply that $L^N = 0$ or $L = 1$. The composition of nonzero linear transformations may be zero. Note that the statement you are trying to prove is stated for an arbitrary linear transformation $L \colon V \to V$, not just nilpotent ones or the identity.
Instead, observe that
$$V \supseteq L(V) \supseteq L^2(V) \supseteq \cdots,$$
thus
$$\dim_F(V) \geq \dim_F(L(V)) \geq \dim_F(L^2(V)) \geq \cdots.$$
Can you see why there must exist $N$ such that $\dim_F(L^{N + 1}(V)) = \dim_F(L^N(V))$, which implies $L^{N + 1}(V) = L^N(V)$?
|
{
"pile_set_name": "StackExchange"
}
|
Q:
How to send a data from req.body using nodejs
How can I send data from body using nodejs?
I am writing a code in node.js in which the user inputs a data in the body. And based on that input, the program fetches the data from the database and displays it in JSON format.
I have written the following code:
app.post('/city', (req,res) => {
var id = parseInt(req.body.id);
pool.connect(function (err, client, done) {
if (err) {
console.log("Can not connect to the DB" + err);
}
client.query(`SELECT * FROM city WHERE state_id=${id}`, function (err, result) {
done();
if (err) {
console.log(err);
res.status(400).send(err);
}
res.status(200).send(result.rows);
})
})
});
I feel that something is wrong with var id = parseInt(req.body.id);. Because, when I am running the code, it says it is not able to recognize the id?
Also, when I run this in Postman, I get the following error:
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Error</title>
</head>
<body>
<pre>TypeError: Cannot read property 'id' of undefined
<br> at app.post (F:\DatabaseProject15\routes\common.js:36:32)
<br> at Layer.handle [as handle_request] (F:\DatabaseProject15\node_modules\express\lib\router\layer.js:95:5)
<br> at next (F:\DatabaseProject15\node_modules\express\lib\router\route.js:137:13)
<br> at Route.dispatch (F:\DatabaseProject15\node_modules\express\lib\router\route.js:112:3)
<br> at Layer.handle [as handle_request] (F:\DatabaseProject15\node_modules\express\lib\router\layer.js:95:5)
<br> at F:\DatabaseProject15\node_modules\express\lib\router\index.js:281:22
<br> at Function.process_params (F:\DatabaseProject15\node_modules\express\lib\router\index.js:335:12)
<br> at next (F:\DatabaseProject15\node_modules\express\lib\router\index.js:275:10)
<br> at expressInit (F:\DatabaseProject15\node_modules\express\lib\middleware\init.js:40:5)
<br> at Layer.handle [as handle_request] (F:\DatabaseProject15\node_modules\express\lib\router\layer.js:95:5)
</pre>
</body>
</html>
Details:
var id = parseInt(req.body.id);
is at F:\DatabaseProject15\routes\common.js:36:32
Error at console:
TypeError: Cannot read property 'id' of undefined
at app.post (F:\DatabaseProject15\routes\common.js:36:32)
at Layer.handle [as handle_request] (F:\DatabaseProject15\node_modules\express\lib\router\layer.js:95:5)
at next (F:\DatabaseProject15\node_modules\express\lib\router\route.js:137:13)
at Route.dispatch (F:\DatabaseProject15\node_modules\express\lib\router\route.js:112:3)
at Layer.handle [as handle_request] (F:\DatabaseProject15\node_modules\express\lib\router\layer.js:95:5)
at F:\DatabaseProject15\node_modules\express\lib\router\index.js:281:22
at Function.process_params (F:\DatabaseProject15\node_modules\express\lib\router\index.js:335:12)
at next (F:\DatabaseProject15\node_modules\express\lib\router\index.js:275:10)
at expressInit (F:\DatabaseProject15\node_modules\express\lib\middleware\init.js:40:5)
at Layer.handle [as handle_request] (F:\DatabaseProject15\node_modules\express\lib\router\layer.js:95:5)
CODE:
app.js
const pg = require('pg');
const express = require('express');
const app = express();
var common = require('./routes/common')
app.use('/common', common)
app.listen(4600, function () {
console.log('Server is running.. on Port 8000');
});
router/common.js
const pg = require('pg');
const express = require('express');
const app = express();
const config = {
user: 'postgres',
database: 'mydb',
host: '40.83.121.72',
password: 'abc',
port: 5432
};
const pool = new pg.Pool(config);
app.post('/', (req, res, next) => {
pool.connect(function (err, client, done) {
if (err) {
console.log("Can not connect to the DB" + err);
}
client.query('SELECT * FROM city', function (err, result) {
done();
if (err) {
console.log(err);
res.status(400).send(err);
}
res.status(200).send(result.rows);
})
})
});
app.post('/city', (req,res) => {
//var id = parseInt(req.params.id);
var id = parseInt(req.body.id);
pool.connect(function (err, client, done) {
if (err) {
console.log("Can not connect to the DB" + err);
}
client.query(`SELECT * FROM city WHERE state_id=${id}`, function (err, result) {
done();
if (err) {
console.log(err);
res.status(400).send(err);
}
res.status(200).send(result.rows);
})
})
});
app.post('/app/state/:id', (req,res) => {
var id = parseInt(req.params.id);
pool.connect(function (err, client, done) {
if (err) {
console.log("Can not connect to the DB" + err);
}
client.query(`SELECT * FROM state WHERE id=${id}`, function (err, result) {
done();
if (err) {
console.log(err);
res.status(400).send(err);
}
res.status(200).send(result.rows);
})
})
});
module.exports = app
A:
In app.js above your routes add
app.use(express.json());
this will let you parse application/json, if you need to parse application/x-www-form-urlencoded you need to add
app.use(express.urlencoded({ extended: true }));
|
{
"pile_set_name": "StackExchange"
}
|
Internal Republican polls show ex-coal CEO and former convict Don Blankenship in the lead a day before West Virginia’s Republican Senate primary, prompting more GOP fears about a Blankenship surge.
An internal poll from one of Blankenship’s rivals taken on Saturday and Sunday found Blankenship slightly ahead with 31 percent of the vote, according to The Weekly Standard. Rep. Evan Jenkins Evan Hollin JenkinsWest Virginia New Members 2019 Republican Carol Miller holds off Democrat in West Virginia House race Trump to fundraise for 3 Republicans running for open seats: report MORE came in second, with 28 percent, and state Attorney General Patrick Morrisey in third, with 27 percent.
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Another internal survey taken on Friday and Saturday also showed Blankenship with a narrow lead with 28 percent of the vote. This poll found Morrisey in second place, with 27 percent, while Jenkins received just 14 percent.
Republicans are sounding the alarm as it appears Blankenship, who spent a year in prison for violating mining safety regulations following an explosion that killed 29 miners, is leading the pack again ahead of Tuesday’s primary. The winner of the GOP nomination will go on to face vulnerable Sen. Joe Manchin Joseph (Joe) ManchinThe Hill's Morning Report - Sponsored by Facebook - Trump, GOP allies prepare for SCOTUS nomination this week Trump meets with potential Supreme Court pick Amy Coney Barrett at White House Names to watch as Trump picks Ginsburg replacement on Supreme Court MORE (D), a top Republican target.
The GOP views Manchin's seat as a prime pick-up opportunity to expand the party’s narrow majority in the Senate. President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE won West Virginia by more than 40 points in 2016.
Some Republicans worry Blankenship’s controversial past could jeopardize their chances at unseating Manchin.
In a last-ditch effort to suppress Blankenship, Trump on Monday urged voters to reject the former coal executive and instead vote for either Jenkins or Morrisey on Tuesday.
“To the great people of West Virginia we have, together, a really great chance to keep making a big difference,” the president wrote on Twitter.
“Problem is, Don Blankenship, currently running for Senate, can’t win the General Election in your State...No way! Remember Alabama. Vote Rep. Jenkins or A.G. Morrisey!”
Blankenship fired back in a response to Trump’s tweet.
"As some have said I am Trumpier than Trump, and this morning proves it,” Blankenship said in a statement.
|
{
"pile_set_name": "OpenWebText2"
}
|
Introduction
============
Brucellosis is the collective name of a group of zoonotic diseases afflicting a wide range of domestic and wild mammals ([@B75]; [@B77]). In domestic livestock brucellosis is manifested mostly as abortions and infertility, and contact with infected animals and consumption of unpasteurized dairy products are the sources of human brucellosis, an incapacitating condition that requires prolonged antibiotic treatment ([@B78]). Eradicated in a handful of countries, brucellosis is endemic or even increasing in many areas of the world ([@B33]; [@B18]; [@B39]).
This disease is caused by facultative intracellular parasites of the genus *Brucella*. Taxonomically placed in the α-2 *Proteobacteria* ([@B51]), the brucellae are close to plant pathogens and endosymbionts such as *Agrobacterium, Sinorhizobium*, and *Rhizobium* and to soil bacteria such as *Ochrobactrum*, the latter including some opportunistic pathogens, and comparative analyses suggest that soil bacteria of this group are endowed with properties that represent a first scaffold on which an intracellular life style develops ([@B70]; [@B50]; [@B5]). The brucellae owe their pathogenicity mainly to their ability to multiply within dendritic cells, macrophages, and a variety of other cells. Due to their ability to control intracellular trafficking and be barely detected by innate immunity, these bacteria are able to reach a safe intracellular niche before an effective immune response is mounted, and to multiply extensively ([@B25]; [@B4]). A mechanism used by *Brucella* to scape from the host immune response is the interference with the toll-like receptor (TLR) signaling pathway by the injection of active effectors such as BtpA and BtpB through the Type IV secretion system T4SS. Both effector proteins contain a TIR domain that interferes with TLR signaling by directly interacting with MyD88 ([@B12]; [@B61], [@B60]; [@B11]) and contribute to the control of dendritic cell (DC) activation during infection. Moreover, *Brucella* has modified outer membrane (OM) components in order to reduce the pathogen-associated molecular patterns (PAMP) of the cell envelope. In Gram-negative bacteria, these PAMP are created by the conserved composition of the OM lipopolysaccharide (LPS) and the free lipids on which the topology of the OM also depends. However, in addition to free-lipid species present in most Gram-negative bacteria (i.e., cardiolipin, phosphatidylglycerol, and phosphatidylethanolamine), *Brucella* also possesses phosphatidylcholine and amino lipids. Phosphatidylcholine is a eukaryotic-type phospholipid required for *Brucella* full virulence ([@B13]; [@B15]). Among the amino lipids, only the ornithine lipids (OL) have been investigated which unlike their counterparts in *Bordetella*, do not trigger the release of IL-6 or TNF-α by macrophages, possibly on account of their longer acyl chains that reduce the OL PAMP ([@B55]). Concerning the LPS, most bacteria carry C1 and C4′ glucosamine disaccharides with C12 and C14 acyl and acyl-oxyacyl chains. This highly amphipathic structure, named lipid A, is adjacent to additional negatively charged groups of the core oligosaccharide, namely the heptose phosphates and 2-keto-3-deoxyoctulosonate carboxyl groups ([@B36]; [@B52]). This lipid A-core PAMP is so efficiently detected by the innate immunity system that some pathogens partially conceal it by removing phosphate groups or substituting them with arabinosamine and/or ethanolamine, or by hydroxylating the acyl chains ([@B67]; [@B43]; [@B48]; [@B54]; [@B44]; [@B69]). In contrast, *Brucella* lipid A is a diaminoglucose disaccharide amide-linked to long (C16, C18) and very long (C28--C30) acyl chains ([@B70]; [@B31]; [@B21]). Furthermore, negative charges in lipid A phosphates and 2-keto-3-deoxyoctulosonate are counterbalanced by four glucosamine units present in the core ([@B38]; [@B21]). As illustrated by the unusually reduced endotoxicity of the *Brucella* LPS this structure is defectively detected by the innate immune response ([@B40]; [@B47]; [@B14]). It remains unknown, however, whether *Brucella* LPS undergoes post-synthetic modifications that have been described for other bacteria that could alter its PAMP potential and contribution to virulence. In this work, we investigated in *Brucella* the role of gene homologs to phosphatases, phospho-ethanolamine (pEtN) transferases, and acyl hydroxylases (**Figure [1](#F1){ref-type="fig"}**) that have been shown in other Gram-negative pathogens to act on LPS and to contribute to overcoming innate immunity defenses.
{#F1}
Materials and Methods {#s1}
=====================
Bacterial Strains and Growth Conditions
---------------------------------------
The bacterial strains and plasmids used in this study are listed in Supplementary Table [S1](#SM1){ref-type="supplementary-material"}. Bacteria were routinely grown in standard tryptic soy broth or agar either plain or supplemented with kanamycin at 50 μg/ml, or/and nalidixic at 5 or 25 μg/ml or/and 5% sucrose. All strains were stored in skim milk at -80°C.
DNA Manipulations
-----------------
Genomic sequences were obtained from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database^[1](#fn01){ref-type="fn"}^. Searches for DNA and protein homologies were carried out using the National Center for Biotechnology Information (NCBI^[2](#fn02){ref-type="fn"}^) and the European Molecular Biology Laboratory (EMBL) -- European Bioinformatics Institute server^[3](#fn03){ref-type="fn"}^. Primers were synthesized by Sigma-Genosys (Haverhill, United Kingdom). DNA sequencing was performed by the "Servicio de Secuenciación del Centro de Investigación Médica Aplicada" (Pamplona, Spain). Restriction--modification enzymes were used under the conditions recommended by the manufacturer. Plasmid and chromosomal DNA were extracted with Qiaprep Spin Miniprep (Qiagen) and Ultraclean Microbial DNA Isolation Kits (Mo Bio Laboratories), respectively. When needed, DNA was purified from agarose gels using the Qiack Gel Extraction Kit (Qiagen).
Mutagenesis
-----------
To obtain *BmeΔlptA, BaΔlpxE*, and *BmiΔolsC* in-frame deletion mutants, directed mutagenesis by overlapping PCR were performed using genomic DNA as template and pJQK ([@B63]) as the suicide vector. The corresponding gene was deleted using allelic exchange by double recombination as previously described ([@B15]).
For the construction of the *BmeΔlptA* mutant, we first generated two PCR fragments: oligonucleotides *lptA-*F1 (5′-GAACGCGAGACTATGGAAAC-3′) and *lptA-*R2 (5′-TGGTGAACGCCAGAAGATAGA-3′) were used to amplify a 400-bp fragment including codons 1--26 of *BmelptA* ORF, as well as 324 bp upstream of the *BmelptA* start codon, and oligonucleotides *lptA-*F3 (5′-TCTATCTTCTGGCGTTCACCGCACGACAATCTCTTC-3′) and *lptA*-R4 (5′-AATATTCCATGGCGCATTTC-3′) were used to amplify a 472-bp fragment including codons 506--544 of the *lptA* ORF and 353-bp downstream of the *lptA* stop codon. Both fragments were ligated by overlapping PCR using oligonucleotides *lptA*-F1 and *lptA*-R4 for amplification, and the complementary regions between *lptA*-R2 and *lptA*-F3 for overlapping. The resulting fragment, containing the *lptA* deleted allele, was cloned into pCR2.1 (Invitrogen, Barcelona, Spain), sequenced to ensure maintenance of the reading frame, and subcloned into the *Bam*HI and the *Xba*I sites of the suicide plasmid pJQK. The resulting mutator plasmid (pRCI-32) was introduced in *B. melitensis 16M* by conjugation using the *Escherchia coli* S.17 strain ([@B64]).
For the construction of the *BaΔlpxE* mutant, we first generated two PCR fragments: oligonucleotides *lpxE*-F1 (5′-CGCGTGTGCCATAGGTATATT-3′) and *lpxE-*R2 (5′-TATAGGCAGGGCGCAGAA-3′) were used to amplify a 482-bp fragment including codons 1--29 of *lpxE* ORF, as well as 394 bp upstream of the *lpxE-*1 start codon, and oligonucleotides *lpxE-*F3 (5′-TTCTGCGCCCTGCCTATAGATTCGTTTCCGCATGGT-3′) and *lpxE-*R4 (5′-CCAATACAC CCGTCATGAGA-3′) were used to amplify a 577-bp fragment including codons 226--255 of the *lpxE* ORF and 488-bp downstream of the *lpxE* stop codon. Both fragments were ligated by overlapping PCR using oligonucleotides *lpxE-*F1 and *lpxE-*R4 for amplification, and the complementary regions between *lpxE*-R2 and *lpxE*-F3 for overlapping. The resulting fragment, containing the *lpxE* deleted allele, was cloned into pCR2.1 (Invitrogen, Barcelona, Spain), sequenced to ensure maintenance of the reading frame, and subcloned into the *Bam*HI and the *Xba*I sites of the suicide plasmid pJQK ([@B63]). The resulting mutator plasmid (pRCI-36) was introduced in *B. abortus* 2308 by conjugation using the *E. coli* S.17 strain ([@B64]).
For the construction of the *BmiΔolsC* mutant, we first generated two PCR fragments: oligonucleotides *olsC-*F1 (5′-TGCTGGATCGTATTCGTCTG-3′) and *olsC-*R2 (5′-GCCATAAGCCGATGGAACTA-3′) were used to amplify a 334-bp fragment including codons 1--15 of *olsC* ORF, as well as 289 bp upstream of the *olsC* start codon, and oligonucleotides *olsC-*F3 (5′-TAGTTCCATCGGCTTATGGCAGGAGGGGCTAGACAACCAC-3′) and *olsC*-R4 (5′-AACCAGCGACAGGGTAAGC-3′) were used to amplify a 320-bp fragment including codons 286--313 of the *olsC* ORF and 237-bp downstream of the *olsC* stop codon. Both fragments were ligated by overlapping PCR using oligonucleotides *olsC*-F1 and *olsC*-R4 for amplification, and the complementary regions between *olsC*-R2 and *olsC*-F3 for overlapping. The resulting fragment, containing the *lptA* deleted allele, was cloned into pCR2.1 (Invitrogen, Barcelona, Spain), sequenced to ensure maintenance of the reading frame, and subcloned into the *Bam*HI and the *Xba*I sites of the suicide plasmid pJQK ([@B63]). The resulting mutator plasmid (pRCI-65) was introduced in *B. microti* CM445 by conjugation using the *E. coli* S.17 strain ([@B64]).
Deletion of each gene was checked with oligonucleotides *gene*-F1 and *gene*-R4 and internal primers hybridizing in the non-deleted regions.
Complementation of Deleted Genes
--------------------------------
For pBME*lpxE* and pBME*lptA* construction we took advantage of the *Brucella* ORFeome constructed with the Gateway cloning Technology (Invitrogen) ([@B17]). The clones carrying Bme*lpxE* or Bme*lptA* were extracted and the DNA containing the corresponding ORF was subcloned in plasmid pRH001 ([@B28]) to produce pBME*lpxE* and pBME*lptA*. For pBMI*olsC, olsC* was amplified using genomic DNA of Bmi-parental as DNA template. The primers used were *olsC*-F6 (5′-GCTTTCCGAACAAGCACTGA-3′) and *olsC*-R7 (5′-GCCTCCCTTCACCGGTTATT-3′). The resulting PCR product, containing the ORF from 342 bp upstream to 84 bp downstream, was then cloned into pCR2.1 TOPO (Invitrogen) plasmid by "TA cloning" (Life Technologies). The resulting plasmid was sequenced to ensure that the gene was correctly cloned. Then, the gene was subcloned into the *BamHI* and the *XbaI* sites of the replicative plasmid pBBR1 MCS ([@B37]) pBME*lpxE*, pBME*lptA*, and pBMI*olsC* were introduced into *Brucella* by conjugation using *E. coli* S.17-1 strain and the conjugants harboring corresponding plasmid were selected by plating onto TSA-Nal-Cm plates.
Sensitivity to Cationic Peptides
--------------------------------
Exponentially growing bacteria were adjusted to an optical density equivalent to one of the McFarland scale and the minimal inhibitory concentrations (MICs) of polymyxin B were determined by the *e*-test method on Müller--Hinton agar (Izasa) or by the serial dilution method in a similar broth.
LPS Preparation
---------------
Lipopolysaccharide was obtained by methanol precipitation of the phenol phase of a phenol--water extract ([@B42]). This fraction \[10 mg/ml in 175 mM NaCl, 0.05% NaN~3~, 0.1 M Tris--HCl (pH 7.0)\] was then purified by digestion with nucleases \[50 μg/ml each of DNase-II type V and RNase-A (Sigma, St. Louis, MO, United States), 30 min at 37°C\] and three times with proteinase K (50 μg/ml, 3 h at 55°C), and ultracentrifuged (6 h, 100,000 × *g*) ([@B1]). Free lipids (OLs and phospholipids) were then removed by a fourfold extraction with chloroform--methanol \[2:1 (vol/vol)\] ([@B70]).
Infections in Mice
------------------
Seven-week-old female BALB/c mice (Charles River, Elbeuf, France) were kept in cages with water and food ad libitum and accommodated under biosafety containment conditions 2 weeks before the start of the experiments. To prepare inocula, tryptic soy agar (TSA) grown bacteria were harvested and suspended in 10 mM phosphate buffered saline (pH 6.85), and 0.1 ml/mouse containing approximately 5 × 10^4^ colony forming units (CFU) for *B. melitensis* or *B. abortus* and 1 × 10^4^ CFU for *B. microti* was administered intraperitoneally. The exact doses assessed retrospectively by plating dilutions of the inocula. Number of CFU in spleens was determined at diferent time after inoculation. For this, the spleens were aseptically removed and individually weighed and homogenized in 9 volumes of PBS. Serial 10-fold dilutions of each homogenate were performed and each dilution was plated by triplicate. Plates were incubated at 37°C for 5 days. At several points during the infection process, the identity of the spleen isolates was confirmed by PCR. The individual data were normalized by logarithmic transformation, and the mean log CFU/spleen values and the standard deviations (*n* = 5) were calculated.
Intracellular Multiplication Assays
-----------------------------------
Bone marrow cells were isolated from femurs of 7--8-week-old C57Bl/6 female and differentiated into dendritic cells \[bone-marrow derived dendritic cells (BMDCs)\] as described by [@B30]. Infections were performed by centrifuging the bacteria onto the differentiated cells (400 x *g* for 10 min at 4°C; bacteria:cells ratio of 30:1 followed by incubation at 37°C for 30 min under a 5% CO~2~ atmosphere). BMDCs were gently washed with medium to remove extracellular bacteria before incubating in medium supplemented with 50 μg/ml gentamicin for 1 h to kill extracellular bacteria. Thereafter, the antibiotic concentration was decreased to 10 μg/ml. To monitor *Brucella* intracellular survival at different time-points post-infection, BMDC were lysed with 0.1% (vol/vol) Triton X-100 in H~2~O and serial dilutions of lysates were plated onto TSA plates to enumerate the CFU.
Flow Cytometry
--------------
To assess activation and maturation, BMDC were analyzed for surface expression of classical maturation markers at 24 h post-treatment with the different *Brucella* strains and derived mutants. Cells were labeled with fluorochrome-conjugated antibodies specific for mouse CD11c:APC-Cy7 (clone N418), IA-IE:PE (MHC class II clone M5/114.15.2) (PE), CD86:FITC (Clone GL-1), CD40:APC (clone 3/23), and CD80:PE-Cy5 (clone 16-10A1), all from BioLegend. Labeled cells were then subjected to multi-color cytometry using a LSR II UV (Becton Dickinson) and the data analyzed using FlowJo Software by first gating on the CD11c^+^ population (100,000 events) prior to quantifying expression of receptors. Cells were stimulated with *E. coli* LPS (055:B5) as a positive control.
Lipid A Extraction
------------------
Five milligrams of LPS was hydrolyzed in 5 ml 1% acetic acid by sonication, heating to 100°C for 30 min, and cooling to room temperature. Concentrated HCl was added to the mixture until the pH was 1--2. The solution was converted to a two-phase acidic Bligh--Dyer mixture by adding 5.6 ml of chloroform and 5.6 ml of methanol. Phases were mixed by inverting the tubes and separated by centrifugation at 4000 × *g* for 20 min. The lower phases containing lipid A were collected, washed two times with water, and dried under a stream of nitrogen. Extraction was repeated, and the lower phases (11.2 ml) were combined and neutralized with a drop of pyridine. Samples were evaporated to dryness under a stream of nitrogen.
Mass Spectrometry
-----------------
Mass spectrometra were acquired on a Bruker Autoflex^®^Speed TOF/TOF Mass Spectrometer (Bruker Daltonics Inc.) in negative reflective mode with delayed extraction. The ion-accelerating voltage was set at 20 kV. Each spectrum was an average of 300 shots. A peptide calibration standard (Bruker Daltonics Inc.) was used to calibrate the Matrix Assisted Laser Desorption/Ionization Time-of-Flight (MALDI-TOF), and lipid A extracted from *E. coli* strain MG1655 grown in LB medium at 37°C.
Extraction and Analysis of Envelope Lipids
------------------------------------------
The free-lipid fraction was extracted as described by [@B7], and analyzed on a silica gel 60 high-performance thin layer chromatography (HPLC) plates (Merck, Darmstadt, Germany). Chromatography was performed either monodimensionally with chloroform--methanol--water \[14:6:1 (volume)\] or bidimensionally with chloroform--methanol--water \[14:6:1 (volume)\] first and chloroform--methanol--acetic acid \[13:5:2 (volume)\] in the second dimension ([@B74]). Plates were developed with 0.2% ninhydrin in acetone at 180°C or 15% sulfuric acid in ethanol at 180°C.
Results
=======
The *Brucella lptA* Orthologs Encode a Lipid A Phosphate-Ethanolamine Transferase
---------------------------------------------------------------------------------
A genomic search in the KEGG database revealed that all *Brucella* spp. carry an ORF (BMEI0118 in *B. melitensis*) homologous to *Neisseria meningitidis lptA*, a pEtN transferase that modifies lipid A ([@B16]). Strikingly, in *B. abortus* but not in other *Brucella* spp., all genomic sequences available at KEGG show a deletion of a thymine in position 774 that should result in a truncated protein lacking the amino acids related to the enzymatic activity ([@B53]; **Figure [1](#F1){ref-type="fig"}** and Supplementary Figure [S1](#SM4){ref-type="supplementary-material"} and Supplementary Table [S2](#SM2){ref-type="supplementary-material"}). In addition to LptA, two other pEtN transferases have been identified in *N. meningitidis*: Lpt-3 and Lpt-6, which, respectively, modify the LPS core at the third and sixth position of heptose II ([@B45]; [@B76]). By multiple sequence alignment, the *B. melitensis* putative pEtN transferase showed highest homology with *Neisseria* LptA and also displayed the LptA membrane-associated domains not present in Lpt-3 and Lpt-6 (ORFs NMB1638, NMB2010, and NMA0408, respectively). Accordingly, it can be predicted that ORF BMEI0118 (henceforth BME*lptA*) encodes a pEtN transferase that acts on lipid A, a hypothesis fully consistent with the absence of heptose in the *Brucella* LPS core ([@B31]; [@B21]).
To test this hypothesis, we constructed a *B. melitensis* non-polar mutant (BmeΔ*lptA*) lacking the LptA enzymatic domain (amino acids 26--506), which as expected maintained a smooth (S) phenotype (negative crystal violet test and positive coagglutination with anti-S-LPS antibodies). As a consequence of the increased positive charge of the amino group, pEtN has been shown to decrease binding of the polycationic lipopeptide polymyxin B to LPS, and to increase resistance to this antibiotic in a variety of bacteria ([@B54]; [@B69]; [@B29]). In keeping with this possibility, the BmeΔ*lptA* mutant was more sensitive to polymyxin B than the parental strain *B. melitensis* 16M (Bme-parental) (**Figure [2A](#F2){ref-type="fig"}**). In contrast, and consistent with the frame-shift in its *lptA* homolog, *B. abortus* 2308 (Ba-parental) displayed polymyxin B sensitivity similar to that of BmeΔ*lptA*. Moreover, complementation of BmeΔ*lptA* with the multi-copy plasmid pBME*lptA* or its introduction into *B. abortus* 2308 leads to restoration of polymyxin B resistance in BmeΔ*lptA* or an increase up to *B. melitensis* level in *B. abortus* (**Figure [2A](#F2){ref-type="fig"}**). As expected both constructs kept the S type features (negative crystal violet test and positive coagglutination with anti-S-LPS antibodies) of the parental strains. *N. gonorrhoeae* shows increased resistance to the action of complement in non-immune serum that is dependent on lipid A-linked pEtN ([@B43]). Testing for a similar contribution here, we found that BmeΔ*lptA* was more sensitive than either the parental strain or the complemented mutant (25% vs. no decrease in viability after 3 h of incubation in normal sheep serum) relevant given that *B. melitensis* is characteristically resistant to killing by normal serum.
{#F2}
By MALDI-TOF analysis, the lipid A of Bme-parental was found to contain four main clusters of ions (A, B, C, and D in **Figure [2B](#F2){ref-type="fig"}**). BmeΔ*lptA* lipid A was qualitatively identical to Bme-parental with respect to groups A, B, and C but clearly differed in group D (**Figure [2B](#F2){ref-type="fig"}** and Supplementary Table [S3](#SM3){ref-type="supplementary-material"}). In group D, the 2191 m/z″ species of Ba-parental was consistent with the isotopic mass of a molecule (C~120~H~232~N~4~O~25~P~2~) formed by a hexaacylated and bisphosphorylated diaminoglucose disaccharide carrying the hydroxylated long and very long chain acyl groups characteristic of *Brucella* ([@B70]; [@B20]). According to this interpretation, the signal(s) at 2112 m/z (mass of - H~2~PO~3~ o - HPO~3~ -, 80.9 - 79.9) could correspond to a monophosphorylated (C~120~H~232~N~4~O~25~P) 2191 m/z″ equivalent. Substitution of this monophosphorylated form with pEtN (^+^H~3~NCH~2~-CH~2~- HPO~3~ mass 125) should account for signal m/z 2237, in keeping with the fact that m/z 2237 did not appear in the spectrum of the lipids A from either BmeΔ*lptA* or Ba-parental (**Figure [2B](#F2){ref-type="fig"}**). Although a clear cut demonstration requires direct analyses of the enzymatic analyses of LptA, these results and the homologies with LptA of other bacteria are consistent with the hypothesis that LptA acts as a pEtN transferase in *B. melitensis* and lacks functionality in *B. abortus*. It is remarkable that pEtN activity was detected for only a fraction (D) of lipid A species. This could be explained by a preferential activity of the enzyme for higher MW lipid A molecules.
The *Brucella lpxE* Orthologs Encode a Phosphatase Involved in the Remodeling of the OM
---------------------------------------------------------------------------------------
As described above, MALDI-TOF analyses showed the presence of molecular species with a mass compatible with monophosphorylated lipid A. Since lipid A synthesis produces C1 and C4′ bisphosphorylated disaccharide backbones ([@B57]), a possible explanation could be its dephosphorylation by a phosphatase such as LpxE, an inner membrane enzyme that in the phylogenetic neighbor *Rhizobium leguminosarum* removes the lipid A phosphate at C1 ([@B58]). A search in KEGG showed that all *Brucella* spp. carry an ORF homologous to *R. leguminosarum lpxE* (Supplementary Table [S2](#SM2){ref-type="supplementary-material"}). However, the start codon in the *B. melitensis* 16M homolog (BMEI1212) is annotated to a position different from that determined for other brucellae (Supplementary Table [S2](#SM2){ref-type="supplementary-material"}), including other *B. melitensis* strains. Thus, whereas the *B. abortus* homolog (BAB1_0671) is predicted to encode a protein of 255 amino acids, the *B. melitensis* one could encode a protein of either 235 or 255 amino acids (**Figure [1](#F1){ref-type="fig"}**). Both proteins conserve the consensus sequence of the lipid phosphatase superfamily \[KX6RP-(X12--54)-PSGH-(X31--54)-SRX5HX3D\] ([@B66]) which is also present in LpxE from *R*. *leguminosarum, Sinorhizobium meliloti*, and *Agrobacterium tumefaciens* ([@B34]). Although BAB1_0671 and BMEI1212 code for proteins that contain the three motifs conserved in the LpxF phosphatase from *Francisella*, they lack two amino acids of the central motif, NCSFX2G, which seems LpxF specific ([@B72], [@B73]). Thus, the *Brucella* proteins were named BALpxE and BMELpxE.
To study whether BALpxE actually acts as a lipid A phosphatase, we constructed a non-polar mutant (BaΔ*lpxE*) and tested it against polymyxin B, since the permanence of a phosphate group in an OM molecule should increase sensitivity to this antibiotic. Mutant BaΔ*lpxE* was eight times more sensitive than the parental strain (MIC 0.2 and 1.6 μg/ml, respectively). Moreover, when we introduced a plasmid containing the BME*lpxE* ortholog into BaΔ*lpxE*, the resistance to polymyxin B was restored (MIC 1.6 μg/ml). Although final confirmation of this interpretation would require to assay the enzymatic activity of the protein, these results are consistent with the predicted role of *lpxE* as a phosphatase and its functionality in both *B. abortus* and *B. melitensis* 16M, a strain where the annotation of the start codon was a source of ambiguity.
By MALDI-TOF analysis, the Ba-parental lipid A spectrum showed three of the four predominant clusters of ions (A, B, and C) found in *B. melitensis* (**Figure [2B](#F2){ref-type="fig"}** and Supplementary Table [S3](#SM3){ref-type="supplementary-material"}). Cluster A (m/z 2173) was consistent with an hexaacylated bisphoshorylated diaminoglucose disaccharide (C~120~H~232~N~4~O~24~P~2~) and the signal at 2093 m/z, which differed in the mass of one phosphate group (i.e., 80), was consistent with the cognate monophosphorylated lipid A (C~120~H~232~N~4~O~25~P) (A-Pi, **Figure [2](#F2){ref-type="fig"}**). Other signals differing in a mass of 14 or 28 units should result from the heterogeneity in acyl chain length that is typical of lipid A. The B and C clusters also contained signals differing in 80 mass units that could correspond to bis- and mono-phosphorylated species. The mass spectrum of BaΔ*lpxE* lipid A (not shown) did not differ significantly from that of Ba-parental, and again showed acyl chain heterogeneity in the A, B, C clusters, as well as the -80 m/z signals indicative of mono- and bisphoshorylated lipid A species. As mutation of lpxE is concomitant with an increase in polymyxin B sensitivity, it is tempting to speculate that LpxE directly or indirectly modulates *Brucella* cell envelope by removing an accessible phosphate group from a substrate different from lipid A. Further studies need to be performed to clarify the role of LpxE.
The *Brucella lpxO* Orthologs Encode an Acyl Hydroxylase Acting on Ornithine Lipids
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The genomes of all *Brucella* species available at KEGG contain an ORF homologous to *Salmonella lpxO* ([@B23]), which encodes an enzyme hydroxylating the 3′-secondary acyl chain of lipid A. In all *Brucella* spp. except *B. microti* and *B. vulpis* this ORF presents a frame-shift leading to a truncated protein that lacks the consensus of the aspartyl/asparaginyl β-hydroxylases family to which LpxO belongs (**Figure [1](#F1){ref-type="fig"}** and Supplementary Table [S2](#SM2){ref-type="supplementary-material"}). These characteristics are consistent with chemical studies that previously failed to observe S2 hydroxylated fatty acids in *B. abortus* lipid A ([@B70]). Moreover, a *lpxO* homolog is present in *Ochrobactrum anthropi* where S2 hydroxylated fatty acids were also not observed in the lipid A ([@B70]), indicating that a role similar to that of *Salmonella* LpxO is unlikely. Thus, the *lpxO* homologs present in these *B. microti* and *O. anthropi* could be acting on a free lipid and, in fact, it has been reported that the corresponding *R. tropici* homolog is a β-hydroxylase acting on OLs ([@B71]). If this were the case in *O. anthropi* and the brucellae, the end product \[a hydroxylated OL (OH--OL)\] of the pathway described previously in members of the *Rhizobiaceae* (**Figure [3A](#F3){ref-type="fig"}**) should be observed in *O. anthropi* and *B. microti* (and *B. vulpis*) but not in other *Brucella* spp.
![The *Brucella lpxO* orthologs encode an acyl hydroxylase acting on ornithine lipids. **(A)** Pathway of synthesis of ornithine lipids in α-2 *Proteobacteria* (adapted from [@B22]); the ORFs of *B. abortus* and *B. microti* are indicated, whereas *B. microti, B. vulpis*, and *O. anthropi* contain an intact *olsC* acyl hydroxylase gene, *B. abortus* and other *Brucella* spp. carry a frame-shift in the *olsC* homolog. **(B)** Lipid profile of *B. abortus* wild-type (Ba-parental) and *B. microti* wild-type (Bmi-parental) showing the absence or presence, respectively, of OH--OL. **(C)** Amino lipid profile of *B. abortus* wild-type (Ba-parental), *B. microti* wild-type (Bmi-parental), *B. microti* deleted in *olsC* (BmiΔ*olsC*), the cognate reconstituted mutant (BmiΔ*olsC*pOlsC), and *B. abortus* wild-type carrying a plasmid with the *B. microti olsC* gene (Ba-parentalpOlsC).](fmicb-08-02657-g003){#F3}
To investigate these hypotheses, we compared the free lipids of *B. abortus, B. melitensis, B. suis, B. ovis, B. microti*, and *O. anthropi*. As can be seen in **Figure [3B](#F3){ref-type="fig"}**, *B. microti* but not *B. abortus* produced an amino lipid with the migration pattern predicted for OH-OL ([@B71]), and results similar to those of *B. microti* were obtained for *O. anthropi* but not for the other *Brucella* spp. tested (not shown). These observations support the interpretation that *O. anthropi* and *B. microti* LpxO are OL hydroxylases and are fully consistent with the aforementioned genomic and chemical evidence. Accordingly, *Brucella lpxO* should be named *olsC.* To confirm this, we examined the amino lipids of a non-polar *olsC* mutant in *B. microti* (BmiΔ*olsC*). As predicted, this mutant did not synthesize OH--OL and complementation with a plasmid containing *B. microti olsC* restored the wild-type phenotype (**Figure [3C](#F3){ref-type="fig"}**). Furthermore, introducing this plasmid or a plasmid carrying *O. anthropi olsC* into *B. abortus* resulted in the synthesis of OH--OL (**Figure [3C](#F3){ref-type="fig"}** and Supplementary Figure [S2](#SM5){ref-type="supplementary-material"}). No difference in polymyxin sensitivity was observed in these constructs or the mutant BmiΔolsC when compared to the corresponding parental strains.
LptA, LpxE, and OlsC Are Not Required for *Brucella* Virulence in Laboratory Models
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*Brucella abortus, B. melitensis*, and *B. suis* have been shown to multiply in murine and human monocyte-derived dendritic cells while interfering with their activation and maturation and reducing both antigen presentation and an effective adaptive response ([@B6]; [@B47]; [@B14]; [@B26]; [@B56]). To assess whether LptA, LpxE, and OL β-hydroxylase (OlsC) were involved, we compared parental and mutant strains of *B. melitensis, B. abortus*, and *B. microti* in mouse BMDCs. As shown in **Figure [4](#F4){ref-type="fig"}**, the kinetics of multiplication of the mutants and wild-type strains were similar. We also performed a phenotypic characterization of MHC II and co-stimulatory receptors CD86 and CD80 (**Figure [5](#F5){ref-type="fig"}**). In agreement with previous studies, these analyses showed that activation and maturation was only partially induced in BMDC infected with *B. melitensis* and *B. abortus* ([@B47]). In addition, a similar partial-activation profile was evident both for *B. microti*, for which no previous studies exist in infected BMDC, and all of the tested mutants obtained for each of the three *Brucella* spp.
{#F4}
{#F5}
The mouse model has been widely used for testing *Brucella* virulence ([@B27]). In this model, the LptA and LpxE mutants and the parental strains behaved identically (**Figure [6](#F6){ref-type="fig"}** upper panels). Deletion of *olsC* in *B. microti* did not alter the CFU/spleen profile produced by this species which is characterized by a lower lethal dose in mice as well as a faster clearance from mouse spleens ([@B32]; **Figure [6](#F6){ref-type="fig"}**, lower left panel). Moreover, when we tested whether the expression of *B. microti olsC* in *B. abortus* could affect virulence, we found no differences between the *B. microti olsC*-carrying and the wild-type *B. abortus* strains (**Figure [6](#F6){ref-type="fig"}**, lower right panel).
{#F6}
Discussion
==========
In this work we investigated three *Brucella* ORFs that according to homologies with genes of known function in other pathogens could modify the lipid A and contribute to further altering the LPS PAMP of representative *Brucella* species. The results show that, whereas *Brucella* LptA modifies the lipid A, this is not the case for *lpxE* and *lpxO* (redesignated *olsC*), the former encoding a putative phosphatase acting on an unidentified OM molecule and the latter for an enzyme with OlsC activity.
Our data strongly suggest that *B. melitensis* LptA is involved in the addition of pEtN to lipid A, homologous proteins carrying out this function are not uncommon in Gram-negative pathogens and modulate the properties of lipid A. In *Salmonella* Typhimurium, *Shigella flexneri, E. coli, Vibrio cholerae, Helicobacter pylori, Haemophilus ducreyi, N. gonorrhoeae*, and *N. meningitidis* pEtN reduces the binding of cationic bactericidal peptides by balancing the negative charge of lipid A ([@B54]; [@B69]). Conversely, pEtN promotes binding to *N. gonorrhoeae* lipid A of factors that downregulate the complement cascade and thwart building of the membrane-attack complex and opsonophagocytosis ([@B43]). *N. meningitidis* pEtN also promotes adhesion of non-encapsulated bacteria to endothelial cells ([@B67]). Indeed, properties that parallel some of those observed for the above-listed pathogens can also be attributed to the pEtN transferase counterpart in *Brucella*. An intact *lptA* was related to polymyxin B resistance in *B. melitensis* and the introduction of *B. melitensis lptA* into *B. abortus* increases polymyxin B resistance to the level of *B. melitensis*, suggesting that LptA function is severally impaired in *B. abortus*. This is in agreement with the presence of a frame-shift in *B. abortus lptA* encompassing the consensus sequence, which makes likely that it codes for a protein with no or residual enzymatic activity. Previous analyses are contradictory with regard to the presence ([@B10]) or absence ([@B51]) of ethanolamine in *B. abortus* lipid A but the materials analyzed differ in methods of extraction and presence of *B. abortus* lipid A markers, such as very long chain fatty acids (VCLFA). Although further chemical and enzymatic analyses are necessary for a definite conclusion, our results strongly suggest that, if present, pEtN is in much less amounts in *B. abortus* than in *B. melitensis* lipid A. It is also worth noting that such genetic and phenotypic differences in the lipid A of *B. abortus* and *B. melitensis* could relate to differences in biological properties. The LPS of *B. abortus* and *B. melitensis* is a poor activator of the complement cascade, and this property has been traced to the core and lipid A structure ([@B49]; [@B14]; [@B21]). Since *B. abortus* is less resistant than *B. melitensis* to normal serum ([@B24]), it is tempting to suggest that, like in *N. gonorrhoeae, B. melitensis* pEtN could sequester regulatory elements enhancing complement resistance in this species.
Concerning LpxE, phosphatases acting on lipid A have at least been shown in *Francisella tularensis, H. pylori, Porphyromonas gingivalis*, and *Capnocytophaga canimorsus*, bacteria where lipid A dephosphorylation is involved both in resistance to bactericidal peptides and the reduction of TLR-4-dependent recognition ([@B54]). Although these properties are displayed by the LPS of *B. abortus* and *B. melitensis* ([@B46]; [@B41]; [@B14]), our results do not support a role for BALpxE as a lipid A phosphatase. This is consistent with genomic analysis showing that, whereas in bacteria where LpxE acts on lipid A the gene is located together with *lptA* in an operon ([@B68]; [@B59]), *Brucella lpxE* is instead located upstream of three sequences annotated as pseudogenes and downstream, but in the opposite direction, of a cystathionine beta-lyase. On the basis of the data shown here, the origin of monophosphoryl lipid A in *Brucella* remains to be explained. Further, we believe it unlikely to be an artifact resulting from the hydrolytic steps used to obtain lipid A and instead favor the hypothesis of the existence of an as yet unidentified lipid A phosphatase.
LpxE belongs to the type 2 family of phosphatases that can act on lipid A but also on phosphatidylglycerol phosphate, phosphatidic acid, sphingosine phosphate, and lysophosphatidic acid ([@B9]; [@B62]). Significantly, LpxE from *Agrobacterium*, although predicted to be a lipid A phosphatase, dephosphorylates phosphatidyl glycerophosphate ([@B35]) to generate phosphatidylglycerol, a cell envelope phospholipid. Indeed, a hypothetical phosphatidyl glycerophosphate phosphatase activity of *Brucella* LpxE could account for both the polymyxin B sensitivity of the mutated bacteria and the unaltered mass spectra of the lipid A of the mutant. Such a modification of a phospholipid could be meaningful by itself on account of the LpxE-dependent bactericidal peptide resistance but there are other possibilities. In some bacteria (i.e., *Rhizobium*) phosphatidylglycerol is a precursor for the synthesis of amino lipids such as lysyl-phosphatidylglycerol. This synthesis is induced by acid pH and brings about resistance to daptomycin and polymyxin B ([@B65]; [@B19]; [@B2]). Interestingly, whereas the BaΔ*lpxE* mutant is impaired for growth at pH 6, the parental *B. abortus* becomes more resistant to cationic peptides (L. Palacios-Chaves and R. Conde-Álvarez, Unpublished observations). These observations suggest the existence in *Brucella* of pH-dependent envelope modifications that require a functional LpxE. Research is in progress to elucidate the mechanisms behind the increased resistance at acid pH and the implication regarding a role for LpxE.
In *S.* Typhimurium, *Pseudomonas aeruginosa, Bordetella bronchispetica, Legionella pneumophila*, and *Klebsiella pneumonia*, LpxO is a Fe2+/α-ketoglutarate-dependent dioxygenase that catalyzes the hydroxylation of the 3′-secondary acyl chain of lipid A. LpxO has been implicated indirectly in stress responses at the envelope level ([@B54]) and, in *K. pneumoniae*, it has been shown to be relevant *in vivo* by increasing bactericidal peptide resistance and reducing the inflammatory responses ([@B44]). However, as discussed above, previous chemical analysis ([@B70]) of lipid A and the evidence presented here indicate that the *Brucella lpxO* homolog is not a lipid A hydroxylase but rather an OlsC whose mutation, in contrast with LpxO, does not result in increased sensitivity to polymyxin B. This absence of an effect on polycation resistance is in keeping with both the lack of activity on lipid A and the fact that OL do no play a major role in resistance to polycationic bactericidal peptides in *B. abortus* ([@B55]). At the same time, it would also appear to rule out, the involvement of this protein in the metabolism of succinate in *B. microti* as has been previously suggested ([@B3]).
Previous data showing *lptA, lpxE*, and *lpxO* to be involved in modulating the properties of the OM in a way that in some cases confers *in vitro* resistance to innate immunity bactericidal peptides, complement, and cytokine responses ([@B54]) have been drawn upon as evidence for a role in virulence. However, to the best of our knowledge, a role *in vivo* has thus far been shown only for *lpxO* from *K. pneumoniae* ([@B44]). Moreover, contrasting results have been obtained with mutants both showing bactericidal peptide sensitivity *in vitro* and no phenotype *in vivo* have been reported for at least *H. ducreyi* ([@B69]) and may reflect the complexities of the infection processes and/or the inadequacies of the currently available *in vivo* models. Despite their effect on the envelope, our results show that *Brucella lptA, lpxE*, or *olsC* do not play a role in the ability of *Brucella* to replicate in BMDC and do not modulate the activation and maturation profile in these cells. Similarly, the mouse model did not reveal any effect on its ability to colonize and multiply in the spleen. However, further experimental work in the natural hosts and alternative routes of infection might provide evidence on the role in virulence of these genes. The fact that *lptA* and *olsC* are not functional in all *Brucella* spp. must therefore be considered in the context of the models used. While the absence of a functional *lptA* in *B. abortus* suggests that the gene is not essential for the virulence of this species we cannot conclude it to be totally irrelevant. Differences between *B. melitensis* and *B. abortus* related to *lptA* could explain the higher invasiveness of the former species noted by early researchers in studies carried out in guinea pigs, animals that are highly susceptible to brucellosis ([@B8]). This possibility together with the presence of intact *lptA* and *olsC* in *Ochrobactrum* and *B. microti* is also compatible with the hypothesis that they represent ancestral characters that are liable to be lost in the absence of a selective pressure during the intracellular life cycle or, in the case of *lptA*, that is no longer present in the ruminant host species (i.e., cattle) to which *B. abortus* is characteristically associated.
Ethics Statement
================
Female BALB/c mice (Charles River, France) were kept in cages with water and food *ad libitum* under P3 biosafety conditions in the facilities of "Centro de Investigación Médica Aplicada" (registration code ES31 2010000132) 2 weeks before and during the experiments. The procedures were in accordance with the current European (directive 86/609/EEC) and Spanish (RD 53/2013) legislations, supervised by the Animal Welfare Committee of the University of Navarra, and authorized by the "Gobierno de Navarra" \[CEEA045/12 and E36-14 (045-12E1)\].
Author Contributions
====================
IM, MI, J-PG, JB, and RC-Á conceived the study. RC-Á, LP-C, YG-R, MB-V, MS-B, BA-A, EM-G, AZ-R, MdM, TLB, SH, M-JG, MV-G, and VA-G carried out the experimental work. IM, MI, and RC-Á wrote the paper. All authors participated in the presentation and discussion of results.
Conflict of Interest Statement
==============================
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
**Funding.** This research was supported by the Institute for Tropical Health funders (Obra Social la CAIXA, Fundaciones Caja Navarra and Roviralta, PROFAND, Ubesol, ACUNSA, and Artai) and grants MINECO (AGL2014-58795-C4-1-R, Bru-Epidia 291815-FP7/ERANET/ANIHWA), Aragón Government (Consolidated Group A14), and Marie Curie Career Integration Grant U-KARE (PCIG13-GA-2013-618162). TLB is the recipient of a Ph.D. Fellowship funded by the Department for Employment and Learning (Northern Ireland, United Kingdom).
The authors thank A. Delgado-López for excellent technical assistance in the extraction and purification of LPS.
<http://www.genome.jp/kegg/>
<http://www.ncbi.nlm.nih.gov/>
<http://www.ebi.ac.uk/>
Supplementary Material
======================
The Supplementary Material for this article can be found online at: <https://www.frontiersin.org/articles/10.3389/fmicb.2017.02657/full#supplementary-material>
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[^1]: Edited by: *Axel Cloeckaert, Institut National de la Recherche Agronomique (INRA), France*
[^2]: Reviewed by: *Diego J. Comerci, Instituto de Investigaciones Biotecnológicas (IIB-INTECH), Argentina; Roy Martin Roop II, East Carolina University, United States*
[^3]: This article was submitted to Infectious Diseases, a section of the journal Frontiers in Microbiology
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Elesa at MACH Exhibition, Birmingham, NEC
12 February 2018
The Elesa range of standard machine elements is designed around the needs of manufacturing in all industry sectors, many of which will be on display at the 2018 MACH Exhibition, taking place on 9-13 April at NEC Birmingham.
Featured on the Elesa stand – Hall 6, No. 72 - will be its IP65-7 direct dial digital position indicators with electronic mechanism for easy set up and readout.
These are coupled with the Elesa wireless spindle positioning system which enables faster and more reliable machine set up by use of a wireless connected profile controller, which displays the initial set up values on each of up to 36 electronic position indicators. The operator can simply choose the appropriate menu then quickly re-set each spindle to its correct start position and the machine is “good to go”. This saves time and takes out much of the possibility of human error.
The Elesa LMHD hygienic levelling feet (EHEDG certified) for use in bio-hazard areas such as food processing or other hygiene sensitive areas, feature mounting holes which provide rugged adjustable equipment mounting and facilitate reduced cleaning work – which can be up to 25 percent of the production time. Thus leaving more time available for production, with less use of resources such as fresh water, energy and cleaning agents, also with less waste water to process, and so lower total costs.
A wide range of industrial levelling feet complement the needs of equipment manufacturers, many are in stainless steel for heavy duty application and special designs with vibration damping pads to prolong equipment life or for use on conveyor systems.
The Elesa IP67 CFSW safety switch and hinge unit also on display facilitates safe operation of access panels and control equipment.
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Travel Guide: Oman
by WatchMojo Videos
2:36 mins
Travel Guide: Oman
by WatchMojo Videos
2:36 mins
In this http://www.WatchMojo.com Presents video, we continue our travel series with a look at the Sultanate of Oman, which is an the Arab state in southwest Asia and is also the seventh stop of the 2012 Red Bull Cliff Diving World Series.
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Ischemia-reperfusion injury represents a pathological condition characterized by an initial undersupply of blood to an area or organ followed by a restoration of perfusion and concomitant reoxygenation (= reperfusion). Ischemia typically occurs in the presence of embolism or thrombosis but can also be triggered by surgery and transplantation. Anyway, the disturbance in perfusion results in a severe imbalance between metabolic supply and demand, subsequently causing tissue hypoxia \[[@B1]\]. Notably, these initial changes cause time-dependent molecular and structural alterations. In this context, it is also important to consider that all tissues and organs are susceptible to ischemia, but susceptibility to an ischemic insult differs between organ systems. Whereas the brain can endure ischemia only a few minutes, other tissues (e.g., muscle) are able to withstand ischemia for a long time without signs of irreversible damage.
Interestingly, restoration of blood flow and reoxygenation is commonly associated with an exacerbation of tissue injury and a profound inflammatory response ("reperfusion injury") \[[@B1], [@B2]\]. Ischemia-reperfusion injury contributes to pathology in a wide range of conditions.
For example, myocardial ischemia followed by reperfusion typically manifests in microvascular dysfunction, death of myocytes, and myocardial stunning or dysfunction.
Ischemia-reperfusion injury (IRI) of the lung, for example, following transplantation, is characterized by nonspecific alveolar damage, edema formation, and hypoxemia. The clinical spectrum of pulmonary IRI may range from mild hypoxemia to acute respiratory distress syndrome.
In contrast to other organs, the brain is particularly susceptible to ischemia and irreversible neuronal damage already occurs after only 5 minutes of complete ischemia \[[@B3]\]. For brain ischemia, as occurring in the setting of stroke, reestablishing reperfusion seems to be only beneficial, if carried out within a short time period after the onset of ischemia. Reperfusion of ischemic stroke seems to be very critical, as patients may suffer from cerebral reperfusion injury manifesting in fatal cerebral edema formation and intracranial hemorrhage.
IRI of the kidney may occur in the setting of transplantation and cardiac arrest and during cardiac surgery. Here it is important to note that renal injury is usually associated with a high morbidity and mortality. The cortical-medullary region is the most susceptible region to tubular injury, inflammation, and vascular alterations.
Generally, IRI of a single organ causes the release of different proinflammatory mediators, which may subsequently induce inflammation in other organs, thereby potentially contributing to multiple organ dysfunction or even failure \[[@B4]\].
Different pathological processes contribute to tissue injury secondary to ischemia-reperfusion. During ischemia, limited oxygen availability leads to an impaired endothelial cell barrier function with a concomitant increase in vascular permeability and leakage due to decreases of intracellular cAMP levels caused by a reduced adenylate cyclase activity \[[@B1]\]. Furthermore, ischemia-reperfusion induces cell death due to apoptosis, necrosis, and autophagy \[[@B5]\]. During the ischemic period, alterations in the transcriptional control of gene expression likewise occur. Another mechanism implicated in the pathophysiology of injury during ischemia is the inhibition of oxygen-sensing prolyl hydroxylase (PHD) enzymes, because they require oxygen as a cofactor. Hypoxia-triggered inhibition of PHD enzymes induces the posttranslational activation of hypoxia and inflammatory signaling cascades, which in turn regulate the stability of the transcription factors, hypoxia-inducible factor (HIF) and nuclear factor-*κ*B (NF-*κ*B) \[[@B2]\].
Reperfusion of ischemic tissue activates a complex inflammatory response without the involvement of pathogenic triggers, a phenomenon also referred to as sterile inflammation. During the initiation of this inflammatory response, endogenous molecules act as alarmins or danger-associated molecular patterns (DAMPs) \[[@B6]\]. The inflammatory process is stimulated through self-antigens, which are functional components of intact cells but become stimulators of innate immunity when released from injured or dying cells \[[@B6]\]. In 1996, Weiser et al. discovered and described a novel mechanism for reperfusion injury that involves antibody deposition and activation of the complement system leading to an acute inflammatory response \[[@B7]\]. One decade later, the concept of innate autoimmunity was introduced, which is based on the discovery that circulating natural antibodies recognize self-antigens and elicit an acute inflammatory response involving the complement system \[[@B8]\]. Although ischemia-reperfusion is typically established in a sterile environment, activation of innate and adaptive immune responses occurs and contributes to injury, including activation of pattern-recognition receptors such as TLRs and inflammatory cell trafficking into the injured organ \[[@B9]\]. During this inflammatory process, the coagulation system is also activated, because the innate immune system and coagulation system are highly interconnected \[[@B10]\]. As ischemia-reperfusion injury is a common clinical problem and is associated with relevant complications, it is important to identify therapeutic approaches which prevent or at least mitigate ischemia-reperfusion-induced organ injury and organ dysfunction.
This special issue is devoted to the modulation of ischemia-reperfusion injury by different measures and contains eight original papers addressing this clinically relevant topic. These papers are accompanied by two review articles dealing with the effects of anesthetics on ischemia-reperfusion injury. Papers from B. U. Togrul et al., D. Dohman et al., and Y. Demirci et al. are focusing on ischemia-reperfusion injury of the liver. In two of these three papers, different therapeutic interventions on hepatic ischemia-reperfusion injury are evaluated, whereas the third paper is a retrospective study in which the authors investigated the efficacy and safety of intermittent portal triad clamping with low central venous pressure during liver resection. In this context, it has been reported that remote ischemic preconditioning and therapeutic interventions can reduce liver damage after inducing ischemia-reperfusion injury. The studies by S. C. Karahan et al., B. Michèle et al., S. C. Karahan et al., D. Dohman et al., and G. Altun et al. elucidate the effects of different anesthetic techniques and drugs on ischemia-reperfusion injury. These eight papers are entitled as follows:*"The effects of remote ischemic preconditioning and N-acetylcysteine with remote ischemic preconditioning in rat hepatic ischemia-reperfusion injury model"* by B. U. Togrul et al.,*"The effects of spinal, inhalation, and total intravenous anesthetic techniques on ischemia-reperfusion injury in arthroscopic knee surgery"* by S. C. Karahan et al.,*"Efficacy and safety of hepatectomy performed with intermittent portal triad clamping with low central venous pressure\"* by D. Dohman et al.,*"Adalimumab ameliorates abdominal aorta cross clamping induced liver injury in rats"* by Y. Demirci et al.,*"Evidence for the use of isoflurane as a replacement for chloral hydrate anesthesia in experimental stroke: an ethical issue"* by B. Michèle et al.,*"The effect of dexmedetomidine on oxidative stress during pneumoperitoneum"* by S. C. Karahan et al.,*"The comparison of the effects of sevoflurane inhalation anesthesia and intravenous propofol anesthesia on oxidative stress in one lung ventilation"* by D. Dohman et al., and*"Role of ethyl pyruvate on systemic inflammatory response and lung injury in an experimental model of ruptured abdominal aortic aneurysm"* by G. Altun et al.
*Alexander Zarbock* *Ahmet Eroglu* *Engin Erturk* *Can Ince* *Martin Westphal*
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and investment services for over 35 years, TDAmeritrade offers a full spectrum of powerful solutions and innovative ... Ameritrade Holding Corporation (NYSE: AMTD). TDAmeritrade is a trademark jointly owned by TDAmeritrade IP Company and...
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News
Successful Race Weekend
The male and female riders of Steylaerts 777 had a successful weekend in Tabor, CZ and Hamme, BE with two wins and important podium placings.
Team Steylaerts 777 experienced a very successful weekend: On Saturday, Annemarie Worst and Alice Maria Arzuffi rode to second and third place in the 4th World Cup race of the season in Tabor, CZ. On Sunday Timo Kelich won the U23 race and Annemarie Worst won the Women’s Elite competition at the DVV trophy in Hamme, Belgium.
In Tabor Annemarie Worst rode the complete race in front, in the later part accompanied by her team mate and fellow Super Prestige rider Maria Arzuffi. Both entered the final lap together with Lucinda Brand and Sanne Cant – but without hearing the bell announcing the final lap and therefore assuming there was another lap to go. This way Lucinda Brand could jump ahead by an intermediate sprint and keep the lead until the finish.
Annemarie Worst after the race: “I simply did not hear the bell.” Alice Maria Arzuffi and many other competitors confirmed this. The European Champ continued: “So I was about to wait until what I thought was the final lap to save my power until the very end, but suddenly it was all over.” She was accordingly bewildered at the finish. Despite the confusion and the missed chances Arzuffi though was pleased with her third place.
In the Men’s race Mathieu van der Poel wins in superior fashion ahead of Michael Vanthourenhout and Lars van der Haar. Wout van Aert comes in seventh. Also riding a STEVENS Super Prestige, Tim Merlier of team Crélan-Charles finishes 18th and Gianni Vermeersch von Steylaerts 777 after a vigorous chase from very far behind comes in 20th. Tom Lindner gained his best result in the U19 category so far. Thanks to a strong performance he wins third place ahead of Jakub Toupalik from the Czech Republic.
Double Victory in Hamme, All Team Riders in Top TenOnly one day later in the women’s race everything was alright about the bell and Annemarie Worst was well prepared for the sprint against her team mate Alice Maria Arzuffi and Sanne Cant. Arzuffi began sprinting, yet a little too early, and was eventually passed by Worst, Cant und Ellen van Loy. Before Arzuffi had escaped on a solo break-away and which kept the pace high and the race exciting until the end.
In the Men’s Elite Gianni Vermeersch was in front during the whole race, yet was defeated in the final sprint and ended up in 4th place.
In the U23race Timo Kielich had to make a decision: His was well positioned in the lead group when his shoe suffered a defect. Instead of stopping at the tech zone, he went for an intermediate sprint to open a gap the competition was not able to close – good choice! “I’m so happy that it worked out today”, said the Belgian U23 Cross Country Champion. In addition Gert Smets also finishes in the top ten in 9th place – to round off a satisfactory weekend for Steylaerts 777.
|
{
"pile_set_name": "Pile-CC"
}
|
The Bankruptcy Court for the District of Oregon awarded a married couple damages for emotional distress plus attorneys' fees due to the IRS's violation of an automatic stay of collection activities after the couple filed for protection under the Bankruptcy Code. According to the court, sovereign immunity did not protect the government from liability for the damages.
Facts: On Nov. 5, 2012, Jonathan and Cheryl Hunsaker filed a petition for relief under the Bankruptcy Code. By law, the filing automatically stopped collection efforts by their creditors, which included the IRS, to which they owed $9,301. After filing the petition, the couple made all payments required under the bankruptcy plan. From Dec. 12, 2013, to Dec. 8, 2014, the Hunsakers received four notices from the IRS that included demands for payment, two of which were notices to levy on Jonathan Hunsaker's Social Security benefits.
The taxpayers notified their attorney, who told them any collection efforts by the IRS were illegal. The attorney twice wrote to the IRS, stating the Hunsakers were in bankruptcy and requesting that the Service stop its collection efforts. All of the notices created stress for the Hunsakers, but the notices to levy on the Social Security benefits caused greater stress, because that income was crucial for the couple to make their required bankruptcy plan payments. The couple petitioned the Bankruptcy Court for damages from the IRS due to its violations of the automatic stay.
Issues: A debtor injured by a willful violation of the automatic bankruptcy stay may recover damages including court costs and attorneys' fees and may in certain cases receive punitive damages. Damages for emotional distress from a creditor's violating the automatic stay provisions have been allowed if the debtor can clearly establish he or she suffered significant harm and can demonstrate a causal connection between the violation and the harm (Dawson v. Washington Mutual Bank, 390 F.2d 1139 (9th Cir. 2004)).
While the doctrine of sovereign immunity often protects the federal government from litigation, federal law (11 U.S.C. §106) waives sovereign immunity for awards of compensatory damages (except punitive damages) related to violations of the automatic stay provisions of bankruptcy laws. The IRS admitted it had violated the automatic stay provisions but argued it was not liable for damages for emotional distress because the provisions that waive sovereign immunity do not specifically allow for the award of damages for emotional distress.
Holding: The Bankruptcy Court awarded the Hunsakers damages of $4,000 plus reasonable attorneys' fees. The court stated that excluding any type of damages because they are not specifically listed in the sovereign immunity waiver rules would enable "the government to escape liability for any form of damages." The court also held that the taxpayers satisfied the tests of Dawson because (1) the IRS violated the automatic stay, (2) a reasonable person would suffer significant emotional harm from such a violation, and (3) the Hunsakers sustained significant emotional damages due to the additional stress caused by the IRS's violating the stay.
Hunsaker, No. 14-06218 (Bankr. D. Or. 1/13/16)
—By Charles J. Reichert, CPA, instructor of accounting, University of Minnesota—Duluth.
|
{
"pile_set_name": "OpenWebText2"
}
|
Q:
Call web API from client app
I used to use ASMX web services, however have since read (and been told) that a better way to request data from a client etc is to use web API's with MVC.
I have created an MVC 4 web api application and getting to grips with how it works.
Currently I have a single public string in my valuesControllers -
public class ValuesController : ApiController
{
// GET api/values/5
public string Get(int id)
{
return "value";
}
}
And I am currently trying to call this in my client like this -
class Product
{
public string value { get; set; }
}
protected void Button2_Click(object sender, EventArgs e)
{
RunAsync().Wait();
}
static async Task RunAsync()
{
using (var client = new HttpClient())
{
try
{
client.BaseAddress = new Uri("http://localhost:12345/");
client.DefaultRequestHeaders.Accept.Clear();
client.DefaultRequestHeaders.Accept.Add(new MediaTypeWithQualityHeaderValue("application/json"));
// HTTP GET
HttpResponseMessage response = await client.GetAsync("api/values/5");
if (response.IsSuccessStatusCode)
{
Product product = await response.Content.ReadAsAsync<Product>();
Console.WriteLine("{0}", product.value);
}
}
catch(Exception ex)
{
Console.WriteLine(ex.Message.ToString());
}
}
}
On debugging I can step through the request and enter the web API code successfully however on the line -
Product product = await response.Content.ReadAsAsync<Product>();
This fails and enters my catch with the exception -
Error converting value "value" to type 'myDemo.Home+Product'. Path '', line 1, position 7.
Why is this?
A:
Why is this?
Because from your controller action you are returning a string, not a Product which are 2 quite different types:
public string Get(int id)
{
return "value";
}
so make sure that you are consistently reading the value on the client:
if (response.IsSuccessStatusCode)
{
string result = await response.Content.ReadAsAsync<string>();
Console.WriteLine("{0}", result);
}
Of course if you modified your API controller action to return a Product:
public Product Get(int id)
{
Product product = ... go fetch the product from the identifier
return product;
}
your client code would work as expected.
|
{
"pile_set_name": "StackExchange"
}
|
Dulce De Leche
Take a trip south of the border with this flavor! Dulce de leche comes from slowly heated milk where the consistency thickens and color darkens. This is the caramel of the mild family! Sweet and creamy!
|
{
"pile_set_name": "Pile-CC"
}
|
function json=saveubjson(rootname,obj,varargin)
%
% json=saveubjson(rootname,obj,filename)
% or
% json=saveubjson(rootname,obj,opt)
% json=saveubjson(rootname,obj,'param1',value1,'param2',value2,...)
%
% convert a MATLAB object (cell, struct or array) into a Universal
% Binary JSON (UBJSON) binary string
%
% author: Qianqian Fang (fangq<at> nmr.mgh.harvard.edu)
% created on 2013/08/17
%
% $Id: saveubjson.m 460 2015-01-03 00:30:45Z fangq $
%
% input:
% rootname: the name of the root-object, when set to '', the root name
% is ignored, however, when opt.ForceRootName is set to 1 (see below),
% the MATLAB variable name will be used as the root name.
% obj: a MATLAB object (array, cell, cell array, struct, struct array)
% filename: a string for the file name to save the output UBJSON data
% opt: a struct for additional options, ignore to use default values.
% opt can have the following fields (first in [.|.] is the default)
%
% opt.FileName [''|string]: a file name to save the output JSON data
% opt.ArrayToStruct[0|1]: when set to 0, saveubjson outputs 1D/2D
% array in JSON array format; if sets to 1, an
% array will be shown as a struct with fields
% "_ArrayType_", "_ArraySize_" and "_ArrayData_"; for
% sparse arrays, the non-zero elements will be
% saved to _ArrayData_ field in triplet-format i.e.
% (ix,iy,val) and "_ArrayIsSparse_" will be added
% with a value of 1; for a complex array, the
% _ArrayData_ array will include two columns
% (4 for sparse) to record the real and imaginary
% parts, and also "_ArrayIsComplex_":1 is added.
% opt.ParseLogical [1|0]: if this is set to 1, logical array elem
% will use true/false rather than 1/0.
% opt.NoRowBracket [1|0]: if this is set to 1, arrays with a single
% numerical element will be shown without a square
% bracket, unless it is the root object; if 0, square
% brackets are forced for any numerical arrays.
% opt.ForceRootName [0|1]: when set to 1 and rootname is empty, saveubjson
% will use the name of the passed obj variable as the
% root object name; if obj is an expression and
% does not have a name, 'root' will be used; if this
% is set to 0 and rootname is empty, the root level
% will be merged down to the lower level.
% opt.JSONP [''|string]: to generate a JSONP output (JSON with padding),
% for example, if opt.JSON='foo', the JSON data is
% wrapped inside a function call as 'foo(...);'
% opt.UnpackHex [1|0]: conver the 0x[hex code] output by loadjson
% back to the string form
%
% opt can be replaced by a list of ('param',value) pairs. The param
% string is equivallent to a field in opt and is case sensitive.
% output:
% json: a binary string in the UBJSON format (see http://ubjson.org)
%
% examples:
% jsonmesh=struct('MeshNode',[0 0 0;1 0 0;0 1 0;1 1 0;0 0 1;1 0 1;0 1 1;1 1 1],...
% 'MeshTetra',[1 2 4 8;1 3 4 8;1 2 6 8;1 5 6 8;1 5 7 8;1 3 7 8],...
% 'MeshTri',[1 2 4;1 2 6;1 3 4;1 3 7;1 5 6;1 5 7;...
% 2 8 4;2 8 6;3 8 4;3 8 7;5 8 6;5 8 7],...
% 'MeshCreator','FangQ','MeshTitle','T6 Cube',...
% 'SpecialData',[nan, inf, -inf]);
% saveubjson('jsonmesh',jsonmesh)
% saveubjson('jsonmesh',jsonmesh,'meshdata.ubj')
%
% license:
% BSD, see LICENSE_BSD.txt files for details
%
% -- this function is part of JSONLab toolbox (http://iso2mesh.sf.net/cgi-bin/index.cgi?jsonlab)
%
if(nargin==1)
varname=inputname(1);
obj=rootname;
if(isempty(varname))
varname='root';
end
rootname=varname;
else
varname=inputname(2);
end
if(length(varargin)==1 && ischar(varargin{1}))
opt=struct('FileName',varargin{1});
else
opt=varargin2struct(varargin{:});
end
opt.IsOctave=exist('OCTAVE_VERSION','builtin');
rootisarray=0;
rootlevel=1;
forceroot=jsonopt('ForceRootName',0,opt);
if((isnumeric(obj) || islogical(obj) || ischar(obj) || isstruct(obj) || iscell(obj)) && isempty(rootname) && forceroot==0)
rootisarray=1;
rootlevel=0;
else
if(isempty(rootname))
rootname=varname;
end
end
if((isstruct(obj) || iscell(obj))&& isempty(rootname) && forceroot)
rootname='root';
end
json=obj2ubjson(rootname,obj,rootlevel,opt);
if(~rootisarray)
json=['{' json '}'];
end
jsonp=jsonopt('JSONP','',opt);
if(~isempty(jsonp))
json=[jsonp '(' json ')'];
end
% save to a file if FileName is set, suggested by Patrick Rapin
if(~isempty(jsonopt('FileName','',opt)))
fid = fopen(opt.FileName, 'wb');
fwrite(fid,json);
fclose(fid);
end
%%-------------------------------------------------------------------------
function txt=obj2ubjson(name,item,level,varargin)
if(iscell(item))
txt=cell2ubjson(name,item,level,varargin{:});
elseif(isstruct(item))
txt=struct2ubjson(name,item,level,varargin{:});
elseif(ischar(item))
txt=str2ubjson(name,item,level,varargin{:});
else
txt=mat2ubjson(name,item,level,varargin{:});
end
%%-------------------------------------------------------------------------
function txt=cell2ubjson(name,item,level,varargin)
txt='';
if(~iscell(item))
error('input is not a cell');
end
dim=size(item);
if(ndims(squeeze(item))>2) % for 3D or higher dimensions, flatten to 2D for now
item=reshape(item,dim(1),numel(item)/dim(1));
dim=size(item);
end
len=numel(item); % let's handle 1D cell first
if(len>1)
if(~isempty(name))
txt=[S_(checkname(name,varargin{:})) '[']; name='';
else
txt='[';
end
elseif(len==0)
if(~isempty(name))
txt=[S_(checkname(name,varargin{:})) 'Z']; name='';
else
txt='Z';
end
end
for j=1:dim(2)
if(dim(1)>1) txt=[txt '[']; end
for i=1:dim(1)
txt=[txt obj2ubjson(name,item{i,j},level+(len>1),varargin{:})];
end
if(dim(1)>1) txt=[txt ']']; end
end
if(len>1) txt=[txt ']']; end
%%-------------------------------------------------------------------------
function txt=struct2ubjson(name,item,level,varargin)
txt='';
if(~isstruct(item))
error('input is not a struct');
end
dim=size(item);
if(ndims(squeeze(item))>2) % for 3D or higher dimensions, flatten to 2D for now
item=reshape(item,dim(1),numel(item)/dim(1));
dim=size(item);
end
len=numel(item);
if(~isempty(name))
if(len>1) txt=[S_(checkname(name,varargin{:})) '[']; end
else
if(len>1) txt='['; end
end
for j=1:dim(2)
if(dim(1)>1) txt=[txt '[']; end
for i=1:dim(1)
names = fieldnames(item(i,j));
if(~isempty(name) && len==1)
txt=[txt S_(checkname(name,varargin{:})) '{'];
else
txt=[txt '{'];
end
if(~isempty(names))
for e=1:length(names)
txt=[txt obj2ubjson(names{e},getfield(item(i,j),...
names{e}),level+(dim(1)>1)+1+(len>1),varargin{:})];
end
end
txt=[txt '}'];
end
if(dim(1)>1) txt=[txt ']']; end
end
if(len>1) txt=[txt ']']; end
%%-------------------------------------------------------------------------
function txt=str2ubjson(name,item,level,varargin)
txt='';
if(~ischar(item))
error('input is not a string');
end
item=reshape(item, max(size(item),[1 0]));
len=size(item,1);
if(~isempty(name))
if(len>1) txt=[S_(checkname(name,varargin{:})) '[']; end
else
if(len>1) txt='['; end
end
isoct=jsonopt('IsOctave',0,varargin{:});
for e=1:len
val=item(e,:);
if(len==1)
obj=['' S_(checkname(name,varargin{:})) '' '',S_(val),''];
if(isempty(name)) obj=['',S_(val),'']; end
txt=[txt,'',obj];
else
txt=[txt,'',['',S_(val),'']];
end
end
if(len>1) txt=[txt ']']; end
%%-------------------------------------------------------------------------
function txt=mat2ubjson(name,item,level,varargin)
if(~isnumeric(item) && ~islogical(item))
error('input is not an array');
end
if(length(size(item))>2 || issparse(item) || ~isreal(item) || ...
isempty(item) || jsonopt('ArrayToStruct',0,varargin{:}))
cid=I_(uint32(max(size(item))));
if(isempty(name))
txt=['{' S_('_ArrayType_'),S_(class(item)),S_('_ArraySize_'),I_a(size(item),cid(1)) ];
else
if(isempty(item))
txt=[S_(checkname(name,varargin{:})),'Z'];
return;
else
txt=[S_(checkname(name,varargin{:})),'{',S_('_ArrayType_'),S_(class(item)),S_('_ArraySize_'),I_a(size(item),cid(1))];
end
end
else
if(isempty(name))
txt=matdata2ubjson(item,level+1,varargin{:});
else
if(numel(item)==1 && jsonopt('NoRowBracket',1,varargin{:})==1)
numtxt=regexprep(regexprep(matdata2ubjson(item,level+1,varargin{:}),'^\[',''),']','');
txt=[S_(checkname(name,varargin{:})) numtxt];
else
txt=[S_(checkname(name,varargin{:})),matdata2ubjson(item,level+1,varargin{:})];
end
end
return;
end
if(issparse(item))
[ix,iy]=find(item);
data=full(item(find(item)));
if(~isreal(item))
data=[real(data(:)),imag(data(:))];
if(size(item,1)==1)
% Kludge to have data's 'transposedness' match item's.
% (Necessary for complex row vector handling below.)
data=data';
end
txt=[txt,S_('_ArrayIsComplex_'),'T'];
end
txt=[txt,S_('_ArrayIsSparse_'),'T'];
if(size(item,1)==1)
% Row vector, store only column indices.
txt=[txt,S_('_ArrayData_'),...
matdata2ubjson([iy(:),data'],level+2,varargin{:})];
elseif(size(item,2)==1)
% Column vector, store only row indices.
txt=[txt,S_('_ArrayData_'),...
matdata2ubjson([ix,data],level+2,varargin{:})];
else
% General case, store row and column indices.
txt=[txt,S_('_ArrayData_'),...
matdata2ubjson([ix,iy,data],level+2,varargin{:})];
end
else
if(isreal(item))
txt=[txt,S_('_ArrayData_'),...
matdata2ubjson(item(:)',level+2,varargin{:})];
else
txt=[txt,S_('_ArrayIsComplex_'),'T'];
txt=[txt,S_('_ArrayData_'),...
matdata2ubjson([real(item(:)) imag(item(:))],level+2,varargin{:})];
end
end
txt=[txt,'}'];
%%-------------------------------------------------------------------------
function txt=matdata2ubjson(mat,level,varargin)
if(isempty(mat))
txt='Z';
return;
end
if(size(mat,1)==1)
level=level-1;
end
type='';
hasnegtive=(mat<0);
if(isa(mat,'integer') || isinteger(mat) || (isfloat(mat) && all(mod(mat(:),1) == 0)))
if(isempty(hasnegtive))
if(max(mat(:))<=2^8)
type='U';
end
end
if(isempty(type))
% todo - need to consider negative ones separately
id= histc(abs(max(mat(:))),[0 2^7 2^15 2^31 2^63]);
if(isempty(find(id)))
error('high-precision data is not yet supported');
end
key='iIlL';
type=key(find(id));
end
txt=[I_a(mat(:),type,size(mat))];
elseif(islogical(mat))
logicalval='FT';
if(numel(mat)==1)
txt=logicalval(mat+1);
else
txt=['[$U#' I_a(size(mat),'l') typecast(swapbytes(uint8(mat(:)')),'uint8')];
end
else
if(numel(mat)==1)
txt=['[' D_(mat) ']'];
else
txt=D_a(mat(:),'D',size(mat));
end
end
%txt=regexprep(mat2str(mat),'\s+',',');
%txt=regexprep(txt,';',sprintf('],['));
% if(nargin>=2 && size(mat,1)>1)
% txt=regexprep(txt,'\[',[repmat(sprintf('\t'),1,level) '[']);
% end
if(any(isinf(mat(:))))
txt=regexprep(txt,'([-+]*)Inf',jsonopt('Inf','"$1_Inf_"',varargin{:}));
end
if(any(isnan(mat(:))))
txt=regexprep(txt,'NaN',jsonopt('NaN','"_NaN_"',varargin{:}));
end
%%-------------------------------------------------------------------------
function newname=checkname(name,varargin)
isunpack=jsonopt('UnpackHex',1,varargin{:});
newname=name;
if(isempty(regexp(name,'0x([0-9a-fA-F]+)_','once')))
return
end
if(isunpack)
isoct=jsonopt('IsOctave',0,varargin{:});
if(~isoct)
newname=regexprep(name,'(^x|_){1}0x([0-9a-fA-F]+)_','${native2unicode(hex2dec($2))}');
else
pos=regexp(name,'(^x|_){1}0x([0-9a-fA-F]+)_','start');
pend=regexp(name,'(^x|_){1}0x([0-9a-fA-F]+)_','end');
if(isempty(pos)) return; end
str0=name;
pos0=[0 pend(:)' length(name)];
newname='';
for i=1:length(pos)
newname=[newname str0(pos0(i)+1:pos(i)-1) char(hex2dec(str0(pos(i)+3:pend(i)-1)))];
end
if(pos(end)~=length(name))
newname=[newname str0(pos0(end-1)+1:pos0(end))];
end
end
end
%%-------------------------------------------------------------------------
function val=S_(str)
if(length(str)==1)
val=['C' str];
else
val=['S' I_(int32(length(str))) str];
end
%%-------------------------------------------------------------------------
function val=I_(num)
if(~isinteger(num))
error('input is not an integer');
end
if(num>=0 && num<255)
val=['U' data2byte(swapbytes(cast(num,'uint8')),'uint8')];
return;
end
key='iIlL';
cid={'int8','int16','int32','int64'};
for i=1:4
if((num>0 && num<2^(i*8-1)) || (num<0 && num>=-2^(i*8-1)))
val=[key(i) data2byte(swapbytes(cast(num,cid{i})),'uint8')];
return;
end
end
error('unsupported integer');
%%-------------------------------------------------------------------------
function val=D_(num)
if(~isfloat(num))
error('input is not a float');
end
if(isa(num,'single'))
val=['d' data2byte(num,'uint8')];
else
val=['D' data2byte(num,'uint8')];
end
%%-------------------------------------------------------------------------
function data=I_a(num,type,dim,format)
id=find(ismember('iUIlL',type));
if(id==0)
error('unsupported integer array');
end
% based on UBJSON specs, all integer types are stored in big endian format
if(id==1)
data=data2byte(swapbytes(int8(num)),'uint8');
blen=1;
elseif(id==2)
data=data2byte(swapbytes(uint8(num)),'uint8');
blen=1;
elseif(id==3)
data=data2byte(swapbytes(int16(num)),'uint8');
blen=2;
elseif(id==4)
data=data2byte(swapbytes(int32(num)),'uint8');
blen=4;
elseif(id==5)
data=data2byte(swapbytes(int64(num)),'uint8');
blen=8;
end
if(nargin>=3 && length(dim)>=2 && prod(dim)~=dim(2))
format='opt';
end
if((nargin<4 || strcmp(format,'opt')) && numel(num)>1)
if(nargin>=3 && (length(dim)==1 || (length(dim)>=2 && prod(dim)~=dim(2))))
cid=I_(uint32(max(dim)));
data=['$' type '#' I_a(dim,cid(1)) data(:)'];
else
data=['$' type '#' I_(int32(numel(data)/blen)) data(:)'];
end
data=['[' data(:)'];
else
data=reshape(data,blen,numel(data)/blen);
data(2:blen+1,:)=data;
data(1,:)=type;
data=data(:)';
data=['[' data(:)' ']'];
end
%%-------------------------------------------------------------------------
function data=D_a(num,type,dim,format)
id=find(ismember('dD',type));
if(id==0)
error('unsupported float array');
end
if(id==1)
data=data2byte(single(num),'uint8');
elseif(id==2)
data=data2byte(double(num),'uint8');
end
if(nargin>=3 && length(dim)>=2 && prod(dim)~=dim(2))
format='opt';
end
if((nargin<4 || strcmp(format,'opt')) && numel(num)>1)
if(nargin>=3 && (length(dim)==1 || (length(dim)>=2 && prod(dim)~=dim(2))))
cid=I_(uint32(max(dim)));
data=['$' type '#' I_a(dim,cid(1)) data(:)'];
else
data=['$' type '#' I_(int32(numel(data)/(id*4))) data(:)'];
end
data=['[' data];
else
data=reshape(data,(id*4),length(data)/(id*4));
data(2:(id*4+1),:)=data;
data(1,:)=type;
data=data(:)';
data=['[' data(:)' ']'];
end
%%-------------------------------------------------------------------------
function bytes=data2byte(varargin)
bytes=typecast(varargin{:});
bytes=bytes(:)';
|
{
"pile_set_name": "Github"
}
|
Quantitative determinations of immunoglobulins and complement components in human aortic atherosclerotic wall.
Saline and acid eluates of intima with only fatty streaks, fibrous plaque and intima surrounding the fibrous plaque were obtained from 42 human aortae. IgG, IgA, IgM, C1q, C3c, C4, C9, C3A, C-reactive protein, alpha-1-antitrypsin, alpha-2-macroglobulin, albumin, transferrin and fibrinogen were quantitatively determined in these eluates using the radial immunodiffusion technique. Saline extracted IgG and IgA were significantly higher in the fibrous plaque and adjacent tissue than in the fatty streak intima, where IgM was the highest. IgG and IgA were only present in acid eluates. The complement components were present in all saline eluates, but only traces of C3c and C1q in some acid eluates. Statistically significant differences were found for C1q and C9. C-reactive protein was present in 23 samples. The results could suggest an involvement of immune mechanisms in the progression of the atherosclerotic lesion.
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Q:
Visual Studio 2013 crash on start
Yesterday I studied a little MVC5 before bed.
Today, I open Visual Studio 2013 and while loading, the following exception occurs:
Exception Details
System.ArgumentNullException was unhandled
Message: An unhandled exception of type 'System.ArgumentNullException' occurred in mscorlib.dll
Additional information: Buffer cannot be null.
Parameter name: buffer
I have already repaired Visual Studio and nothing has changed.
Does anyone know what's going on?
A:
The Update 5 worked for me. However you need to be part of Dev Essentials in order to download this update.
https://my.visualstudio.com/Downloads?q=Visual%20Studio%202013%20Update%205
|
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"pile_set_name": "StackExchange"
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{
"status_code": 200,
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"PaginationToken": "",
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---
abstract: 'In this article we study the homology of spaces ${{\rm Hom}}({{\mathbb Z}}^n,G)$ of ordered pairwise commuting $n$-tuples in a Lie group $G$. We give an explicit formula for the Poincaré series of these spaces in terms of invariants of the Weyl group of $G$. By work of Bergeron and Silberman, our results also apply to ${{\rm Hom}}(F_n/\Gamma_n^m,G)$, where the subgroups $\Gamma_n^m$ are the terms in the descending central series of the free group $F_n$. Finally, we show that there is a stable equivalence between the space ${{\rm Comm}}(G)$ studied by Cohen–Stafa and its nilpotent analogues.'
address:
- 'Indiana University - Purdue University Indianapolis, Indianapolis, IN 46202'
- 'Tulane University, New Orleans, LA 70118'
author:
- 'Daniel A. Ramras'
- Mentor Stafa
title: 'Hilbert–Poincaré series for spaces of commuting elements in Lie groups'
---
Introduction
============
Let $G$ be a compact and connected Lie group and let $\pi $ be a discrete group generated by $n$ elements. In this article we study the rational homology of the space of group homomorphisms ${{\rm Hom}}(\pi,G)\subseteq G^n$, endowed with the subspace topology from $G^n$. In particular, when $\pi$ is free abelian or nilpotent we give an explicit formula for the Poincaré series of ${{\rm Hom}}(\pi,G)_1$, the connected component of the trivial representation, in terms of invariants of the Weyl group $W$ of $G$.
The topology of the spaces ${{\rm Hom}}(\pi,G)$ has been studied extensively in recent years, in particular when $\pi$ is a free abelian group [@adem2007commuting; @bairdcohomology; @BJS; @gomez.pettet.souto; @pettet.souto; @stafa.comm; @stafa.comm.2]; in this case ${{\rm Hom}}({\mathbb{Z}}^n, G)$ is known as *the space of ordered commuting $n$-tuples in $G$*. The case in which $\pi$ is a finitely generated nilpotent group was recently analyzed by Bergeron and Silberman [@bergeron; @bergeron2016note]. These spaces and variations thereon, such as the space of almost commuting elements [@borel2002almost], have been studied in various settings, including work of Witten and Kac–Smilga on supersymmetric Yang-Mills theory [@witten1; @witten2; @kac.smilga].
Our formula for the Poincaré series of the identity component ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$ builds on work of Baird [@bairdcohomology] and Cohen–Reiner–Stafa [@stafa.comm]. In fact, we give a formula for a more refined *Hilbert–Poincaré series*, which is a tri-graded version of the standard Poincaré series that arises from a certain cohomological description of these spaces due to Baird. Work of Bergeron and Silberman [@bergeron2016note] then leads immediately to results for nilpotent groups. The formula we produce is obtained by comparing stable splittings of ${{\rm Hom}}({{\mathbb Z}}^n,G)$ and of the space ${{\rm Comm}}(G)$ introduced in [@stafa.comm]. The latter space is an analogue of the James reduced product construction for commuting elements in $G$; see Section \[Comm-sec\].
Main results
------------
The main purpose of this paper is to give an explicit formula for the Poincaré series of the component ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$.
\[thm: Poincare series of Hom INTRO\] The Poincaré series of ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$ is given by $$P({{\rm Hom}}({{\mathbb Z}}^n,G)_1;q)=\frac{\prod_{i=1}^r (1-q^{2d_i})}{|W|}
\left(\sum_{w\in W} \frac{ \det(1+qw)^n}{\det(1-q^2w)} \right),$$ where the integers $d_1,\dots,d_r$ are the characteristic degrees of the Weyl group $W$.
A similar formula for the homology of the character variety ${{\rm Hom}}({{\mathbb Z}}^n, G)/G$ appears in Stafa [@Stafa-char-var].
Some comments are in order regarding the above formula. Let $T \subset G$ be a maximal torus with lie algebra $\mathfrak{t}$. Then the Weyl group $W$ acts on the dual space $\mathfrak{t}^*$ as a finite reflection group, and the determinants in the formula are defined in terms of this linear representation of $W$. The characteristic degrees of $W$ arise by considering the induced action of $W$ on the polynomial algebra ${{\mathbb R}}[x_1, \ldots, x_r]$, where the $x_i$ form a basis for $\mathfrak{t}^*$ (so $r ={{\rm rank\,}}(G)$). It is a theorem of Shephard–Todd [@shephard1954finite] and Chevalley [@chevalley1955invariants] that the $W$–invariants ${{\mathbb R}}[x_1, \ldots, x_r]^W$ form a polynomial ring with $r$ homogeneous generators. The characteristic degrees of $W$ are then the degrees of the homogeneous generators for ${{\mathbb R}}[x_1, \ldots, x_r]^W$. These degrees are well-known, and are displayed in Table \[table: characteristic degrees\]. For further discussion of these ideas, see Section \[FRG\].
The spaces ${{\rm Hom}}(\pi,G)$ are not path-connected in general; see for instance [@giese.sjerve] where the path components of ${{\rm Hom}}({{\mathbb Z}}^n,SO(3))$ are described. However, if there is only one conjugacy class of maximal abelian subgroups in $G$, namely the conjugacy class of maximal tori, then ${{\rm Hom}}({{\mathbb Z}}^n,G)$ and ${{\rm Comm}}(G)$ are both path-connected. This is true, for instance, if $G=U(n)$, $SU(n)$, or $Sp(n)$; on the other hand, ${{\rm Hom}}({{\mathbb Z}}^n,SO(2n+1))$ is disconnected for $n{\geqslant}2$ and ${{\rm Hom}}({{\mathbb Z}}^n,G_2)$ is disconnected for $n{\geqslant}3$. In fact, Kac and Smilga have classified those compact, simple Lie groups for which ${{\rm Hom}}({{\mathbb Z}}^n, G)$ is path connected [@kac.smilga]. Moreover, when $G$ is semisimple and simply connected, it is a theorem of Richardson that ${{\rm Hom}}({{\mathbb Z}}^2, G)$ is an irreducible algebraic variety, and hence is connected [@richardson1979commuting].
Theorem \[thm: Poincare series of Hom INTRO\] can also be applied to nilpotent groups. Let $F_n \unrhd \Gamma^2_n \unrhd \Gamma^3_n \cdots$ be the descending central series of the free group $F_n$. Bergeron and Silberman [@bergeron2016note] show that for each $m{\geqslant}2$, the identity component ${{\rm Hom}}(F_n/\Gamma^m_n,G)_1$ consists entirely of abelian representations. In fact, they show that if $N$ is a finitely generated nilpotent group, then the natural map $${{\rm Hom}}(N/[N,N], G)\longrightarrow {{\rm Hom}}(N, G)$$ restricts to a homeomorphism between the identity components. Since $G$ admits a neighborhood $U$ of the identity that contains no subgroup other than the trivial subgroup, every representation in the identity component of ${{\rm Hom}}(N/[N,N], G)$ kills the torsion subgroup of $N/[N,N]$. Thus our main result also yields the homology of the identity component in ${{\rm Hom}}(N, G)$.
The assumption that $G$ is compact is not in fact very restrictive, since if $G$ is the complex points of a connected reductive linear algebraic group over ${{\mathbb C}}$ (or the real points if $G$ is defined over ${{\mathbb R}}$) and $K{\leqslant}G$ is a maximal compact subgroup, then Pettet and Souto [@pettet.souto] showed that ${{\rm Hom}}({{\mathbb Z}}^n,G)$ deformation retracts onto ${{\rm Hom}}({{\mathbb Z}}^n,K)$. For simplicity, we refer to such groups $G$ simply as [reductive]{} Lie groups. Bergeron [@bergeron] generalized this result to finitely generated nilpotent groups (in fact, Bergeron’s result also allows $G$ to be disconnected). It should be emphasized, however, that for other discrete groups $\pi$ it is known that the homotopy types of ${{\rm Hom}}(\pi, G)$ and ${{\rm Hom}}(\pi, K)$ can differ; examples appear in [@adem2007commuting].
The above descending central series can be used to define a filtration of the James reduced product of $G$, denoted $J(G)$, which is also known as the free monoid generated by the based space $G$. The filtration is given by the spaces $${{\rm Comm}}(G)={{\rm X}}(2,G)\subset {{\rm X}}(3,G) \subset \cdots \subset {{\rm X}}(\infty,G)=J(G)$$ defined in Section \[sec: topology Hom\], and was studied by Cohen and Stafa [@stafa.comm]. Here we show that all the terms in the filtration have the same Poincaré series.
\[thm: Poincare series of X(q,G) Intro\] The inclusion $$P({{\rm Comm}}(G)_1;q){\hookrightarrow}P({{\rm X}}(m, G)_1;q)$$ induces an isomorphism in homology for every $m\geq 2$ .
Structure of the paper
----------------------
We start in Section \[sec: topology Hom\] by giving some basic topological properties of the spaces of homomorphisms ${{\rm Hom}}({{\mathbb Z}}^n,G)$ and we define the spaces ${{\rm X}}(m, G) \subset J(G)$ considered above. In particular, we explain how all these spaces decompose into wedge sums after a single suspension. We prove Theorems \[thm: Poincare series of Hom INTRO\] and \[thm: Poincare series of X(q,G) Intro\] in Sections \[sec: Poincare series of Hom(Zn,G)\] and \[sec: Poincare series of X(q,G)\], respectively. In Section \[ungraded-sec\], we consider the ungraded cohomology and the rational complex $K$–theory of ${{\rm Hom}}({{\mathbb Z}}^n, G)_1$. Finally, we give examples of Hilbert–Poincaré series in Section \[sec: examples Poincare\], most notably for the exceptional Lie group $G_2$.
[**Acknowledgements:**]{} We thank Alejandro Adem and Fred Cohen for helpful comments, and Mark Ramras for pointing out the Binomial Theorem, which simplified our formulas.
Topology of commuting elements in Lie groups {#sec: topology Hom}
============================================
Let $G$ be a compact and connected Lie group. Fix a maximal torus $T{\leqslant}G$ and let $W = N_G(T)/T$ be the Weyl group of $G$. The map $$\label{c}G \times T \to G$$ conjugating elements of the maximal torus by elements of $G$ has been studied as far back as Weyl’s work, and can be used to show that the rational cohomology of $G$ is the ring of invariants $[H^\ast(G/T) \otimes H^\ast(T)]^W$. To study the rational cohomology of ${{\rm Hom}}({{\mathbb Z}}^n,G)$ we can proceed as follows. The action by conjugation of $T$ on itself is trivial, so (\[c\]) descends to a map $G/T\times T \to G$, which is invariant under the $W$–action $([g],t)\cdot [n] = ([gn],n^{-1}tn)$, where $n\in N_G (T)$. In [@bairdcohomology] Baird showed that the induced map $$\begin{aligned}
\label{theta}
\begin{split}
\theta_n: G/T\times_{W} T^n &\to {{\rm Hom}}({{\mathbb Z}}^n,G)\\
[g,t_1,\dots,t_n] &\mapsto (gt_1g^{-1},\dots, gt_ng^{-1})
\end{split}\end{aligned}$$ surjects onto ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$ and induces an isomorphism of rational cohomology groups $$\label{Baird}
H^\ast({{\rm Hom}}({{\mathbb Z}}^n,G)_1;{{\mathbb Q}}) {\cong}[H^\ast(G/T;{{\mathbb Q}})\otimes H^\ast(T^n;{{\mathbb Q}})]^W.$$ This recovers the above fact about the cohomology of $G$ when $n=1$. Baird in fact shows that all torsion in $H^\ast({{\rm Hom}}({{\mathbb Z}}^n,G)_1;{{\mathbb Z}})$ has order dividing $|W|$, but little else is known about the torsion in these spaces, beyond the case of $SU(2)$ [@BJS] and the fact that $H_1 ({{\rm Hom}}({{\mathbb Z}}^n,G)_1; {{\mathbb Z}})$ is torsion-free [@gomez.pettet.souto].
We note that as an ungraded ${{\mathbb Q}}W$-module, the ring $H^\ast(G/T;{{\mathbb Q}})$ is simply the regular representation ${{\mathbb Q}}W$, a well-known fact that dates back to Borel [@borel1953cohomologie] – a proof can be found for instance in the exposition by M. Reeder [@reeder1995cohomology]. This fact implies that the ungraded cohomology of the homomorphism space is just a regraded version of the cohomology of $T^n$. As we will see, various topological constructions related to the maps $\theta_n$ enjoy a similar structure in their cohomology.
Adem and Cohen [@adem2007commuting] showed that there is a homotopy decomposition of the suspension of ${{\rm Hom}}({{\mathbb Z}}^n,G)$ into a wedge sum of *smaller* spaces as follows $$\label{eqn: stable decomp Hom}
\Sigma {{\rm Hom}}({{\mathbb Z}}^n,G) \simeq \Sigma \bigvee_{1\leq k \leq n}
\bigvee_{n \choose k} \widehat{{{\rm Hom}}}({{\mathbb Z}}^k,G),$$ where $\widehat{{{\rm Hom}}}({{\mathbb Z}}^k,G)$ is the quotient of $ {{\rm Hom}}({{\mathbb Z}}^n,G)$ by the subspace consisting of all commuting $n$–tuples $(g_1, \ldots, g_n)$ such that $g_i=1$ for at least one coordinate $i$. This decomposition, along with the analogous decomposition of ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$ given in Lemma \[dec\], will play a key role in our study of homology.
Recall that the descending central series of a group $\pi$ is the sequence of subgroups of $\pi$ given by $
\pi=\Gamma^1 \unrhd \Gamma^2=[\pi,\pi] \unrhd
\cdots \unrhd \Gamma^{k+1} \unrhd \cdots,
$ where inductively $\Gamma^{k+1}=[\pi,\Gamma^{k}]$. Let $\Gamma^k_n$ be the $k$-th stage in the descending central series of the free group $F_n$, and note that $\Gamma_n^\infty = \bigcap_{k=1}^\infty \Gamma^k_n = 1$. Then we obtain a filtration $$\label{eq: filtration of G^n}
{{\rm Hom}}(F_n/\Gamma^2_n,G)\subset {{\rm Hom}}(F_n/\Gamma^3_n,G)
\subset \cdots \subset {{\rm Hom}}(F_n/\Gamma^\infty_n,G)=G^n$$ of the space $G^n$ by subspaces of nilpotent $n$-tuples, where the first term of the filtration is the space of commuting $n$-tuples $F_n/\Gamma^2_n=F_n/[F_n,F_n]={{\mathbb Z}}^n$. It should be noted that this filtration need not be exhaustive; that is, $\bigcup_{k=1}^\infty {{\rm Hom}}(F_n/\Gamma^k_n,G)$ is in general a proper subset of $G^n$. Also note that $T^n \subset F_n/\Gamma^2_n = {{\rm Hom}}({{\mathbb Z}}^n,G)$, a fact that will be used later. We obtain the following stable decompositions of the connected components of the trivial representations for nilpotent $n$-tuples.
\[dec\] Let $G$ be either a compact connected Lie group or a reductive connected Lie group. For each $m\geq 2$ there is a homotopy equivalence $$\begin{aligned}
\Sigma {{\rm Hom}}(F_n/\Gamma^m_n,G)_1 \simeq \Sigma
\bigvee_{1\leq k \leq n} \bigvee_{n \choose k}
\widehat{{{\rm Hom}}}(F_k/\Gamma^m_k,G)_1.\end{aligned}$$ In particular there is a homotopy equivalence $$\begin{aligned}
\Sigma {{\rm Hom}}({{\mathbb Z}}^n,G)_1 \simeq \Sigma
\bigvee_{1\leq k \leq n} \bigvee_{n \choose k}
\widehat{{{\rm Hom}}}({{\mathbb Z}}^k,G)_1.\end{aligned}$$
This is a minor modification to the arguments in [@villarreal2016cosimplicial Corollary 2.21], where the corresponding decompositions for the full representation spaces are obtained. The spaces $\{{{\rm Hom}}(F_n/\Gamma^m_n,G)\}_n$ form a simplicial space, which Villarreal shows is simplicially NDR in the sense defined in [@adem.cohen.gitler.bahri.bendersky]. The face and degeneracy maps in these simplicial spaces preserve the identity components, so $\{{{\rm Hom}}(F_n/\Gamma^m_n,G)_1\}_n$ is also a simplicial space, and is again simplicially NDR. The decompositions now follow from the main result of [@adem.cohen.gitler.bahri.bendersky Theorem 1.6].
The James reduced product
-------------------------
The *James reduced product* $J(Y)$ can be defined for any CW-complex $Y$ with basepoint $*$. In our discussion $Y$ is usually a compact Lie group with basepoint the identity element. Define $J(Y)$ as the quotient space $$J(Y):= \bigg( \bigsqcup_{n\geq 0} Y^n \bigg)/\sim$$ where $\sim$ is the relation $(\dots,*,\dots) \sim (\dots,\widehat{*},\dots)$ omitting the coordinates equal to the basepoint. This can also be seen as the free monoid generated by the elements of $Y$ with the basepoint acting as the identity element. It is a classical result that $J(Y)$ is weakly homotopy equivalent to $\Omega\Sigma Y$, the loops on the suspension of $Y$. Moreover, the suspension of $J(Y)$ is given by $$\Sigma J(Y) \simeq \Sigma \bigvee_{n \geq 1} \widehat{Y^n},$$ where $\widehat{Y^n}$ is the $n$-fold smash product. It was first observed by Bott and Samelson [@bott1953pontryagin] that the homology of $J(Y)$ is isomorphic as an algebra to the tensor algebra ${{\mathcal T}}[\widetilde{H}_\ast(Y;R)]$ generated by the reduced homology of $Y$, given that the homology of $Y$ is a free $R$-module. This is a central result used in our calculation.
The spaces ${{\rm X}}(m,G)$ {#Comm-sec}
---------------------------
Now consider the case in which $Y = G$, a connected Lie group with basepoint the identity element $1\in G$. A filtration of the free monoid $J(G)$ is given by $$\label{eq: filtration of J(G)}
{{\rm X}}(2,G)\subset {{\rm X}}(3,G) \subset
{{\rm X}}(4,G) \subset \cdots \subset {{\rm X}}(\infty,G)=J(G),$$ where each space is defined by $${{\rm X}}(m,G):=\bigg(\bigsqcup_{n\geq 0} {{\rm Hom}}(F_n/\Gamma^m_n,G) \bigg)/\sim$$ where $\sim$ is the same relation as in $J(G)$. The spaces ${{\rm X}}(m,G)$ and ${{\rm Comm}}(G)={{\rm X}}(2,G)$ were studied in [@stafa.comm], where it was shown that ${{\rm Comm}}(G)$ carries important information about the spaces of commuting $n$-tuples ${{\rm Hom}}({{\mathbb Z}}^n,G)$. However, note that in general the spaces ${{\rm X}}(m,G)$ do not have the structure of a monoid for any $m$. As in the case of spaces of homomorphisms, the spaces ${{\rm X}}(m,G)$ need not be path connected. For instance, the space ${{\rm X}}(2,SO(3))$ has infinitely many path components, as shown in [@stafa.thesis]. We can define the connected component of the trivial representation for each space ${{\rm X}}(m,G)$ by $${{\rm X}}(m,G)_1:=\bigg(\bigsqcup_{n\geq 0}
{{\rm Hom}}(F_n/\Gamma^m_n,G)_1 \bigg)/\sim$$ with ${{\rm X}}(2,G)_1={{\rm Comm}}(G)_1.$ Cohen and Stafa [@stafa.comm Theorem 5.2] show that there is a stable decomposition of this space as follows: $$\label{eqn: stable decomp Comm}
\Sigma {{\rm X}}(m,G) \simeq \Sigma
\bigvee_{k \geq 1} \widehat{{{\rm Hom}}}(F_k/\Gamma^m_k,G).$$
We have an analogous result for the identity components.
\[prop: X(q,G) decomposition\] Let $G$ be either a compact connected Lie group or a reductive connected Lie group. For each $m\geq 2$ there is a homotopy equivalence $$\Sigma {{\rm X}}(m,G)_1 \simeq \Sigma
\bigvee_{k \geq 1} \widehat{{{\rm Hom}}}(F_k/\Gamma^m_k,G)_1.$$ This is true in particular for ${{\rm Comm}}(G)_1$.
This follows from the proof of [@stafa.comm Theorem 5.2].
[Poincaré series of ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$]{} {#sec: Poincare series of Hom(Zn,G)}
=========================================================
For a topological space $X$ the (rational) *Poincaré series* is the series $$P(X; q):=\sum_{k\geq 0} {{\rm rank\,}}_{{\mathbb Q}}(H_k(X;{{\mathbb Q}})) q^k.$$ In this section we describe the Poincaré series of ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$. Following [@stafa.comm], we will refine the usual grading of cohomology and introduce tri-graded *Hilbert–Poincaré series* for $X = {{\rm Hom}}({{\mathbb Z}}^n,G)$, ${{\rm Comm}}(G)$, or ${{\rm X}}(m,G)$. These additional gradings will facilitate the computation of the Poincaré series itself.
For the remainder of this section, we will drop the coefficient group ${{\mathbb Q}}$ from our notation for (co)homology. The statements are true for any field with characteristic 0 or relatively prime to $|W|$.
The maps $\theta_{n}: G/T\times_{W} T^n \to {{\rm Hom}}({{\mathbb Z}}^n,G)$ can be assembled to give a map $$\label{Theta}
\Theta : G/T\times_{W} J(T) \to {{\rm Comm}}(G)$$ which surjects onto the connected component ${{\rm Comm}}(G)_1.$ It was shown in [@stafa.comm] that $\Theta$ induces isomorphisms on the level of rational (co)homology, so rationally we obtain $$\label{Comm}
H^\ast({{\rm Comm}}(G)_1) \cong [H^\ast(G/T)\otimes H^\ast(J(T))]^W
\cong [H^\ast(G/T)\otimes {{\mathcal T}}^*[\widetilde{H}_*(T)] ]^W,$$ where ${{\mathcal T}}^*$ denotes the dual of the tensor algebra. This interpretation of the cohomology in terms of Weyl group invariants allows us to make the following definition. Define the Hilbert–Poincaré series of ${{\rm Comm}}(G)_1$ as the tri-graded series $$P({{\rm Comm}}(G)_1;q,s,t)=\sum_{i,j,k \geq 0} {{\rm rank\,}}A(i,j,k)^W\,\, q^i s^j t^m,$$ where $$A(i,j,k) := H^i (G/T) \otimes {{\mathcal T}}^*[\widetilde{H}_*(T)]_{j,m}$$ and ${{\mathcal T}}^*[\widetilde{H}_*(T)]_{j,m}$ is the dual of the submodule of ${{\mathcal T}}[\widetilde{H}_*(T)]$ generated by the $m$–fold tensors of total cohomological degree $j$.
To recover the ordinary Poincaré series we can set $s$ equal to $q$ and $t$ equal to 1 since the tensor degree does not affect the (co)homological degree. In order to understand this tri-graded version of the Poincaré series, we take a short diversion to discuss the characteristic degrees of a finite reflection group.
Finite reflection groups {#FRG}
------------------------
A finite reflection group is a finite subgroup $W\subset GL_k(\mathbf{k})$, with $\mathbf{k}$ a field of characteristic 0, such that $W$ is generated by reflections. Equivalently, consider an $n$-dimensional vector space $V$ over $\mathbf{k}$ equipped with the action of a finite subgroup $W \subset GL (V)$. There is a corresponding action on the symmetric algebra $R$ of $V$, which is isomorphic to the polynomial algebra $R:=\mathbf{k}[x_1,\dots,x_n]$[^1]. It is a classical result of Chevalley [@chevalley1955invariants] and Shephard–Todd [@shephard1954finite] that when $W$ is generated by reflections, the invariant elements of the $W$-action also form an algebra generated by $n$ elements, and these generators can be chosen to be (algebraically independent) homogeneous polynomials $f_1,\dots,f_n$. Hence the $W$-invariant subalgebra is given by $R^W=\mathbf{k}[f_1,\dots,f_n]$. The degrees of the $f_i$ are independent of the choice of the homogeneous generators. The degrees $d_i={\rm deg}(f_i)$ are called the *characteristic degrees* of the reflection group $W$. See [@springer1974regular; @broue.reflextion.gps] for a thorough exposition.
Let $W$ be the Weyl group of a compact and connected Lie group $G$, which is finite. Then $W$ is a unitary reflection group: $W$ acts on the maximal torus $T$ of $G$, and there is an induced action of $W$ on the Cartan subalgebra $\mathfrak{t}$ of the Lie algebra $\mathfrak{g}$. The actions of $W$ on $\mathfrak{t}$ and its dual $\mathfrak{t}^\ast$ are faithful, so $W$ can be considered as a subgroup of $GL(\mathfrak{t}^\ast)$. Moreover, $W$ is generated by reflections. This action of $W$ has associated characteristic degrees $d_1,\dots,d_r$, where $r$ is the rank of the maximal torus $T$, and it is a well-known fact that $|W|=\prod_i d_i$. Characteristic degrees of reflection groups have many other remarkable properties, outside the scope of this paper.
Type Lie group Rank $W$ $|W|$ Characteristic degrees
------- ------------ ---------- ---------------------------------------------- ------------------- ------------------------- -- -- -- -- -- --
$A_n$ $SU(n+1)$ $n\geq1$ $\Sigma_{n+1}$ $(n+1)!$ $2,3,...,n+1$
$B_n$ $SO(2n+1)$ $n$ ${{\mathbb Z}}_2^n\rtimes\Sigma_n$ $n!2^n$ $2,4,\dots,2n$
$C_n$ $Sp(n)$ $n$ ${{\mathbb Z}}_2^n\rtimes\Sigma_n$ $n!2^n$ $2,4,\dots,2n$
$D_n$ $SO(2n)$ $n$ $H_n \rtimes\Sigma_n$ $n!2^{n-1}$ $2,4,\dots,2n-2,n$
$G_2$ $G_2$ 2 $D_{2^2\cdot 3}$ 12 $2,6$
$F_4$ $F_4$ 4 $D_{2^7\cdot 3^2}$ 1,152 $2,6,8,12$
$E_6$ $E_6$ 6 $O(6,{{\mathbb F}}_2)$ 51,840 $2,5,6,8,9,12$
$E_7$ $E_7$ 7 $O(7,{{\mathbb F}}_2)\times {{\mathbb Z}}_2$ 2,903,040 $2,6,8,10,12,14,18$
$E_8$ $E_8$ 8 $\widehat{O(8, {{\mathbb F}}_2)}$ $2^{14}3^5 5^2 7$ $2,8,12,14,18,20,24,30$
: Characteristic degrees of Weyl groups $W$[]{data-label="table: characteristic degrees"}
As an example consider the unitary group $U(n)$ with Weyl group the symmetric group $\Sigma_n$ on $n$ letters. The rank of $U(n)$ is $n$ and the $\Sigma_n$ acts on the maximal torus $T=(S^1)^n$ by permuting the coordinates, so it acts on $\mathfrak{t}$ by permuting the basis vectors. Therefore, as a subgroup of $GL(\mathfrak{t}^\ast)$ the Weyl group $\Sigma_n$ consists of permutation matrices. The invariant subalgebra is then generated by the elementary symmetric polynomials $\epsilon_1,\dots,\epsilon_n$, with degrees $d_i={\rm deg}(\epsilon_i)=i$ for $i=1,\dots,n.$
Table \[table: characteristic degrees\] summarizes the Weyl groups and their associated characteristic degrees for families of simple Lie groups, including exceptional Lie groups. In the column for $W$, the group $H_n$ is the kernel of the multiplication map ${{\mathbb Z}}_2^n = \{\pm 1\}\to {{\mathbb Z}}_2$ (so $H_n$ consists of $n$–tuples containing an even number of $-1$’s), $D_n$ denotes the dihedral group of order $n$, and $\widehat{O(8, {{\mathbb F}}_2)}$ is a double cover of ${O(8, {{\mathbb F}}_2)}$. Similar information about characteristic degrees can also be found in [@springer1974regular p. 175] and [@humphreys1992reflection p. 59].
As shown in [@stafa.comm], the information in Table \[table: characteristic degrees\] and the realization of the Weyl group $W$ as a subgroup of $GL(\mathfrak{t}^\ast)$ suffice to describe the rational cohomology of ${{\rm Comm}}(G)_1.$ This information will be used below to describe the corresponding Hilbert–Poincaré series for ${{\rm Hom}}({{\mathbb Z}}^k,G)_1$.
Hilbert–Poincaré series
-----------------------
Suppose $G$ has rank $r$. Let us denote by $A_W (q)$ the quantity $$A_W (q):=\frac{\prod_{i=1}^r (1-q^{2d_i})}{|W|},$$ where $d_1,\dots,d_r$ are the characteristic degrees of $W$. It was shown by Cohen, Reiner and Stafa [@stafa.comm] that the Hilbert–Poincaré series of ${{\rm Comm}}(G)_1$ is given by the following infinite series.
Let $G$ be a compact and connected Lie group with maximal torus $T$ and Weyl group $W$. Then the Hilbert–Poincaré series of the connected component of the trivial representation in ${{\rm Comm}}(G)$ is given by $$\label{eqn: Poincere series Comm 3}
\ds P(Comm(G)_1;q,s,t) =
A_W (q) \sum_{w\in W}
\frac{1}{\det(1-q^2w)(1-t(\det(1+sw)-1))}.$$
Using this theorem and stable decompositions of ${{\rm Comm}}(G)_1$ given above, we will now describe the Hilbert–Poincaré polynomial of the space of ordered pairwise commuting $n$-tuples. We begin with the following result, which is the fundamental step in our calculation of Poincaré polynomials for homomorphism spaces.
\[prop: homology of hom hat\] For $m{\geqslant}1$, the reduced Hilbert–Poincaré series of $\widehat{{{\rm Hom}}}({{\mathbb Z}}^m,G)_1$ is given by $$\label{Phat}
P(\widehat{{{\rm Hom}}}({{\mathbb Z}}^m,G)_1;q,s) =
A_W (q) \sum_{w\in W} \frac{(\det(1+sw)-1)^m}{\det(1-q^2 w)}.$$ In particular, setting $s=q$ gives the reduced Poincaré series of $\widehat{{{\rm Hom}}}({{\mathbb Z}}^m,G)_1$.
When $m=0$, the same formulas yield the (unreduced) Hilbert–Poincaré and Poincaré series of the one-point space $\widehat{{{\rm Hom}}}({{\mathbb Z}}^0,G)_1$.
When $m=0$, this result asserts that the above series reduces to the constant series 1. An algebraic explanation of this fact, in terms of Molien’s Theorem, is given at the end of this section.
The bigrading in this Hilbert–Poincaré series arises from applying the homology isomorphism (\[hom-hat-iso\]) described in the proof, together with the Künneth Theorem. More specifically, let $\widehat{T^m}$ denote the $m$–fold smash product of the maximal torus $T{\leqslant}G$ with itself. Then the coefficient of $q^i s^j$ in the above Hilbert–Poincaré series is the rank of the subspace $[H^i (G/T) \otimes H^j( \widehat{T^m})]^W$ of $W$–invariant elements.
First rearrange the terms in the Hilbert–Poincaré series of ${{\rm Comm}}(G)_1$: $$\begin{aligned}
\ds P({{\rm Comm}}(G)_1;q,s,t)
&= A_W (q) \sum_{w\in W}\frac{1}{\det(1-q^2w)
(1-t(\det(1+sw)-1))}\\
&= A_W (q) \sum_{w\in W}\frac{\sum_{m=0}^\infty
(t(\det(1+sw)-1)))^m}{\det(1-q^2w)}\\
&= A_W (q) \sum_{w\in W} \sum_{m=0}^\infty \frac{
(\det(1+sw)-1))^m t^m}{\det(1-q^2w)}\\
&= A_W (q) \sum_{m=0}^\infty \sum_{w\in W} \frac{
(\det(1+sw)-1))^m t^m}{\det(1-q^2w)}\\
&= \sum_{m=0}^\infty \left( A_W (q) \sum_{w\in W} \frac{
(\det(1+sw)-1))^m}{\det(1-q^2w)}\right) t^m.\\\end{aligned}$$ We claim that after setting $s=q$, the coefficient of $t^m$ in $P({{\rm Comm}}(G)_1;q,s,t)$ is the Poincaré series of the stable wedge summand $\widehat{{{\rm Hom}}}({{\mathbb Z}}^m,G)_1$ appearing in the decomposition of ${{\rm Comm}}(G)_1$ given by Proposition \[prop: X(q,G) decomposition\].
Recall that our tri-grading of the (co)homology of ${{\rm Comm}}(G)_1$ comes from the natural map $$\Theta\co G/T \times_W J(T){\longrightarrow}{{\rm Comm}}(G)_1,$$ (see (\[Theta\])) which induces isomorphisms in (rational) cohomology. On the left-hand side, we have $$H^*(G/T \times_W J(T)) {\cong}\big(H^*(G/T)\otimes H^*(J(T))\big)^W
{\cong}\big(H^*(G/T)\otimes {{\mathcal T}}^*[{\widetilde{H}_*(T)}]\big)^W.$$ Let ${{\mathcal T}}^*_m[{\widetilde{H}_*(T)]}$ denote the dual of the submodule $${{\mathcal T}}_m[{\widetilde{H}_*(T)}]\subset {{\mathcal T}}[{\widetilde{H}_*(T)}]$$ of $m$–fold tensors. The action of $W$ preserves these submodules, so we obtain a decomposition $$H^*(G/T \times_W J(T)) {\cong}\bigoplus_m \big(H^*(G/T)\otimes {{\mathcal T}}^*_m[{\widetilde{H}_*(T)}]\big)^W.$$ Note that for $m>0$, the terms in this decomposition are in fact the reduced cohomology of $G/T{\times}_W \widehat{T^m}$, where $\widehat{T^m}$ denotes the $m$–fold smash product of $T$ with itself, so the coefficient of $t^m$ in $P({{\rm Comm}}(G)_1;q,s,t)$ is the (bigraded, reduced) Hilbert–Poincaré series of $G/T{\times}_W \widehat{T^m}$. Similarly, the $m=0$ term in this decomposition is unreduced cohomology of $G/T{\times}_W \widehat{T^0} = (G/T)/W$. Note that the rational cohomology of $G/T{\times}_W 1{\cong}(G/T)/W$ is trivial, since the action of $W$ on $H^* (G/T)$ is the regular representation.
To complete the proof, it will suffice to show that the map $$\label{hom-hat-iso}G/T{\times}_W \widehat{T^m} {\longrightarrow}\widehat{{{\rm Hom}}}({{\mathbb Z}}^m,G)_1$$ is an isomorphism in (rational) cohomology. As shown in the proof of [@stafa.comm Theorem 6.3], the induced map $$\big(G/T{\times}_W \widehat{T^m} \big)/(G/T{\times}_W 1) {\longrightarrow}\widehat{{{\rm Hom}}}({{\mathbb Z}}^m,G)_1$$ induces an equivalence in rational cohomology. But the map $$G/T{\times}_W \widehat{T^m} {\longrightarrow}\big(G/T{\times}_W \widehat{T^m} \big)/(G/T{\times}_W 1)$$ is also an equivalence in rational cohomology, because the rational cohomology of $G/T{\times}_W 1{\cong}(G/T)/W$ is trivial, as noted above.
Baird’s formula (\[Baird\]), together with the Künneth Theorem, provides a bigraded Hilbert–Poincaré series for ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$, in which the coefficient of $q^i s^j$ records the rank of $[H^i (G/T)\otimes H^j(T^n)]^W$. We now compute this series.
\[thm: Poincare series of Hom\] The homology of the component of the trivial representation in the space of commuting $n$-tuples in $G$ is given by the following Hilbert–Poincaré series: $$\label{eqn: Hilb-Poincare series of Hom(Zn,G)1}
P({{\rm Hom}}({{\mathbb Z}}^n,G)_1;q,s)=A_W (q)\sum_{w\in W}
\left(\sum_{k=0}^n {n \choose k} \frac{(\det(1+sw)-1)^k}{\det(1-q^2w)} \right).$$ The Poincaré series of ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$ is given by $$\label{eqn: Poincare series of Hom(Zn,G)1}
P({{\rm Hom}}({{\mathbb Z}}^n,G)_1;q)=A_W (q) \sum_{w\in W} \frac{\det(1+qw)^n}{\det(1-q^2w)}.$$
Consider the bigraded series $$\label{PHomqs}
P({{\rm Hom}}({{\mathbb Z}}^n,G)_1;q,s)= \sum_{k=0}^n {n \choose k} A_W (q)
\left(\sum_{w\in W} \frac{(\det(1+sw)-1)^k}{\det(1-q^2w)} \right),$$ which in which the summands are the Hilbert–Poincaré series from Proposition \[prop: homology of hom hat\]. Since the terms in this sum match the terms from the stable decomposition of the space ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$ in equation (\[eqn: stable decomp Hom\]), we see that setting $q=s$ in (\[PHomqs\]) yields the Poincaré series of $\widehat{{{\rm Hom}}}({{\mathbb Z}}^m,G)_1$: $$\begin{aligned}
P({{\rm Hom}}({{\mathbb Z}}^n,G)_1;q)= &A_W (q)\sum_{k=0}^n {n \choose k}
\left(\sum_{w\in W} \frac{(\det(1+qw)-1)^k}{\det(1-q^2w)} \right)\\
=& A_W (q)
\sum_{w\in W} \frac{\sum_{k=0}^n {n \choose k} (\det(1+qw)-1)^k}{\det(1-q^2w)}.\end{aligned}$$ Setting $x = \det(1+qw)-1$ in the binomial expansion $$(1+x)^n = \sum_{k=0}^n {n \choose k} x^k$$ gives $$\sum_{k=0}^n {n \choose k} (\det(1+qw)-1)^k = \det(1+qw)^n,$$ yielding the simplified form (\[eqn: Poincare series of Hom(Zn,G)1\]).
Finally, we check that the bigrading in $P({{\rm Hom}}({{\mathbb Z}}^n,G)_1;q,s)$ agrees with the bigrading arising from the Künneth Theorem applied to (\[Baird\]). More precisely, we want to show that for each $i, j{\geqslant}0$, $$\label{qisj} {{\rm rank\,}}[H^i (G/T) \otimes H^j (T^n)]^W
= \sum_{k=0}^n {n\choose k} {{\rm rank\,}}[H^i (G/T) \otimes H^j (\widehat{T^k})]^W.$$ The spaces $G/T {\times}T^n$ form a simplicial space $G/T {\times}T^\bullet$ as $n$ varies, where the simplicial structure arises from the bar construction on $T$ (so the face and degeneracy maps are the identity on the $G/T$ factors). The main result of [@adem.cohen.gitler.bahri.bendersky] provides a stable splitting of the spaces $G/T{\times}T^n$: $$\gamma\co {\Sigma}(G/T {\times}T^n)
{\stackrel{{\simeq}}{{\longrightarrow}}}
\bigvee_{k=0}^n \bigvee_{{n\choose k}} {\Sigma}(G/T {\times}\widehat{T^k}).$$ In fact, the stable splittings from [@adem.cohen.gitler.bahri.bendersky] apply to any (sufficiently nice) simplicial space, and are natural with respect to simplicial maps. In particular, we can consider the simplicial maps $$G/T \longleftarrow G/T {\times}T^\bullet {\longrightarrow}T^\bullet,$$ where $G/T$ is viewed as a constant simplicial space, and $ T^\bullet$ is the bar construction on $T$. Naturality of the splittings yields a commutative diagram
(G/T) & &\
(G/T) & (G/T T\^n) & T\^n,\
in which the vertical maps are weak equivalences. Commutativity implies that the map on cohomology induced by $\gamma$ respects the Künneth decompositions of $H^p ({\Sigma}(G/T {\times}T^n))$ and $H^p ({\Sigma}(G/T {\times}\widehat{T^k}))$ ($p{\geqslant}1$), so that $\gamma$ induces isomorphisms $$\label{gamma*}\bigoplus_{k=0}^n \bigoplus_{{n\choose k}} (H^i(G/T)\otimes H^j( \widehat{T^k}))
{\stackrel{{\cong}}{{\longrightarrow}}} H^i (G/T)\otimes H^j ( \widehat{T^k})$$ for each $i,j{\geqslant}0$. Moreover, $W$ acts simplicially on $G/T{\times}T^\bullet$, so naturality implies that $\gamma$ is $W$–equivariant, and hence the maps (\[gamma\*\]) induce isomorphisms when restricted to $W$–invariants. This establishes the desired equality (\[qisj\]).
Since ${{\rm Hom}}({{\mathbb Z}}^n,G)_{1}$ is path connected, the constant term in its Poincaré series must be 1. This can be understood in terms of a classical theorem of Molien [@molien1897] (also see [@shephard1954finite p. 289]). Let $R=\mathbf{k}[x_1,\dots,x_r]$ and $W$ be as above, with $x_1,\dots,x_r$ in degree 1. Molien’s Theorem states that the number of linearly independent elements in degree $m$ in the invariant ring $R^W=\mathbf{k}[x_1,\dots,x_r]^W$ is given by the coefficients of the generating function $$\sum_{m=0}^{\infty} l_m q^m = \frac{1}{|W|}\sum_{w\in W} \frac{1}{\det(1-qw)} .$$ Moreover, Chevalley [@chevalley1955invariants] and Shephard–Todd [@shephard1954finite] give the following generating function for $R^W=\mathbf{k}[f_1,\dots,f_r]$ $$\sum_{m=0}^{\infty} l_m q^m =\prod_{i=1}^r \frac{1}{(1-q^{d_i})},$$ Therefore, after doubling the degree of $q$ one obtains the equation $$1 =\frac{\prod_{i=1}^r (1-q^{2d_i})}{|W|} \sum_{w\in W} \frac{1}{\det(1-q^2w)},$$ which corresponds to the constant term in the Hilbert–Poincaré series of the spaces of homomorphisms ${{\rm Hom}}({{\mathbb Z}}^n,G)_{1}$ in Theorem \[thm: Poincare series of Hom\].
By work of Gomez–Pettet–Souto [@gomez.pettet.souto], $$\pi_1 ({{\rm Hom}}({{\mathbb Z}}^n, G)_1) \cong (\pi_1 G)^n.$$ It follows that $$\label{GPS}{{\rm rank\,}}(H^1 ({{\rm Hom}}({{\mathbb Z}}^n, G)_1)) = n \cdot {{\rm rank\,}}(H^1 G).$$ This can in fact be seen directly from the formula in Theorem \[thm: Poincare series of Hom\] by analyzing the coefficient of $q$. Indeed, any non-zero coefficient of $q$ must come from one of the terms $\det (1+qw)^n$. We have $$\det (1+qw) = \prod (1+ \lambda(w)q),$$ where $\lambda(w)$ ranges over the eigenvalues of $w$ (counted with multiplicity). Hence the constant term of $\det (1+qw)$ is 1, and the coefficient of $q$ is the trace of $w$ (acting on $\mathfrak{t}^*$). It follows that the coefficient of $q$ in $P({{\rm Hom}}({{\mathbb Z}}^n, G)_1; q)$ is precisely $$\frac{n}{|W|} \sum_{w\in W} {{\rm trace\,}}(w) = n \langle \chi, 1\rangle = n\cdot {{\rm rank\,}}((\mathfrak{t}^*)^W),$$ where $\chi$ is the character of the representation of $W$ on $\mathfrak{t}^*$ and $\langle \chi, 1\rangle$ is the inner product of this character with the trivial 1-dimensional character. Since this representation is isomorphic to the natural representation of $W$ on $H^1 (T; {{\mathbb C}})$, we find that ${{\rm rank\,}}(H^1 ({{\rm Hom}}({{\mathbb Z}}^n, G)_1)) = n\cdot {{\rm rank\,}}(H^1 (T; {{\mathbb C}})^W)$. As discussed above, $H^*(G) {\cong}[H^\ast(G/T) \otimes H^\ast(T)]^W$, and the action of $W$ on $H^*(G/T)$ is the regular representation. Hence $$H^1 (G) {\cong}(H^1(T))^W,$$ and combining the previous two formulas yields (\[GPS\]).
Poincaré series of ${{\rm X}}(m,G)_1$ {#sec: Poincare series of X(q,G)}
=====================================
The following theorem describes the Poincaré series of ${{\rm X}}(m,G)_1$ for all $m \geq 2.$ Note that when $G$ is a compact connected Lie group, it follows from Bergeron–Silberman [@bergeron2016note] that ${{\rm X}}(m,G)_1 = {{\rm Comm}}(G)_1$.
Let $G$ be a reductive connected Lie group. Then the natural inclusion maps $$X(2,G)_1 \hookrightarrow X(3,G)_1 \hookrightarrow
\cdots \hookrightarrow X(m,G)_1 \hookrightarrow \cdots$$ all induce homotopy equivalences after one suspension. In particular, the Hilbert–Poincaré series of ${{\rm X}}(m,G)_1$, for all $m\geq 2$, is given by $$\label{eqn: Poincere series Comm 4}
P({{\rm X}}(m,G)_1;q,s,t) =
A_W (q) \sum_{w\in W}
\frac{1}{\det(1-q^2w)(1-t(\det(1+sw)-1))},$$ where $W$ is the Weyl group of a maximal compact subgroup $K{\leqslant}G$.
By Proposition \[prop: X(q,G) decomposition\], there is a stable decomposition of ${{\rm X}}(m,G)_1$ into a wedge sum $$\label{q-s}
\Sigma {{\rm X}}(m,G)_1 \simeq \Sigma
\bigvee_{k \geq 1} \widehat{{{\rm Hom}}}(F_k/\Gamma^m_k,G)_1.$$ Consider the commutative diagram of cofibrations
S\_[n,2]{}(G) & [[Hom]{}]{}([[Z]{}]{}\^n,G)\_[1]{} &([[Z]{}]{}\^n,G)\_[1]{}\
S\_[n,m]{}(G) & [[Hom]{}]{}(F\_n/\^m\_n,G)\_[1]{} & (F\_n/\^m\_n,G)\_[1]{},\
where $S_{n,m}(G)$ is the subspace of ${{\rm Hom}}(F_n/\Gamma^m_n,G)_{1}$ consisting of $n$-tuples with at least one coordinate the identity, and $m \geq 2$. The middle vertical map $$i\co {{\rm Hom}}({{\mathbb Z}}^n,G)_{1} \hookrightarrow {{\rm Hom}}(F_n/\Gamma^m_n,G)_{1}$$ is a homotopy equivalence: by [@bergeron], up to homotopy we can replace $G$ by a maximal compact subgroup, and by [@bergeron2016note], the map $i$ is a homeomorphism in the compact case. The first vertical map $$S_{n,2}(G) \hookrightarrow S_{n,m}(G)$$ is a homotopy equivalence by the Gluing Lemma [@RBrown], since these spaces can be built up inductively as pushouts of subspaces of the form $$\{(g_1, \ldots, g_n) \,:\, g_i =1 \textrm{ for all } i\in I\}$$ for various $I \subset \{1, \ldots n\}$, and on these subspaces the results from [@bergeron] and [@bergeron2016note] apply. Applying the Gluing Lemma again, the third vertical map $$\widehat{{{\rm Hom}}}({{\mathbb Z}}^n,G)_{1} \to \widehat{{{\rm Hom}}}(F_n/\Gamma^m_n,G)_{1}$$ is a homotopy equivalence as well, and the theorem follows from the decompositions (\[q-s\]).
Ungraded cohomology and $K$–theory {#ungraded-sec}
==================================
The *ungraded cohomology* $H^u (X;R)$ of a space $X$ with coefficients in $R$ refers to the ungraded direct sum of all the cohomology groups of $X$ as an $R$–module. It is a classical result [@borel1953cohomologie] that the ungraded cohomology of $G/T$ with rational coefficients, viewed as a $W$–module, is the regular representation ${{\mathbb Q}}W$. This alone yields some interesting consequences. Let $M$ be a graded ${{\mathbb Q}}W$-module. Then it follows that $(H^u(G/T;{{\mathbb Q}})\otimes M)^W {\cong}M.$ Applying this principle to formulas (\[Baird\]) and (\[Comm\]) yields the following result.
Let $G$ be a compact and connected Lie group. Then
1. the ungraded rational cohomology of the compact and connected Lie group $G$ is the same as the ungraded rational cohomology of its maximal torus: $$(H^u(G/T;{{\mathbb Q}})\otimes H^u(T))^W{\cong}H^u(T);$$
2. the ungraded cohomology of ${{\rm Hom}}(F_n/\Gamma^m_n,G)_1$ is given by $$H^u({{\rm Hom}}(F_n/\Gamma^m_n,G)_1;{{\mathbb Q}}) {\cong}H^u(T^n;{{\mathbb Q}})$$ for all integers $m\geq 2.$
It is quite interesting, although not a surprise, that the maximal torus $T\subset G$ plays a fundamental role in the topology of nilpotent representations into $G$, similar to the role it plays in the topology of $G$ from the classical theory of Lie groups. Recall that the rational cohomology of Lie groups can be described by the cohomology of a product of as many spheres of odd dimension as the rank of $G$ [@reeder1995cohomology]. It would however be very compelling to understand, in a topological manner, the regrading process that produces the cohomology of ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$ and ${{\rm Comm}}(G)_1$ from the cohomology of $T^n$ and $J(T)$, respectively.
\[tot-rk\] Let $G$ be a compact and connected Lie group of rank $r$. Then $$\begin{aligned}
\sum_{k\geq 0} {{\rm rank\,}}( H^k({{\rm Hom}}({{\mathbb Z}}^n,G)_1;{{\mathbb Q}}))=
\sum_{k\geq 0} {{\rm rank\,}}( H^k(T^n;{{\mathbb Q}}) )= 2^{nr}.\end{aligned}$$
Having identified the total rank of the cohomology of these spaces, one can ask if they satisfy Halperin’s Toral Rank Conjecture, which states that if a topological space $X$ has an almost free action of a torus of rank $k$, then the rank of the total cohomology of $X$ is at least $2^k$; see [@halperin1985 Problem 1.4]. In this setting, the conjecture predicts that if a torus $T'$ acts almost freely on the space of homomorphisms ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$, then the rank of $T'$ must be at least $nr.$ Hence it would be interesting to understand almost-free torus actions on these spaces.
Having identified the total rank of the cohomology of ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$, we can also identify its rational complex $K$–theory.
\[K-cor\] Let $G$ be a compact and connected Lie group of rank $r$. Then $$\begin{aligned}
{{\rm rank\,}}( K^i({{\rm Hom}}({{\mathbb Z}}^n,G)_1))= 2^{nr-1}.\end{aligned}$$ for every $i$.
Since ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$ is a finite CW complex, the Chern character provides an isomorphism from $K^i({{\rm Hom}}({{\mathbb Z}}^n,G)_1)\otimes {\mathbb{Q}}$ to the sum of the rational cohomology groups of ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$ in dimensions congruent to $i$ (mod 2). The fibration sequence $$G/T \times T^n {\longrightarrow}G/T \times_W T^n {\longrightarrow}BW$$ implies that the Euler characteristic of $G/T \times_W T^n$ is zero, and the same follows for ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$ by Baird’s result (\[Baird\]). Hence $$\begin{aligned}
\sum_{k \textrm{ even}} {{\rm rank\,}}( H^k({{\rm Hom}}({{\mathbb Z}}^n,G)_1) )=
\sum_{k \textrm{ odd}} {{\rm rank\,}}( H^k({{\rm Hom}}({{\mathbb Z}}^n,G)_1)), \end{aligned}$$ and the result follows from Corollary \[tot-rk\].
When $G$ is a product of groups of the form $SU(r)$, $U(q)$, and $Sp(k)$, Adem and Gomez [@AG-equivK Corollary 6.8] showed that the $G$–equivariant $K$–theory ring $K^*_G ({{\rm Hom}}({{\mathbb Z}}^n, G))$ is free as module of rank $2^{nr}$ over the representation ring $R(G)$ (for such $G$ we have ${{\rm Hom}}({{\mathbb Z}}^n, G)_1 = {{\rm Hom}}(Z^n, G)$). In light of Corollary \[K-cor\], it is natural to ask whether the map $R(G) \otimes K^*({{\rm Hom}}({{\mathbb Z}}^n,G)) \to K_G^* ({{\rm Hom}}({{\mathbb Z}}^n,G))$ is an isomorphism for these groups.
We now explain how to compute ${{\rm rank\,}}(H^u({{\rm Hom}}({{\mathbb Z}}^n,G)_1))$, and the Euler characteristic $\chi({{\rm Hom}}({{\mathbb Z}}^n,G)_1)$, directly from Theorem \[thm: Poincare series of Hom\], by setting $q=1$ or $-1$ in the formula $$\label{p}P({{\rm Hom}}({{\mathbb Z}}^n,G)_1; q) =
A_W (q) \sum_{w\in W} \frac{\det(1+qw)^n}{\det(1-q^2w)}.$$ To do so, we must compute the multiplicities of $\pm 1$ as roots of $A_W (q)$ and of $\det (1-q^2 w)$ ($w\in W)$. We have $$A_W (q) = \frac{1}{|W|}\prod_{i=1}^r (1-q^{d_i})(1+q^{d_i}),$$ so the multiplicity of $\pm 1$ as a root of $A_W (q)$ is $r = {{\rm rank\,}}(G)$. On the other hand, $$\det (1-q^2 w) = \prod_i (1-q^2 \lambda_i (w))^{n_i},$$ where the numbers $\lambda_i (w)$ are the eigenvalues of $w$ (acting on $\mathfrak{t}^\ast$) and $n_i$ is the dimension of the corresponding eigenspace. So the multiplicity of $\pm 1$ is the dimension of the eigenspace for $\lambda_i (w) = 1$, which is strictly less than ${{\rm rank\,}}(G)$ unless $w = 1$, in which case it is exactly ${{\rm rank\,}}(G)$. Canceling factors of $1\pm q$ in $$\frac{\prod_{i=1}^r (1-q^{d_i})(1+q^{d_i})}{\det(1-q^2w)}\det(1+qw)^n$$ and plugging in $q=\pm 1$, we see that all terms for $w\neq 1$ are zero.
Now consider what happens when we plug in $q=-1$ into (\[p\]). The term for $w=1$ contains the determinant of $I +qI= I-I = 0$ as a factor, so it too vanishes. This gives another proof that $\chi ({{\rm Hom}}({\mathbb{Z}}^n, G)_1) = 0$.
To calculate ${{\rm rank\,}}(H^u ({{\rm Hom}}({\mathbb{Z}}^n, G)_1))$, we must analyze the $w=1$ term of (\[p\]) more closely. This term has the form $$\begin{aligned}
\frac{\prod_{i=1}^r (1+q^{d_i})(1-q^{d_i})}{|W|} \cdot & \frac{\det((1+q)I)^n}{\det((1-q^2)I)}\\
= &\frac{\prod_{i=1}^r (1+q^{d_i})(1-q^{d_i})}{|W|} \cdot \frac{(1+q)^{rn}}{(1-q^2)^r}\\
= &\frac{\prod_{i=1}^r (1+q^{d_i})(1+q+q^2 +\cdots +q^{d_i-1})}{|W|} \cdot \frac{(1+q)^{rn}}{(1+q)^r}.\end{aligned}$$ Plugging in $q=1$, we find that $${{\rm rank\,}}(H^u ({{\rm Hom}}({\mathbb{Z}}^n, G)_1)) =
\frac{\left(\prod_{i=1}^r 2d_i \right) 2^{rn}}{|W| \cdot 2^r}
=2^{rn},$$ where we have used the equation $\prod_{i=1}^r d_i = |W|$.
Examples of Hilbert–Poincaré series {#sec: examples Poincare}
===================================
Using Theorem \[thm: Poincare series of Hom\] and Table \[table: characteristic degrees\], one can obtain explicit formulas for the Hilbert–Poincaré and Poincaré series described in this article. We demonstrate this for some low-dimensional Lie groups and for the exceptional Lie group $G_2$. We give only the formulas for the Poincaré series. The Hilbert–Poincaré series can then be deduced similarly from Theorem \[thm: Poincare series of Hom\] and are left to the reader.
The maximal torus of $SU(2)$ has rank 1 and the Weyl group is isomorphic to $W={{\mathbb Z}}_2$. The dual space $\mathfrak{t}$ is 1-dimensional, and $W$ is represented as $\{1,-1\} \subset GL(\mathfrak{t}^\ast)$. The only characteristic degree of $W$ is $d_1=2$. Therefore, we have $A_W (q)=(1-q^4)/2$ and $\det(1+qw)$ equals $1+q$ and $1-q$, for $w$ equal to 1 and -1, respectively, and $$\frac{\det(1+qw)^n}{\det(1-q^2w)}=
\begin{cases}
\ds\frac{(1+q)^n}{1-q^2} & \mbox{if $w=1$}, \\
\\
\ds\frac{(1-q)^n}{1+q^2} & \mbox{if $w=-1$}. \\
\end{cases}$$ We know the space of commuting $n$-tuples in $SU(n)$ is path connected, so it equals the component of the trivial representation. $$\begin{aligned}
P({{\rm Hom}}({{\mathbb Z}}^n,SU(2));q)&= A_W (q) \sum_{w\in {{\mathbb Z}}_2} \frac{\det(1+qw)^n}{\det(1-q^2w)}\\
&= \frac{1}{2}\bigg((1+q)^n (1+q^2) + (1-q)^n(1-q^2)\bigg), \end{aligned}$$ which agrees with calculations in [@bairdcohomology].
The maximal torus of $U(2)$ has rank 2, the Weyl group $W {\cong}{{\mathbb Z}}_2$ acts on $\mathfrak{t}^*$ via the matrices $$\left\{\left(
\begin{array}{cc}
1 & 0 \\
0 & 1 \\
\end{array}
\right), \left(
\begin{array}{cc}
0 & 1 \\
1 & 0 \\
\end{array}
\right)\right\},$$ and the characteristic degrees of $W$ are $d_1=1,d_2=2$. We know the space of commuting $n$-tuples in $U(n)$ is path connected, so again it equals the component of the trivial representation. We have $A_W (q)=(1-q^2)(1-q^4)/2$ and $$\frac{\det(1+qw)^n}{\det(1-q^2w)}=
\begin{cases}
\ds\frac{(1+q)^{2n}}{(1-q^2)^2} & \mbox{if $w=1$}, \\
\\
\ds\frac{(1-q^2)^n}{1-q^4} & \mbox{if $w\neq 1$}. \\
\end{cases}$$ Therefore, we get the following Poincaré series $$P({{\rm Hom}}({{\mathbb Z}}^n,U(2));q)=\dfrac{1}{2}\bigg((1+q)^{2n} (1+q^2) + (1-q^2)^{n+1}\bigg).$$ For example, we get $$\begin{aligned}
P({{\rm Hom}}({{\mathbb Z}}^2,U(2));q)&= 1+2q+2q^2+4q^3+5q^4+2q^5,\\
P({{\rm Hom}}({{\mathbb Z}}^3,U(2));q)&= 1 + 3q + 6q^2 + 13q^3 + 18q^4 +13q^5 + 6q^6 + 3q^7 + q^8,\\
P({{\rm Hom}}({{\mathbb Z}}^4,U(2));q)&= 1 + 4q + 12q^2 + 32q^3 + 54q^4 +56q^5 + 44q^6 + 32q^7\\
&\,\,\,\,\,\,\,\,\,\,\, + 17q^8+4q^9.\end{aligned}$$
The maximal torus has rank 3 and the Weyl group is the symmetric group on 3 letters $$W=\Sigma_3=\{e,(12),(13),(23),(123),(132)\}.$$ The characteristic degrees of $W$ are $1$, $2$, and $3$, so $$A_W (q) = \frac{1}{6}(1-q^2)(1-q^4)(1-q^6).$$ The matrix representations $W \leqslant GL(\mathfrak{t}^\ast)$ can be obtained by applying each permutation in $\Sigma_3$ to the rows of the $3\times 3$ identity matrix $I_{3\times 3}$. This can be done in general for the Weyl group $\Sigma_n$ of $U(n).$ For the transpositions $w=(12), (13), (23)\in W$ and for the 3-cycles we obtain the same determinants, respectively, since they are in the same conjugacy class. Hence we get $$\ds
\frac{\det(1+qw)^n}{\det(1-q^2w)}=
\begin{cases}
\ds\frac{(1+q)^{3n}}{(1-q^2)^3} & \mbox{if $w=e$}, \\
\\
\ds\frac{(1+q)^n(1-q^2)^n}{(1-q^2)(1-q^4)} & \mbox{if $w=(12), (13), (23)$}, \\
\\
\ds\frac{(1+q^3)^n}{1-q^6} & \mbox{if $w=(123),(132)$}. \\
\end{cases}$$ Therefore, the Poincaré series is given by $$\begin{aligned}
P({{\rm Hom}}&({{\mathbb Z}}^n,U(3)),q)
=\frac{1}{6} \bigg(
(1+q^2)(1+q^2+q^4)(1+q)^{3n} \\ &+
3 (1-q^6)(1+q)^n(1-q^2)^n +
2 (1-q^2)(1-q^4)(1+q^3)^n
\bigg).\end{aligned}$$ In particular, the following are the Poincaré series for pairwise commuting pairs, triples, and quadruples in $U(3)$, respectively: $$\begin{aligned}
P({{\rm Hom}}({{\mathbb Z}}^2,U(3)),q) = & 1+2q+2q^2+ 4q^3+7q^4+10q^5+11q^6+8q^7+8q^8\\
&+8q^9+3q^{10}\\
P({{\rm Hom}}({{\mathbb Z}}^3,U(3)),q)= & \,1 +3q + 6q^2 + 14q^3 + 30q^4 + 54q^5 + 73q^6 + 75q^7 + 75q^8\\
& \,\,\,\,+ 73q^9 + 54q^{10} + 30q^{11} + 14q^{12} + 6q^{13} + 3q^{14} + q^{15}, \\
P({{\rm Hom}}({{\mathbb Z}}^4,U(3)),q)= & \,1 +4q + 12q^2 + 36q^3 + 96q^4 + 212q^5 + 357q^6 + 472q^7 \\
& \,\,\,\,+555q^8+ 604q^9 + 574q^{10} + 468q^{11} + 330q^{12} + 204q^{13} \\
& \,\,\,\,+ 113q^{14} + 48q^{15} + 10q^{16}.\end{aligned}$$
Now consider the exceptional Lie group $G_2$, a 14 dimensional submanifold of $SO(7)$, which has rank 2 and Weyl group the dihedral group $W=D_{12}$ of order 12 with presentation $\langle s,t | s^2,t^6,(st)^2 \rangle.$ We can write $W=\{1,t,t^2,t^3,t^4,t^5,s,st,st^2,st^3,st^4,st^5\}$ as a subgroup of $GL(\mathfrak{t}^\ast)$ by setting $$s=\left(
\begin{array}{cc}
1 & 0 \\
0 & -1 \\
\end{array}
\right),
\text{ and }
t=\frac{1}{2}\left(
\begin{array}{cc}
1 & \sqrt{3} \\
-\sqrt{3} & 1 \\
\end{array}
\right).$$ The characteristic degrees of $W$ are 2 and 6 as given in Table \[table: characteristic degrees\]. The space ${{\rm Hom}}({{\mathbb Z}}^n,G_2)$ is not path-connected since it has an elementary abelian 2–subgroup of rank 3, which is non-toral. Setting $t=1$ and $q=s$ the Poincaré series of ${{\rm Hom}}({{\mathbb Z}}^n,G_2)_1$ is calculated using Equation \[eqn: Poincare series of Hom(Zn,G)1\]: $$\begin{aligned}
P(& {{\rm Hom}}({{\mathbb Z}}^n,G_2)_1;q)= 1 + \frac{1}{12}
\big[(2{q}^{14}-2{q}^{12}-2{q}^{2}+2)(-{q}^{2}+1)^{n-1}\\
&+ (2{q}^{12}-2{q}^{10}-2{q}^{8}+4{q}^{6}-2{q}^{4}-2{q}^{2}+2)({q}^{2}-q+1)^{n}\\
&+ (2{q}^{12}+2{q}^{10}-2{q}^{8}-4{q}^{6}-2{q}^{4}+2{q}^{2}+2)( {q}^{2}+q+1)^{n}\\
&+ ({q}^{12}-2{q}^{10}+2{q}^{8}-2{q}^{6}+2{q}^{4}-2{q}^{2}+1)(-1+q)^{2n}
+(-4{q}^{12}+4)(-{q}^{2}+1)^{n} \\
&+ ({q}^{12}+2{q}^{10}+2{q}^{8}+2{q}^{6}+2{q}^{4}+2{q}^{2}+1)(q+1)^{2n}\big].\end{aligned}$$ For example, for $n=1,2,3$ we obtain: $$\begin{aligned}
P({{\rm Hom}}({{\mathbb Z}}^1,G_2)_1;q)=&1+q^3+q^{11}+q^{14}=P(G_2;q),\\
P({{\rm Hom}}({{\mathbb Z}}^2,G_2)_1;q)=&1+q^2+2q^3+q^4+2q^5+q^6+q^{10}+2q^{11}+2q^{13}+3q^{14},\\
P({{\rm Hom}}({{\mathbb Z}}^3,G_2)_1;q)=&1+3q^2+3q^3+6q^4+9q^5+3q^6+3q^7+3q^8+2q^9+3q^{10}\\
& \,\,\,+3q^{11}+3q^{12}+9q^{13}+6q^{14}+3q^{15}+3q^{16}+q^{18}.\end{aligned}$$
It can be observed from the above formula for the Poincaré series that the *rational homological dimension* of the spaces of commuting $(2k-1)$-tuples in $G_2$ is the same as that for commuting $2k$-tuples, namely $12+4k$. However, it is not clear if there is a topological reason for this phenomenon.
The above formulas suggests that for odd $n$, ${{\rm Hom}}({{\mathbb Z}}^n,G)_1$ is a [rational Poincaré duality space]{}; in particular, the coefficients of the above Poincaré series are palindromic for $n$ odd. A geometric proof of this fact was provided to us by Antolín, Gritschacher, and Villarreal (private communication). Briefly, Baird’s theorem (as discussed in Section \[sec: topology Hom\]) reduces us to showing that for $n$ odd, the action of $W$ on the manifold $G/T {\times}T^n$ is [orientation preserving]{}. From the case $n=1$, where $H^*(G)$ is known, we can see that for each $w\in W$ the action of $w$ on $G/T$ is orientation-preserving if and only if the action of $w$ on $T$ is orientation preserving. Since $W$ acts diagonally on $T^n$, the result follows.
[10]{}
A. Adem, A. Bahri, M. Bendersky, F. R. Cohen, and S. Gitler. On decomposing suspensions of simplicial spaces. , 15(1):91–102, 2009.
A. Adem and F. R. Cohen. Commuting elements and spaces of homomorphisms. , 338(3):587–626, 2007.
Alejandro Adem and José Manuel Gómez. Equivariant [$K$]{}-theory of compact [L]{}ie group actions with maximal rank isotropy. , 5(2):431–457, 2012.
T. Baird. Cohomology of the space of commuting [$n$]{}-tuples in a compact [L]{}ie group. , 7:737–754, 2007.
T. Baird, L. C Jeffrey, and P. Selick. The space of commuting $n$-tuples in [[[SU]{}]{}]{}$(2)$. , 55(3):805–813, 2011.
M. Bergeron. The topology of nilpotent representations in reductive groups and their maximal compact subgroups. , 19:1383––1407, 2015.
M. Bergeron and L. Silberman. A note on nilpotent representations. , 19(1):125–135, 2016.
A. Borel. . , 57(1):115–207, 1953.
A Borel, R. Friedman, and J. Morgan. . Number 747 in Mem. Amer. Math. Soc. AMS, 2002.
R. Bott and H. Samelson. . , 27(1):320–337, 1953.
M. Brou[é]{}. , volume 1988 of [*Lecture Notes in Mathematics*]{}. Springer-Verlag, Berlin, 2010.
Ronald Brown. . BookSurge, LLC, Charleston, SC, 2006.
C. Chevalley. Invariants of finite groups generated by reflections. , 77(4):778–782, 1955.
F. R. Cohen and M. Stafa. . In [*[Configurations Spaces: Geometry, Topology and Representation Theory]{}*]{}, volume [14]{} of [*[Springer INdAM series]{}*]{}, pages [ 361–379]{}. [Springer]{}, [2016]{}.
F. R. Cohen and M. Stafa. . , 161(3):381–407, 2016.
J. G[ó]{}mez, A. Pettet, and J. Souto. On the fundamental group of [${\rm Hom}({\Bbb Z}^k,G)$]{}. , 271(1-2):33–44, 2012.
L. C. Grove and C. T. Benson. , volume 99 of [*Graduate Texts in Mathematics*]{}. Springer-Verlag, New York, second edition, 1985.
S. Halperin. , pages 293–306. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge 1985.
J. E. Humphreys. , volume 29. , 1992.
V. Kac and A. Smilga. . , pages 185–234, 2000.
Th. [Molien]{}. , 1897:1152–1156, 1897.
A. Pettet and J. Souto. Commuting tuples in reductive groups and their maximal compact subgroups. , 17(5):2513–2593, 2013.
M. Reeder. . , 41:181–200, 1995.
R. W. Richardson. Commuting varieties of semisimple [L]{}ie algebras and algebraic groups. , 38(3):311–327, 1979.
G. C. Shephard and J. A. Todd. Finite unitary reflection groups. , 6(2):274–301, 1954.
D. Sjerve and E. Torres-Giese. Fundamental groups of commuting elements in [L]{}ie groups. , 40(1):65–76, 2008.
T. A. Springer. Regular elements of finite reflection groups. , 25(2):159–198, 1974.
M. Stafa. . PhD thesis, University of Rochester, 2013.
Mentor Stafa. Poincaré series of character varieties for nilpotent groups. , 2017.
Bernardo Villarreal. Cosimplicial groups and spaces of homomorphisms. , 17(6):3519–3545, 2017.
E. [Witten]{}. . , 202:253–316, July 1982.
Edward Witten. Toroidal compactification without vector structure. , (2):Paper 6, 43 pp., 1998.
[^1]: Some authors (e.g. Grove and Benson [@Grove-Benson Chapter 7], or Humphreys [@humphreys1992reflection Chapter 3]) replace $V$ by its dual $V^*$ in this discussion.
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//
// Copyright (c) Microsoft. All rights reserved.
// Licensed under the MIT license.
//
// Microsoft Cognitive Services (formerly Project Oxford): https://www.microsoft.com/cognitive-services
//
// Microsoft Cognitive Services (formerly Project Oxford) GitHub:
// https://github.com/Microsoft/Cognitive-Speech-TTS
//
// Copyright (c) Microsoft Corporation
// All rights reserved.
//
// MIT License:
// Permission is hereby granted, free of charge, to any person obtaining
// a copy of this software and associated documentation files (the
// "Software"), to deal in the Software without restriction, including
// without limitation the rights to use, copy, modify, merge, publish,
// distribute, sublicense, and/or sell copies of the Software, and to
// permit persons to whom the Software is furnished to do so, subject to
// the following conditions:
//
// The above copyright notice and this permission notice shall be
// included in all copies or substantial portions of the Software.
//
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// MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
// OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
// WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
//
import UIKit
class ViewController: UIViewController, UITextFieldDelegate {
override func viewDidLoad() {
super.viewDidLoad()
}
func textFieldDidBeginEditing(_ textField: UITextField) {
textField.becomeFirstResponder()
}
func textFieldShouldReturn(_ textField: UITextField) -> Bool {
textField.resignFirstResponder()
if let text = textField.text {
DispatchQueue.global().async {
TTSVocalizer.sharedInstance.vocalize(text)
}
}
return false
}
}
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version https://git-lfs.github.com/spec/v1
oid sha256:e3bae3afdb8853e7a104d47e408c9c76538ad9fc938ad382363fc9fbaa9bb12c
size 1460
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Q:
How to set color of child QLabels while hover parent QFrame with QSS?
I'm trying to set the hover state color of 2 labels inside a QFrame with a stylesheet, but the frame takes the hover states regardless if there is an actual hover:
See screenshot:
I've got a QFrame with QLabels. I set the default colors to green and purple. While i hover the QFrame, the color of both labels should go red.
The exact same CSS does work with html, but i can't seem to get it to work with the QT stylesheets.
div{background-color:black; width:200px; height:100px;}
#label1{color: green;}
#label2{color: purple;}
div:hover #label1 {color: red;}
div:hover #label2 {color:red;}
A:
You could not do it with QLabel. It's limitation of QSS. Try to use QToolButton instead of QLabel (and customize QToolButton to look like QLabel).
Possible you shuld use QToolButton instead of QFrame too.
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27
For this people's heart has grown dull, and their ears are hard of hearing, and they have shut their eyes; so that they might not look with their eyes, and listen with their ears, and understand with their heart and turn— and I would heal them.'
New Revised Standard Version Bible, copyright 1989, Division of Christian Education of the National Council of the Churches of Christ in the United States of America. Used by permission. All rights reserved.
(New Revised Standard Bible Version Online)
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Categorizers are often used in data mining applications, where data contained in a database (or multiple databases) is analyzed and used for various purposes (such as to determine customer purchasing habits and preferences or for other purposes). A categorizer looks at a data item (e.g., article, product, customer, stock, support call, and so forth), and decides, based on information associated with the item (e.g., text, cost, date, duration, buying history, trade volume, and so forth), whether the item should be associated with a particular category or multiple categories. The categorizer decides which of a set of potential categories most likely applies, describes, or should be associated with the data item in question. A “category” refers to a label, annotation, or some other form of identifying indicator.
A categorizer has to be trained to enable the categorizer to perform categorization tasks. Various conventional algorithms exist to train categorizers. The categorizer implemented according to a given algorithm is associated with a set of parameters that the categorizer uses to make its decision. Often, the parameters are in the form of weights attached to the presence or absence of various features (words, purchases, and so forth). The parameters can be set manually (e.g., by an expert creating categorization rules) or deduced automatically from data. Most conventional techniques for training categorizers rely on the notion of a labeled training set, which is a set of training cases each annotated with a category (or multiple categories). The annotated category, or categories, constitutes the “correct answer” for each training case. The correctness of the categorizer is judged based on the errors the categorizer makes with respect to the categorizations of cases in the training set. Often the correctness will be judged based on the errors the categorizer makes with respect to a subset of the cases in the training set, the subset (called a “validation set”) not being used otherwise in training the categorizer.
With many conventional approaches, training a categorizer involves two separate stages. In a first stage, a training set is acquired. Then, the training set is used to train the categorizer. To acquire a training set, several approaches are used. A first approach involves acquiring training sets where the “correct answer” can be ascertained at some point after a prediction is made. However, this training approach may not be useful for circumstances where the correct answer cannot be objectively ascertained at some later point in time.
A second approach to acquire a training set involves obtaining desired information about a subset of observed cases by asking people to divulge information about themselves, such as purchasing information or other information. In one example, people can be asked to complete surveys. Alternatively, the information can be purchased from a third party or some other data source, or by physically measuring an object or plural objects. This second approach is usually expensive in terms of time and effort. Additionally, if surveys or other techniques of acquiring information are not designed properly, the training set acquired may not provide the desired level of accuracy in training categorizers.
In an approach used in the customer service call center context for acquiring a training set, customer support representatives are asked to choose categorizations (also referred to as issue paths) from a set of possibilities at the time that a customer call occurs. However, many customer support representatives may not be properly trained to recognize all possible answers, so that the categorization performed by such customer support representatives may not be accurate. Also, it may be expensive to train people to properly recognize all possible categorizations. Additionally, customer support representatives may not be properly motivated to spend the time to provide accurate categorizations, since the performance of customer support representatives may be measured on how quickly they resolve calls, not on how accurately they categorize the calls. Also, the set of possibilities may not include a category that accurately describes the customer call.
Another approach for acquiring a training set involves asking an expert to provide a correct answer for a randomly drawn subset of cases. The expert usually has to be prepared to distinguish among all possible categories (dozens or even hundreds of possible categories) to find the correct answer for each particular case. Also, an expert may not be qualified to recognize cases for certain categories. In addition, an expert may have to look at a large number of cases to accurately find a sufficient number of examples for certain types of categories. This training approach can be relatively expensive and may not produce sufficiently accurate results for training categorizers.
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Well thanks for some replies so far. Sadly i am in norway right now and only online occasionally through a phone to read and rarely reply so dont expect a long reply til like in a week.
As for the name and the potential offensive chatter i can only say that there likely exist only a very few word that aint offensive or generally got a negative conotation in any other region in the world. That is a general problem we got in any intercultural communications. Someone says something normal and neutral while another person takes it very offensive even though never intended by the senser of that message.
Click to expand...
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The Dumbest of the New #MinnesotaStateFair Food
I love fair food. Every year state fairs around the country bring us new and amazing fair foods. Some are always dumb, but mostly, they're awesome. Like the Belgian waffle made with bacon bits baked right in! But this year, the new dumbest food needs to be called out. And I'm just the guy to do it.At this year's Minnesota State Fair, the waffle is available...so are...
Bacon Fluffernutter: A Grilled cinnamon bun sandwch with a bacon, peanut butter and marshmallow cream filling. Find it at The Sandwich Stop on the west side of Clough St. between Carnes & Judson avenues
Two great examples of YUM! And the new list is full of yum (check it out here).
There's one really dumb one, tho..
Cheesy Nacho Corn on the Cob: Roasted corn on the cob lightly coated with crushed Dorito® corn chips and nacho cheese. Find it at Texas Steak Out on the west side of Underwood St. between Lee & Randall avenues.
So, what's up with roasting corn (best way to cook it!), then coating it in Doritos and nacho cheese? It's corn on the cob, mannnn! One of natures most perfect foods. Plain, or with a bit of butter and salt, it is exactly what it needs to be.
anna1311
Nacho chips need cheese, peanut butter does very well with jelly, and walk/don't walk have been saving lives for years. But corn on the cob?
COTC is a loner, only occasionally is it good at making friends. It took over 150 years for COTC to consider butter and salt its buddy. And here you are forcing chip and cheese on it?
Well, I say no. NO! This is where I draw the sand in the line, this far I will not cross.
Stop it already...and apologize to corn on the cob. He's quite understanding.
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concussions
Plante Show: Jacques Plante indicates where a puck hit his mask in May of 1970. Visiting is Mrs. Ruth Frohlichstein, a St. Louis neighbour of the goaltender’s who was also described by some contemporary newspaper captioneers as Plante’s “favourite bridge partner.”
“Did you ever see how they kill cattle?” Jacques Plante said. “They use a sledgehammer and the cattle just drop dead. That’s how the shot felt when it hit me. Without the mask I wouldn’t be here today.”
•
He was in the Jewish Hospital in St. Louis by then, early May of 1970. Eleven years had passed since he’d first donned his famous mask and started a hockey revolution. At 41, with seven Stanley Cup championships to his name, he was nearing the end of his playing days, but he wasn’t there yet. In his second year with St. Louis, he was a favourite of fans, and had helped the Blues reach their third consecutive appearance in the Stanley Cup finals.
Coach and GM Scotty Bowman had used three goaltenders through the early rounds of the playoffs. As the Blues prepared to face Boston in the finals, Bruins’ coach Harry Sinden said, “We recognize Plante as their number one goalie, and I never want to see him in the nets against us.” Bowman didn’t oblige: Plante was the starter on Sunday, May 3, as the Blues opened the series at home at The Arena.
•
Boston’s Johnny Bucyk scored in the first period, Jim Roberts tied the score for St. Louis early in the second. Then, as recalled next day in The St. Louis Post-Dispatch: “The 41-year-old Blues goalie was struck on the fiberglass mask above the left eye on a deflection of a shot by the Boston Bruins’ Fred Stanfield.” Another correspondent from the same paper had him “felled by a puck.”
UPI: “nearly had his head torn off Fred Stanfield’s screamer.”
Stanfield’s “brow-bender,” was Harold Kaese’s contribution, in The Boston Globe.
“The Boston player’s drive, which started out low, glanced off Phil Esposito’s stick and smashed into the veteran goalie’s mask, cracking it.” (Post-Dispatch)
He fell facedown. For two minutes he lay unconscious on the ice. Blues’ doctor J.G. Probstein and trainer Tommy Woodcock “worked on” him, the AP said. After about five minutes, they got him to his feet. He wobbled. They brought out a stretcher, but he wanted to skate off.
•
Ernie Wakely, 28, was the Blues’ back-up. He came in and did his best, but the Bruins kept coming, and won by a score of 6-1 with the aid of Bucyk’s hattrick.
•
Later, Dr. Probstein said it was a concussion and that while Plante’s condition was “satisfactory,” he’d be hospitalized “for an indefinite period of time.”
Plante’s first words (“after his head cleared”) were said to be: “The mask saved my life.”
He phoned his wife Jacqueline in Montreal. “She was relieved to hear from me,” he said later. She made a habit of not watching her husband on TV, but his children had the game on that night. It was almost when she passed through the room and noticed that Plante was absent from the net. Only then did the youngest son calmly mention what had happened.
•
Monday, a reporter among many visiting Room 223 at Jewish Hospital described the patient: “He had a whelp over his left eye and a slight cut and he smiled very little for his audience.”
Plante: “My head hurts every time I move it.”
•
Joe Falls was there, sports editor of The Detroit Free Press.
“Hockey writers,” he’d write, “happen to like old Jacques.”
He’s a good guy and always good for a story and so before we went up to see him I chipped in two bucks with a couple of Montreal writers and we bought him some flowers.
Jacques, he like that very much. He is a very sensitive man and was moved by the sentiment.
“Merci beaucoup, merci beaucoup,” he kept repeating.
Of course we’d signed the card: “From Fred Stanfield, with love.” He pretended not to notice.
•
Did Plante change rooms? Also Monday, Boston Globe columnist Fran Rosa found him asleep in 219. Barclay Plager had spent the night at the hospital, too, and he was the one to wake Plante up. The Blues defenceman was admitted after passing out on the Blues’ bench during the third period of Sunday’s game; now he was being released.
Plante talked about his future. “I don’t think I’ll be here next season.” With Buffalo and Vancouver coming into the league, summer would see an expansion draft. Plante didn’t think he’d be protected.
“Look,” he said, “Hall is three years younger than me and Wakely is the goalie of the future so what do they want with me?”
Plager had injured himself trying to hipcheck Boston’s Johnny McKenzie, damaging ribs when he bounced off and hit the boards. “The doctor didn’t exactly call it a fracture,” he confided. “He seems to think it was a separation. He said he hadn’t seen anything like it before and he’s going to write a paper on it.”
•
Monday, the Bruins held a light practice. Towards the end, coach Harry Sinden called the players together and led them in an off-key rendition of “Happy Birthday.” Fred Stanfield was turning 26.
•
Plante said he’d never been hit so hard. From his Montreal days, he recalled a tough night against Toronto: “Red Kelly shot and hit me in the face and the rebound went to Mahovlich. When I dove for the puck, it hit me where the mask protects my eyes. All I had that time was a nosebleed. No cuts.”
•
Dan Stoneking of The MinneapolisStar phoned Plante on Monday, said he sounded “groggy.” He also noted his “unmistakable French-Canadian accent.”
Another report from Plante’s bedside noted his “slight French accent.”
“I’ve got the world’s biggest hangover,” was another quote in another paper.
“Nothing ever felt like this,” Joe Falls heard. “My head, it is still spinning. I feel like I am floating. I feel like I want to throw up all the time.”
“I can still feel it in my head,” was another thing Plante said on the Monday. “The way I feel right now, I don’t feel like playing any more. That’s today. I don’t feel like eating or anything. Then I know as I get better I’m sure I’ll play again. But I do not know I will play in this series. I just don’t know.”
•
Also on Monday, Mrs. Ruth Frohlichstein dropped by. That’s her, above. The newspapers who ran photographs of her visit described her variously: as “a neighbourhood friend” and “Plante neighbour and favourite bridge partner.”
St. Louis coach and general manager Scotty Bowman had yet another goaltender waiting in the wings, 37-year-old Glenn Hall. Originally, Bowman had said he’d wanted to see how Plante played in the first game before he made any decisions on later starters. “He doesn’t play well in Boston,” Bowman said, “Glenn Hall plays well there.” With Plante out, the coach didn’t waver from that: Wakely would keep the net for Game Two in St. Louis before giving way to Hall when the series moved to Boston.
Bodycheck: St. Louis defenceman Al Arbour arrives on the scene in the moments after Fred Stanfield’s shot laid Plante low.
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Hat Trick: A hospitalized Reggie Fleming poses with Chicago policemen in his Hawk days in the early 1960s. In all his 14 years as a hockey professional, he never wore a helmet on the ice. (Image: Chris Fleming)
A version of this post appeared on page 132 of The Story of Canada in 150 Objects, published jointly by Canadian Geographic and The Walrus in January of 2017.
Reggie Fleming’s brain made its NHL debut somewhere in the middle of January of 1967—that, at least, is how the newspapers framed it.
By then, at age 30, six full seasons into his professional hockey career, Fleming knew the league’s penalty boxes better than its nets. He was a policeman, in the parlance, valued for his strength, bravado and professional surliness. Born with a black eye, a wag in the press wrote in 1961. He was a knuckleman, a bulldozer, a wild bucko. Reviews of his work are filled with references to his truculence and fistic prowess, his battle-scarred face.
But here was Emile Francis telling reporters that Fleming’s brain had caught up with his brawn. He wasn’t taking foolish penalties, only wise ones; he was scoring goals. “He’s playing it real smart,” said the coach of Fleming’s New York Rangers.
The truth is, Fleming could always play. He was just very, very good at being (as another chronicler put it) “one of hockey’s most brutal, meanest players.” Like hockey fighters before and since, Fleming was a beloved figure to teammates and fans alike, and much nicknamed: Reg The Ruffian, The Horse, Mr. Clean, Hardrock.
“He had a ferocious left hook, a decent right and a beautiful head butt,” Earl McRae would write in a famous profile that’s still known as one of the most penetrating pieces of hockey prose. “He fought all the tough ones: Howe, Fontinato, Lindsay, Harris, Ferguson — and seldom lost. His only clear defeats came in the last few years; he lost to age.”
Once he retired from the game, Fleming and his wild years might have lapsed into the background, the way the careers of workaday players do, enshrined on hockey cards and in the fond dimming memories of those who saw him play.
Something else happened. When he died in 2009, his family donated his brain for study by pathologists in Boston. What they discovered was a shock to both those who loved him and to the hockey world he’d inhabited for all his skating years. It not only shifted Fleming’s legacy, but it transformed — and continues to transform — the conversation about the calamitous toll hockey can take on those who play.
•••
If for some sinister reason you had to invent from scratch a comprehensive system for putting the human brain at risk, hockey might be what you’d conjure. The speed of the game, its accelerations and sudden stops, the potential for impacts in unyielding ice and boards, all those weaponized sticks and fists and elbows — just how is an innocent mass of neural tissue afloat in cerebrospinal fluid supposed to protect itself?
For much of the game’s history, guarding the head wasn’t exactly a priority. Toronto Maple Leafs’ star winger Ace Bailey underwent two brain surgeries in 1933 when he was knocked to the ice in Boston; he survived, though he never played again. Scared, many of his fellow NHLers donned helmets after that. Most of them soon vanished: they were cumbersome, hot. Even when they started to make a comeback in the late 1960s, hockey’s protocol for concussion cases remained simple: Got your bell rung? Shake it off, get back out there.
Not long before the Bailey incident, a pathologist in Newark, New Jersey by the name of Dr. Harrison Martland was studying boxers. In a landmark paper he published in 1928, he wrote about what every fan of the sweet science had witnessed, a fighter staggered by a blow to the head that didn’t knock him out acting “cuckoo,” “goofy,” “sluggy nutty” — “punch drunk.”
Dr. Martland was the first to propose that repeated blows to the head were doing deeper damages within fighter’s heads, and that it was cumulative, causing “multiple concussion hemorrhages in the deeper portions of the cerebrum.” His conclusions on “punch drunk” syndrome were limited — he may have been circumscribed, too, by the outrage he stirred among fight fans annoyed by his medical meddling in a sport they loved so well.
If Dr. Martland conceived that hockey players might be suffering similar injuries, he never wrote about it. Why wasn’t anyone making the connection between hockey and head trauma earlier? “I think because it’s an invisible injury,” says Dr. Ann McKee, a leading pathologist who heads Boston University’s Chronic Traumatic Encephalopathy Center. “Because players aren’t getting pounded in the head like they are in boxing. You see a hook to the jaw, you think, ah. It’s not a big jump for the layperson to say that might be hurting their brain.”
But hockey players? “They look invincible. There’s no blood, no pain, usually, so I think it was just — I think even the field of medicine didn’t recognize that these low-level hits, the ones that aren’t even causing concussions or any symptoms — just the repetitive impact injuries are leading to long-term loss of quality. We were all sort of oblivious.”
•••
Reggie Fleming didn’t mind talking about the role he played on the ice. He was open, affable — “a soft-spoken, mild-mannered quipster,” one interviewer wrote. Born in 1936 into a large Catholic family in east-end Montreal, he first stirred tempers as a star for the Junior Canadiens. His mother hated to watch. Seeing his cuts, the blood he wore home from games, she wanted to talk to coach Sam Pollock. Her son told her no. That’s my job, he told her, the only way I’ll make it.
Pollock went on to a management job with the big-league Canadiens, and Fleming eventually followed him there, first as a fill-in defenceman, always as a willing warrior when a teammate wanted revenging, or Canadiens felt a need to send one of hockey’s proverbial messages to their opponents. Although I guess there’s such a thing as message overload — as the story goes, Pollock traded Fleming to Chicago in the summer of 1960 after he roughed up a couple of teammates in practice.
Got To Knock Them Down: Reggie Fleming as a Hawk, c. the early 1960s.
Rudy Pilous was the coach of the Black Hawks when Fleming arrived in the early 1960s. “We can’t skate with most teams,” he was explaining around that time, “we’ve got to knock them down.” Fleming remembered his first game with his new team for the brawl he viewed from the bench. Unacceptable, Pilous told him: he should have been out there in the middle of the messing. “So I went out and fought,” Fleming recalled later. “I didn’t do it to be cruel, I was just following orders.”
His time in penalty boxes would eventually tick up to total 1,468 career minutes, or just over 24 hours. The websites that archive and revel in hockey’s fights don’t have a good fix on just how many he fought: at least 69, but maybe 96, and (almost certainly) many more. Still, he was relatively restrained compared to some of his heirs, the fearsome likes of Tie Domi (338 fights in 1,020 games) or Bob Probert (302 in 935).
A ledger of the punishments he dispensed and received during his career isn’t hard to coax out of the newspaper archives. There’s a whole angry thesaurus of NHL violence in there: Fleming struck Jack McCartan with a vicious right (1960), slugged Wally Boyer (1969). The NHL fined him $175 for charging a referee (1964). Other uproars he sparked by swiping a goalie (1967) and trying to cross-check Bobby Hull’s face (1972). Eddie Shack clotheslined Fleming with his stick (1964), sending him to hospital with a concussion and cuts that needed 21 stitches to close. He was incoherent when he left the rink, the papers reported.
Fleming was a proficient penalty-killer, too, and he was a key asset of Chicago’s when they won the 1961 Stanley Cup. One year, in Boston, he found the net 18 times.
“I would rather have been recognized as a guy who scored a lot of goals like a Bobby Hull or a Stan Mikita,” he’d say in 1979, aged 43. “But I did something I loved: played hockey. If it meant I had to be a tough guy, then I was a tough guy. I was brought up in an area where you had to fight to survive. I worked my butt off to get to the top in hockey, and I had to work twice as hard to stay there.”
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Gaye Stewart was the last Toronto Maple Leaf to lead the NHL in goalscoring: in 1945-46 he finished the season with 37 goals. Maybe that’s how you know the name. He was also the first NHLer to win a Stanley Cup before he won the Calder Trophy as the league’s best rookie, long before Danny Grant, Tony Esposito, or Ken Dryden got around to doing it. The Cup came in the spring of 1942, when he was 18; the Calder came the following year. He won a second Cup with the Leafs in 1947, then later the same year found himself on his way to Chicago in the big trade that brought Max Bentley to Toronto.
Stewart did fine for himself in Chicago, even as the team struggled. He was named captain of the Black Hawks for the 1948-49 season. It was in January of ’49 that he was photographed, above, with his goaltender’s son: Tom Henry was Sugar Jim’s two-and-a-half-year-old.
Stewart, 25, was only just back in Chicago following a hospital stay in Toronto. Struck by another puck, not the one depicted here, he’d left the Hawks’ January 8 game, a 3-3 tie with the Leafs, a few days earlier. Jim Vipond of The Globe and Mail was on hand to watch. In the second period, as he told it,
The ex-Leaf left winger was struck over the right eye by a puck lifted by Garth Boesch as the Toronto defenseman attempted to clear down the ice.
Stewart returned to action after a brief rest but collapsed in the shower after the game. After being removed to the Gardens hospital, his condition became so serious that a rush call was put in for an ambulance and arrangements made for an emergency operation.
Fortunately the player rallied soon after reaching Toronto General Hospital and surgery was not necessary. His condition was much improved last night [January 9], with the injury diagnosed as a bruise on the brain.
“I forgot to duck,” he was joshing by the time he was back in Chicago, as hockey players did, and do. Brain bruises, The Globe was reporting now. “I’m feeling fine,” Stewart said. “The accident was just one of those things. I expect I’ll start skating next week.” The Associated Press called it a concussion, and had the player’s side of the story to offer:
Stewart said that he when he returned to action in the game he felt tired. He remembered his mates coming into the dressing after the game, but then blacked out until he woke up in hospital.
There wasn’t much news, after that, of Stewart’s head or his recovery — not that made it into the newspapers, anyway. It was three weeks or so before he returned to play, back in Toronto again at the end of January, having missed six games. The two teams tied this time, too, 4-4. They met again in Chicago the following day. The Black Hawks won that one, 4-2, with Stewart scoring the winning goal.
All in all, it was ended up another fruitless year for Chicago. When the playoffs rolled around in March, they were on the outside looking in for the third consecutive season. When Tribune reporter Charles Bartlett buttonholed coach Charlie Conacher before he departed for Toronto, he asked him how he felt about his players.
“I’m not satisfied with any of them,” he answered. “It never pays to be satisfied with any team in sports. Creates a weak attitude. What I am pleased with, however, is the morale of the Hawks. I think their fifth place finish, and the fact that they won only won game less than Toronto will mean a lot when we start training at North Bay in September.”
He thought the team had played pretty well through December. But then Doug Bentley got sick and Stewart concussed, and Bill Mosienko and Metro Prystai had played that stretch of games with their wonky shoulders …
Conacher was headed home to his summer job — his oil business, Bartlett reported. A couple of Hawks were staying in Chicago for the duration, Ralph Nattrass to work in real estate and Jim Conacher at an auto agency. The rundown on their teammates as went their separate ways looked like this:
Goalie Jim Henry will join with his Ranger rival, Chuck Rayner, in operating their summer camp in Kenora, Ont. Red Hamill will go a talent scouting tour of northern Ontario. Doug Bentley and brother Max of the Leafs will play baseball and run their ice locker plant in De Lisle, Sask. Mosienko will return to Winnipeg, where he owns a bowling center with Joe Cooper, former Hawk defenseman.
Roy Conacher, who received a substantial bonus from the Hawks for winning the league’s scoring title, is headed for Midland, Ont., where he plans to open a sporting goods store. Gaye Stewart will run a soft drink agency in Port Arthur, Ont. A fish business will occupy Ernie Dickens in Bowmanville. Doug McCaig is enrolled in a Detroit accounting school. Adam Brown will assist his dad in their Hamilton filling station.
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As the Toronto Maple Leafs approach their centennial, the team is thinking of maybe updating, altering, or otherwise rejigging their logo — possibly. That was the news today, from the website sportslogos.net, quoting “sources” and hinting at plans for new sweaters, some of which may or may not be St. Patricks-green.
“Centennial plans will be announced in the New Year,” Dave Haggith, senior director of communications for Maple Leafs Sports and Entertainment, was telling Kevin McGran, from The Toronto Star. “We won’t be commenting until that time. There’s some fun stuff planned.”
Erik Karlsson is the most game-changing defenceman since Bobby Orr, said Adam Gretz this week at CBS Sports. And he is only getting better. (Italics his.)
The city of Edmonton commissioned artist Slavo Cech to fashion a small steel sculpture of a bison to present to former Oilers coach and GM and dynasty-builder Glen Sather this week. Cech, an Oilers fan, was honoured. “It’s not hockey-related,” he said, “but he’s more than hockey, right?”
“It’s difficult for me to put in my words the gratitude I feel for this honour,” Sather said on Friday night as a banner bearing his name lifted to the rafters of Rexall Place. “My sincere wish is that every one of you in this building gets to experience something, anything in your life that makes you feel like I’m feeling right now: the luckiest person on earth.”
Brand New: A Globe and Mail correspondent browsed the aisles at a Jordanian refugee camp earlier this week.
“I say,” tweeted Don Cherry, “what kind of a world would we live in without the police?”
Everyone who paid attention to the New York Rangers’ advanced stats saw their struggles coming, said someone, on social media, somewhere.
On the ice in Boston a week or two back, it’s possible that a Bruin winger, Brad Marchand, may have kneed a Ranger goaltender, Henrik Lundqvist, in the head. Boston coach Claude Julien said that Lundqvist was acting.
“Who would you rather have as a son,” said his New York counterpart, Alain Vigneault, “Henrik or Brad Marchand?”
David Akin of The Toronto Sun reported this week that hockey historian Stephen J. Harper has been sighted just twice in the House of Commons in Ottawa since he lost his day-job as prime minister of Canada in October. Akin writes:
His front-row seat is immediately to the left of the Speaker. That location lets the former prime minister enter and exit the House with little fanfare and without having to go near the press.
Paul Martin used the same seat after his Liberals lost the 2006 election.
To pass the albeit brief time he’s spent in the Commons, Harper arrived last time with a book: A just published biography by Eric Zweig of Art Ross, the Hockey Hall of Famer, NHL founding father, and long-time member of the Boston Bruins. Harper is a big hockey history buff.
Speaking of the Speaker, there’s a new one, Harperside: Nova Scotia Liberal MP Geoff Regan. He was on CTV’s Question Period today comparing the House of Commons to a hockey game.
“Only certain people get to play and it’s shaped in a lot of ways like an arena, with the two sides,” said Regan.
“And the people who aren’t actually in the game, they’d like to be in the game, and sometimes want to react to something, want to say something, the way you’d see at a game. But we’re not in a rink. We’re in the House of Commons.”
Sather was a master psychologist: that’s what a defenceman who worked his blueline, Steve Smith, told Jim Matheson of The Edmonton Journal. “You can take Roger Neilson, maybe the best Xs and Os guy, but he didn’t win, maybe because he didn’t have the players elsewhere. But Glen managed all these personalities in Edmonton. That’s a special art to manage all those guys and keep them happy. It’s like Phil Jackson in basketball. He understood his players in Chicago and what buttons to push.”
“It was the managing of people that made Glen really good.”
No Logo: Leaf fans weighed in at The Toronto Star earlier today, hours after word of a possible new logo emerged online.
Fighting is on its way out of the NHL, mostly everybody agreed this week — as they have been agreeing, more or less, since the season started in early October.
A kinder, gentler NHL is taking shape, said Dave Feschuk of The Toronto Star:
Given the rise in concern about the permanent nature of head injuries, there is also, in some eyes, a growing mutual awareness of the ultimate fragility of the human condition.
“Back in the day it used to be pretty malicious,” said Nazem Kadri, the only Leafs player who’s been penalized for fighting this season. “I think guys now respect the game and respect each other’s bodies and hope nobody gets seriously injured. I mean, anytime you see someone go down, it’s a frightening feeling because you know it could be you.”
Back in October, The Globe and Mail ran an editorial at that time to bid farewell to the age of the goon, noting that the NHL might even be showing signs of getting serious about dealing with its concussion problem. And yet:
… if players are still allowed to punch each other in the head during prolonged, staged fights, what’s the point? It is hypocritical to express concern for concussions on the one hand, and allow fighting on the other.
Pierre LeBrun of ESPN was wondering the same thing this week. “Shouldn’t we be asking why the NHL still allows bare-knuckle fighting?” he wrote in a piece you’re advised to read for yourself. “I’ve said this before, but it just seems so hypocritical to have introduced Rule 48 (illegal hit to the head) in 2010 but still allow bare-knuckle punches.”
More required reading: writing at Vice Sports, Dave Bidini’s take on the complicated cultural significance of fighting is a smart, counterintuitive view you haven’t heard before.
“He was a guy who brought everyone together; he seemed like a great button-pusher. Having that much skill and that much talent on your team isn’t an easy thing.”
Blackhawks preternatural confidence rubs off on new players
was a recent headline on a Mark Lazerus feature in Chicago’s Sun-Times in which the coach praised his captain, Jonathan Toews:
Joel Quenneville calls it a “competitive” nature, that the Hawks, perhaps more than any team he’s ever played for or coached, are better physically prepared and better mentally equipped to handle any situation. And he said it starts at the top, with the captain.
“As a coaching staff, you’re in a good spot knowing that the message is always there [about] doing things the right way,” Quenneville said. “Guys definitely notice Jonny’s intensity and professionalism right off the bat.”
Don Cherry gave another Postmedia interview, this one to Michael Traikos:
Q: Is it OK that enforcers have been run out of the league?
A: I never ever believed in guys that should sit there for two periods and then get thrown out there for a minute and fight. I never believed in that. I call that ‘Mad Dog Thinking.’ I remember with my Boston Bruins, we had more tough guys than any team and every one of them got 20 goals. That’s what they have now. Every one of them can play the game. And that’s the way it should be. You should never have a guy sitting on the bench like a mad dog.
A Nashville rookie named Viktor Arvidsson used his stick to neck-check a Buffalo defenceman, Carlo Colaiacovo. The former left the game with a five-minute major and a game misconduct on his record; the latter departed with what the Sabres at first classed, inevitably, as an upper body injury.
His coach, Dan Bylsma, had an update following the game: “Carlo is doing OK. He got the cross check to the throat. He did go to the hospital; he’s there now. I guess they’re saying he has a dented trachea.”
When you tell people how you learned to skate later in life, they’ll think you’re messing with them. They’re not going to believe how your handyman father would clear off the frozen creek across from your house after a snowstorm. You know how he walks out there at twilight with a big machete and floods the creek by chopping up a beaver dam? That’s not a normal thing. Other kids’ dads have Zambonis, or at least a hose. Your dad has a machete and some Canadian know-how. Thanks, Mr. Beaver.
Sometimes you just have to go out to the beaver dam with a machete and start chopping wood.
Brandon Prust of the Vancouver Canucks paid $5,000 last week to spear Boston’s Brad Marchand in the groin.
“Best money I’ve ever spent,” Prust told reporters.
Why did he do it? “It was frustrations,” Prust explained. “It happens out there. I wasn’t trying to injure him. I was just coming back as the puck was coming back up the boards. On my swing by, I got my stick active.”
“It wasn’t that hard,” he said. “He sold it pretty good. I saw him laughing on the bench afterwards.
Marchand, for his part, was only too glad to talk about what happened to Amalie Benjamin of The Boston Globe. “I think it was Prust,” he said. “I didn’t really see who did it when it happened, but just kind of gave me a jab, got me in the fun spot.”
Assuming it was who it may have been, Marchand understood. “Honestly,” he continued, “even if he wasn’t fined, I wouldn’t have been upset. It’s fine that he is, but I wouldn’t want to see him lose that much money over what happened. I think suspensions are worthy when guys get hurt or it’s a really bad shot. Like I said, I’ve done that before, lots of guys do that all the time. It is what it is. It’s part of the game.”
On he went, and on:
“It clearly doesn’t feel good,” Marchand said. “It hurts, so whether you’re upset at someone or you want to take a shot, it’s an easy place to target. You know it’s going to hurt. I think that’s why a lot of guys do it.
“A lot of guys take cheap shots, when there’s that much emotion in the game and it happens all the time. If you’re down by a few goals, if you’re having a bad game, someone takes a shot at you, someone says the wrong thing, guys get upset and they take shots at guys. I think it’s just human nature.
“There’s a lot of good players that take jabs at guys. People can say whatever they want. I’m not overly upset about what happened. It’s part of the game. I’ve done it. I’m sure he’s done it before. I’m sure it won’t be the last. It won’t be the last time I do it. It is what it is. It’s part of hockey.”
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Hello, Canada, and hockey fans in the United States and Newfoundland: Franklin Arbuckle painted Foster Hewitt at work for the cover of Maclean’s that found newsstands on March 3, 1956.
Max Pacioretty, Montreal’s leading scorer, was in the news this week, having left a game last week and unsettling Canadiens fans everywhere. Sniper was a word used to describe him; we learned that his nicknames include Pax and Max Pac. Midweek, the nhl.com was reporting:
Pacioretty appeared to sustain an upper-body injury at 5:48 of the first period against the Florida Panthers on Sunday when he hit his head against the boards after being checked by Panthers defenseman Dmitry Kulikov and then getting his feet tangled with Panthers defenseman Alex Petrovic.
A former Hab, Sergio Momesso, who now works on the radio in Montreal for TSN690 said he’d seen Pacioretty looking, quote, groggy and not good.
From the Canadiens:
Head coach Michel Therrien confirmed that Max Pacioretty met with team doctors on Wednesday morning. He will not play against Detroit on Thursday night or in the regular season finale on Saturday night in Toronto. Pacioretty’s condition will be re-evaluated next week. Therrien did not rule out Pacioretty returning to the lineup as soon as next week, too.
“We know exactly what he has,” Therrien told reporters on Thursday. “He won’t play the next two games. He will be re-evaluated next week and we’ll have more details next week.”
At habseyesontheprize.com, Andrew Berkshire was among those fearing the worst:
Max Pacioretty has been involved in 34.5% of the Canadiens’ goals, among the highest marks of any player in the NHL. Can the Habs survive without him?
Answer: nope, sorry, don’t think so,
Saturday. Pacioretty skated in Montreal while his team prepared for its game in Toronto. Therrien: “He’s reacted really well to the treatment that he got.”
Patrick Kane skated this week in Chicago. “He’s progressing real well,” commented his coach, Joel Quenneville. Kane’s collarbone was broken on the left side on February 24. Quenneville: “Every day it seems like he’s getting a little stronger. His skating has always been fine, he’s handling the puck extremely well. It’s good signs every day, seeing the progress.”
The Philadelphia Flyers handed out their in-house trophies today before the last game of their non-playoff season. As team MVP, Jacob Voracek won the Bobby Clarke Trophy (reported Sam Carchidi of the Philadelphia Inquirer) while Mark Streit got the Barry Ashbee as the as top defenceman. The Pelle Lindbergh Memorial Trophy (most improved) went to Chris VandeVelde. Streit also took the Yanick Dupre Class Guy Memorial Award. Claude Giroux won the Toyota Cup, reflecting his accumulation of three-star selections over the course of the season.
“We know how to play in order to have success,” said Boston winger Milan Lucic on the last day of the regular season, as his team tottered on the lip of the playoffs, “we’ve got to bring that here tonight and hope that things go our way.” Continue reading →
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In The Paint: Montreal’s Classic Auctions closed out another big sale last week. Big-money items included a 1980 Miracle-On-Ice U.S.A. number-23 sweater worn by Rob McClanahan (sold for US$$86,220, including a buyer’s premium); four different gold-and-diamond Stanley Cup rings of Billy Smith’s (one of which went for US$ $36,563); a Herb Cain game-worn woolen number-four Bruins’ sweater (US$25,937); and one of Andy Warhol’s iconic 1984 “Wayne Gretzky #99” screenprints signed by both artist and subject (US$$8,249). Also on the block was this 1964 oil painting by brushtender Jacques Plante. Bidding started at US$300 with the final price climbing to US$2,014.
Carey Price is 6 foot 3, reported The Globe and Mail’s Sean Gordon, and his thighs are as stout as 50-year-old timber.
From Stan Butler, who coaches the OHL’s Brampton Battalion, came a tweet last week:
Evgeni Malkin told Sport Express about some of the keys to the success he’s been enjoying in his ninth NHL season. Language was one of them: as soon as English ceased to be a problem, he said, came “looseness and confidence.” Also, he has a good Russian cook now, who prepares soups and pancakes. His fridge, now, is filled with “tasty and familiar food, not the typical American chips and stuff.”
“Thank God,” said Malkin, “all is well and I am happy in life.”
When, last week, Philadelphia GM Ron Hextall traded a defenceman, Kimmo Timonen, to Chicago’s Blackhawks, he said that he was sending them not just a skilled and experienced player, “but a damn good person, too.”
“I’m comfortable and strong,” said Toronto captain Dion Phaneuf.
An entomologist who discovered a new species of wasp in Kenya’s Teita Hills of Kenya, being a Bruins fans, named it Thaumatodryinus tuukkaraski, writes Carolyn Y. Johnson of The Boston Globe. And so Tuukka Rask —
“This species is named after the acrobatic goaltender for the Finnish National ice hockey team and the Boston Bruins, whose glove hand is as tenacious as the raptorial fore tarsus of this dryinid species,” the authors wrote in the paper, which has been accepted and will be published in April.
Robert S. Copeland, an entomologist at the International Centre of Insect Physiology and Ecology in Nairobi who grew up in Newton, said naming this particular wasp after Rask reflected his admiration for a player who has “had an outstanding career in one of the most difficult positions in sports.”
The name also fit for other reasons. The project that led to the discovery of the species was underwritten by the government of Finland, Rask’s home country. The wasp is yellowish and black, similar to the Bruins’ colors. The grasping front legs of the female have claspers that look vaguely like goalie gloves.
Alert: if you happen to be browsing Player Bios filed by the Detroit Red Wings, and you come across captain Henrik Zetterberg’s he does not, in fact, collect smoke-detectors. The actual wording is this:
OTHER: Hosts guests from local children’s hospitals at DRW home games in his Zetterberg Foundation Suite… Serves as the team spokesperson for the annual smoke detector collection…Scored the Stanley Cup-clinching goal in 2008.
Last month, while Michal Neuvirth was still a goaltender for the Buffalo Sabres, he paid US$2,000 to dive and embellish his distress after Nashville’s Mike Santorelli took a penalty for running into him. Neuvirth, who was trade on Monday to New York’s Islanders, is the first goaltender to pay the price, apparently; he’ll pay more if he does it again, says the NHL, up to a maximum of $5,000.
Headline on an NBC Sports item ahead of Detroit’s game in Anaheim Monday last:
Zetterberg (Jamie Benn head punch) doubtful for tonight
Two days earlier in Dallas it happened, during the second period of a 7-6 win by the Red Wings. Benn took a roughing minor for the punch; Zetterberg played on until the end of the period and missed the third.
Of the game, Pavel Datsyuk said, “We play not really good today. We happy we win.”
Regarding Zetterberg, reporters in a scrum that included Mike Heika of The Dallas Morning News asked coach Mike Babcock whether his captain might have a concussion. “Yeah,” he said, “I don’t really know that. I didn’t talk to the guys. Let’s just say he’s got an upper-body injury and I don’t know if he’s fine tomorrow or not fine tomorrow, so we’ll see him tomorrow. We’ll practice tomorrow and then play the following day, so we’ll see where he’s at.”
“You go through this whole range of feelings when things aren’t going well,” said Cam Neely, president of the Boston Bruins, for whom he once used to skate the wing. The team’s season, if you haven’t been paying attention, has been lacklustrous. “I’ve been frustrated. I’ve had some anger tossed in there. And now, for the first time, I’ve landed on disappointed.”
Detroit GM Ken Holland: “He got punched in the head, didn’t feel great after the game, so anytime you have any kind of head injury, you don’t feel good and we’re not going to put you in the lineup.”
From Ken Dryden, writing in this month’s Walrus about Scotland’s referendum, tells of visiting the house in Harwick, in Scotland, that his ancestors left in 1834 to come to Canada. A man named Norman Huggan lives there now; afterwards, Dryden went to a local pub called the Waverley.
Longtime NHL referee (ret’d) Kerry Fraser wrote about Benn’s punch in his column on TSN.ca, specifically the question of why wasn’t the Stars’ captain punished with more than the merest minor penalty.
Historically and currently a punching motion with the hand or fist, with or without the glove on the hand, normally directed at the head of an opponent is roughing. Roughing is a minor altercation that is not worthy of a major penalty to either participant. (An altercation is a situation involving two players with at least one to be penalized). A minor penalty shall be imposed on a player who strikes an opponent with his hand or fist. (Rule 51.1)
In reviewing this altercation that resulted from a Detroit end zone face-off, the initial push-off and subsequent glove punch that Jamie Benn administered to the head/helmet of Henrik Zetterberg fell completely within the parameters of this roughing rule. The altercation began as a result of Zetterberg tying up Benn with a stick between the legs and a left-hand shoulder wrap after the Stars captain won the draw back toward the top of the face-off circle.
Benn attempted a ‘crow-hop’ to break free from Zetterberg’s restraint/interference to get to the front of the net without success. As the shot and eventual save was made by Jimmy Howard, Benn created separation with a forearm push and subsequent glove punch to the lower right side of Zetterberg’s helmet. Unless there is a change in the rule and operating procedure, this play will continue to be enforced as a minor penalty for roughing. Continue reading →
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Minnesota’s Ryan Suter paid US$81,058.72 to elbow Pittsburgh’s Steve Downie in the head. That was a while ago. More recent was Zac Rinaldo, of Philadelphia, for whom the price of charging Kris Letang from the Penguins, and also boarding him, was US$73,170.72.
And Dan Carcillo? Of Chicago? For him, the cost of cross-checking Winnipeg’s Mathieu Perreault and upper-body-injuring him was US$40,243.92
Sports Illustrated wondered: Are the New York Islanders for real? (Answer: yes.)
It’s a while back, now, hard to recall, but Randy Carlyle was coaching the Toronto Maple Leafs earlier this year. On his last day on the job, he was in North Bay, Ontario, when GM Dave Nonis called him to set up a meeting early next morning in Toronto. “I’m not going to drive five hours back and through a snow storm to get fired,” Carlyle told him. “You might as well do it now.”
“We’re trying,” Toronto’s Phil Kessel has said subsequently, of the losing Leafs. “I don’t know if people see that. We are trying. I don’t know. We can’t find it right now.”
At The Walrus, the new editor, Jonathan Kay, profiled the Kelowna man who steered a 10,000-pound truck to the 2012 World Freestyle Championship at the Monster Jam Finals in Las Vegas. “It’s hard to imagine a more gentlemanly monster trucker than Cam McQueen,” he wrote. “He’s like the Jean Béliveau of car crushing.”
Via Aaron Portzline, meanwhile, of The Columbus Dispatch, we got to know the Blue Jackets All-Star goaltender Sergei Bobrovsky, who comes from Novokuznetsk in Russia, where the average temperature in January is -18 degrees and (quote) living in the Siberian city of 600,000 is neither easy nor glamorous.
As a six-year-old there, Bobrovsky wanted to play in goal. When his family couldn’t afford to buy equipment, his coach, Alexei Kitsyn, bought (says Portzline) “some bulk leather.”
“He made the equipment for me,” Bobrovsky said, his eyes getting big with emphasis. “He made it. By himself. By his hands. He made the pads and the glove. My parents bought me the rest of it.” …
“It sounds crazy,” Bobrovsky said. “If you know how some kids today get the best gear, how much money they spend … and that’s how it started for me.”
Another Columbus All-Star was ruminating this week, Nick Foligno, son of former NHLer Mike. “My dad has always said that if you treat the game of hockey well, it will treat you well,” Nick said. “He’s been bang-on with that.”
“Morale is good,” said the Leafs’ new coach, Peter Horachek, at some point. Continue reading →
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From Greystone Books. Available in bookstores in Canada and the United States. 2014 Hockey Book of the Year, as per www.hockeybookreviews.com. "Funny, smart, unlike any hockey book I've read," Dave Bidini has said; "Joycean," Charles Foran called it. "It’s rare to find a book that makes me proud to be Canadian," is what Michael Winter wrote: "A funny, myth-busting, life-loving read."
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poem
Thankful that I never
played against
Wayne Gretzky
in an NHL playoff series;
I probably would have had to break his hand.
I would not have wanted to injure Gretzky, mind you;
I loved the guy.
I never touched him on the ice
in a regular season game.
I had too much respect
for how he played
and how he carried himself.
But I can say without question
I would have tried to hurt him
if we had been matched up
in the playoffs.
In my mind,
there are no friends
in a playoff series
I’m not talking about
elbowing someone in the head
or going after someone’s knees.
I’m talking about a strategic slash.
To me, slashing someone’s hand or breaking someone’s fingers was nothing.
It was part of the game.
Broken hands heal.
Fingers heal.
The pain that comes from losing does not.
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Kate Bush has penned an emotional tribute to choreographer Lindsay Kemp.
Kemp, who famously collaborated with David Bowie as well as Bush herself, died while in Italy last week at the age of 80. David Haughton, his closest friend and collaborator for 45 years, said Kemp had remained busy and active right till the end, saying “he suddenly said he felt ill, and a minute and a half later he was gone.”
Having worked closely with Bowie, Kemp went on to mentor Bush after she saw his 1974 show “Flowers” and asked him to work with her. Following his passing, Bush described Kemp as “a truly original and great artist of the stage,” adding, “to call him a mime artist is like calling Mozart a pianist.”
The statement appeared on Bush’s official website under a post titled “a message for Lindsay”. Here it is in full:
“The world has lost a truly original and great artist of the stage. To call him a mime artist is like calling Mozart a pianist. He was very brave, very funny and above all, astonishingly inspirational. There was no-one quite like Lindsay. I was incredibly lucky to study with him, work with him and spend time with him. I loved him very much and will miss him dearly. Thank you, dear Lindsay.”
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