text:
package com.opengamma.engine.depgraph;

import static org.testng.Assert.fail;
import static org.testng.AssertJUnit.assertEquals;

import java.util.Collection;
import java.util.HashMap;
import java.util.Map;

import org.testng.annotations.Test;

import com.opengamma.engine.function.CompiledFunctionDefinition;
import com.opengamma.engine.function.FunctionDefinition;
import com.opengamma.engine.function.exclusion.AbstractFunctionExclusionGroups;
import com.opengamma.engine.function.exclusion.FunctionExclusionGroup;
import com.opengamma.engine.function.exclusion.FunctionExclusionGroups;
import com.opengamma.engine.function.resolver.FunctionPriority;
import com.opengamma.util.test.TestGroup;
import com.opengamma.util.test.TestLifecycle;

/**
 * Tests the function exclusion group mechansim.
 */
@Test(groups = TestGroup.UNIT)
public class DepGraphExclusionTest extends AbstractDependencyGraphBuilderTest {

  private static abstract class Group extends AbstractFunctionExclusionGroups {

    protected abstract String getKey(int functionId);

    @Override
    protected String getKey(final FunctionDefinition function) {
      return getKey(Integer.parseInt(function.getUniqueId()));
    }

  }

  private DependencyGraph test(final FunctionExclusionGroups exclusions) {
    TestLifecycle.begin();
    try {
      final DepGraphTestHelper helper = helper();
      final Map<CompiledFunctionDefinition, Integer> priority = new HashMap<>();
      priority.put(helper.addFunctionRequiringProducing(helper.getRequirement1Bar(), helper.getValue1Foo()), 5); // 0
      priority.put(helper.addFunctionRequiringProducing(helper.getRequirement2Bar(), helper.getValue1Bar()), 5); // 1
      priority.put(helper.addFunctionRequiringProducing(helper.getRequirement2Foo(), helper.getValue2Bar()), 5); // 2
      priority.put(helper.addFunctionProducing(helper.getValue1Foo()), 1); // 3
      priority.put(helper.addFunctionProducing(helper.getValue1Bar()), 1); // 4
      priority.put(helper.addFunctionProducing(helper.getValue2Bar()), 1); // 5
      priority.put(helper.addFunctionProducing(helper.getValue2Foo()), 1); // 6
      final DependencyGraphBuilder builder = helper.createBuilder(new FunctionPriority() {
        @Override
        public int getPriority(final CompiledFunctionDefinition function) {
          return priority.get(function);
        }
      });
      builder.setFunctionExclusionGroups(exclusions);
      builder.addTarget(helper.getRequirement1Foo());
      return builder.getDependencyGraph();
    } finally {
      TestLifecycle.end();
    }
  }

  public void noGroups() {
    final DependencyGraph graph = test(new FunctionExclusionGroups() {

      @Override
      public FunctionExclusionGroup getExclusionGroup(final FunctionDefinition function) {
        return null;
      }

      @Override
      public boolean isExcluded(final FunctionExclusionGroup current, final Collection<FunctionExclusionGroup> existing) {
        return false;
      }

      @Override
      public Collection<FunctionExclusionGroup> withExclusion(final Collection<FunctionExclusionGroup> existing, final FunctionExclusionGroup newGroup) {
        // Should never be called
        fail();
        throw new UnsupportedOperationException();
      }

    });
    assertEquals(4, graph.getSize()); // 6 -> 2 -> 1 -> 0
  }

  public void singleGroups() {
    final DependencyGraph graph = test(new Group() {
      @Override
      protected String getKey(final int function) {
        return Integer.toString(function);
      }
    });
    assertEquals(4, graph.getSize()); // 6 -> 2 -> 1 -> 0
  }

  public void group01group2() {
    final DependencyGraph graph = test(new Group() {
      @Override
      protected String getKey(final int function) {
        switch (function) {
          case 0:
          case 1:
            return "A";
          case 2:
            return "B";
          default:
            return null;
        }
      }
    });
    assertEquals(2, graph.getSize()); // 4 -> 0
  }

  public void group0group26() {
    final DependencyGraph graph = test(new Group() {
      @Override
      protected String getKey(final int function) {
        switch (function) {
          case 0:
            return "A";
          case 2:
          case 6:
            return "B";
          default:
            return null;
        }
      }
    });
    assertEquals(3, graph.getSize()); // 5 -> 1 -> 0
  }

  public void group02() {
    final DependencyGraph graph = test(new Group() {
      @Override
      protected String getKey(final int function) {
        switch (function) {
          case 0:
          case 2:
            return "A";
          default:
            return null;
        }
      }
    });
    assertEquals(4, graph.getSize()); // 6 -> 2 -> 1 -> 0
  }

  public void group014() {
    final DependencyGraph graph = test(new Group() {
      @Override
      protected String getKey(final int function) {
        switch (function) {
          case 0:
          case 1:
          case 4:
            return "A";
          default:
            return null;
        }
      }
    });
    assertEquals(1, graph.getSize()); // 3
  }

}

redpajama_set_name: RedPajamaGithub


text:
Fmr NYC Police Commissioner Bernie Kerik remembers Sept. 11, 2001
Former New York City Police Commissioner Bernie Kerik remembers standing in downtown Manhattan on Sept. 11, 2001, looking up at the burning buildings and thinking, "What the hell just happened?"
"About three or four minutes after I got there, there was this enormous explosion," Kerik told Dean Obeidallah Friday. "Nobody ever imagined this kind of attack… We didn't realize we under attack until the second plane hit."
Kerik and Mayor Rudy Giuliani learned about the simultaneous attacks on the World Trade Center and Pentagon after phoning Vice President Dick Cheney. When they hung up the call with the White House, which was in the process of evacuating, Kerik remembers "the building we were in started to move, started to shake."
"The door slammed open, Chief [James] Esposito … he yells 'get down, it's coming down!' … it was tower 2. It was imploding and it imploded basically on top of us."
Kerik, Giuliani and the entire cabinet were "trapped inside 75 Barclay for about 25 minutes" before they were able to make their escape onto Church Street in downtown Manhattan.
"We called for the evacuation of City Hall, Police Headquarters, the Empire State Building — every major building we could think of, we had to make sure they were evacuated. We didn't know how many more planes there would be, did they have ground attacks planned, were they going to do something in the mass transit system — we knew none of this."
Fifteen years later, two images remain ingrained in Kerik's memory; witnessing people jumping off the side of the tower and walking into NYPD headquarters to meet with the families of the 23 members of the force that were missing.
"It was a horrific time for us," Kerik said. "No department in the country had taken those kind of loses."
In remembrance of the 15th anniversary of September 11th, SiriusXM Insight Ch. 121 will air special programming of "the Dean Obediallah Show" with interviews including with Kerik, Fareed Zakaria, Soledad O'Brien, Ayman Mohyeldin, Joy Reid and Bill Carter on Saturday, September 10th at 10 am ET and Sunday, September 11th at 12 am ET, 8 am ET and 4 pm ET
News, News and Issues, Politics
Urban View Votes hits the road to mobilize the youth vote
Olivier Knox named new chief Washington correspondent for SiriusXM
Honoring Dr. King's life and legacy, 50 years later

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: parsing dates in R I have this input: 2020-03-11 and I want to return 03-11, How can I do that in R?. For example, if I want to have only month, I can assign the month this way: Month=lubridate::month(data)

A: Here are a few ways. All are vectorized, i.e. x can be a vector of such strings. No packages are used.
x <- "2020-03-11"  # input

substring(x, 6)

sub("\\d+-", "", x)

trimws(trimws(x, "left", "\\d"), "left", "-")

format(as.Date(x), "%m-%d")

A different approach is to create an S3 subclass of Date that represents a Date but displays just the month and day storing the full date so that it is recoverable.  as.md constructs an object of this new class, as.Date.md converts it back to Date class and format.md formats it.  If we print such as object it will look for print.md but we have not defined it so it will use print.Date, the print method of the super class of md, and that method calls format invoking format.md.
as.md <- function(x, ...) structure(as.Date(x), class = c("md", "Date"))
as.Date.md <- function(x, ...) structure(x, class = "Date")
format.md <- function(x, format = "%m-%d", ...) format(as.Date(x), format = format, ...)

y <- as.md(x)

y
## [1] "03-11"

as.Date(y)  # recover the full date
##[1] "2020-03-11"

data.frame(x, y)
##            x     y
## 1 2020-03-11 03-11

A: One easy way to do this is:
library(lubridate)
x <- "2020-03-11"
month <-month(x)
day <- day(x)
paste(month,"-",day)

and here is the result:
"3 - 11"

So, basically, I used lubridate to extract day and month and then used paste function to put those two together.
Another alternative is to use the code below (no lubridate):
format(as.Date(x), "%m-%d")

here is the result:
"03-11"

redpajama_set_name: RedPajamaStackExchange


text:
CAROLINE's Interview with Music of the Future
What is your name? CAROLINE
What is your genre of music? Pop
Give us a little bio about you. I've been singing and dancing my whole life, and I started writing music at 12. I've always felt that music is such an amazing and universal language that brings people together and I couldn't live without it.
What made you go into music? I write songs about everything, it's how I process what's going on in my mind and the world. I've always had an indescribable passion for particular pop music, live performances, and being able to connect with people. I never saw myself going into music because I'm not naturally a risk taker but I had to go for it because it's one of the only things that make me happy.
You released your new single ' Already There', tell us more about the single. I'm really excited about this single because it sends a message of bravery and confidence. I also adopted a fun mermaid theme for the song because when I hear the I think of the beach. I've been doing a lot of fun things with this song from a 50 part video series, a podcast, daily listening parties and there's even more fun stuff coming!
What is the meaning behind 'Already There'? The meaning behind the song is telling the person who you like how you feel and taking a risk.
Describe the track in two words. Chill, and Beachy
Will we see an EP or Album this year? Hopefully!
Do you have any shows coming up? I had some but due to the Coronavirus they have been cancelled for health reasons.
Do you have any collaborations coming up with any upcoming artists? Not right now but I'd love to in the future!
Would you be up for collaborations if other musicians wanted one with you? and who would they have to contact? For sure and you could DM on Instagram @carolines_music
You are very entrepreneurial, with your own fashion brand, book and more, tell us more about how all these came about. The fashion brand came because a lot of people were asking for merch but I wanted to do something a little more than merch and create necessities that are glitterful. I've always wanted to write a book so I started with a children's book because children are the future and it's so important that they are exposed to things like kindness and empathy. That's where the inspiration came from for CAROLINE's Life Lessons.
Let us know where they can be purchased from. Everything can be purchased at my website
Will we see anything new coming in 2020 in this side of things as well as the music? Yes, I'm currently writing my second book, planning new issues of the magazine and working on music.
Do you play any instruments? I play the keyboard.
Who are your influences? My influences are Madonna and Taylor Swift.
How do you get inspiration to write songs? I write about everything from a day at school to something really dramatic that just happened to fictional fantasies.
Where do you see yourself now in 5 Years? Hopefully still putting out music!
When you're not doing music, what do you do? I love to dance!
What was the song you listened to most that influenced you to go more into the music scene? I don't really have one, probably a Britney Spears or Christina Aguilera song.
What's the best advice you have ever been given? Don't care what anyone else thinks.
What advice would you give to aspiring musicians not about the industry and just as an artist? Don't care what anyone else thinks.
What quote or saying do you always stick by? Kindness is not a weekend.
Where in your hometown is a must go to visit? The Grove is really cool.
Your coming off tour; 1/ Where do you go first? I'd probably go home 2/ Who do you see first? see a friend 3/What do you eat first? eat whatever's in the fridge.
When you are at a gig, what are 5 things you cannot forget? An aux-cord, a phone, a video camera, a jacket, and a hat or sunglasses.
Do you have social media accounts so your fans can follow you? Instagram Facebook: CAROLINE Tik Tok: Carolines_music
CATCH-UP WITH CAROLINE - Jan 3rd
Hi, Today was a fun day!! Here's a recap of what happened! I turned my little black dress into a sparkly pink and black stage costume: Also, did a lot of singing of some of my favorite songs such as E
pretend music video
Everything you need to know before Pretend comes out!
my brand new song pretend will be out tonight at midnight est!! this is my favorite song that I've ever put out and I am soooo excited for you to hear it! here's the link it will be live at tonight -


text:
Poodle Sock It to Me: Irish dance hosiery regulations and origins
S.J. Velasquez
A few years ago, the Irish dance scene was buzzing over a proposed hosiery mandate that would force ladies aged 18 and older to wear black tights in competition, banning adult ladies from feising in the standard white poodle sock. The call to prohibit the popular mid-calf white quilted socks among mature dancers was dismissed, but the discussion opened up a whole can of worms regarding dancers' footwear.
When it comes down to it, there is no standard sock rule in the An Coimisiún le Rincí Gaelacha list of regulations. The only related entry deals with the density of tights worn by dancers. It states:
"Where tights are worn, they must be of a denier of not less than 70."
There's no other mention of sock style or color, so how did the popular white poodle sock become the stocking of choice for CLRG dancers -- and dancers of other organizations, for that matter -- around the world?
"Presumably, they thought of it in Ireland, and it spread like wildfire over here," Brian Sexton, ADCRG, suggested.
Sexton is one of the few dance teachers who's taken advantage of vague sock rule wording. For 25 years, dancers from his New Jersey school have been dancing in "lemony yellow" poodle socks in competition and for shows. His thought behind dyeing white socks yellow is simple: yellow socks match the yellow uniform blouse. "That is the costume," Sexton said. "This is standard."
The popular poodle sock wasn't always the standard style, though. Dr. John Cullinane, author of Irish dance history books including "Irish Dancing Costumes, Their Origins and Evolution," asserts that the white ankle sock was the go-to dance sock before the poodle variety emerged on the scene.
"Socks are nearly always white and tights are nearly always black but by choice and not by legislations."
Just as Sexton chose to put yellow socks on his dancers, a few other dance teachers have made colored tights part of the uniform. The Claddagh Dance Company of California turned heads when its ceili team captured the gold medal in burgundy stockings at the 2009 World Irish Dancing Championships.
And while some teachers and judges aren't too keen on the idea of experimental sock hues and non-black tights, Sexton isn't fazed by a touch of color on the feet. "I think we're supposed to be judging the dancing," he said.
Have you spotted any colorful hosiery at a feis or major competition? I'd love to see how other dance schools have interpreted the footwear regulations established by CLRG. And non-CLRG dancers and teachers, do you have more strict rules on socks and tights? Email me, or leave a comment below.
For more Irish dancing news from North America's favorite magazine delivered to your mailbox, subscribe today!


Will my home insurance in Washington, DC, cover breakdown of electrical appliance?
Most homeowners policies cover a lot of things, but the appliances in the home are often excluded. That's largely because these appliances aren't a fixed part of the home. In order to determine whether your Washington, DC insurance policy covers the breakdown of an electrical appliance, it's important to be clear about what your policy really offers. Too many homeowners aren't sure what their insurance documents actually say, so they don't really know the coverage provided by the company. By talking to an independent agent like us, you can avoid all of that.
For example, there are different companies with many different types of policies. Independent agents like us work with a lot of these companies, so we can help you find a policy that works for you. You'll have more choices for coverage and cost, and that's always a good thing. We can find you insurance that will protect the things that matter most to you, and if you want to have your appliances covered we can look for companies that provide that type of coverage. If it's not standard in the policies, you may be able to get a rider that will give you that coverage.
Often, adding something else onto a policy does not cost that much in premiums, unless the value of the added items is extremely high. Even top of the line appliances aren't incredibly expensive when compared to how much your home costs, so the additional premiums wouldn't be that much. Still, you want the best deal you can get. Come in and talk to us, and let us find you the right company, coverage, and price for your needs.
Will Replacement cost vary if I renovate/upgrade my house in Washington, DC?
If you renovate or upgrade your house in Washington, DC, your insurance should also be upgraded. By talking to an independent agent like us, you can find out how the renovations you've made have changed the replacement value of your home. The money you've put into your house is important, and you want to make sure you can get that money back if your home becomes severely damaged and has to be reconstructed. Because of that, you'll want to make adjustments to your insurance policy in order to make sure you're covered for the right amount.
The value of your home can vary based on the changes you made, and the cost of your insurance premiums may also be affected. Anytime you raise the value, or replacement cost, for the home, your premiums will also be higher. However, you can't put a price on the peace of mind you'll have when you know your home is properly insured no matter what happens to it. You can't always predict when something might go wrong, but you can make sure you're financially prepared for it when it does. Insurance is the best way to do that, but it won't really help you if you don't have enough of it.
Keep in mind that some upgrades can actually lower your insurance cost, overall. That doesn't mean that updating your house will make your replacement cost go down, but it can make your premiums lower based on discounts you'll receive. Come in and talk to us about your options before you renovate, so you can be sure what will really benefit you the most from an insurance standpoint. Then you can work on your renovations with all the knowledge you need to make the right choices.
What is Motor Vehicle Act in Laurel, Maryland?
As a driver in Laurel, Maryland there are times that you will have to renew your license, pull your motor vehicle records, renew registrations and even other minor things. To help with your auto needs Maryland has setup a website to help facilitate your needs. After all no one ever wants to stand in long lines just to prove your car insurance is still valid. Here are some details of this website and how it can help you save time.
You can now renew your registration online by following some simple steps. Provide the necessary information, pay all the fees associated with the request and wait for your registration to arrive.
You can even check your own driving record from this site which can be a huge benefit when you are shopping for car insurance. Once all of your items have fallen off your record you can have your agent look at the reports and start saving money right away.
Get the information you need about driver education programs offered by the state. Some insurance companies offer a discount for people who have completed a defensive driver course.
You can even register a change of address and even perform many other minor jobs on the website.
If you live in the Laurel, Maryland area and have any questions regarding your car insurance or what you need to drive legally, then you need to contact your independent agent today. As your agent, we can help give you the information that you need to protect yourself from costly accidents and trouble with the state. It is important that you give us a call so that we can give you specific details for your circumstances so you can drive knowing you are fully compliant.
What is the time frame within which an NCB can be transferred in Laurel, Maryland?
No one ever wants to be involved in auto accident. Just the thought of having to wade through all the insurance paperwork and dealing with the repair shop can be tiring. To help encourage people to drive safely insurance companies have started provided a No-claim bonus for safe drivers. Here are some things that you need to think about when getting a car insurance no-claim bonus.
Your no-claim bonus is something that is given to you for not filing a claim. The longer you are claim free the more your bonus will be.
Your bonus is not transferable to another person. It is issued to the person that deserves it. However, you may be able to have it transferred to another car. Just make sure to call your insurance provider before making the change.
The bonus can have a time frame for up to three years. It really depends on which company is offering the bonus to you. Before you wait too long make sure that you have a clear understanding of when the bonus will expire.
This type of bonus can save you a lot of money. If you have a record that needs work, try and drive safely so you can earn your no-claim bonus soon and stop mission out on the savings.
If you have questions and live in Laurel, Maryland, then you are encouraged to contact your independent agent today. As your auto insurance agent we can assist you by answering all of your questions. It is important that you give us a call so that we can give you specific details for your circumstances so we can help you maximize your benefits regarding your auto insurance policy.


text:
catherinebroad
What the Hell is the Deal with the Oakland County Child Killer Investigation?
OCCK Case Overview
930 Knox Street
Posted: September 4, 2021 | Author: cathybroad | Filed under: Uncategorized | 20 Comments
930 Knox Street, Birmingham, Michigan, was built and sold in 1996 to the late Senator Jack Faxon. I can't remember if that was an empty lot back in 1977 or if perhaps there was a home there that was torn down for this build. I do remember Knox Street very well. It would have been the last street my brother Tim walked on before he was abducted. It was a short, quiet, dark street.
Route-to-Hunter-Maple-Download
We've discussed Jack Faxon, whose name appears in investigative notes concerning the investigation into pedophiles Ted Lamborgine and Richard Lawson. https://catherinebroad.blog/2020/08/24/ex-michigan-senator-jack-faxon/. An April 11, 1979 article in The Decatur Herald (Decatur, IL) opens with ""Somehow, when you're talking to Jack Faxon, you can never be quite sure which Jack Faxon will answer." The reporter was referring to Faxon as state senator, school headmaster, or artist-performer. We wouldn't know for decades after that there was yet another side. Faxon's side where he was friends with convicted pedophiles Kent Shultz ("best friends" according to Shultz, see https://www.hebrewmemorial.org/obituaries/Jack-Faxon/#!/TributeWall) and Josiah Tazelaar (https://catherinebroad.blog/wp-content/uploads/2020/08/ex-michigan-senator-jack-faxon.pdf).
While it is unclear whether the late Faxon ever lived on Knox before 1996, it appears he did have a home in Birmingham while he was still in the Michigan senate. Faxon retired from the senate in 1994, two years before this home was built. See memory posted on obituary page from a man who was caretaker at Faxon's home in Birmingham while Faxon went back and forth to serve in Lansing. https://www.hebrewmemorial.org/obituaries/Jack-Faxon/#!/TributeWall.
Faxon, "something of an arts doyen" (see Hugh McDiarmid's column in The Detroit Free Press, April 6, 1996, p. 3A, discussing a lawsuit filed by a dentist who purchased art from Faxon and later claimed he had been duped and the subsequent defamation action Faxon filed against the GOP for mentioning this lawsuit in campaign materials), managed to amass quite the art collection. As a reader pointed out, it is curious how Faxon began collecting art in his 30s while a school teacher.
DuMouchelles and Sotheby's have already been through Faxon's home. An estate sale is in progress.
Estate-SaleDownload
I thought you might like to see some of the art that is left for sale:
IMG-4481Download
And this classic book:
Dr. Richard Golden, the Southfield dentist who sued Faxon over the 1981 art sale, told McDiarmid in 1996 that the lawsuit was settled when Faxon bought back all but two of the items–two paintings by Faxon himself. Dr. Golden said Faxon did not want them back and that Golden "still [had] 'em. I think they are in a closet."
Feels like there is a lot in the closet here.
Not again.
"I love it when you say that."
Relevant handwRiting
Pig.
"A demon who disguised himself as a man of God."
washingtonpost.com/nation…
detroitnews.com/story/new…
baycountylibrary.org/even…
mdocweb.state.mi.us/otis2…
ncbi.nlm.nih.gov/pmc/arti…
sonomawest.com/sonoma_wes…
freep.com/story/news/educ…
L. Brooks Patterson
Noteworthy Predators
Other Ass-Hats
Powered by WordPress.com. Mid Mo Design.


text:
Before Facebook and the era of social media, it was estimated that the average person was exposed to some 2000 ads every day - billboards, television commercials, signs in grocery stores and storefronts, etc, etc.
Since then, that number has probably doubled. This makes promotion very tricky. How do you successfully promote your music when there is so much competition? Below are 6 things you must do to stand out in a sea of clutter, make a dent with your music, and continue to grow your fanbase.
First and foremost, no matter what it is you're promoting, the key is to sound like YOU. Sound like a human. Don't be a robot or take the tone of a marketer or that dude on the TV commercial who reads the fine-print at top speed.
You never know what feedback you're gonna get when you share a new song, video, or show details. Promoting is a difficult task as it is. When you use phrases like "Only $20 for a limited time", or "get yours now!", you just sound cheesy and superficial. Make sure to sound like a human. Sound like YOU.
Use a Newsletter
"Email marketing is 40 times as effective as Facebook and Twitter, combined."
Your newsletter is not just your greatest tool; it is your best friend! No one can keep up to speed with every post in their news feed. No one reads every tweet or every status update. They just can't. Who has that much time in the day?
When you send a newsletter out, it should be an extension of your presence. It should take on the same tone that you use on stage. It's the longer version of a 140 character tweet. It tells a fuller story of that photo you shared on Instagram. It tells the backstory behind the music video you just released.
Newsletters inform your fans of what's to come, tell them what happened in the past, and fill in the gaps to create a more cohesive story of who you are as an artist. Newsletters are essentially your opportunity to brand yourself.
By the way, Email marketing is 40 times as effective as Facebook and Twitter, combined. Artists, writers, corporations, organizations...they all use it. They realize it's so much more powerful than social media.
[Why Email Newsletters Are Still a Vital Marketing Tool for Musicians]
Think of Your Fans
Sounds silly, but it's what works. Instead of thinking about how you want to do something, think about what your fans really want you to do. I would liken this to a live show. You might have a really excellent cover of a Beatles song. Problem is, you're playing to a demographic that is more likely to enjoy Paul Simon. What are you gonna do? Hint: Play Paul Simon!
Promotion is just like this. Instead of posting yet another photo of a product at your online store, post something that is more engaging. Maybe that means your update will have nothing to do with merch. Maybe instead of talking about yourself or your music, you ask fans to share their favorite song. It might not seem like promotion, but that's the kind of stuff that really engages people, brings traffic to your page, and comes off as more personal.
Know When to Post
The key to promotion is knowing when to do it. You won't see a diaper commercial come on during a sports game. It's just not gonna happen. In the same way, you can't post about your show at midnight when the average person is asleep. Your posts need to happen during high-traffic times and to the right audience. They also need to happen when people can adequately respond to them.
Need to tell a long drawn out story about something that happened at your gig last night? Don't do it at 9am when the average person is beginning their work day. 9am posts are great for questions like "Hey, what cover should I do at this Fridays show?". Posts like this not only serve as a reminder about the show, but they also get your fans posting about their favorite songs and tunes they think would be perfect for your voice.
Same goes for your newsletter. Don't send a newsletter out on Friday morning! You'll get plenty of Out-of-Office responses. Statistically the best times to send newsletters are Tuesday and Wednesday - in the heart of the work week when more people are checking their email.
Good promo has a lot to do with planning well. Artists who plan well get the best feedback from fans. If your next show is 6 weeks out, planning well means dropping a "save the date" post on your social media for fans who need that extra heads up.
It means sending posters to the venue 3-4 weeks out so you can get the attention of everyday foot traffic. Planning ahead means communicating with other artists on the bill so that everyone knows the facts and can also do their part in promoting the show. Planning means the Facebook invite is created 2 weeks out and shared with your band mates and other bands on the bill so they can share.
Planning ahead means spacing out your social media posts so your fans have no excuse for not knowing about your show. There's a fine line between too much and not enough. Find it!
Last but not least, tell your story! This pretty much wraps up this blog and reiterates the first point. The one thing that distinguishes you from every other performer is your voice. Your voice (not your singing voice) is unique. You have a story that no one else has. How you shape that story, tell that story, and invite others to identify with that story, is what makes you real to your fans. It's what makes you human, and keeps fans sticking around for the length of your career.
[5 tips for developing your personal blogging voice]
Promoting your music is essentially finding creative ways to tell your story - through content, how you brand that content, and how you share that content.
Joy Ike is a full-time singer/songwriter based out of Philadelphia, PA. She is also the founder and primary writer for Grassrootsy, one of the most-read music business blogs on the internet. She believes the greatest tragedy in the world is having a talent and keeping it to yourself.
Bandzoogle websites have built-in mailing lists and the tools you need to step it up. Sign up free now!


text:
\section{Introduction}

Duality is a powerful tool to study a strongly coupled gauge theory.
Duality enables us to map strongly coupled region in a gauge theory to
weakly coupled region in the dual theory,
so phenomena such as color confinement can be addressed by perturbation from the dual theory.
Several examples are known such as
S duality, Seiberg duality \cite{Seiberg:1994pq}, mirror duality \cite{Intriligator:1996ex},
AdS/CFT duality \cite{Maldacena:1997re}.

Although it is often too difficult to prove duality completely,
one can provide evidence for duality by using a superconformal index.
A superconformal index can be a test of duality
by checking whether indices of both theories agree or not.
Such an analysis was first carried out for the simplest example of AdS$_5$/CFT$_4$ duality,
${\cal N}=4$ super Yang-Mills theory and its gravity dual \cite{Kinney:2005ej}.
The agreement of indices of both theories was confirmed in the large $N$ limit.
Four dimensional indices can be calculated for less supersymmetric gauge theories
and they were applied to various types of duality
\cite{Romelsberger:2005eg,Nakayama:2005mf,Nakayama:2006ur,Gadde:2010en,Benvenuti:2006qr,Romelsberger:2007ec,Dolan:2008qi,Spiridonov:2008zr,Spiridonov:2011hf}.

Similarly,
three dimensional indices can be computed.
Index calculation in three dimension has been performed actively
since ${\cal N}=6$ Chern-Simons theory (ABJM theory) appeared \cite{Aharony:2008ug},
which provides the first example of AdS$_4$/CFT$_3$ duality.
An index for ABJM theory was first computed by taking 't Hooft limit \cite{Bhattacharya:2008bja},
which excludes monopole contribution.
It was confirmed that the index agrees with that of dual type IIA theory.
The index for ABJM theory including monopole contribution can be also calculated \cite{Kim:2009wb}.
It was checked that it coincides with that of dual M-theory in the large $N$ limit.
This kind of analysis can be done for ${\cal N}=5,4,3$ Chern-Simons theories
\cite{Choi:2008za,Imamura:2009hc,Kim:2010vwa}.
An index for a general ${\cal N}=2$ superconformal field theories was first computed
in \cite{Imamura:2011su},
and it can be applied to AdS$_4$/CFT$_3$ duality \cite{Imamura:2011uj,Cheon:2011th},
mirror duality \cite{Imamura:2011su} with refined analysis \cite{Krattenthaler:2011da,Kapustin:2011jm}
and other types of duality
\cite{Jafferis:2011ns,Bashkirov:2011vy,Hwang:2011qt,Gang:2011xp,Hwang:2011ht}.

In the next section,
we make a brief review of a derivation of a three dimensional superconformal index
and give an index formula explicitly.
From this formula,
we can obtain a formula of an index in the large $N$ limit.
In Section \ref{apply},
we apply the formula to several ${\cal N}=2$ gauge theories.
We will give evidence for mirror duality and AdS$_4$/CFT$_3$ duality
by using indices.
The final section is devoted to summary and discussion.

\section{Superconformal index}

The definition of a superconformal index is
\begin{eqnarray}
I&=& \mathrm{Tr}_{{\cal H}} \biggl((-1)^F e^{-\beta'\{Q, S\}} \, C \biggr).
\label{ind}
\end{eqnarray}
Here ${\cal H}$ is the Hilbert space of the theory, $F$ is fermion number operator,
$Q$ is a supercharge satisfying the nilpotent condition,
$S$ is the hermitian conjugate of $Q$,
$C$ is a chemical potential which commutes with $Q$,
and $\beta'$ is a parameter.
Indices are defined so that
they receive contribution only from supersymmetric states.
This is due to the fact that
in a supersymmetric theory
there is one-to-one correspondence between bosons and fermions
in non-supersymmetric states
and their contributions totally cancel thanks to insertion of $(-1)^F$ \cite{Witten:1982df}.
As a result, \eqref{ind} is independent from $\beta'$.
In this section,
we will show a general formula of a three-dimensional superconformal index
and the large $N$ version of the formula.

\subsection{Formula in three dimension}

Before showing a formula of an index,
we make a brief review on how to compute an index.
To calculate an index,
we have to specify the Hilbert space of the theory.
For this purpose,
since the theory is a euclidean conformal field theory,
we use the radial quantization.
In other words,
we consider the theory not on $R^3$ but on $S^2 \times R$
by using a conformal transformation.
Here $R$ is the radial direction of $R^3$.
By regarding this radial direction as time,
we quantize the theory and obtain the Hilbert space as a set of the quantized states.

We compute a superconformal index of this theory in path-integral approach
by using a localization method \cite{Kim:2009wb,Imamura:2011su}.
To do this,
we first compactify the radial direction $R$ to $S^1$ to read off the charge assignment of the states.
Then we add a $Q$-exact term into the original Lagrangian.
Since only BPS states contribute to the index,
this $Q$-exact deformation does not change the index at all.
The point is that
we can choose a $Q$-exact term in such a way that
it becomes kinetic terms of the fields on $S^2\times S^1$ \cite{Kim:2009wb,Kapustin:2009kz}.
Then we look for saddle points of the $Q$-deformed action.
It turns out that
saddle points are given by GNO monopole solutions \cite{Goddard:1976qe},
which is specified by a magnetic flux through $S^2$,
with holonomy, which is a zero-mode of a gauge field on $S^1$.
Note that saddle points are sensitive to the topology of the space.
Then we expand the theory around a saddle point
and take the weak coupling limit,
which can be realized by sending the coupling of the $Q$-exact term to infinity.
After the weak coupling limit,
the total Lagrangian consists of quadratic terms of the fields on a monopole background
and thus we can perform path-integral exactly, which reduces to gaussian integrals.
The index is decomposed in the following form.
\begin{equation}
I=\sum_M t^M\int\! d\alpha e^{-S_{0}} \biggl[\prod_{v} I^{v} \prod_{q} I^q\biggr].
\label{indR3}
\end{equation}
Here we introduce the chemical potential $t$ for a magnetic charge $M$ in a collective notation.
We sum the contribution over all saddle points parametrized by a magnetic charge $M$ and
holonomy $\alpha$.
$e^{-S_{0}}$ is the contribution coming from the original action,
which does not vanish only when it includes a Chern-Simons term
\begin{equation}
S_{0}
= \sum_v i k_v \mathrm{tr}_v( \alpha M),
\end{equation}
where $k_v$ is the Chern-Simons coupling of a vector multiplet $v$
and $\mathrm{tr}_v$ is trace for the gauge group associated with $v$.
$I^v$ and $I^q$ are the contributions coming from a vector multiplet and a chiral multiplet,
respectively.

The result of the path-integral is the following.
The contribution of a vector multiplet is \cite{Kim:2009wb}
\begin{equation}
I^v =
{1 \over \mbox{(sym)}}
\prod_{\substack{\hat v(M)=0}} 2 i\sin\left({\hat v(\alpha)\over 2}\right)\prod_{\hat v} \biggl[
x^{-{1\over2} |\hat v(M)|}
\exp\left[
\sum_{m=1}^\infty\frac{1}{m} \mathfrak{i}^v(e^{im \alpha},x^m)
\right]\biggr].
\end{equation}
$\hat v$ represents a weight of the gauge representation of the vector multiplet $v$.
The factors ${1 \over \mbox{(sym)}}$
and
$\prod_{\substack{\hat v(M)=0}} 2 i\sin\left({\hat v(\alpha)\over 2}\right)$
come from the Weyl symmetry and gauge fixing of the unbroken gauge group, respectively.
When the gauge group $G$ is broken to $\prod_i G_i$ by monopole flux,
(sym) is given by $\prod_i (\mbox{rank} G_i)!$.
The factor $x^{-{1\over2} |\hat v(M)|}$ describes the zero-point energy of a vector multiplet on a monopole background.
$\mathfrak{i}^v$ describes a single excitation of a vector multiplet on a monopole background, called a letter index.
\begin{equation}
\mathfrak{i}^v(x,e^{i\alpha})=
-e^{i\hat v(\alpha)}x^{|\hat v(M)|}.
\label{fvector}
\end{equation}
The following exponential
\begin{equation}
\exp\left[\sum_{m=1}^\infty\frac{1}{n} {\mathfrak i}(e^{im\alpha},x^m,z_i^m)\right]
\label{excitation}
\end{equation}
is called plethystic exponential.
The plethystic exponential of a letter index describes an index of a multi-excitation.

The contribution of a chiral multiplet is  \cite{Imamura:2011su}
\begin{equation}
I^q = \prod_{\hat q} \biggl[
e^{-\frac{i}{2} |\hat q (M)|\hat q (\alpha)}x^{{1\over2}(1-\Delta_q)|\hat q (M)|}z_i^{-{1\over2}|\hat q (M)|F_i}
\exp\left[
\sum_{m=1}^\infty\frac{1}{m} \mathfrak{i}^q(e^{im \alpha},x^m,z_i^n)
\right],
\end{equation}
where $\hat q $ represents a weight of the gauge representation of the chiral superfield $q$.
The structure is the same as that of a vector multiplet.
The first factor in front of plethystic exponential describes the contribution of
zero-point fluctuation of a chiral multiplet.
$\mathfrak{i}^q$ is a letter index of a chiral multiplet.
\begin{equation}
\mathfrak{i}^{q}(e^{i\alpha},x,z_i)=
e^{i\hat q (\alpha)}z_i^{F_i}\frac{x^{|\hat q (M)|+\Delta_q}}{1-x^2}
-e^{-i\hat q (\alpha)}z_i^{-F_i}
\frac{x^{|\hat q (M)|+2-\Delta_q}}{1-x^2},
\label{fchiral}
\end{equation}
where $\Delta_q$ is a conformal dimension of the scalar field in a chiral multiplet.
Plethystic exponential describes a multi-excitation of a chiral multiplet on a monopole background.

When the conformal dimension is canonical, $\Delta_q={1\over2}$,
the formula of indices was derived in \cite{Kim:2009wb}.
We generalized the result of \cite{Kim:2009wb} so that
it can be applicable to theories with non-canonical R-charge assignments \cite{Imamura:2011su}.
It was pointed out that
this formula can be further generalized to
${\cal N}=2$ theories in a non-trivial background gauge field
coupling to global symmetry currents \cite{Kapustin:2011jm}.

\subsection{Large $N$ formula}

From a general formula for an index shown in the previous section,
we can obtain an index formula in the large $N$ limit \cite{Imamura:2011uj}.
In application of the formula,
gauge theories we have in mind are quiver gauge theories,
so
we specify the gauge group as a product of unitary groups $\prod_v U(N_v)_v$ and
representations of the chiral matters as bi-fundamental ones.
It is not difficult to do for other types of gauge group and representation such as
fundamental/anti-fundamental representations.
In this situation, the saddle points are labeled by
the diagonal components of magnetic charges
$M^v_s$ and holonomy $\alpha^v_s$ for each gauge group $U(N_v)_v$,
where $s=1, \cdots, N_v$.
So the formula is rewritten as
\begin{equation}
I(x,z_i)
=\sum_M t^M{1\over (\mbox{\rm sym})}  \int d\alpha e^{-S_{0}}
e^{i b_0(\alpha)}x^{\epsilon_0}z_i^{f_{0i}}
\exp\left[\sum_{m=1}^\infty\frac{1}{n}\mathfrak{i} (e^{ima},x^m,z_i^m)\right].
\label{formula}
\end{equation}
Here the total letter index $\mathfrak{i}$ consists from those of vector and hyper multiplets,
$\mathfrak{i}=\sum_v  \mathfrak{i}^v+\sum_q \mathfrak{i}^q$, where
\begin{eqnarray}
&&\mathfrak{i}^v(e^{i\alpha},x)
=
\sum_{s,t=1}^{N_v}
(1-\delta_{s,t})
\left(-e^{i(\alpha^{v}_s- \alpha^v_t)}x^{| M^v_s- M^v_t|}\right),
\label{fvecdef}\\
&&
\!\!\!\!\!\!\!\!\!\!\!\!\!\mathfrak{i}^q(e^{i\alpha},x,z_i)
=
\sum_{s=1}^{N_{h_q}}
\sum_{t=1}^{N_{t_q}}
\frac{x^{|M^{h_q}_s-M^{t_q}_t|}}{1-x^2}
\left(
e^{i(\alpha^{h_q}_s-\alpha^{t_q}_t)}z_i^{F_i(q)}x^{\Delta(q)}
-e^{-i(\alpha^{h_q}_s-\alpha^{t_q}_t)}z_i^{-F_i(q)}x^{2-\Delta(q)}
\right),
\label{fchdef}
\end{eqnarray}
where we assume that the chiral multiplet $q$ is $(N_{h_q}, \bar N_{t_q})$ representation
for the gauge group $U(N_{h_q})_{h_q} \times U(N_{t_q})_{t_q}$.
The zero-point contributions is
\begin{eqnarray}
\epsilon_0
&=&\frac{1}{2}\sum_{q}
\sum_{s=1}^{N_{h_q}}
\sum_{t=1}^{N_{t_q}}
|M^{h_q}_s-M^{t_q}_t|(1-\Delta(q))
-\frac{1}{2}\sum_{v}
\sum_{s=1}^{N_v}\sum_{t=1}^{N_v}|M^{v}_s-M^{v}_t|,
\label{ep0}\\
f_{0i}
&=&-\frac{1}{2}\sum_{q}
\sum_{s=1}^{N_{h_q}}
\sum_{t=1}^{N_{t_q}}|M^{h_q}_s-M^{t_q}_t|F_i(q),
\label{q0i}
\\
b_0(\alpha)
&=&-\frac{1}{2}\sum_{q}
\sum_{s=1}^{N_{h_q}}
\sum_{t=1}^{N_{t_q}}
|M^{h_q}_s-M^{t_q}_t|
(\alpha^{h_q}_s-\alpha^{t_q}_t).
\label{b0}
\end{eqnarray}

The striking feature of the large $N$ index is that
the index can be factorized into three parts by monopole charges as
\begin{equation}
I= I^{(0)} I^{(+)} I^{(-)}.
\label{factor}
\end{equation}
Here $I^{(0)}, I^{(+)}, I^{(-)}$ are the neutral, positive, negative parts of the index.
Let us explain this below.
To see this factorization,
we can divide the letter index into three parts
\begin{equation}
\mathfrak{i} = \mathfrak{i}^{(0)}+\mathfrak{i}^{(+)}+\mathfrak{i}^{(-)},
\end{equation}
where $\mathfrak{i}^{(*)}= \sum_v \mathfrak{i}^{v(*)}+\sum_q \mathfrak{i}^{q(*)}$ and
\begin{eqnarray}
\!\!\!\!\!\!\!\!&&\!\!\!\!\!\!\!\!\!\!\!\!\!\mathfrak{i}^{v(0)}=
\sum_{s,t=1}^{N_v}
\left(-e^{i(\alpha^{v}_s- \alpha^v_t)}x^{|M^v_s|+|M^v_t|}\right), \\
\!\!\!\!\!\!\!\!&&\!\!\!\!\!\!\!\!\!\!\!\!\!\mathfrak{i}^{v(\pm)}=
\sum_{s,t=1}^{N^{(\pm)}_v}
e^{i(\alpha^{v}_s- \alpha^v_t)}\left(-(1-\delta_{s,t})x^{|M^v_s - M^v_t|}+ x^{|M^v_s|+|M^v_t|}\right), \\
\!\!\!\!\!\!\!\!&&\!\!\!\!\!\!\!\!\!\!\!\!\!\mathfrak{i}^{q(0)}=
\sum_{s=1}^{N_{h_q}}
\sum_{t=1}^{N_{t_q}}
\frac{x^{|M^{h_q}_s|+|M^{t_q}_t|}}{1-x^2}
\left(
e^{i(\alpha^{h_q}_s-\alpha^{t_q}_t)}z_i^{F_i(q)}x^{\Delta(q)}
-e^{-i(\alpha^{h_q}_s-\alpha^{t_q}_t)}z_i^{-F_i(q)}x^{2-\Delta(q)}
\right),\\
\!\!\!\!\!\!\!\!&&\!\!\!\!\!\!\!\!\!\!\!\!\!\mathfrak{i}^{q(\pm)}=
\sum_{s=1}^{N^{(\pm)}_{h_q}}
\sum_{t=1}^{N^{(\pm)}_{t_q}}
{ x^{|M^{h_q}_s-M^{t_q}_t|}- x^{|M^{h_q}_s|+|M^{t_q}_t|} \over 1-x^2}
\left(
e^{i(\alpha^{h_q}_s-\alpha^{t_q}_t)}z_i^{F_i(q)}x^{\Delta(q)}
-e^{-i(\alpha^{h_q}_s-\alpha^{t_q}_t)}z_i^{-F_i(q)}x^{2-\Delta(q)}
\right).
\end{eqnarray}
$\sum_{s=1}^{N^{(\pm)}_v}$ means summation over $s$ satisfying
$M_s {}^{>}\!\!\!\> \!\!{}_{<} 0$, where $M>0 \;(M<0)$ means
that $M$ is non-zero and the components are all non-negative (non-positive).
This is due to the fact that
$\mathfrak{i}^{v(\pm)}$ and $\mathfrak{i}^{q(\pm)}$ vanish unless
$M^v_s, M^v_t$ and $M^{h_q}_s, M^{t_q}_t$ are the same signature, respectively.

We can also divide the factors in front of plethystic exponential by three parts
as follows.
\begin{eqnarray}
S_{0}&=&S_{0}^{(0)}+S_{0}^{(+)}+S_{0}^{(-)},\\
\epsilon_{0}&=&\epsilon_0^{(0)}+\epsilon_{0}^{(+)}+\epsilon_0^{(-)},\\
f_{0i}&=&f^{(0)}_{0i}+f_{0i}^{(+)}+f_{0i}^{(-)},\\
b_{0}&=&b^{(0)}_0+b_{0}^{(+)}+b_{0}^{(-)}.
\end{eqnarray}
The neutral sector is
\begin{eqnarray}
S_{0}^{(0)}&=&0,\\
\epsilon_0^{(0)}
&=&N \sum_v
\left(\sum_{ h_q= v \atop t_q=v}{1-\Delta(q) \over 2} - 1\right) \sum_{s=1}^{N_v} |M^v_s|,
\label{ep00}\\
f_{0i}^{(0)}
&=&-N \sum_v
\left(\sum_{h_q= v \atop t_q=v}{F_i(q) \over 2}\right) \sum_{s=1}^{N_v} |M^v_s|,
\label{fp00}\\
b_0^{(0)}(\alpha)
&=&-\frac{1}{2}\sum_{q}
\sum_{s=1}^{N_{h_q}}
\sum_{t=1}^{N_{t_q}}
\left(|M^{h_q}_s|+|M^{t_q}_t|\right)
(\alpha^{h_q}_s-\alpha^{t_q}_t),
\label{b00}
\end{eqnarray}
The charged sector is
\begin{eqnarray}
\!\!\!\!\!\!\!\!\!\!\!\!S_{0}^{(\pm)}&=&\sum_v\sum_{s=1}^{N^{(\pm)}_v} i k_v \alpha^v_s M^v_s,\\
\!\!\!\!\!\!\!\!\!\!\!\!\epsilon_0^{(\pm)}
&=&\frac{1}{2}\biggl(\sum_{q}
\sum_{s=1}^{N^{(\pm)}_{h_q}}
\sum_{t=1}^{N^{(\pm)}_{t_q}}
{\bf M}(h_q,t_q:s,t)(1-\Delta(q)) -
\sum_{v} \sum_{s=1}^{N^{(\pm)}_v}\sum_{t=1}^{N^{(\pm)}_v}
{\bf M}(v,v:s,t)\biggr),
\label{ep02}\\
\!\!\!\!\!\!\!\!\!\!\!\!f_{0i}^{(\pm)}
&=&-\frac{1}{2}\sum_{q}
\sum_{s=1}^{N^{(\pm)}_{h_q}}
\sum_{t=1}^{N^{(\pm)}_{t_q}}
{\bf M}(h_q,t_q:s,t) F_i(q),
\label{q0i2}\\
\!\!\!\!\!\!\!\!\!\!\!\!b_0(\alpha)
&=&-\frac{1}{2}\sum_{q}
\sum_{s=1}^{N^{(\pm)}_{h_q}}
\sum_{t=1}^{N^{(\pm)}_{t_q}}
{\bf M}(h_q,t_q:s,t)
(\alpha^{h_q}_s-\alpha^{t_q}_t).
\end{eqnarray}
Here we set
\begin{eqnarray}
{\bf M}(a,b:s,t)=|M^{a}_s-M^{b}_t| -|M^{a}_s|-|M^{b}_t|.
\end{eqnarray}
By using these decompositions, $I^{(0)}, I^{(\pm)}$ in \eqref{factor} is written as
\begin{eqnarray}
\!\!\!\!\!\!\!\!\!\!\!\!
I^{(0)}&=& \int d\alpha
e^{i b^{(0)}_0}x^{\epsilon^{(0)}_0}z_i^{f^{(0)}_{0i}}
\exp\left[\sum_{m=1}^\infty\frac{1}{n}\mathfrak{i}^{(0)} (e^{ima},x^m,z_i^m)\right],\\
\!\!\!\!\!\!\!\!\!\!\!\!
I^{(\pm)}
&=&\sum_{M{}^{>}\!\!\!\> \!\!{}_{<} 0} t^M{1\over (\mbox{\rm sym})}  \int d\alpha e^{-S^{(\pm)}_{(0)}}
e^{i b^{(\pm)}_0}x^{\epsilon^{(\pm)}_0}z_i^{f^{(\pm)}_{0i}}
\exp\left[\sum_{m=1}^\infty\frac{1}{n}\mathfrak{i}^{(\pm)} (e^{ima},x^m,z_i^m)\right].
\end{eqnarray}

Let us assume $b_0(\alpha)$ vanishes as is the case with vector-like theories.
Under this assumption,
we can perform the holonomy integral in $I^{(0)}$ in the large $N$ limit.
By using the following notation
\begin{equation}
\lambda_{v,m}
=
\sum_{s=1}^{N_v}
(x^{| M_s|}
e^{i \alpha_s})^m,
\label{lambdadef}
\end{equation}
we can rewrite $\mathfrak{i}^{(0)}$ as
\begin{equation}
\mathfrak{i}^{(0)}
=-\sum_{v}\lambda_{A,+1}\lambda_{A,-1}
+\sum_{q}
\left[
\lambda_{h_q,+1}
\lambda_{t_q,-1}
\frac{z_i^{F_i}x^{\Delta(\Phi)}}{1-x^2}
-
\lambda_{h_q,-1}
\lambda_{t_q,+1}
\frac{z_i^{-F_i}x^{2-\Delta(\Phi)}}{1-x^2}
\right],
\end{equation}
which is quadratic of $\lambda_v$.
Therefore, if we set
$\mathfrak{i}^{(0)} =-\sum_{v,v'}\lambda_{v,+1}M_{v,v'}(x,z_i)\lambda_{v',-1}$,
then $I^{(0)}$ can be calculated as
\begin{eqnarray}
I^{(0)}
&=&\int d\lambda \; x^{\epsilon^{(0)}_0}z_i^{f^{(0)}_{0i}}
\exp\left(-\sum_{m=1}^\infty\frac{1}{m}\sum_{v,v'}M_{v,v'}(x^m,z_i^m)
\lambda_{v,m}\lambda_{v',-m}
\right)
\nonumber\\
&=&x^{\epsilon^{(0)}_0}z_i^{f^{(0)}_{0i}}\prod_{m=1}^\infty\left(\det _{v,v'} M^{-1}_{v,v'}(x^m,z_i^m)\right).
\label{neutralint2}
\end{eqnarray}

\section{Applications}
\label{apply}
In the previous section,
we showed a formula of a superconformal index with a general R-charge assignment.
In this section, testing whether the formula works correctly,
we apply it to ${\cal N}=2$ superconformal field theories
which have a non-canonical R-charge assignment
and show evidence of mirror duality and AdS$_4$/CFT$_3$ duality.

\subsection{Mirror duality}

We apply the formula to a mirror pair of ${\cal N}=2$ gauge theories.
In this paper, we use a mirror pair studied in
\cite{Aharony:1997bx,deBoer:1997ka}.

One of the pair we study is $U(1)$ supersymmetric Maxwell theory (SQED) with a fundamental flavor,
which means a pair of fundamental/anti-fundamental chiral multiplet.
This theory has flavor symmetry $U(1)_L\times U(1)_R$
and toplogical symmetry $U(1)_J$, which is generated by topological current
$J^\mu= \varepsilon^{\mu\nu\rho} F_{\nu\rho}$.
It is easily seen that
the diagonal $U(1)$ group of the flavor symmetry is included
in the gauge symmetry,
so it is sufficient to take account of $U(1)_{L-R}$,
which act on two chiral fields in the same way.
This theory flows to non-trivial fixed point in the infra-red (IR) region.
Let us denote the $U(1)_R$ charge of the chiral fields as $h$.
Then the letter index of the IR theory is
\begin{equation}
\mathfrak{i}_{\rm QED}(x,e^{i\alpha},y)=f_{h,M}(x,e^{i\alpha}y)+f_{h,M}(x,e^{-i\alpha}y),
\end{equation}
where $y$ describes the chemical potential for $U(1)_{L-R}$.
$f$ is defined by
\begin{equation}
f_{\Delta,M}(x,y)=\frac{yx^{|M|+\Delta}-y^{-1}x^{|M|+2-\Delta}}{1-x^2}.
\end{equation}
Notice that the contribution of a vector multiplet becomes trivial since the theory is abelian.
The total index is given by
\begin{equation}
I_{\rm QED}(x,y,t)=\sum_{M\in{\bf Z}}t^{M}\int\frac{d\alpha}{2\pi}x^{(1-h)|M|}y^{-|M|}
\exp\left(\sum_{n=1}^\infty\frac{1}{n}\mathfrak{i}_{\rm QED}(x^n,e^{in\alpha},y^n)\right).
\end{equation}

The mirror dual theory is known as
a Wess-Zumino model of three chiral multiplets $q, \widetilde q, S$ with cubic superpotential, $\widetilde q S q$.
From this superpotential,
we can see two global $U(1)$ symmetries assigned for three fields $q, \widetilde q, S$
as $1, -1, 0$ and $-1, -1, 2$, respectively.
Due to permutation symmetry of three chiral fields,
we can determine the conformal dimension of the fields as two thirds
so that the superpotential has R-charge two.
It will turn out that, however,
this information is not necessary for indices of both theories to match.
To see the agreement of both indices,
we need the relation of conformal dimensions of chiral fields coming from
the correspondence of chiral operators such that
$\widetilde Q Q \leftrightarrow S$, where $Q, \widetilde Q$ are chiral fields of SQED.
From this relation,
the conformal dimensions of three chiral fields $q, \widetilde q, S$ are fixed as $1-h, 1-h, 2 h$,
respectively.
By combining these facts,
we can obtain the letter index of the dual theory
\begin{equation}
\mathfrak{i}_{{\rm WZ}}(x,y',t')
=f_{1-h,0}(x,t'y'^{-1})
+f_{1-h,0}(x,t'^{-1}y'^{-1})
+f_{2h,0}(x,y'^2)
\end{equation}
and the total index
\begin{equation}
I_{{\rm WZ}}(x,y',t')=
\exp\left(\sum_{n=1}^\infty\frac{1}{n}\mathfrak{i}_{{\rm WZ}}(x^n,y'^n,t'^n)\right).
\end{equation}
Here $t', y'$ are the chemical potentials for the two global $U(1)$ symmetries.

By using numerical calculation,
we can show that both indices agree in a series expansion form
by setting $t'=t, y'=y$ \cite{Imamura:2011su}.
\begin{align}
&
I_{\rm QED}(x,y,t)=I_{{\rm WZ}}(x,y,t)\nonumber\\
&=\left(1
+\left(\frac{1}{ty}+\frac{t}{y}\right)a
+\left(\frac{1}{t^2y^2}+\frac{t^2}{y^2}\right)a^2
+\left(\frac{1}{t^3y^3}+\frac{t^3}{y^3}\right)a^3
+\left(\frac{1}{t^4y^4}+\frac{t^4}{y^4}\right)a^4
+{\cal O}(a^5)\right)\nonumber\\
&+\left(y^2-2a^2+\frac{a^4}{y^2}+{\cal O}(a^5)\right)b^2+\left(y^4+\left(\frac{y}{t}+ty\right)a^3-3a^4+{\cal O}(a^5)\right)b^4+{\cal O}(b^6),
\end{align}
where we set
$a=x^{1-h}, b=x^h.$

One can show the agreement of both indices analytically \cite{Krattenthaler:2011da}.
Let us explain the analytic proof briefly.
For this purpose,
it is convenient to define q-shifted factorials following \cite{Krattenthaler:2011da}.
\begin{equation}
(A;q)_{n} = \biggl\{
\begin{array}{lc}
\prod_{k=0}^{n-1} (1-A q^k)  & (n>0)\\
1  & (n=0)\\
\prod_{k=0}^{|n|-1} (1-Aq^{-k-1})^{-1}  & (n<0).
\end{array}
\end{equation}
We also use the abbreviation such that $(A;q)=(A;q)_{\infty}$ and $(A_1, A_2, \cdots, A_l;q)
=(A_1;q) (A_2;q)  \cdots (A_l;q)$.
By using this notation, the indices of SQED and the dual Wess-Zumino model can be rewritten as
\begin{eqnarray}
\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!I_{\rm QED}(x,y,t)
&=&\sum_{M\in{\bf Z}}t^{M}\oint\frac{dz}{2\pi i z} a^{|M|/2}y^{-|M|}
{(z^{-1}y^{-1}a^{1\over2} x^{|M|+1}, zy^{-1}a^{1\over2} x^{|M|+1};x^2)
\over
(zya^{-{1\over2}} x^{|M|+1}, z^{-1}ya^{-{1\over2}} x^{|M|+1};x^2)},
\label{sqed}\\
\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!I_{\rm WZ}(x,y',t')
&=&{(t'^{-1}y' a^{-{1\over2}} x^{2}, t' y' a^{-{1\over2}} x^{2}, y'^{-2} a ;x^2)
\over
(t'y'^{-1} a^{{1\over2}} , t'^{-1} y'^{-1} a^{{1\over2}}, y'^2 a^{-1} x^2 ;x^2)}.
\label{wz}
\end{eqnarray}
The contour integral in \eqref{sqed} is carried out around the unit circle.
The poles of the integrand in \eqref{sqed}
in the unit circle are $z= y a^{-{1\over2}} x^{|M|+1+j}$, where $j\in{\mathbf Z}\geq0$
when $x<a^{{1\over2}}/z<1$.
Picking up these poles,
one can perform the residue calculus of \eqref{sqed}
\begin{equation}
I_{\rm QED}(x,y,t)
=\sum_{M\in{\bf Z}}t^{M} \hat a^{|M|/2}
\sum_{j=0}^\infty {(\hat a x^{-2j}, x^{2(|M|+1+j)};x^2)
\over
(\hat a^{-1} x^{2(|M|+1+j)}, x^{2};x^2) (x^{-2j};x^2)_j},
\end{equation}
where we set $\hat a = y^{-2}a$.
It turns out from a straight forward calculation
that one can perform the summation over $M$ without taking the absolute value for $M$.
By using this fact and a little calculation,
one finds
\begin{equation}
I_{\rm QED}(x,y,t)
=
\sum_{j=0}^\infty \sum_{M\in{\bf Z}}(t\hat a^{{1\over2}})^M {(\hat a^{-1} x^{2(1+j)};x^2)_M
\over
(x^{2(1+j)};x^2)_M}
{(\hat a x^{-2j}, x^{2(1+j)};x^2)
\over
(\hat a^{-1} x^{2(1+j)}, x^{2};x^2) (x^{-2j};x^2)_j}.
\end{equation}
By using Ramanjujan summation formula
\begin{equation}
\sum_{M\in{\mathbf Z}} {(A;q)_M \over (B;q)_M} z^M =
{(q, B/A, Az, q/(Az);q) \over (B,q/A,z, B/(Az);q)},
\end{equation}
one can perform the summation over $M$ as
\begin{eqnarray}
I_{\rm QED}(x,y,t)
&=&
{(\hat a ;x^2)\over (t \hat a^{{1\over2}}, t^{-1} \hat a^{{1\over2}};x^2)}
\sum_{j=0}^\infty {( t^{-1} \hat a^{{1\over2}} x^{-2j}, t \hat a^{-{1\over2}} x^{2(1+j)};x^2)
\over
(\hat a^{-1} x^{2(1+j)};x^2) (x^{-2j};x^2)_j}\\
&=&
{(\hat a, t \hat a^{-{1\over2}}x^2 ;x^2)\over (t \hat a^{{1\over2}}, \hat a^{-1}x^2  ;x^2)}
\sum_{j=0}^\infty {(  \hat a^{-1} x^2 ;x^2)_j \over (x^{2};x^2)_j} (t^{-1} \hat a^{{1\over2}})^j.
\end{eqnarray}
By using binomial theorem
\begin{equation}
\sum_{j=0}^\infty {(A;q)_j \over (q;q)_j} z^j =
{(Az;q) \over (z;q)},
\end{equation}
one can also carry out the summation over $j$ as
\begin{eqnarray}
I_{\rm QED}(x,y,t)
&=&
{(\hat a, t \hat a^{-{1\over2}}x^2, t^{-1} \hat a^{-{1\over2}}x^2 ;x^2)\over (t \hat a^{{1\over2}},  \hat a^{-1}x^2, t^{-1}\hat a^{{1\over2}};x^2)},
\end{eqnarray}
which precisely agrees with $I_{\rm WZ}(x,y,t)$ in \eqref{wz}.

One can study mirror pairs with more flavor case \cite{Imamura:2011su,Krattenthaler:2011da}
and with a more general background \cite{Kapustin:2011jm}.

\subsection{AdS$_4$/CFT$_3$ duality}
\label{ads/cft}

We apply the formula to an ${\cal N}=2$ Chern-Simons-matter theory
which has M-theory dual on AdS$_4 \times Q^{1,1,1}$,
where $Q^{1,1,1}$ is a homogeneous manifold defined by
\begin{equation}
\frac{SU(2)\times SU(2)\times SU(2)}{U(1)\times U(1)}.
\end{equation}
From the definition,
$Q^{1,1,1}$ has the isometry
\begin{equation}
SU(2)_1\times SU(2)_2\times SU(2)_3\times U(1)_R.
\label{isom}
\end{equation}
The last $U(1)_R$ factor is identified with the R-symmetry.

A corresponding gauge theory
is proposed as a quiver Chern-Simons theories studied in \cite{Franco:2008um}.
The field contents and symmetries are
shown in Table \ref{table:q111}.
\begin{table}[htb]
\caption{Symmetries and their charge assignments for the fields of a gauge theory dual to M-theory dual on AdS$_4 \times Q^{1,1,1}$.
In the table, $U(N)_{a,k_a}\,(a=1,2,3,4)$ is $a$-th $U(N)$ gauge group with Chern-Simons level $k_a$,
$U(1)_i\,(i=1,2,3)$ is Cartan subgroup of $SU(2)_i$. }
\label{table:q111}
\begin{center}
\begin{tabular}{ccccccc}
\hline
 Symmetry     & $A_1$ & $A_2$ & $B_1$ & $B_2$ & $C_1$ & $C_2$ \\
\hline
\hline
$U(N)_{1,k}$& $0$ & $0$ & $\bar N$ & $0$ & $0$ & $N$ \\
$U(N)_{2,k}$& $0$ & $0$ & $0$ & $N$ & $\bar N$ & $0$ \\
$U(N)_{3,-k}$& $\bar N$ & $\bar N$ &$N$ & $0$ & $N$ & $0$ \\
$U(N)_{4,-k}$& $N$ & $N$ &$0$ & $\bar N$ & $0$ & $\bar N$ \\
\hline
$U(1)_1$ & $\frac{1}{2}$ & $-\frac{1}{2}$ & $0$ & $0$ & $0$ & $0$ \\
$U(1)_2$ & $0$ & $0$ & $\frac{1}{2}$ & $-\frac{1}{2}$ & $0$ & $0$ \\
$U(1)_3$ & $0$ & $0$ & $0$ & $0$ & $\frac{1}{2}$ & $-\frac{1}{2}$ \\
$U(1)_R$ & $1-2h$ & $1-2h$ & $h$ & $h$ & $h$ & $h$ \\
\hline
\end{tabular}
\end{center}
\end{table}
The superpotential of the theory is
\begin{equation}
W=\mathrm{tr}(\epsilon^{ij}C_2B_1A_iB_2C_1A_j).
\end{equation}
It turns out that the moduli space of the theory is $Q^{1,1,1}/{\bf Z}_k$,
and this theory is expected to be dual to M-theory on AdS$_4\times Q^{1,1,1}/{\bf Z}_k$.
Here ${\bf Z}_k$ is included in the diagonal $SU(2)$ of
$SU(2)_2\times SU(2)_3$,
so ${\bf Z}_k$ breaks $SU(2)_2\times SU(2)_3$ to $U(1)_F\times U(1)_B$.
The manifest global symmetry in the Lagrangian is
\begin{equation}
SU(2)_1\times U(1)_F\times U(1)_B\times U(1)_R.
\label{symq111}
\end{equation}
The charge assignment of $U(1)_B (U(1)_F)$ is
given by the summation (difference) of those of $U(1)_2$ and $U(1)_3$.
Using the symmetry and the fact that
the superpotential has the R-charge $2$,
we can determine R-charges of the chiral fields with one parameter $h$.
If AdS$_4$/CFT$_3$ duality is the case in this model,
then the gauge theory must have the global symmetry \eqref{isom}
rather than \eqref{symq111} when $k=1$ in the large $N$ limit.
In the following,
we give  evidence of this global symmetry enhancement by using a superconformal index.

Since we fix the charge assignments of the fields,
we can compute an index of this theory by applying the formula.
We compute the index of this model numerically up to $x^2$ order when $k=1$.
The neutral part of the index is
\begin{equation}
I^{(0)}(x,z_i)=1+
\chi_\frac{1}{2}(z_1)
\left(\frac{z_2^{1/2}}{z_3^{1/2}}+\frac{z_3^{1/2}}{z_2^{1/2}}\right)
x+
\left[
\chi_1(z_1)\left(2\frac{z_2}{z_3}+1+2\frac{z_3}{z_2}\right)
-3
\right]
x^2+\cdots,
\label{q111i0}
\end{equation}
where $\chi_s(z)$ is the $SU(2)$ character with spin $s$
\begin{equation}
\chi_s(z)=z^s+z^{s-1}+\cdots+ z^{-s}.
\end{equation}
The charged parts are
\begin{eqnarray}
\!\!\!\!\!\!\!\!I^{(+)}&=&1+\chi_\frac{1}{2}(z_1)z_2^{-1/2}z_3^{-1/2}x
+\left[(\chi_1(z_1)-1)(z_2^{-1}+z_3^{-1})
+2\chi_1(z_1)z_2^{-1}z_3^{-1}\right]x^2
+\cdots.
\label{q111ip}\\
\!\!\!\!\!\!\!\!I^{(-)}&=&1+\chi_\frac{1}{2}(z_1)z_2^{1/2}z_3^{1/2}x
+\left[(\chi_1(z_1)-1)(z_2+z_3)
+2\chi_1(z_1)z_2z_3\right]x^2
+\cdots.
\label{q111im}
\end{eqnarray}
To obtain the positive part of index,
we sum up the following contributions including $I^{(+)}_{(0,0,0,0)}(x,z_i)=1$.
\begin{eqnarray}
I^{(+)}_{(1,1,1,1)}(x,z_i)
&=&\chi_\frac{1}{2}(z_1)z_2^{-1/2}z_3^{-1/2}x
+(\chi_1(z_1)-1)(z_2^{-1}+z_3^{-1})x^2
+\cdots,
\nonumber\\
I^{(+)}_{(2,2,2,2)}(x,z_i)
&=&\chi_1(z_1)z_2^{-1}z_3^{-1}x^2
+\cdots,
\nonumber\\
I^{(+)}_{((1,1),(1,1),(1,1),(1,1))}(x,z_i)
&=&\chi_1(z_1)z_2^{-1}z_3^{-1}x^2+\cdots.
\end{eqnarray}

We have several remarks from these results.
First,  we observe that
the index does not depend on $h$.
Second,
we can easily see that the index has the following properties.
\begin{eqnarray}
I^{(*)}(x,z_1,z_2,z_3)&=&I^{(*)}(x,z_1^{-1},z_2,z_3),
\label{q111isym1}\\
I^{(*)}(x,z_1,z_2,z_3)&=&I^{(*)}(x,z_1,z_3,z_2),
\label{q111isym2}\\
I^{(-)}(x,z_1,z_2,z_3)&=&I^{(+)}(x,z_1,z_2^{-1},z_3^{-1}).
\label{q111isym3}
\end{eqnarray}
And each relation comes from symmetry underlying the theory.
(\ref{q111isym1}) comes from $SU(2)_1$ symmetry.
(\ref{q111isym2}) is due to ${\mathbf Z}_2$ symmetry,
which exchanges $B_i$ and $C_i$.
(\ref{q111isym3}) originates in the charge conjugation symmetry,
which exchanges $B_1, C_1$ and $B_2, C_2$, respectively.

To see the flavor symmetry enhancement to $SU(2)^3$,
we compute the total index by using the factorization property \eqref{factor}.
To do this,
we simply multiply (\ref{q111i0}), (\ref{q111ip}), and (\ref{q111im}).
\begin{equation}
I(x,z_i)
=1
+\chi_{\frac{1}{2}}(z_1)\chi_{\frac{1}{2}}(z_2)\chi_{\frac{1}{2}}(z_3)x
+(2\chi_1(z_1)\chi_1(z_2)\chi_1(z_3)-2)x^2
+\cdots.
\label{indexq111}
\end{equation}
This is invariant under the Weyl reflections
$z_i\rightarrow z_i^{-1}$ and under permutations among $z_i$,
which implies that the theory has $SU(2)^3$ symmetry.
This is precisely what we expect from the isometry of $Q^{1,1,1}$.

The comparison with the index of dual M-theory was carried out in \cite{Cheon:2011th}.
The gravity index can be obtained by summing the BPS spectrum
of M-theory on AdS$_4\times Q^{1,1,1}$,
which was investigated in \cite{Merlatti:2000ed}.
It turns out from the spectrum that up to the $x^2$ order
the single particle index receives the contribution only from one hypermultiplet and short vector multiplets.
The result is
\begin{eqnarray}
&&
I^{\rm sp}(x,z_i)=
\chi_\frac{1}{2}(z_1)
\chi_\frac{1}{2}(z_2)
\chi_\frac{1}{2}(z_3)x
\notag\\
&&\qquad+
\left(
\chi_1(z_1)
\chi_1(z_2)
\chi_1(z_3)
-\chi_1(z_1)
-\chi_1(z_2)
-\chi_1(z_3)
-2
\right)x^2+\cdots.
\label{q111sp}
\end{eqnarray}
Note that the positive terms are coming from the hypermultiplet and
the negative terms are from (massless) vector multiplets.
One can easily see that
the multi-particle index for M-theory on AdS$_4\times Q^{1,1,1}$,
which can be obtained as plethystic exponential of (\ref{q111sp}),
agree with \eqref{indexq111} up to the order of $x^2$.

Consult \cite{Imamura:2011uj,Cheon:2011th} for further investigation
such as applications to other ${\cal N}=2$ Chern-Simons matter theories
and their gravity duals.

\section{Summary and discussion}

We have seen aspects of three dimensional superconformal indices.
They can be computed exactly
by using localization method including the contribution of monopole operators,
which play a key role to elucidate the rich structure of
three-dimensional superconformal field theories and their M-theory duals.
We showed that superconformal indices can capture the rich structure
and non-perturbative aspects such as mirror duality, AdS$_4$/CFT$_3$ duality.

In Section \ref{ads/cft},
using a superconformal index
we showed  evidence of a global symmetry enhancement
of a gauge theory dual to M-theory on AdS$_4\times Q^{1,1,1}$
in $k=1$ in the large $N$ limit.
It is natural to ask whether this phenomenon occur in a finite $N$.
We strongly suspect this is not the case at least in this model.
This is simply due to the fact that
in a finite $N$ case
a non-diagonal monopole operator contributes to the index non-trivially
and thus the enhancement doesn't happen.
To discuss this concretely,
let us compute the index of the gauge theory in abelian case.
This can be done simply
by applying the formulas \eqref{formula}, \eqref{fvecdef} and \eqref{fchdef}.
It turns out that
several non-diagonal monopole operators contribute to the index non-trivially like
\begin{eqnarray}
I_{(1,-1,0,0)}(x,z_i)
&=&x^4-\biggl(\frac{1}{z_1^2}+z_1^2\biggr)x^6+\cdots,\\
I_{(0,0,-1,1)}(x,z_i)
&=&x^{2+2h}-4 x^{6+ 2h}
+\chi_{1\over2}(z_1)\biggl({z_2^2\over z_3^2}+{z_3^2 \over z_2^2}\biggr)x^{7+2h}
+\cdots.
\end{eqnarray}
Contributions coming from non-diagonal monopole operators like these
break the invariance under the Weyl reflections and permutations of $z_i$
\footnote{
The contribution of the index only from diagonal monopole operators up to the order of $x^3$
is
\begin{eqnarray}
\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!&&I_{diagonal}(x,z_i)
=1+\chi_{\frac{1}{2}}(z_1)\chi_{\frac{1}{2}}(z_2)\chi_{\frac{1}{2}}(z_3)x
+(\chi_1(z_1)\chi_1(z_2)\chi_1(z_3)-\chi_1(z_1)-\chi_1(z_2)-\chi_1(z_3)-3)x^2 \notag\\
\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!&&\qquad+\chi_{1\over2}(z_1)\chi_{1\over2}(z_2)\chi_{1\over2}(z_3)
(\chi_1(z_1)\chi_1(z_2)\chi_1(z_3)-\chi_1(z_1)\chi_1(z_2)-\chi_1(z_2)\chi_1(z_3)-\chi_1(z_1)\chi_1(z_3)+2)x^3 \notag\\
\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!&&\qquad +{\cal O}(x^4),
\label{indq111finite}
\end{eqnarray}
which is invariant under the Weyl reflections and permutation of $z_i$.
}

Therefore, we naturally expect that
these contributions from non-diagonal monopole operators decouple
after the large $N$ limit.
This expectation is also natural from the dual geometry perspective.
We proposed in \cite{Imamura:2008ji}
that
a non-diagonal monopole operator corresponds to
a M2-brane wrapped on a two-cycle in an internal manifold.
We gave evidence for this on ${\cal N}=4$ Chern-Simons theories
by using supconformal indices \cite{Imamura:2009hc,Imamura:2010sa}.
In case of ${\cal N}=4$ Chern-Simons theories,
such two cycles are vanishing ones coming from orbifold singularities,
so wrapped M2-branes on them are BPS and contribute to the index
of order $1$.
In a general ${\cal N}=2$ Chern-Simons theories, however,
such two cycles have a finite volume.
Therefore, even if wrapped M2-branes on them become BPS and
contribute to the index,
the contribution is of order $x^{\sqrt{N}}$,
so decouple after the large $N$ limit.

It is worth mentioning that
this consideration is not inconsistent with
the earlier study that
the supersymmetry is enhanced from ${\cal N}=6$ to ${\cal N}=8$ in ABJM theory with $k=1, 2$
\cite{Gustavsson:2009pm,Kwon:2009ar,Bashkirov:2010kz,Samtleben:2010eu}.
This is simply because
ABJM theory does not have non-diagonal monopole operators \cite{Imamura:2008ji}.
Indeed, for example,
we can compute the index of abelian ABJM theory with $k=1$ by using the formula.
Here we use the normalization in \cite{Kim:2009wb}.
We can evaluate it analytically and the result is given by the plethystic exponential of the following single-particle index
\begin{eqnarray}
\mathfrak{i}_{ABJM} &=&
(v^{1\over2} \chi_{1/2}(z_A) y+ v^{-{1\over2}} \chi_{1/2}(z_B) y^{-1})
{x^{{1\over2}} \over {1-x^2}} \notag\\
&&- (v^{1\over2} \chi_{1/2}(z_A)  y^{-1} + v^{-{1\over2}} \chi_{1/2}(z_B)y)
{x^{\frac{3}{2}} \over 1-x^2}.
\label{abjmsp}
\end{eqnarray}
Here $z_A$ and $z_B$ are chemical potentials for $SU(2)_A$
and $SU(2)_B$ symmetries rotating the complex scalars $A_1, A_2$ and $B_1, B_2$, respectively.
$v$ is a chemical potential for $U(1)_b$ symmetry and
$y$ is that for the diagonal monopole charge.
By setting $v=1$, which means making the baryonic charge of the fields trivial,
this single-particle index \eqref{abjmsp}
reduces to that of four complex chiral multiplets with a suitable charge assignment.
This is consistent with the expectation that abelian ABJM theory is
an effective field theory of one membrane, which, in particular, has $SO(8)$ R-symmetry.

On the other hand,
a discrepancy was found between
an index for several ${\cal N}=2$ gauge theories calculated by using the large $N$ formula
and that for their gravity duals calculated from the BPS spectrum obtained by Kaluza-Klein analysis at a higher order \cite{Cheon:2011th}.
It will be worthwhile to investigate whether there is a discrepancy in other ${\cal N}=2$ models,
and what is the problem if there is.

We hope we will come back to these issues in the near future.

\vspace*{1ex}
\section*{Acknowledgments}
The auther would like to thank Yosuke Imamura and Daisuke Yokoyama
for early collaboration.
He is also grateful to Yosuke Imamura and Seok Kim for nice comments.
He was supported by National Research Foundation of Korea (NRF) grant No. 2010-0007512,
and No. 2009-0076297.

\bibliographystyle{utphys}

redpajama_set_name: RedPajamaArXiv


Victoria, London is particularly popular with visitors looking to stay in London thanks to its convenient and relatively central location as well as its excellent transport links. There are a total of three underground lines and countless buses which run from the area and radiate out to all parts of London, making it an ideal place to set up base for those looking for hotels in London or hostels or bed and breakfasts. Added to this, the area itself is within easy reach of a number of famous and worthwhile attractions.
For example, located to the north is Buckingham Palace and one of the many royal London parks. From here visitors can walk to Westminster where the Houses of Parliament, London Eye and Westminster Abbey are located, as well as Trafalgar Square on the doorstep of London's West End theatre and entertainment district. London accommodation in Victoria, London therefore tends to be extremely popular and TravelStay boasts a number of different options which are sure to cater for all types of traveller.
Prices for this luxury accommodation start from £59.50 and visitors will also be conveniently located close to the designer stores on Sloane Street and Brompton Cross.
Astors Hotel is a brand-new four-star bed and breakfast which promises quality service to go alongside its prime situation. Prices start at £44.75.
Perfect for backpackers and those studying in the capital, Wigram House offers a choice of single and twin rooms, housed within shared apartments. Each apartment at this budget accommodation in London has its own kitchen and bathroom facilities.
The Surtees Hotel is located a short walk from the station and only a few minutes away from Westminster Cathedral, where visitors can go and enjoy panoramic views across London. A stay in this two-star London hotel close to the hustle and bustle of central London costs just £33.33 per person.
Recently refurbished to a very high standard, Astor Victoria offers quality budget accommodation. Full cooking facilities are available at this residence. This London budget hostel is near Victoria Station and is ideal for students and young travellers on a budget.
Book yourself into Astor Hyde Park now if you want to stay in a brand new budget London hostel which is on the doorstep of major attractions like the Natural History Museum and the Royal Albert Hall in South Kensington. Continental breakfast and access to a TV lounge and games room is included in the amazing price! Please Note: You need to be 18-35 years old to stay here.
Female only quality hostel in Centre of London. Park House Hostel London in Earls Court is a safe and clean London budget hostel for women. Each room is a private single room, so you need not share with someone who snores! The hostel is near the Underground and the friendly bars of Earls Court.


We at AEM Consolidated Pty Ltd are committed to providing you with the highest level of customer service, which includes protecting your privacy.
Information we collect includes details that have been provided to us by yourself for your nominated service. These details may include; Name, Address, Telephone- Mobile phone number, Fax number, Email address, Method of payment i.e. Visa/ MasterCard details.
For customers applying for a commercial credit account with AEM, in addition to the details mentioned in the preceding paragraph, we will also collect information such as, ABN, business name, date of birth, trading history, commercial trading and banking references and guarantor details.
We collect this information in order to further improve our products and services along with general requirements to complete warranty service, normal service and repair. We may use the information to improve our products and services. We will not sell, distribute or lease your personal information to third parties unless we have your permission or are required to do so by law.
We may occasionally send promotional emails about new products, special offers or other information which we think you may find interesting, using the email address you have provided.
We aim to make sure the information we are holding from you is accurate, up to date, complete and relevant. If you believe that any information we are holding on you is incorrect or incomplete, please write or email us as soon as possible at the above address and we will promptly correct the information as necessary.
If you choose not to provide certain information, we may not be able to provide the service to you or the level of customer service that we strive for.
We will take reasonable steps to ensure your personal information will not be misused, interfered with and accessed from unauthorized access and disclosure.
The type of information we collect depends on what information and services you request and use, but generally does not contain or is not linked to your personal information.
AEM Consolidated is committed to working with its customers to obtain a fair resolution of any complaint or concern about privacy.
Call us on 8162 5957 between 8.00am and 5.00pm Monday to Friday.


Please scroll to view all shop items.
Welcome to our KS Teamwear shop.
Please use the below buttons to view full range of our products.
You can always write few more words about this shop- like a little introduction.
Here you can add few words about Mitre and your close relation ship with this sponsor. Also you can add the hyperlink to their website.
Please see their shop Mitre UK.


Please use the form below to get in touch with us. Alternatively you may contact us on the postal address provided below. You may also get in touch with us on telephone numbers provided.
wmvdktsc Help us prevent SPAM!


Hosting No.1 Jalandhar, Punjab provides Linux Shared Web Hosting, Windows Shared Web Hosting, Java Shared Web Hosting, Windows and Linux Reseller Web Hosting, Linux and Windows VPS Hosting, Managed and Self Managed Dedicated Servers in Jalandhar, Punjab, India and abroad as well. You can choose lots of options for your perfect web hosting plan which is available at reasonable prices. We grant 24X7 telephonic support to our clients. We provide safe and secure web services and 99.9% server uptime. Jalandhar, Punjab Hosting No. 1 provides best web hosting services. We offer 100% satisfied web services to our clients.
Jalandhar, Punjab Shared Hosting No.1 grants you nominal prices and secure web hosting services with 100 % telephonic and mail Support. Shared Hosting No. 1 Jalandhar, Punjab provides Shared Windows Web Hosting, Shared Linux Web Hosting, Shared Java Web Hosting, Tomcat Hosting, and Apache Server Hosting. Hosting No. 1 Shared Hosting in Jalandhar, Punjab, India provides higher standard web hosting. With Shared Web Hosting in Jalandhar, Punjab, you can choose plans for business hosting, commercial hosting, corporate hosting, etc. Clients can select WINDOWS Shared Web Hosting, LINUX Shared Web Hosting, or JAVA Shared Web Hosting.
Reseller Hosting No.1 Jalandhar, Punjab provides safe web hosting solutions with 24x7 technical Support at very affordable cost. Hosting No. 1 Reseller Berhampur offers Windows Reseller Hosting, Linux Reseller Hosting, Java Reseller Hosting. Reseller Hosting No. 1 in Jalandhar, Punjab, India offers world class reseller hosting solutions. With Reseller Hosting in Jalandhar, Punjab, India, resellers can select plans as per their requirements. You can select WINDOWS Reseller Hosting, LINUX Reseller Hosting, or JAVA Reseller Hosting.
Hosting No.1 Jalandhar, Punjab provides you with perfect plans for all VPS including Managed Windows VPS, Managed Linux VPS, Self Managed Linux VPS and Self Managed Windows VPS that include 24X7 technical support. All VPS are high configured and fully secure. VPS Hosting No. 1 Jalandhar, Punjab offers you perfect VPS packages at affordable cost.
Dedicated Hosting No.1 Dedicated Server Hosting Jalandhar, Punjab, India offers optimum dedicated server hosting services for Managed Windows Dedicated Server, Managed Linux Dedicated Server, Self Managed Linux Dedicated Server and Self Managed Windows Dedicated Server including 24x7 technical support. All Dedicated Servers at Hosting No. 1 Jalandhar, Punjab are highly configured and totally safe and secure. Hosting No. 1 Dedicated Server Jalandhar, Punjab, India grants perfect Dedicated Server plans at affordable rates.


35th Celebration – You Make it Possible!
Hey Instructors! The 35th Anniversary Training Workshop is coming up and we can use your assistance to help everything run smoothly. Please click the link below and see what volunteer opportunities are available and sign up to help.
What are your favorite Body & Soul memories?
Limitless! What does that mean to you?


QUE: Can I use a rubber hose for very high temperature?
ANS: Generally hydraulic hose can be used up to 100º C for oil. High temperature hoses are also available which works up to 135º C for oil.
QUE: Is it necessary to specify hose Internal Diameter even when thread size is specified?
ANS: It will be very appropriate to specify thread size as well as Internal Diameter of hose to facilitate the desired flow.
QUE: Can I specify "flexible" braided hoses for all my hose requirement?
ANS: No. Though all hoses are flexible, it is necessary to specify the inner core material like rubber, PTFE, stainless steel, silicon, PVC ,food grade rubber etc. and also it is necessary to specify the braiding like steel wire braided, textile braided, SS over-braided , on outer diameter.
QUE: I have a hydraulic hose with me, Can I use this for high temperature water or steam application.
ANS: No. The inner rubber for high temperature water & steam application are different. Hence it is not advised.


Two days after Naseemuddin Siddiqui was shown the exit door by Mayawati, it was entry for former Minister Anis Ahmed urf Phool Babu. Addressing a heavily attended press conference in Lucknow today, he counter levelled serious charges on his former colleague. Accusing him of obstructing the entry of Muslims in BSP. He said that it would be worthwhile to know how many members did Naseemuddin inducted into the party. Infact he accused him of not bringing into the BSP fold the Nadwa Maulana, Muslims educationist, Barielly, and Moradabad muslims. There are about 18% Muslims in the states.
During his period of ministership, he had arranged big rallies at Moradabad, Barielly, Banaras, Kannauj, Kanpur but was removed from the ministry at the behest of him. He further boosted that he will bring into the BSP party, Muslims from all walks of life, and make it a stronger party for the 2019 elections. Naseemuddin did not give any importance to Muslims, OBC and other BC, in the party but it will be his priority to bring them back to BSP. Accusing Naseemuddin of harming him thru his 200 goons, at a meeting in Moradabad, he managed to complete the function with the help of administration and media persons.
Quoting Maula Ali ( RA), Anis Ahmed said that in his wasiyaat to his son, Maula Ali ( RA) had told him that he should not talk when in anger, secondly, he must not make company of foolish persons, and thirdly he must not do Amanat mei Khayanat. Perhaps he was refereeing to Naseemuddin role in membership ghotala, as mentioned by Mayawati. Dismissing his charge that BSP will finish off, Anis said that BSP is a mission, on the lines of Baba sahib Ambedkar and Kanshi Ram. It is a party of Dalits and Muslims.
Anis Ahmed expressed his gratitude to Mayawati for re-inducting him back into the party and he will try to make it stronger. Praising S C Mishra, he said that he is pillar of the party and he is not corrupt, as alleged by Naseemuddin. Amongst his followers Shakil Ahmed Khan, Atal Singh Jaiswal, M S Faridi, Ansar Khan, Jawed Ahmed, Maulana Dildar, Mukarram Ali attended the press conference.
It is to be seen now, whether Anis Ahmed entry into BSP will make any impact in its prospect in 2019 elections or will he able to bring back Muslims back into its fold.


text:
package no.digipost.util;

import no.digipost.function.ThrowingConsumer;

/**
 * An adapter to enable any arbitrary object to be managed by the
 * try-with-resources facility of Java >= 7, i.e. it will have a
 * closing operation invoked when exiting the {@code try}-block.
 *
 * @param <T> The type of the arbitrary object which will have an operation invoked
 *            on exiting from a try-with-resources block.
 * @param <X> The type of exception which may be throwed by the {@code closeOperation}
 */
public final class ThrowingAutoClosed<T, X extends Exception> extends AutoCloseableAdapter<T, X> implements AutoCloseable {

    public ThrowingAutoClosed(T managedObject, ThrowingConsumer<? super T, X> closeOperation) {
        super(managedObject, closeOperation);
    }

}


text:
SYNONYM

#### According to
The Catalogue of Life, 3rd January 2011

#### Published in
Report Dept. of Agric. Uganda 31 (1927)

#### Original name
Alternaria longipedicellata Snowden, 1927

### Remarks
null


LIMA, Peru (AP) — With temperature data showing 2014 currently tied for the hottest year on record, the U.N. weather agency on Wednesday rejected claims that global warming has paused.
"Whether such a period is about to begin, we cannot say but the warm 2014 is a reminder that the warming never stopped and the long term trend is up, up, up," Oppenheimer said.
"Around 93 percent of the excess energy trapped in the atmosphere by greenhouse gases from fossil fuels and other human activities ends up in the oceans. Therefore, the heat content of the oceans is key to understanding the climate system," the WMO said.
While scientists are now 95 percent certain that the temperature rise since the middle of the 20th century is mostly man-made, they can't say with the same confidence how the warming affects different parts of the climate system, including the frequency of tropical storms or hurricanes.
In Lima, delegates from more than 190 countries are trying to lay the groundwork for a global emissions pact that's planned to be adopted next year. Divisions between rich and poor countries have slowed the negotiations over the years, but a U.S.-China emissions deal last month has injected new hope into the talks.
U.N. climate chief Christiana Figueres said temperature data added urgency to the talks, but noted that you don't have to be a scientist to realize that the climate is changing.


text:
Ryan Barrett
Arrival | Barrett signs for Spartans
Blyth Spartans are delighted to confirm the signing of defender Ryan Barrett. The former Wales youth international joins the club following his release from Inverness Caledonian Thistle earlier this month, where he made four appearances this season. Barrett came through the academy at Newcastle United where he featured regularly for the U23s, before departing the Magpies last summer and making the move to Scotland. Barrett will be available and in…


Comments: This 2019 Dodge Challenger GT is complete with top-features such as the backup sensor, push button start, remote starter, backup camera, parking assistance, Bluetooth, braking assist, dual climate control, hill start assist, and stability control. It has a 6 Cylinder engine. This one's on the market for $41,332. This coupe awd scored a crash test safety rating of 5 out of 5 stars. For a good-looking vehicle from the inside out, this car features a dazzling granite exterior along with a black interior. Interested? Call today and schedule a test drive!


In this book, the politics and poetics of cultures in the 1960s literary works of three renowned authors are examined: Savushun, Drama der Trauer by Simin Daneshvar (Iran), La Plaça del Diamant by Rodoreda (Spain), and Der geteilte Himmel by Christa Wolf (GDR). Based on these shared stories from under the authoritarian regimes of the Shah, General Franco and the communist authorities in East Germany, Yahya Kouroshi illuminates the subject of modernity from a cross-cultural perspective and traces the diverse developments from and alternatives to this global cultural and social phenomenon.
Yahya Kouroshi (Dr. phil.) forscht an der Universität Erfurt und am Kunsthistorischen Institut in Florenz (Max-Planck-Institut). Seine Schwerpunkte sind Neuzeitliches Denken und Interkulturalität.


Inspired by working detection dogs, K9 Nose Work is the fun search and scenting activity for virtually all dogs and people.
This easy to learn activity and sport builds confidence and focus in many dogs, and provides a safe way to keep dogs fit and healthy through mental and physical exercise.
K9 Nose Work starts with getting your dog excited about using his nose to seek out a favourite toy or treat reward hidden in one of several boxes, expanding the game to entire rooms, exterior areas, and vehicles.
As your dog grows more confident with his nose, target odours are introduced, and competition skills are taught.


text:
NextWhich Irish Groups Made it Onto Facebook Danger List?
"They lied. They misled you." — Rethink Abortion Rally Held Outside Leinster House
Dáibhí Ó Bruadair on 21/10/2021
The Life Institute's "Rethink Abortion" rally took place outside Leinster House last night.
The protest came in light of the ongoing review of the 2018 abortion legislation.
Attracting a crowd of around 300, the protest sought to draw attention to the reality of abortion in Ireland under the current legislation, and promote the pro-life message as the review proceeds.
Organisers stated their opposition to the review being used as a means to further liberalise abortion laws within the country, which seems to be the intention of many in government.
A press release prior to the rally argued that the review must take into consideration high abortion rates, late-term abortions, abortions targeting the disabled, and pressure being placed on parents to abort.
It also recommended that the 3-day waiting period be retained.
Niamh Uí Bhriain's speech opened proceedings, describing the number of abortions taking place within the state under the current legislation:
"13,243 children were killed by abortion in two years, that's more than the population of Arklow, more than the population of Santry…and we're here to say that must stop".
Uí Bhrian drew attention to the fact that the figures constitute the equivalent of 529 primary school classes (based on average class size). A nationwide billboard campaign highlighting such high abortion figures has taken place in recent weeks, and generated considerable publicity.
Peadar Toibín TD addressed the crowd next, noting the need for on the ground pro-life activism and stating that those fighting abortion stood on the right side of history.
Vicky Wall described her work with "Every Life Counts", a pro-life organisation which offers support to families whose children have been diagnosed with fatal foetal abnormalities. She criticized the tendency within the maternity system for such parents to be pressurised into abortion.
Megan Bopp was next to speak, detailing ongoing youth activism within the pro-life movement:
"If we don't stand up for this, nobody will….but the reality of abortion as hard as it is, it cannot be dismissed and it cannot be ignored. We have to fight to bring this to the forefront, because on average we're losing 18 babies a day."
Bopp also spoke on the misleading rhetoric which had given voters the impression that abortion would be rare and resorted to primarily in cases of fatal foetal abnormalities, emergencies, and threats to the mother's life. 98.1% of abortions in the state have not fallen under such criteria.
The night continued with further speeches, with speakers including Senator Katherine Keogan, Carol Nolan TD, Ben Scanlan and Michael Collins TD. Nolan mentioned late-term abortions taking place under the current legislation, alongside her work with other TD's to introduce a Pain Relief Bill in the Dáil.
The three day waiting period requirement was mentioned, alongside figures which state that almost 900 women have changed their mind on whether to proceed with an abortion during this period. The testimonies of women who had availed of abortions and regretted the decision were read out, detailing their feeling of having been misled over the procedure.
Michael Collins TD noted how politicians had lied in relation to how prevalent abortion would be should a referendum pass. He continued:
"They promised us there would be no late-term abortions. They lied. They misled you. They misled this country bit by bit."
Collins stated his opposition to any measures seeking to further expand abortion access as part of the review, and assured attendees of his commitment to the pro-life cause.
Representatives of the National Party and Aontú were in attendance at the rally.
The event proceeded smoothly and demonstrated the willingness of the Irish pro-life movement to continue its fight in a post-Repeal era. The nature of the legislation review will become clearer in the coming months, with the public being offered the chance to take part in a consultation process.
Tagged in: 8th ammendment, Abortion, pro-choice, Pro-Life, Protest, Referendum
Posted by Dáibhí Ó Bruadair
Mairead Tóibín 22/10/2021 at 9:47 am
Senator Sharon Keoghan
Dave 22/10/2021 at 3:30 pm
Well, of course they lied. It's the left. The left always lies about everything, often just for practice.
Which Irish Groups Made it Onto Facebook Danger List?
The Journal's €350k Brussels Bailout


Picasa displays error "No Images Specified in Gallery XML"
SimpleViewer Forum » WP-SimpleViewer WordPress Plugin » Picasa displays error "No Images Specified in Gallery XML"
Topic: Picasa displays error "No Images Specified in Gallery XML"
Running WP 3.7.1 and SimpleViewer 2.3.2.1. Client is OS X Mountain Lion with both Safari & Chrome.
All works OK when selecting photos from the WP media library however, when specifying a Picasa gallery, nothing shows only the message "No Images Specified in Gallery XML".
I have tried 2 different IDs and several Picasa albums but nothing works. Same for both Safari & Chrome.
Re: Picasa displays error "No Images Specified in Gallery XML"
Try using either villa.ravello or 103574814608072251259 instead.
Hello Steven, many thanks for the speedy reply.
I have tried both suggestions and still no go.
Forgot to mention that on install of the plugin, it wouldn't activate because of permissions. After, setting al permissions correctly and still not able to activate, searched the forum and followed your suggest and commented out a few lines of code that checks for 777 permissions. At that point it activated and was able to create a gallery based on the media library. However, ultimately would like to use the Picasa feature.
That is certainly very strange (and I do not think it is related to the permissions issue you reported).
I notice that you have created a new gallery called 'newgallery' and, using the current version of WP-SimpleViewer (v2.3.2.1), I can display the gallery using any one of your three alternative Picasa User Ids (villa.ravello@gmail.com, villa.ravello or 103574814608072251259) and 'newgallery' as the Picasa Album Name.
When trying to display your 'Villa Ravello Grecamore Photo Gallery', try entering the Picasa Album Name without spaces ('VillaRavelloGrecamorePhotoGallery').
Really appreciate your speedy responses and detailed investigation.
As you probably saw from the site, the current used is called Traveifly v1.4.31. It has a built-in slider for the front page. Is this an issue, conflict? Its seems to be well behaved so far. Also, I deactivated all Plugins except SV.
The error message mentions Gallery XML. Is that a file created from the Picasa feed. If so where is it stored on the host? How is the Picasa feed handled? Does it store temporary data?
Is this an issue, conflict?
The gallery XML file (the file containing the image data) is generated dynamically by WP-SimpleViewer's 'gallery.php' file.
As you can see, there are no <image> entries in the file (which is the reason for the 'No Images Specified' message being displayed).
Try saving the following code into a file named 'picasa.php', upload it to your web server and open it in a browser.
The URLs of all the images and thumbnails in the Picasa Web Album should be listed as text.
The code uses the same routine that WP-SimpleViewer does but with all error trapping turned off.
What output do you see on-screen?
Also, what version of PHP do you have installed on your web server?
Running the script on its own takes both WordPress and WP-SimpleViewer out of the equation and the problem seems to lie somewhere between your own web server, your web server's PHP version/configuration and the script itself.
Try running phpinfo(). Save the following code into a file named 'phpinfo.php', upload it to your web server and open it in a browser.
Please let me know what version of PHP your web server is running and scroll down to (or search for) the SimpleXML section and check whether or not it is enabled. It sounds like it might be disabled and this would certainly account for the problem you are experiencing as the script to fetch the images from Picasa Web Albums relies on the PHP simplexml_load_file() method.
Just try my suggestion and reply to this thread when you can.
Hopefully the results will shed some light on the problem.