UPDATE: Thank you for your interest in the Small Business Solar Pilot program. The program is currently fully subscribed through the end of September 30, 2016. Please continue to check back for further updates.
The EPA approved a joint Total Maximum Daily Load to limit trash in the Anacostia River in the District of Columbia and Maryland.
Review the procedures, protocols, training opporunities and guidance documents for underground storage tanks.
Review the requirements, protocals and procedures for participation in the Voluntary Cleanup Program.
DOEE ensure the success of the Vehicle Emissions Inspection and Maintenance Program by reviewing data collection procedures, calibrating instruments, reviewing the training certification for emissions inspectors, and conducting station performance reviews.
Clean water is essential for human and animal life, for commerce and industry, and for recreation. DOEE administers several programs dedicated to improving water quality within the District.
The mission of the Water Quality Division is to restore and protect the surface and ground waters of the District of Columbia.
Review the legal standards and regulations that support water quality, stormwater management, and watershed protection in the District.
The District's Watershed Implementation Plan (WIP) explains how DC will achieve and maintain the water quality benefits outlined in the Bay TMDL.
DDOE's Watershed Protection Division (WPD) protects and restores the environmental health of our watersheds through stormwater management and sediment and erosion control regulations.
The Weatherization Assistance Program (WAP) provides technical and financial assistance to help low-income residents reduce their energy bills by making their homes more energy efficient.
The District is a densely populated city that is also home to a wide assortment of wildlife. Occasionally, these two populations interact and sometimes it isn't welcomed.
DOEE's Fisheries and Wildlife Division works to enhance wildlife populations and conserve sensitive species by protecting them and by improving their habitat.


Tannenbaum declined to get into details about Tannehill's health, choosing to respect the quarterback's privacy.
But a source close to Tannehill this week told The Herald the quarterback's knee is stable. The same source said alternative medicines have seriously considered to promote healing in Tannehill's knee, including stem cell injections and platelet rich plasma (PRP) injections, although clinical studies on the treatments are mixed.
Tannenbaum would not confirm or deny the alternate medical approaches have even been studied. He did, however, express confidence Tannehill will be good to go for the 2017 season.
One of Tannehill's favorite receivers last season was Stills, who led the team with nine touchdown catches. NJ.com reported Wednesday the Philadelphia Eagles will make Stills a top target in free agency if the Dolphins don't sign him before the start of free agency.
But Tannenbaum seemed to confirm a team source saying the Dolphins are not rushing to sign their free agents at the moment because, in part, agents are not overly motivated to get deals done a month out from free agency.
"All those players have earned the right to become free agents," Tannenbaum said. "We appreciate their contributions. We're constantly in contact with their agents -- [general manager] Chris Grier, [senior director of football administration] Brandon Shore, myself. We'll see where things go.
The NFL Scouting Combine is Feb. 28-March 6 and the Dolphins will see and continue talking to agents who represent their players, including Landry and Jones. And the team expects to give both players contract extensions although they are signed for 2017.
But barring a sudden willingness by the agents to do bargain extensions, it will come in due time. And due time is apparently not before players who are unsigned.
The Dolphins had a breakout year in 2016, posting a 10-7 record and making the playoffs for the first time since 2008. But Tannenbaum seemed to strike a sober tone about where people in the organization believes that performance of a year ago has left them.
"We were encouraged by last year. Adam and his staff in particular did an excellent job, particularly with all the bumps in the road we had with a 1-4 start, the injuries, and our quarterback getting hurt," Tannenbaum said. "To go to the playoffs is very hard to do and its an accomplishment that we're proud of and feel good about.
Based on that, do not look for the Dolphins to do what they did in 2015 when they went out and signed the most expensive player in free agency in Ndamukong Suh. This team does not believe it is one player away from winning a championship.
This team believes it must address multiple needs to keep improving.
That also includes restricted free agents. Kiko Alonso and Michael Thomas are arguably the most significant of those and will likely be tendered by the team so that it retains their rights. But Tannenbaum would not discuss at what level that tender offer, which would tie the players to the time for 2017, will come.
Tender numbers are not yet out for 2017, but same-round tenders are expected to be around $1.8 million while first-round tenders climb to about $3.6 million.
So do the Dolphins tender Alonso, who led the team in tackles and was a key contributor at middle linebacker, the lesser figure and save $2 million while also exposing him to possibly being signed away? Any team signing him would then owe the Dolphins a second-round pick, because that is the round Alonso was drafted in.
Or would the Dolphins tender Alonso at the first-round figure, practically assuing no team will give up its first rounder to sign the linebacker?
Tannenbaum would not say and it is possible that decision has not yet been made.
This much is clear: Last year the Dolphins lost significant and talented players. Rishard Matthews, Lamar Miller, Olivier Vernon, and Derrick Shelby left via free agency and that stung for a while. The Dolphins don't wish to see their own talent leak onto other rosters like that.
But, it should also be noted, the Dolphins lost all those players and improved from 6-10 in 2015 to their winning record. So the team doesn't want to lose talent but replacing players that go elsewhere is possible.


The annual plan of estimated storage shutdown for the period between 1/1/2015 and 31/12/2015.
The annual plan of estimated storage shutdown for the period between 1/1/2016 and 31/12/2016.
The annual plan of estimated storage shutdown for the period between 1/1/2017 and 31/12/2017.
The annual plan of estimated storage shutdown for the period between 1/1/2018 and 31/12/2018.
The annual plan of estimated storage shutdown for the period between 1/1/2019 and 31/12/2019.


If you are interested in Playing "AA" travel baseball or have questions please come to our Outlaws Baseball Parent Info night!!!
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-Find out about the evaluation Process, commitment, cost, get all your questions answered.


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text:
На́хид Курба́н Не́нши (, р. 2 февраля 1972) — канадский политик, на калгарийских муниципальных выборах 2010 избранный мэром Калгари (Альберта), сменив на этом посту Дейва Бронконье.

Биография
Ненши родился в Торонто (Онтарио), но вырос в Калгари (Альберта). Его родители Нурджа и Курбан были канадскими иммигрантами южноазиатского происхождения из Танзании и воспитывали двух детей: сына и дочь.

Он окончил Калгарийский университет, получив в 1993 степень бакалавра коммерции, а в 1998 стал магистром государственной политики Школы управления Джона Ф. Кеннеди Гарвардского университета. Несколько лет до открытия своей консалтинговой конторы Ненши работал в McKinsey & Company.

Ненши является автором работ о том, как города могут удержать молодых специалистов и стал соавтором идеи создания двух групп горожан, имеющих целью совершенствование городского управления Калгари. Он был преподавателем некоммерческого управления в Школе бизнеса Биссетта в Университете Маунт-Ройял и вёл рубрику в Калгари геральд, посвящённую городским делам.

Участие в выборах мэра в 2010

Ненши впервые занялся политикой в 2004, когда неудачно выступил на выборах в Городской совет Калгари. В своей кампании 2010 особое значение он придал использованию таких социально-сетевых сайтов, как Facebook и Twitter для продвижения своей позиции и привлечения избирателей. В конце сентября опрос показал, что его кампания заинтересовала их, так как он имел 8 % поддержки, однако, был далеко позади лидеров гонки: олдермена Рика Макайвера (42 %) и деятеля местных СМИ Барб Хиггинс (28 %). Растущая популярность привела к большему вниманию к его взглядам и даже к общественной полемике с главой Полицейской службы Калгари Риком Хэнсоном о стоимости обслуживания города полицией.

Незадолго до выборов опрос Калгари геральд показал, что популистская кампания Ненши продолжала набирать обороты, так как его поддерживало уже 30 % определившихся избирателей и он фактически сравнялся с Макайвером и Хиггинс. По опросу он имел наибольшую поддержку молодых избирателей, что, возможно, стало результатом его кампании в социальных СМИ. Рост популярности Ненши продолжался до самих выборов, на которых он победил, получив 40 % голосов и на 28 000 голосов опередив Макайвера.

Выиграв выборы, Ненши стал первым мусульманином (к тому же исмаилитом), занявшим должность мэра крупного канадского города. Его победа рассматривалась как прорыв в использовании социальных СМИ в качестве предвыборного инструмента, а учитывая его вероисповедание и происхождение, попала и в заголовки газет по всему миру. Особенно была удивлена Восточная Канада, считавшая Калгари консервативным городом. Его избрание воспринимается как знак изменений в альбертской и калгарийской политике.

Вскоре после своей победы Ненши изложил четыре приоритета: преобразование управления городским советом, устранение дефицита бюджета, строительство тоннеля под новой запланированной взлётно-посадочной полосой международного аэропорта Калгари и сохранение финансирования проектируемой юго-восточной ветви городской сети Си-Трейна.

6 апреля 2021 года Ненши объявил, что не будет переизбираться после трёх сроков пребывания на посту мэра Калгари.

Примечания

Ссылки

 TEDxCalgary — Нахид Ненши — Калгари 3.0

Выпускники Школы управления Джона Ф. Кеннеди
Мэры Калгари
Танзанийцы
Выпускники Университета Калгари
Канадские исмаилиты

redpajama_set_name: RedPajamaWikipedia


text:
Q: In Sqlalchemy Strange behaviour while appending an object twice in class relationship attribute I am facing some odd problems while learning SQLAlchemy. I am using 0.7.2 version of it. These are my test classes:
    class User(Base):
        __tablename__ = 'users'

        id = Column('user_id',Integer,primary_key = True)
        name = Column('user_name',String(20))

        addresses = relationship("Address",backref="user")

        def __repr__(self):
              return "<User(%s)>" % self.name

    class Address(Base):
          __tablename__ = 'addresses'

          id = Column('adress_id',Integer,primary_key = True)
          address = Column('address',String(30))
          user_id = Column('user_id',ForeignKey('users.user_id'))

          def __repr__(self):
               return "<Address(%s)>" % self.address

*

*I accidentally ran my main file twice which made following code run twice
Session = sessionmaker()
session = Session(bind=engine)
q=session.query(User)
a=q.get(3)
a.addresses.append(Address(address='myaddress'))
session.flush()
print a.addresses[0].id,a.addresses[0].address

I initially thought that a.addresses would have got two address object with 'myaddress'. But actually there is only one object whose address_id got updated. I mean to say when I ran file first it printed
1,'myaddress'

and then in second run it printed

2,'myaddress'

I confirmed existence of only Address object by printing a.addresses and it shows only object in it.
Should it not add a second Address object in a.addresses on append instead of updating id of existing address object?
Note there is no session.commit() command executed. I simply ran the file twice and noticed this behaviour.
Edit : Added code which creates new session and is responsible for the problem as suggested by van below in the answer

A: This cannot be seen in your code, but I assume that the code that is executed twice is also executed within two different sessions. This would explain all the side effects you observe:

*

*only one address: because second session is not aware of the first one (not commit-ed)

*address ID is increased: this happens because of flush() in the first session where the identifier is assigned to the object. This is not an update to the previous Address though, but rather an ID assignment to the new Address.

redpajama_set_name: RedPajamaStackExchange


We recently got two DCX8510-8 backbones and need help in our SAN topology architecture to utilize them effectively as we apparently paid more for backbones instead of less for a few smaller individual switches.
What kinds of things should we do differently with backbones than switches from the zoning architecture perspective?
We've half-populated each backbone with 8Gbps GBICs on these backbones.
The number of ports available in these backbones are more than enough for the number of servers/storage we have in our environment for a while, and we don't plan to connect any other switches/directors to these backbones for next few years, even considering growth of our environment.
From my previous environment, I connected several small- and mid-sized switches together via ISLs to form the full-mesh single fabric topology (that is, only one SAN island), and it worked out very well for the size and purpose of my previous environment for the past few years.
As I just joined this new environment, we've just got those two backbones instead, and I'd like to know if we should do something different in terms of zoning. One example would be if we utilize the new feature Virtual Fabrics or not.
- so that if we make a human error/mistake when creating zones in one backbone (e.g., bringing down the whole fabric), the other backbone stays up and serves the data, etc.
I know it's a manual HA strategy that may or may not be used elsewhere but this is the manual HA architecture that my new environment has been using with older director models that we're going to migrate and replace to these new DCX8510-8.
I'd like to hear advices from savvy folks out there for now.
hi, your current plan looks good. i don't think i can add anyting. good luck!
young.song, in addition, I've attached the "Secure SAN Zoning Best Practice Guide". Its a high-level guide to zoning, but i refer to it for mental refreshers from time to time. Hope it helps.


The Pattaya Sports Club Association was founded in 1979, and in 1996 became a registered, government recognized, non-profit association whose main objective is to promote sporting events and contribute to local charities. As our club membership has grown over the years, so has our ability to donate to children, the handicapped and the underprivileged.
All committee members of the Pattaya Sports Club volunteer their time and energy to work for the Association and all of us involved with the Pattaya Sports Club are proud and dedicated to improving the community that we live in and improving the lives of those less fortunate.


HAVE YOU EVER WONDERED WHAT WOULD HAPPEN IF THE CHURCH LEFT THE BUILDING AND SHOWED UP IN THE COMMUNITY DEMONSTRATING THE KINGDOM WITH COMPASSION AND AUTHORITY?
The Healing on the Streets model is a simple, but beautiful way, to reach out to the lost and hurting on the streets of your town or city. It enables you to connect with your community every week, powerfully expressing God's love in the market place, whatever the weather. We simply invite people to sit on chairs so we can pray for them.
Over time we build relationships, creating stepping-stones for people to come to Jesus and be healed along the way.
The healing on the streets network is currently taking a break over the summer while we review it. Check back in the Autumn to find out more.


So you saw the good... now here's the bad, ugly, chewy and blinky.
Seriously, this was his worst picture. The man does. not. blink.
On the contrary, this was one of my better pictures. I'm a blinkaholic.
I'm pretty sure he thinks this is a cute face.
The photographer had candy in her bag. Chew, chew, chew.
This is basically what he did the whole time.
We're a hot mess and I'm loving it. Hah!
ROFL you are too funny! Love them all!
I love when they think they've got their "cute face" on. (My daughter's still learning how to smile on demand, too.) And thank goodness for candy in the bag!
I love the outtakes. You guys are so cute. And I must say, I love how often you attempt a family photo. I am so scared after we have ours that I wait years before we get another one.
I love the outtakes too. Babies love their fingers..........so nummy!!
funny faces or not, you all still look great!


text:
Anubis, The God of Mumification and the Hereafter - Egypt History, Where the whole story begins : Pharaonic History of Egypt : Ancient Egyptian Religion And Myths : - Egypt :
Anubis is one of immortal gods in the ancient Egyptian mythology whose importance is attributed to his great role in the underworld as the protector of the dead bodies. He was called as the Lord of Mummy Wrapping. Moreover, in the papyrus of Nisti-Ta-Nebet-Taui that dates back to the 21 dynasty, he is called the "Lord of the Holy Land" who brings gifts and blessings for the people as a present for Osiris Anubis. The usual depiction of Anubis is as a Jackal headed man or a complete Jackal. The reason for associating the figure of this animal in particular with Anubis is the fact that jackals were usually seen nearby the cemeteries and thus the people thought that they were protecting the dead bodies. Some historians argue that these animals were surrounding the cemeteries to feed on the sacrifices left there. As indicated in the Coffin Texts, Anubis was the son of Nephthys that was claimed to be the son of Seth but Isis realized that he was the result of the secret affair between Osiris and Nephthys.
As mentioned in the myth of Osiris, Nephthys tried to get ride of her son at the moment of his birth, but Isis saved him and managed to gain the support and trust of him and his mother who helped her in searching for her husband's body. He was responsible for protecting Isis and was truly faithful to her and he helped her to escape from the prison of Seth. It was known that Anubis was knowledgeable of the human language and the art of mummification and many other things. Thus he was commanded by Ra to help Isis in reassembling the body of Osiris and embalming it in the white clothes of the dead. One of the vignettes of the Book of the Dead highlight that he uttered some words that helped Osiris to return to life again and this made the people dignify him hoping that he would treat them in the same way he dealt with his father in the afterlife. Anubis is depicted performing various roles in the underworld including the role of the "Counter of Heats" who receives the recently deceased bodies and mummifies it to protect the mortal parts of the body. This justifies the appearance of the priests with the head of jackal of Anubis while mummifying the kings.
He is presented on the walls of the kings' temples standing next to the "God's Booth" with the jars of the essential needs for glorifying the deceased king. Other inscriptions of Anubis demonstrate that he once occupied the post of the god who weighs the heart of the deceased and write his judgment. Some wall paintings present Anubis in the scene of supporting the mummy while opening the mouth of the dead. One of the most interesting old myths says that Ammit, or the eater of the dead, is the god responsible for destroying those who fail in the arbitration of Anubis i.e. whose heart's weight exceeds the weigh of the feather. Ammit was depicted as a supernatural animal with the head of a crocodile, the body of a lion, and the head hippopotamus. There are many statues for Anubis and wall paintings depicting him performing several roles. The most admired depictions for Anubis can be found in the tombs in Abydos and Aswan in addition to the handsome paintings of him in the Book of the Dead. The tomb of Tutankhamun was also supplied with a large number of statues for Anubis in the jackal form, displayed in the Egyptian Museum now.
This myth was used to serve a crucial political purpose which id the desire of the members of the 5th dynasty and the members of the family of Cheops in particular to give themselves the legitimacy of

redpajama_set_name: RedPajamaCommonCrawl


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text:
Cas Haley
by Main Course
Sun, Oct 10, 2021, 7:00 PM EDT
The Main Course
Sometimes when one door closes, another one opens. Texas singer-songwriter Cas Haley never imagined that in the year of the pandemic, both doors would belong to a 2020 Lincoln Corsair that would take him on a musical adventure across the country. But maybe he shouldn't have been surprised. It was just the latest soulful swerve in the musical ebb and flow of a career that's been both full of challenges and mightily blessed.Fresh off a battle with his wife Cassy's cancer diagnosis, Cas and his family learned in January 2020 that out of 1,600 competitors, he had won the grand prize in Lincoln's "Chart Your Course" songwriting contest with his song "Every Road I'm On." The prize included that new Lincoln Corsair, but the vehicle came with a purpose: a cross-country journey to meet and work with famed songwriters and musicians to perfect and arrange his winning song, fittingly titled "Every Road I'm On."The road trip also came with some valuable advice – and a spiffy new hat – courtesy of an unexpected new friend by the name of Matthew McConaughey. It culminated with a recording at the legendary Capitol Studios in Hollywood, CA with multiple-Grammy-winning producer Al Schmidt (Steely Dan, George Benson, Quincy Jones). And Lincoln featured Cas and McConaughey in a commercial that debuted at the Grammy Awards in Los Angeles, with Cas in attendance, and that's now everywhere.
The whole road-trip saga was also captured in a captivating 25-minute documentary, where we meet Cas and his family and witness him working out song arrangements with the likes of Ruthie Foster, Jon Batiste, Tank of Tank and the Bangas, and Grammy winner Jon Cleary.
Lights, camera, action. It's in the bag. Print it!……and then the pandemic hit. Touring, promotions, the Lincoln campaign – everything was put on hold.Cas wasn't fazed. The philosophy he'd lived by all along held true and carried him through: "Success," he says, "is an accumulation of being in balance, going with your gut, and following your bliss." Or, as he put it in the context of his 2019 album Lessons and Blessings: "It's about wanting to get out of one's head, feel connected, get back to one's roots and body and self."Roots are everywhere on Cas's new album, All the Right People, set for an early-2021 release on Jimmy Buffet's Mailboat Records label. The video for the infectious title track features Cas and his family, bandmates, and friends all singing together and celebrating the power of music and love. A vintage funky pop flavor dominates tracks like "Kellie's Song"; "Misunderstood" and "Long Shadow" hark way back to old-timey sounds and traditional folk; and "Take It All Back" is pure delicious R&B balladry.Together, the new album and the Lincoln adventure sum up a fascinating career journey.Cas grew up immersed in ska/punk/skateboard culture and the classic reggae-pop of bands like UB40 and Sublime. After a dramatic runner-up finish on an early season of America's Got Talent, he worked with indie reggae label Easy Star Records, sharing stages with the likes of UB40, Mike Love, and Trevor Hall.
All along he followed his bliss, going his own independent way, bouncing back from setbacks. He built an enviable career on the road and in the studio, dividing his time between touring and spending time with Cassy and their two kids on his Texas farm.
Today, music is more a family affair than ever for Cas, who collaborates with Cassy on songwriting and now hits the road with his son Eben on bass and his daughter Nolah on fiddle.
What he says about "All the Right People" applies to his whole approach to music and life. American Songwriter calls the song an "instantly memorable singalong," but Cas goes deeper: "It's a feeling, inspired by that energizing emotion that happens when things are in balance and you know you're exactly where you're supposed to be. That magnetic flow that happens when you recognize and honor all the relationships that have helped shape the person you are, and being able to cultivate presence in your life wherever you're at and to find that internal sanctuary, whatever tragedy you might be going through."
Tragedies come and go; what Cas Haley gets at in his songs is that internal sanctuary – whether it's the interior of a brand new SUV or something more ethereal. "Blessings always come rearranged," he sings in "Every Road I'm On." "The only plan I have is here right now…Every road I'm on is my home."
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Organizer Main Course
Organizer of Cas Haley
Main Course features five state-of-the-art simulator bays, including a Champion Suite for the ultimate experience. In addition to the bays, there are two well-appointed bars along with a new menu of mouthwatering entrees and appetizers specifically designed by a team of chefs. Main Course is complete with a live entertainment venue with weekly live music, comedy, and special events at 1626. Come explore one of Columbia's favorite social spots, 1626 at Main Course is the perfect place for dining and special events.
EATERTAINMENT is now on the 1600 Block of Main Street. 1626 Main Street is the perfect place downtown for Cuisine, Spirits & Brews, Entertainment, Virtual gaming, and great parking. We are your Main Eatertainment Destination.
Reserve a table & enjoy our incredible food and cocktails before the show here!
Cas Haley at The Main Course
1624 Main Street, Columbia, SC 29201
Fri, Apr 29 6:00 PM
On the Border- The Ultimate Eagles Tribute
Icehouse Amphitheater, Lexington
Trey Lewis
Skyline Club, West Columbia
Jazz Fest 2022
North Springs Park, Columbia
#CharityCauses #Performance
Wed, Mar 16 6:00 PM
Touché Amoré, vein.fm, Gleemer, Thirdface
New Brookland Tavern, West Columbia
Sat, Mar 26 6:00 PM
David Nail
For The Love Of Arts Open Mic Night
623 12th St, West Columbia
Fri, Mar 18 6:30 PM
RAGEFEST: ATTILA, HE IS LEGEND, ISLANDER, CROWN MAGNETAR, AND BACKSLIDE
The Red Jumpsuit Apparatus, Astoria State, Parris Bridge, Dull Mourning
Ryley Walker at If Art Gallery
If Art Gallery, Columbia
Ward Davis at NBT
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text:
Ruptured TETCO Pipeline in PA Offline Until November
June 27, 2016 Accidents, Energy Services, Industrywide Issues, Pennsylvania, Pipelines, Spectra Energy, Westmoreland County
An update on Spectra Energy's Texas Eastern Transmission's (TETCO) "Delmont Line 27" which exploded in Westmoreland County, PA on April 29 (see Texas Eastern Pipeline Explodes near Pittsburgh, Antis Celebrate). We previously told you that not only was Line 27 out of commission, so too were three other pipelines running through the same corridor, meaning 1 billion cubic feet of natural gas per day is not reaching certain mid-Atlantic markets (see Update on Spectra Pipeline Explosion Near Pittsburgh). The early evidence points to corrosion along welded seams, although the jury is still out and the exact cause may not be known for months (see Preliminary Guess on TETCO Pipeline Explosion Cause: Corrosion). One of the four lines that was offline (Line 19) was examined and certified by the Pipeline and Hazardous Materials Safety Administration (PHMSA) in early May to go back online (see TETCO Pipeline Up & Running Post-Explosion; Antis Exploit Accident). However, the other three lines have remained idle pending further investigation (see TETCO PA Pipeline Explosion Still Limiting NatGas Flow Month Later). We now have an estimate of what else needs to be done, and how long it will take to do it…
Big Green Groups Oppose STRONGER Review of VA Drilling Rules
What Happens in PA When No Mineral Rights Owner is Found?


text:
Q: C# windows form progress bar with background worker I am attempting to add a progress bar in my c# excel add in.  The progress bar appears but it does not indicate any progress until the function is finished executing.
These are the functions in the Windows Form Class:
    public void backgroundWorker1_DoWork(object sender, DoWorkEventArgs e)
    {
        for (int i = 0; i < 100; i++)
        {

            Thread.Sleep(100);

            backgroundWorker1.ReportProgress(i); //run in back thread

        }

    }

    public void backgroundWorker1_ProgressChanged(object sender, ProgressChangedEventArgs e) //call back method
    {

        progressBar1.Value = e.ProgressPercentage;

    }

    public void backgroundWorker1_RunWorkerCompleted(object sender, RunWorkerCompletedEventArgs e) //call back method
    {

        progressBar1.Value = progressBar1.Maximum;

    }

This is how I call the function from the add in button:
    private void buttonClicked(object sender, RibbonControlEventArgs e)
    {
        AddInPlanView.Form1 pBar = new AddInPlanView.Form1();

        pBar.Visible = true;

        pBar.backgroundWorker1.WorkerReportsProgress = true;

        pBar.backgroundWorker1.ProgressChanged += new System.ComponentModel.ProgressChangedEventHandler(pBar.backgroundWorker1_ProgressChanged);

        pBar.backgroundWorker1.DoWork += new System.ComponentModel.DoWorkEventHandler(pBar.backgroundWorker1_DoWork);

        pBar.backgroundWorker1.RunWorkerCompleted += new System.ComponentModel.RunWorkerCompletedEventHandler(pBar.backgroundWorker1_RunWorkerCompleted);

        pBar.backgroundWorker1.RunWorkerAsync();

        FUNCTIONTORUN();

        pBar.Visible = false;

    }

How should I change this so that the progress bar will not stop working during the execution of FUNCTIONTORUN()?  The progress bar is initialized using the Visual Studio designer.  The name of the progressbar object in the form class is progressbar1.
Thank YOU!

A: The DoWork event for your progress bar should be (or contain) FUNCTIONTORUN().  FUNCTIONTORUN() should use the ReportProgress method.

A: What does FUNCTIONTORUN do? It is very likely blocking the UI thread, causing your updates to the progress bar to not be seen until it returns. More than likely, FUNCTIONTORUN needs to run in a background worker, and have it periodically report progress, and that's where you'd update the progress bar.

A: I would like to expand on the following statement.  Matt Greer can correct me if I am wrong.

What does FUNCTIONTORUN do? It is very likely blocking the UI thread,
  causing your updates to the progress bar to not be seen until it
  returns. More than likely, FUNCTIONTORUN needs to run in a background
  worker, and have it periodically report progress, and that's where
  you'd update the progress bar.

What I believe he means by this is you need to update progressBar1.Value within
FUNCTIONTORUN();  you can still use a similar method.


text:
Faurecia Accelerates Website Experiences Worldwide Using Limelight Networks Content Delivery Services
Company Release - 11/28/2018 9:50 AM ET
Leading Automotive Supplier Counts on Limelight to Deliver Dynamic Content Around the Globe
TEMPE, Ariz.--(BUSINESS WIRE)-- Limelight Networks (Nasdaq: LLNW), a leading provider of edge cloud services, today announced that Faurecia is using its private global network and technology to quickly deliver dynamic content around the world.
Founded in 1997, Faurecia, a French company, has grown to become a major player in the global automotive industry. With 290 sites including 30 R&D centers and 109,000 employees in 35 countries, Faurecia is a global leader in its three areas of business: automotive seating, interior systems and clean mobility. The company chose Limelight's CDN with website acceleration and HTTPS to ensure reliability and the best possible website performance for its growing and global customer base.
"Speed and stability of our website are key to people visiting our website," said Olivier Dumont, Group Digital Communications at Faurecia. "It's essential that they can quickly access relevant and sometimes time-sensitive information online. Using Limelight, we can seamlessly deliver content to visitors no matter where they're located."
Limelight's technology allows Faurecia.com visitors to instantly access the detailed information they need to learn more about the company, its services and solutions. Faurecia counts on Limelight's private network and innovative technology to avoid potential congestion and reliably deliver content worldwide. As the company expands into new markets, they can easily expand their websites in new countries and handle spikes in online traffic seamlessly. In addition, with Limelight's SmartPurge, Faurecia is able to improve workflows and easily update content in under two seconds.
"It's important for Faurecia to be able to quickly update its website so that product information is always current for their global customer base," said Didier Nguyen, Sales Director at Limelight Networks. "Limelight provides Faurecia with an easy to use workflow and reliable and scalable platform that can easily handle their growing business including any spikes in online traffic demand."
About Faurecia
Founded in 1997, Faurecia has grown to become a major player in the global automotive industry. With 290 sites including 30 R&D centers and 109,000 employees in 35 countries, Faurecia is now a global leader in its three areas of business: automotive seating, interior systems and clean mobility. Faurecia has focused its technology strategy on providing solutions for smart life on board and sustainable mobility. In 2017, the Group posted total sales of €17.0 billion. Faurecia is listed on the Euronext Paris stock exchange and is a component of the CAC Next 20 index. For more information, please visit www.faurecia.com.
About Limelight Networks
Limelight Networks Inc., (NASDAQ: LLNW), a leading provider of digital content delivery, video, cloud security, and edge computing services, empowers customers to provide exceptional digital experiences. Limelight's edge services platform includes a unique combination of global private infrastructure, intelligent software, and expert support services that enable current and future workflows. For more information, visit www.limelight.com, follow us on Twitter, Facebook, and LinkedIn.
Stephanie Epstein, 617-779-1845
Source: Limelight Networks Inc.


text:
China says 23 children sickened in suspected poisoning
Posted Apr 02 2019 04:32AM CDT
Updated Apr 03 2019 07:29AM CDT
BEIJING (AP) - Authorities in eastern China say 23 kindergarteners were sickened in a suspected act of deliberate poisoning by their teacher.
Police in the city of Jiaozuo said Tuesday that a teacher identified by the surname Wang is believed to have adulterated the children's food with sodium nitrite and has been arrested.
Overexposure to sodium nitrite can be toxic and possibly fatal. Police said they were still looking for a motive in last week's incident.
Schoolchildren in China have been the target of often fatal attacks by people bearing grudges or considered mentally ill.
In 2002, 42 people, mostly schoolchildren, died after eating snacks laced with rat poison in the eastern city of Nanjing. The killer was swiftly sentenced to death and executed.
More International News Stories
Man shouting 'You die' kills more than 30 at Japan anime studio
By MARI YAMAGUCHI, Associated Press
Posted Jul 18 2019 08:19AM CDT
A man screaming "You die!" burst into an animation production studio in Kyoto, Japan, and set it on fire Thursday, authorities said, leaving more than 30 people dead, shocking anime fans in and outside Japan.
A Japanese fire official says the death toll from a Kyoto animation studio fire is now 33 and nobody else is believed to be still missing.
Kyoto fire department official Kazuhiro Hayashi says 36 others have been injured, 10 of them critically.
Pamplona festival ends with 3 gorings in final bull run
PAMPLONA, Spain (AP) - A bull broke from the pack and gored two Australians and a Spaniard during Sunday's final bull run of this year's San Fermin festival, health officials from the northern Spanish city of Pamplona said.
That took the number of gorings to eight for the eight bull runs that provide a high-adrenaline morning rush to the non-stop party that draws around 1 million people each year.
While five of the bulls stayed in a group Sunday and charged through the twisting streets with their guiding steers, one bull drifted back and provoked havoc in the crowds of runners. The bull flipped one man over its horns and slammed him onto the cobblestone street. It then clipped another two runners who were trapped against a wall.
Man charged for allegedly trying to use case of beer as booster seat for toddler
By Gabrielle Moreira
A 22-year-old man in Ontario, Canada, was charged on suspicion of failing to properly secure a toddler by using a case of beer as a booster seat.
Around 2:30 a.m. Tuesday, an officer with the Ontario Provincial Police West Region pulled over the driver near the North Perth area.
The officer then noticed the toddler, who was 2 years old, sitting on a 30-can case of beer in the passenger seat. Authorities believe the driver used the case of a beer as a substitute for a booster seat.


text:
Q: Get specific ".." with PHP regex? I have a variable ($page) that contains HTML code as follows:

    head

        12
        recommendations

        50
        connections

Now I want to get the number of connections (in this case it's 50) with a regular expression in PHP, so I use this:
preg_match('#(.*)#', $page, $connections)

But this gets 12, not 50. How can I solve this problem?

A: preg_match('/([0-9]*)<\/strong>\s+connections/', $page, $connections);

echo $connections[1]; // 50

A: With the caveat that Regular Expressions should not be used to parse HTML, take a look at preg_match_all(). If the HTML follows that structure, you are interested in the second match.


There is nothing worse than a false charge of a crime you didn't commit. When Mary's groom appears under arrest, accused of a robbery of a jewelry store, Mary goes out to investigate - because she was sure that George is innocent.
Participate in investigation full of dangers together with Mary. Believe in yourself and justice, and find the true culprit!


Full Time Customer Service position.
Saturday from 8:15am – 12:15pm.
• Comfortable using computer programs.
Regularly stand, talk and hear.
Regularly lift/move up to 10 pounds, occasionally lift/move up to 25 pounds.
Additional details of duties and responsibilities described during interview process.
Interested in learning more and applying?
© Osgood State Bank. All Rights Reserved.


text:
Five Key Questions
What Does the Ending Mean?
Act I, scene ii
Act I, scene ii (continued)
Act II, scene i
Act II, scene ii
Act III, scene i
Act III, scene ii
Act III, scene iii
Act IV, scene i
Act V, scene i & Epilogue
Plot Analysis
Where Are All the Women?
Quotes By Theme
Prospero's Threats
Obedience and Disobedience
Wonder/admiration
Quotes By Section
Quotes By Character
Who Was Prospero?
Shakespeare's Sources for The Tempest
Act 1, scene ii
Act 1, scene ii (continued)
Act 5, scene i & Epilogue
Companion Texts
Sample A+ Essay
How To Cite No Fear The Tempest
If by your art, my dearest father, you have
Put the wild waters in this roar, allay them. (I.ii.)
Miranda's words open the play's second scene, and with them she makes a plea to her father to calm the violent tempest he has roused. From her very first lines, Miranda identifies herself as an empathetic figure, a mediator who wants to calm tensions and make peace. Her plea for peace is both literal and figurative: literal because she wants the storm to cease, and figurative because she wants her father's rage (i.e., the source of the tempest) to settle.
Your tale, sir, would cure deafness. (I.ii.)
Miranda utters these words of horror in response to Prospero's story about the failed attempt on his life. Her powerful words express empathy for her father, but even more so they also indicate her own sense of shock. After all, this tale belongs to her as well, and her overstatement suggests just how overwhelmed the story makes her feel.
I should sin
To think but nobly of my grandmother.
Good wombs have borne bad sons. (I.ii.)
Miranda says these lines after Prospero implies that he could no longer consider Antonio a brother after his act of betrayal. By emphasizing that her grandmother must have given birth to one good son and one bad one, Miranda at once insists that Antonio is indeed Prospero's brother and that Antonio's sins cannot tarnish Prospero's goodness. On the one hand, her words seek to soothe her father's anger. She may also mean to convince herself of her father's innate goodness, since she has personally born witness to Prospero's violent temper on numerous occasions.
I pitied thee,
Took pains to make thee speak, taught thee each hour
One thing or other. When thou didst not, savage,
Know thine own meaning, but wouldst gabble like
A thing most brutish, I endowed thy purposes
With words that made them known. (I.ii.)
With these words, Miranda tries to instill a sense of gratitude in Caliban for the education she gave him. Like Prospero, Miranda sees Caliban as an ungrateful creature, a "savage" who needed to be saved from his own "brutish" nature. Her insistence on the importance of education and civilized speech demonstrates that Miranda functions in some ways as an extension of Prospero's imperialist attitudes.
When this burns,
'Twill weep for having wearied you. (III.i.)
Miranda says these words to Ferdinand near the top of Act III. She refers to the pile of wood that he has moved at Prospero's command, and she wittily suggests that when Prospero burns the wood, the wood will experience a kind of deathbed regret at having driven Ferdinand to exhaustion. Her playful comment at once shows her empathy for Ferdinand and her attraction to him.
How features are abroad
I am skilless of, but, by my modesty,
The jewel in my dower, I would not wish
Any companion in the world but you,
Nor can imagination form a shape
Besides yourself to like of. (III.ii.)
Here Miranda explicitly expresses her faith in and commitment to Ferdinand. Miranda admits that she knows nothing of the world beyond the island. Nevertheless, she solemnly swears by her modesty (i.e., "The jewel in my dower") that she wants no other companion than Ferdinand.
Sweet lord, you play me false. (V.i.)
Miranda lovingly chastises Ferdinand for cheating in a game of chess. Although her tone is lighthearted, her suggestion that Ferdinand has cheated has an important symbolic resonance. Each player in a game of chess attempts to capture (i.e., kill) their opponent's king, and as such chess is an allegory for regicide. The Tempest has already told of three separate assassination plots, including two against Prospero and one against Alonso. Each of these plots is characterized by unexpected treachery. Ferdinand's alleged cheating at chess recalls all of these plots, and may be an ill omen for the future that otherwise seems so positive at the end of the play.
O wonder!
How many goodly creatures are there here!
How beauteous mankind is! O brave new world
That has such people in 't! (V.i.)
These words form Miranda's most famous lines. She delivers the lines in the play's final act, upon first seeing Alonso and his company of men. Aside from Prospero and Ferdinand, Alonso and his men are the only people she has ever laid eyes on, and the sight fills her with a great deal of hope at the idea of a "brave new world" populated by such "beauteous" individuals. In the larger emotional arc of the play, Miranda's words of wonder express optimism about the possibility of new beginnings.
Prospero Next
Prospero: Character Analysis


text:
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    var pluginName = "bcToc",
        defaults = {
            contentAreaID: 'content',
			contentLinkClass: 'contentLink',
			addClassToLink: ''
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    function Plugin( element, options ) {

        this.element 	= element; //create original element object
		this.jele 		= $(element); //create jquery object of element

        this.options 	= $.extend({}, defaults, options); //add otpions onto default for full list

        this._defaults 	= defaults;
        this._name 		= pluginName;

		this._links 	= $('#'+this._defaults.contentAreaID+' .'+ this._defaults.contentLinkClass);

		this.init();

    }

    Plugin.prototype =
	{

        init: function()
		{

			this.getItems(this.element, this.options);

        },
		getItems: function (el, options)
		{

			var thisObj = this;

			$(this._links).each(function(index, element)
			{
				var title		= $(this).data('title'),
					links 		= '#' + $(this).data('name'),
					newAncor 	= '';

				thisObj.setItems(title, links, thisObj.options.addClassToLink);

				$(this).before(newAncor);
			});
		},
		setItems: function(title, links, classes)
		{
			newLine = '
' + title + '
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			this.jele.append(newLine);
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    // A really lightweight plugin wrapper around the constructor,
    // preventing against multiple instantiations
    $.fn[pluginName] = function ( options )
	{
        return this.each(function ()
		{
            if (!$.data(this, "plugin_" + pluginName))
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                $.data(this, "plugin_" + pluginName, new Plugin( this, options ));
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    };

})( jQuery, window, document );

redpajama_set_name: RedPajamaGithub


text:
\section{Introduction}
\label{sec:introduction}

Percolation is the study of long-range connectiveness in systems such as  graphs or lattices in which the sites
or bonds are randomly occupied with probability $p$. There is a well-defined threshold $p_c$ at which the average
size of a cluster first becomes infinite. The threshold can also be defined by considering finite systems (say an
$L \times L$ square), and studying the probability that a single cluster connects or spans two opposite sides. The
average value of $p$ at which spanning first occurs yields an estimate for $p_c(L)$, and using finite-size scaling
one can predict the value of $p_c$ for $L \to \infty$.   In this  case, the threshold is sharp as $L \to \infty$.  For a square lattice with bond percolation, for example,
one has $p_c = 1/2$ \cite{StaufferAharony94,ReynoldsStanleyKlein80}.

\rev{Percolation has received a great deal of
attention over the years; some recent papers include a study of regular and inverse percolation of rigid rods \cite{RamirezCentresRamirezPastor18},
continuum percolation of overlapping polyhedra \cite{XuZhuJiangJiao19},
percolation over varied ranges of transmission \cite{KunduManna},
percolation on a distorted lattice
\cite{MitraSahaSensharma19},
percolation of $k$-mers undergoing random sequential adsorption \cite{SlutskiiBarashYuTarasevich18},
percolation disassortativity on random networks \cite{MizutakaHasegawa18},
percolation for random sequential adsorption with relaxation \cite{KunduAraujoManna18}, percolation over a range of interactions \cite{OuyangDengBlote18},
percolation in high dimensions and on a random graph \cite{HuangHouWangZiffDeng18},
percolation on hypercubic lattices in high dimensions \cite{MertensMoore18,MertensMoore18b},
percolation of  the elastic backbone \cite{FilhoAndradeHerrmannMoreira18},
universality in explosive percolation \cite{SabbirHassan18},
crossing probabilities for polygons \cite{FloresSimmonsKlebanZiff17},
rigorous bounds for percolation thresholds \cite{Wierman17},
percolation on random jammed sphere packings \cite{ZiffTorquato17}, and percolation on hyperbolic manifolds \cite{KryvenZiffBianconi19}.  Clearly, percolation remains a very active field.}

For the ordinary percolation problem in $d$ dimensions, the connectivity is usually considered between the pair of opposite
$(d-1)$ dimensional hypersurfaces. Naturally, the question arises, what happens if the connectivity is considered
between the $(d-2)$, $(d-3)$, .... dimensional hypersurfaces? In this paper, we try with the simplest possible situation,
that is the connectivity between the $(d-2)$ dimensional hypersurfaces in $d = 2$. More specifically, we study the
percolation problem between the $k$ widely separated points (dimension 0) on the two-dimensional square lattice, or between
a single point and the boundary of the system.

The first threshold we consider is defined as the average value of $p$ at which a point in the center of a square
system first connects to any point on the boundary.  This defines the threshold $\overline p_{c1}$.  The other
thresholds are defined as the average value of $p$ at which $k$ points separated far apart in a periodic system all
first connect; we call those thresholds $\overline p_{ck}$.   These thresholds are all greater than $p_c$, indicating
that we are in the supercritical regime of percolation where there is a percolating net throughout the system. Being
in a supercritical state is expected since connecting a large  cluster to a specific single point at the normal
critical point $p_c$  occurs with low probability (unlike connecting to a boundary, for example, which can occur
through many paths and is much easier).  Connecting to a boundary is a universal property that survives at the
critical point when the lattice spacing goes to zero, while in that limit the probability of connecting to a
single point goes to zero.  When going to the supercritical regime, the probability of connecting to a point
can be raised to a significant value, and this allows different points to connect together simultaneously with
a sufficient probability to be observed.

We carried out  computer simulations to find the values of $\overline p_{ck}$ directly for $k = 1, 2, 3$ and 4.
We also developed a theory to connect $\overline p_{ck}$ to $P_\infty$, the percolation function that gives the
probability a given point belongs to the infinite cluster, or the largest cluster for a finite system.  By directly
simulating $P_\infty$ for this system, we are able to verify numerically that the relation to $\overline p_{ck}$
is valid.  The analysis also shows that, unlike in the case of the usual percolation threshold, the distribution
of $\overline p_{ck}$ for individual systems is broad and does not become sharp as the system size goes to infinity.
That is, there are large fluctuations in the states of these systems defined by these percolation criteria.

In Fig.\ \ref{fig:pic} we show pictures of simulations of a $64 \times 64$ periodic system in which the first
connection between the two anchor points occurred when 4415 bonds were placed down, or at $p_{c2} = 4415/8192 \approx 0.53894$,
and the same system at the standard threshold $p = 4096/8192 = 1/2 = p_c$, at which point no connection exists
between the two anchor points for this system. The value of $p_{c2}$ for this sample is close to the average
value $\overline p_{c2} = 0.5312$ found by averaging over many realizations. It can be seen that, at $p_{c2}$, there is one overwhelming ``infinite''
cluster throughout the system,  and finite clusters are very small.  This behavior illustrates the idea behind
our conjecture that in the supercritical region, the probability that $k$ points are connected together is equal
to $[P_\infty(p)]^k$.

In Fig.\ \ref{fig:pic2} we show a very rare case where the connection between the anchor points occurred at a
value substantially below $p = 1/2$; for large systems such cases appear with very low probability.

      We also studied a ratio involving three-point correlations and two-point correlations,
   and show how that varies with the separation of the points compared with the size of the
   system. This ratio has been studied previously at the critical point only
   \cite{SimmonsZiffKleban09,DelfinoViti10}; here we study it for all $p$.

      In section \ref{sec:theory} we develop our theory for $\overline p_{ck}$, including
    the scaling of the estimates. In section
   \ref{sec:methods} we describe our simulation methods, and in section \ref{sec:results}
   we give the results of our simulations. In section \ref{sec:correlations} we consider
   the problem of the three-point correlation ratio.  In section \ref{sec:discussion} we
   discuss our results and give our conclusions.

\section{Theoretical analysis}
\label{sec:theory}

      Here we develop a theory to predict $\overline p_{ck}$ from $P_\infty(p)$, and develop a scaling analysis
   that allows one to predict the convergence exponents for the $\overline p_{ck}$.

\subsection{Relation to $P_\infty$}

     The first assumption is that we must be in the supercritical state, since only then will the $k$ points be
  able to connect together via the infinite network.  At $p_c$, the infinite cluster is tenuous and fractal,
  and does not connect to given points with a significant probability (for a large system), and below $p_c$ the clusters are all
  small and it would be virtually impossible for points far apart to connect together.

Thus, for $k$ widely separated points to be all connected together, we hypothesize that they \rev{must be}  part of the infinite cluster
in the supercritical state.   The probability a single point belongs to the infinite cluster is denoted as $P_\infty(p)$;
for a finite system we can define $P_\infty(p,L) = s_\mathrm{max}/L^2$ where $s_\mathrm{max}$ is the number of sites in
the largest cluster in the system.  Thus, we conjecture that the probability that $k$ widely separated points are connected must be equal to
$[P_\infty(p)]^k$.  The probability \rev{density} that they first connect when the occupation probability is $p$ is then
\begin{equation} \rev{P_r =}(d/dp)[P_\infty(p)]^k = k[P_\infty(p)]^{k-1} P_\infty'(p)
\label{eq:Pransatz}
\end{equation}
and the average value of $p$ at which the $k$
points first connect will be given by
\begin{equation}
\overline p_{ck} = \langle p \rangle =  \int_0^1 p (d/dp) [P_\infty(p)]^k  dp
\label{eq:pck1}
\end{equation}
Integrating by parts, we find
\begin{equation}
\overline p_{ck} = 1 - \int_0^1 [P_\infty(p)]^k  dp = \int_0^1 (1-[P_\infty(p)]^k)  dp
\label{eq:pck}
\end{equation}

For the problem of a single site connected to the boundary (corresponding to $\overline p_{c1}$), the above
formulas also apply, taking $k = 1$.  In this case, the largest cluster surely connects to the boundary, so
we are asking for just the probability that a point connects to the largest cluster, which is given by $P_\infty(p)$.   \rev{Note, for the case of $k = 1$, we do not use periodic boundary conditions.}

For $k>1$ the value of $\overline p_{ck}$ should be independent of the exact configuration of the $k$ points,
as long as their relative distances grow with $L$, so that they become infinitely far apart as $L \to \infty$
and greater than the correlation length $\xi$, which is finite for any given $p > p_c$.
For finite systems, the specific configuration of the points will be relevant for the precise threshold.

We can make a very useful approximation for calculating $\overline p_{ck}$ from $P_\infty(p)$ for finite systems
by simply assuming $P_\infty(p)=0$ for $p < p_c$, which is true for an infinite system. Then the integrand in
the second form of equation (\ref{eq:pck}) is exactly 1 in the interval $0 < p < p_c$, and we can write as an
alternative to (\ref{eq:pck})
\begin{equation}
\overline p_{ck} = p_c + \int_{p_c}^1 (1-[P_\infty(p)]^k)  dp
\label{eq:pckalt}
\end{equation}
\rev{where $p_c = 1/2$ for bond percolation on the square lattice.}
Equations (\ref{eq:pck}) and (\ref{eq:pckalt}) are identical when $L \to \infty$, but it will turn out that
(\ref{eq:pckalt}) gives a much better estimate of $\overline p_{ck}$ for finite $L$.

\begin{figure}[htbp]
   \centering
   \includegraphics[width=3.0 in]{picL064pcfor53894043} \\
   (a) \\
   \includegraphics[width=3.0 in]{picL064pc2for53894043} \\
   (b) \\
   \caption{
   Two illustrations of the system are presented for a lattice of size $64\times64$
   with periodic boundary conditions, and with $k = 2$ anchor points (marked by filled
   blue circles) separated by a distance of $32$ lattice units. Bonds of the largest
   occupied cluster are shown in red \rev{(grey)}, and all other occupied bonds are shown in black.
   (a) A system where the number of bonds is exactly 4096 or $p = 4096/8192= 1/2 = p_c$,
   without connection between the two anchor points. (b) The same system where the
   number of occupied bonds is increased to 4415 bonds or $p_{c2} = 4415/8192 \approx 0.53894$, at
   which point connection between the anchors first occurred. This is a typical example
   where the threshold is near the average value of $\overline p_{c2} = 0.5322$ and shows that in
   this supercritical regime there is a percolating network that goes essentially
   throughout the entire system.
   } \label{fig:pic}
\end{figure}

\begin{figure}[htbp]
   \centering
   \includegraphics[width=3.0 in]{picL064pc271} \\
   (a) \\
   \includegraphics[width=3.0 in]{picL064pc71} \\
   (b) \\
   \caption{
   (a) Here the density of occupied bonds at the first connection occurs at $p = p_{c2} =
   3660/8192= 0.44678$. (b) The same system where $p$ is increased to $p_c = 1/2$ is shown.
   This is a very rare system in which the connection between the anchor points first
   occurs substantially below $p_c$, where the point connecting cluster \rev{(magenta or light grey bonds)}
   is different from the largest cluster \rev{(red or grey bonds)}. In fact, the spanning cluster is
   relatively small and does not extend over the whole system. Such behavior where spanning
   occurs below $p_c$ can only happen in smaller systems. In most cases, the individual
   values of $p_{c2}$ are larger than $p_c$ and the cluster connecting them is the
   ``infinite" cluster that spreads over virtually the entire system \rev{as in Fig.\ \ref{fig:pic}(b).}
   }
   \label{fig:pic2}
\end{figure}

\subsection{Scaling of the estimates}

If we assume that the mapping of our problem to $[P_\infty(p)]^k$ is correct for finite systems
characterized by $P_\infty(p,L)$,  we can then estimate the scaling behavior of the estimates
from finite-size scaling theory.  That theory states that for  $L \to \infty$ and  $p - p_c \to 0$
with $(p-p_c) L^{1/\nu}$ constant,
\begin{equation}
P_\infty(p,L) \sim a L^{-\beta/\nu} F(b(p-p_c) L^{1/\nu})
\label{scaling}
\end{equation}
where $a$ and $b$ are system-dependent constants (``metric factors") while $\beta$, $\nu$ and $F(z)$
are universal quantities, having the same values and behavior for all systems of a given dimensionality,
and also a given system shape for the case of $F(z)$.  For $d = 2$, one has $\beta = 5/36$ and $\nu = 4/3$
\cite{StaufferAharony94}.

We will apply this \rev{scaling} to the estimate for $\overline p_{ck}$ given by Eq.\ (\ref{eq:pck}).
First we  consider the  interval $p = (0,p_c)$.  In this interval, we assume that the finite-size
effects are essentially those given by the scaling function $F(z)$, because when $p<p_c$,
$P_\infty(p,\infty) = 0$.  That is, we assume the non-scaling corrections are unimportant for
large $L$ for $p<p_c$.

Putting (\ref{scaling}) into the integral in Eq.\ (\ref{eq:pck}) over the interval $p = (0,p_c)$, we find
\begin{equation}
\int_0^{p_c} [P_\infty(p)]^k  dp  = a^k \int_0^{p_c} L^{-k \beta/\nu} [F(b(p-p_c)L^{1/\nu})]^k dp
\end{equation}
and a change of variables yields
\begin{eqnarray}
 \int_0^{p_c} [P_\infty(p)]^k  dp  &=&  a^k b^{-1} L^{-(k \beta+1)/\nu}  \int_{-b p_c L^{1/\nu}}^{0}  [F(z)]^k dz \cr \cr
 &\approx&  a^k b^{-1}  L^{-(k \beta+1)/\nu}  \int_{-\infty}^{0}  [F(z)]^k dz
 \label{eq:scaling2}
\end{eqnarray}
where $z = b(p-p_c) L^{1/\nu}$.  In the second integral in (\ref{eq:scaling2}) we extended the lower limit to
$-\infty$, valid for large $L$ because the integrand decays exponentially for negative $z$.

Therefore, this contribution to the integral in (\ref{eq:pck}) should scale as $L^{-1/\nu_k}$ with
\begin{equation} 1/\nu_k = (k \beta + 1)/\nu = \frac{36+5k}{48} \label{eq:nuk}\end{equation}
 so that $1/\nu_1 = 41/48 = 0.854166$ and $1/\nu_2 =  23/24 = 0.958333$ etc.

For $p > p_c$, it is not clear how to attack the finite-size corrections of the integral in (\ref{eq:pck}) because
there are large non-scaling contributions to $P_\infty$ whose behavior we do not know, but it seems reasonable to
assume that the finite-size corrections for $p>p_c$ scale the same as those we found for $p < p_c$, so we conjecture
that the exponents $\nu_k$ above should characterize the full finite-size corrections to $\overline p_{ck}$.  \rev{That is,  we conjecture
\begin{equation}
\overline p_{ck}(L) = \overline p_{ck} + c L^{-1/\nu_k}
\label{eq:pckscaling}
\end{equation}
where $c$ is a constant and $\nu_k$ is given by Eq.\ (\ref{eq:nuk}).  The constant term
on the right-hand side, $\overline p_{ck}$, derives from the non-scaling parts of $P_\infty$ for $p > p_c$.

\rev{Note that it also follows from the scaling arguments above that $P_r = k [P_\infty(p)]^{k-1} P'_\infty(p)$ behaves with $L$ in the scaling regime as
 \begin{eqnarray}
 P_r &\sim&  k a^{k-1}  L^{-(k-1) \beta/\nu} [F(b(p-p_c)L^{1/\nu})]^{k-1}\cr
 &\times& a L^{-\beta/\nu}F'(b(p-p_c)L^{1/\nu})  b L^{1/\nu} \cr
 &\sim&  L^{ -(k \beta - 1)/\nu} G(b(p-p_c)L^{1/\nu})
 \label{eq:Prscaling}
  \end{eqnarray}
  }
}

\begin{figure}[t]
   \centering
   \includegraphics[width=3.0in]{Prpc.pdf}
   \caption{ Simulation result: (a) The probability distribution $P_r(p_{c2},L)$ of the
   percolation threshold $p_{c2}$ of connecting two anchor points has been plotted
   against $p_{c2}$ for $L$ = 128 \rev{(black or lower curve)}, 256 \rev{(green or middle curve)}, 512 \rev{(red or upper, most peaked curve)}. (b) The scaling plot
   of the probability distribution $P_r(p_{c2},L)L^{(2\beta-1)/\nu}$ against
   $(p_{c2}-p_c)L^{1/\nu}$ with $\beta=5/36, \nu=4/3$ with $p_c=1/2$. \rev{Bottom to top $L = 128$, 256, and 512.}
   }
   \label{fig:Prpc}
\end{figure}

\begin{figure}[htbp]
   \centering
   \includegraphics[width=3.0 in]{mannaP2p.pdf}
   \caption{ Plots of $\rev{P_r(p,L) = }2 P_\infty(p) P'_\infty(p)$ for $L = 128,$ 256 and 512, bottom to top at peaks. These
   are the analogous curves as given in Fig.\ \ref{fig:Prpc}(a), calculated
   from  $P_\infty(p)$ rather than by direct simulation \rev{of $P_r$.
   Note here $p$ is equivalent to $p_{c2}$ used in Fig.\ \ref{fig:Prpc}.}}
   \label{fig:mannaP2p}
\end{figure}

\begin{figure}[htbp]
   \centering
   \includegraphics[width=3.0in]{ScalingPlotManna}
   \caption{ Scaling plot of $L^{(2 \beta-1)/\nu} 2 P_\infty(p) P'_\infty(p)$
   vs.\ $(p-p_c)L^{1/\nu}$ for $L = 128,$ 256 and 512 (bottom to top). The curves collapse well
   to a universal curve, except for the tail for large $(p-p_c)L^{1/\nu}$ which
   represents the non-scaling part of this quantity.  \rev{This plot is comparable with Fig.\ \ref{fig:Prpc}(b), here evaluated through $P_\infty$ rather than the direct measurement of $P_r$}.  Here $p$ is equivalent to $p_{c2}$ in Fig.\ \ref{fig:Prpc}.}
   \label{fig:ScalingPlotManna}
\end{figure}

\section{Simulation methods}
\label{sec:methods}

\subsection{Simulation method to find $\overline p_{ck}$}

      We carried out computer simulations of these processes on systems of size $L \times L$
   for bond
   percolation, with periodic boundary conditions. For the case $k = 1$, we consider $L$ odd and
   add bonds until the center point connects to the boundary for $p = p_{c1}$. Repeating this
   process many times, we average the values of $p_{c1}$ to find $\overline p_{c1}$. For $k$ = 2, 3 and 4, we
   consider periodic $L \times L$ systems with $L = 2^n$, $n = 5, 6, \ldots 12$. For $k = 2$ we
   consider the connectivity between a point at the origin (0,0) and a point at $(0,L/2)$. For $k = 3$,
   the connectivity between the three points (0,0), $(L/2,0)$, and $(0,L/2)$, and for $k = 4$, the
   connectivity between the four points (0,0), $(L/2,0)$, $(0,L/2)$, and $(L/2,L/2)$ is considered.  \rev{Note that for $k = 3$, the three points are the vertices of a
   right triangle rather than an equilateral triangle, so the distances between pairs of
   points are not identical, but this is not important --- all that matters is that the
   three points are relatively far apart from each other. }
   The average value of $p$ at the first connection gives $\overline p_{ck}$.

      It is  clear from Eq.\ (\ref{eq:Pransatz}) that the values of the thresholds $\overline p_{ck}$ should
   depend only on the value of $k$, and not on the actual distribution of the $k$ points. We
   have numerically verified this issue for $k=2$ by randomly distributing these two points on the
   lattice for every configuration. Our simulation results show that the values of $\overline p_{c2}$ remain unchanged.

      We also studied the average $p$ at which the origin connects to point $x = 1$, $x = 2$, \ldots,
   $x = L/2$ and $y = 0$ \rev{for systems of different $L$}. We discovered that $p_{c2}(x)$ does not noticeably depend upon $L$  as along as $x \ll L$,
   indicating that the size of the system is \rev{unimportant} for shorter-range connections.

\subsection{Simulation method to find $P_\infty$}

      To test the conjecture relating $\overline p_{ck}$ to $P_\infty$, we carried out
   measurements of $P_\infty(p)$ using the method of Newman and Ziff (NZ)
   \cite{NewmanZiff00,NewmanZiff01}, which involves adding bonds one at a time to the
   system and using the union-find procedure to merge clusters and keep track of the
   cluster distribution. This method allows one to effectively measure a quantity
   $Q(p)$ (such as $P_\infty(p))$ for all values of $p$ in a single simulation. In this
   method, one first determines the ``microcanonical'' $Q_n$ (here $P_{\infty,n}$) when
   exactly $n$ bonds have been placed down, and then determines the ``canonical''
   $Q(p)$ (here $P_\infty(p)$) by carrying out a convolution with the binomial distribution
   $B(N,n,p)={N \choose n} p^n (1-p)^{N-n}$:
\begin{equation}
Q(p) = \sum_{n=0}^N {N \choose n} p^n (1-p)^{N-n} Q_n
\label{eq:convolution}
\end{equation}
   where $N$ is the total number of bonds in the system, in this case $2L^2$. For large
   systems, the differences between the microcanonical $Q_n$ with $n=p N$ and $Q(p)$ are
    small, except for regions of high curvature or second derivative, but the convolution serves a
   further purpose of smoothing out the data, and connecting it with a continuous curve,
   rather than the discrete values $p = 1/N, 2/N, \ldots$. To integrate $P_\infty(p)$
   (as required for $\overline p_{c1}$ according Eqs.\ (\ref{eq:pck}) or (\ref{eq:pckalt})),
   one can just as well sum the microcanonical values, because of the identity \cite{ZiffNewman02}
\begin{eqnarray}
\int_0^1 Q(p) dp &=& \sum_{n=0}^N
  {N \choose n}  Q_n \int_0^1 p^n (1-p)^{N-n} dp  \cr
&=& \frac{1}{N+1}  \sum_{n=0}^N Q_n
\end{eqnarray}
   Likewise it follow that
\begin{eqnarray}
\int_0^1 p Q(p) dp
&=& \frac{1}{(N+1)(N+2)}  \sum_{n=0}^N (n+1) Q_n
\end{eqnarray}
   To integrate $[Q(p)]^k = [P_\infty(p)]^k$ for $k>1$ with respect to $p$, it is most
   straightforward to first carry out the convolution to find $P_\infty(p)$, and then
   numerically integrate the $[P_\infty(p)]^k$ at equally spaced values of $p$.

Derivatives of $Q(p)$ can also be found directly from the $Q_n$ \cite{ZiffNewman02}:
\begin{eqnarray}
Q'(p) &=& \sum_{n=0}^N  {N \choose n}   \rev{Q_n} \frac{d}{dp} \left( p^n (1-p)^{N-n}\right)  \cr
&=& \frac{1}{p(1-p)}  \sum_{n=0}^N  (n-Np) {N \choose n} ( p^n (1-p)^{N-n})Q_n \cr
&= &\frac{\langle( n - N p)Q_n \rangle }{p(1-p)}
\label{eq:derivative}
\end{eqnarray}
and likewise

\begin{eqnarray}
 &\textstyle{Q''(p)}&=\textstyle{ \frac{\langle n^2 Q_n \rangle    -(2(N-1)p+1) \langle n Q_n \rangle + N(N-1)p^2\langle Q_n \rangle}{p^2(1-p)^2} \hspace{1 em}} \cr
&\textstyle{=}&\textstyle{\hspace{-1.1em} \frac{\langle (n-Np)^2 Q_n\rangle+(2 p - 1)   \langle (n - N p) Q_n\rangle - N p (1-p)\langle Q_n \rangle }{p^2(1-p)^2} }
\label{eq:secondder}
\end{eqnarray}
where the averages are over the binomial distribution $B(N,n,p)$.  Note that in Ref.\ \cite{ZiffNewman02},
there is a typo in Eq.\ (32) for $Q''(p)$, in which the last term should have the factor $(N-n-1)$ rather than $(N-n+1)$.

\begin{figure}[htbp]
   \centering
   \includegraphics[width=3 in]{FigMannaPk.pdf}
   \caption{ A plot of $(d/dp) [P_\infty(p)]^k$ vs.\ $p$ for $k = 1$ (red, highest peak)), $k = 2$
   (orange, second-highest peak), $k=3$ (green, second-lowest peak),
   and $k=4$ (blue, lowest peak) for a system with $L = 512$, calculated
   from the results of the numerical simulations of $P_\infty(p)$, including using Eq.\ (\ref{eq:derivative}) to find $P'_\infty(p)$. The
   estimates of $\overline p_{ck}$ are the means of these distributions according to
   Eq.\ (\ref{eq:pck1}), and it can be seen that the distribution spreads to the
   right as $k$ increases, yielding larger values of $\overline p_{ck}$. To find the
   accurate values of $\overline p_{ck}$, one has to  consider systems of different $L$
   and take the limit that $L \to \infty$, although \rev{the change is small} for systems
   larger than $L = 512$.  Note that the distribution is broad and the large fluctuations in the
   individual values of $p_{ck}$ persist as $L \to \infty$.}
   \label{fig:Pk}
\end{figure}

      To find $P_\infty(p)$ we simulated $10^7$ samples each for $L = 64, 128, 256$
   and 512 on $L \times L$ periodic systems, saving the $2 L^2$ microcanonical values
   of $s_\mathrm{max}$ in a file. For the largest system $L = 512$, the simulations took
   several days on a laptop computer. Then we used a separate program to read the
   files and calculate $P_\infty(p) = s_\mathrm{max}/L^2$ for $10^4$ points $p = 0, 0.0001,
   \ldots, 1.0000 $ using the convolution (\ref{eq:convolution}).  We also calculated
   $P'_\infty(p)$ and $P''_\infty(p)$ using the formulas of Eqs.\ (\ref{eq:derivative})
   and (\ref{eq:secondder}).   We used the recursive method described in Ref.\
   \cite{NewmanZiff01} to calculate the binomial distribution for each $p$. To find the
   integrals of $[P_\infty(p)]^k$ \rev{for Eqs.\ (\ref{eq:pck}) and (\ref{eq:pckalt})}, we carried out numerical integration of the $10^4$
   points using the trapezoidal rule (namely counting the two endpoints with \rev{relative} weight 1/2
   and all other points with weight 1).  We compared some of the integrals using $10^3$
   and $10^5$ points and did not find significant difference in the results, and used
   $10^4$ values of $p$ in our calculations.

\section{Results}
\label{sec:results}

\rev{Figure \ref{fig:Prpc}(a) shows the probability distribution $P_r(p_{c2},L)$ of the
  percolation threshold $p_{c2}$ of connecting two anchor points, from direct
  measurements.  Note $p_{c2}$ is the value of $p$ at which the connection first
  takes place in a given sample, as opposed to $\overline p_{c2}$ which is the
  average value over many samples.   Figure \ref{fig:Prpc}(b)  shows a scaling plot of the data, using the
  scaling implied in Eq.\ \ref{eq:Prscaling}.}

\rev{Figure \ref{fig:mannaP2p} shows the predicted behavior of $P_r$ from
the ansatz of Eq.\ \ref{eq:Pransatz}, using the simulation results of $P_\infty$ rather than measuring
 $P_r$ directly.  These curves can be compared with those of Fig.\  \ref{fig:Prpc}(a), and
 the two can be seen to agree.}

\rev{Figure \ref{fig:ScalingPlotManna} shows the predicted scaling behavior of $P_r$ from
the ansatz of Eq.\ \ref{eq:Pransatz}, and the results can be seen to be similar to the scaling plot of the directly measured $P_r$ given in Fig.\ \ref{fig:Prpc}(b).}

Figure \ref{fig:Pk} shows plots of the predicted distributions of the probabilities of first connection,
 $(d/dp) [P_\infty(p)]^k$, for $k = 1$, 2, 3, and 4, based upon measurements $P_\infty(p)$, for a system
of $L = 512$.   As can be seen, the distributions are broad, meaning that the
 thresholds we find $p_{ck}$ have large
 fluctuations from system to system and persist as $L \to \infty$.

\begin{figure}[htbp]
   \centering
   \includegraphics[width=3 in]{figurek1.pdf}
   \caption{
   Values of $\overline p_{c1}(L)$ found from  simulations of connections of
   a point at the center to the boundary of an $(L+1) \times (L+1)$ square system
   (triangles), by integrating $P_\infty(p)$ on $L \times L$ periodic systems
   using Eq.\  (\ref{eq:pck}) for $k = 1$  (squares), and by integrating
   $P_\infty(p)$ using Eq.\  (\ref{eq:pckalt}) (circles). The estimates are all
   plotted vs.\  $L^{-41/48}$ according to the prediction of Eq.\  (\ref{eq:nuk}).
   The equations of the linear fits through the points are $\overline p_{c1} =
   a + b L^{-41/48} $ with $a=0.55520$, $b=-0.33805$ (squares),
   $a=0.55532$, $b=-0.27962$ (triangles), $ a=0.55530$, $b=-0.06323$ (circles).
   }
   \label{fig:pc1}
\end{figure}

      In Fig.\ \ref{fig:pc1} we plot estimates for $\overline p_{c1}$ found from direct simulations with the point
   in the center of an $(L+1) \times (L+1)$ system, for $L = 64, 128, \ldots, 4096$, and secondly using the
   formulas of Eqs.\  (\ref{eq:pck}) and  (\ref{eq:pckalt}) \rev{for $k=1$} based upon $P_\infty(p)$.  The data are
   plotted based on the predicted scaling $L^{-41/48}$ \rev{from Eq.\ (\ref{eq:nuk})}.  We do not expect that the values of $\overline p_{c1}(L)$
   would be the same for finite $L$ from the two methods (direct simulation and via $P_\infty$); however, we expect that the extrapolation as
   $L \to \infty$ should be the same, because in that limit the probability the point connects to the boundary
   should exactly be the probability the point belongs to the largest cluster, namely $P_\infty$.  Furthermore,
   we expect the two estimates of $\overline p_{c1}$ should scale with $L$ with the same exponent
   $1/\nu_1 = 41/48$, and indeed that plot confirms that expectation.  The two different approaches suggest a
   threshold of $\overline p_{c1} = 0.51749(5)$.

      It can clearly be seen that the estimate based upon (\ref{eq:pckalt}), which assumes $P_\infty(p,L)=0$
   for $p < p_c$, converges much more quickly than the estimate based upon (\ref{eq:pck}). On a more expanded
   scale, the convergence to this estimate is also shown to obey the $L^{-41/48}$ scaling, but is not shown
   here.  The results for $k = 2$, 3 and 4 are shown in Figs.\ \ref{fig:pc2}, \ref{fig:pc3}, and \ref{fig:pc4}.
  Our values of $p_{ck}$ are given in Table \ref{tab:01}.

\begin{figure}[htbp]
   \centering
      \includegraphics[width=3 in]{figurek2.pdf}
   \caption{ Values of  $\overline p_{c2}(L)$ found from direct simulations on an $L
   \times L$ periodic system with the two points at (0,0) and (0,$L/2$) (triangles),
   and the predictions from Eqs.\ (\ref{eq:pck}) (squares)
   and (\ref{eq:pckalt}) (circles) based upon measurements of $P_\infty(p)$ on an $L \times L$
   periodic system, all plotted as a function of $L^{-46/48}=L^{-23/24}$ as
   predicted by Eq.\ (\ref{eq:nuk}). Here  $L = 32$, 64, 128, 256, and 512 for
   the upper two sets of data, and also $L = 1024$ for the lower set.
   }
   \label{fig:pc2}
\end{figure}

\begin{figure}[htbp]
   \centering
   \includegraphics[width=3 in]{figurek3.pdf}
   \caption{ Values of  $\overline p_{c3}(L)$ found from direct simulations on an
   $L \times L$ periodic system with the three points at (0,0), $(0,L/2)$ and ($L/2,0$)
   (triangles), and the predictions from Eqs.\ (\ref{eq:pck}) (squares) and (\ref{eq:pckalt})
    (circles) based upon measurements of $P_\infty(p)$ on an
   $L \times L$ periodic system, all plotted as a function of $L^{-51/48}=L^{-17/16}$
   as predicted by Eq.\ (\ref{eq:nuk}).
   }
   \label{fig:pc3}
\end{figure}

\begin{figure}[htbp]
   \centering
   \includegraphics[width=3 in]{figurek4.pdf}
   \caption{ Values of $\overline p_{c4}(L)$ found from direct simulations on an
   $L \times L$ periodic system with the four points at the corners of a square of
   length $L/2$ (triangles), and the predictions based upon $P_\infty(p)$
   using Eq.\ (\ref{eq:pck}) (squares) and Eq.\ (\ref{eq:pckalt}) (circles),
   both based upon  measurements of $P_\infty(p)$ on an $L \times L$ periodic system. All data are
   plotted as a function of $L^{-56/48}=L^{-7/6}$ as predicted by Eq.\ (\ref{eq:nuk}).
   Lines show linear fits through the data. It can be seen that estimates based upon
   Eq.\ (\ref{eq:pckalt}) exhibit the fastest convergence with system size.
  }
   \label{fig:pc4}
\end{figure}

\section{Correlations}
\label{sec:correlations}

We also considered a related question for two- and three-point correlations.
Studying this problem sheds light on the correlations that occur in the system in the critical vs.\ the post-critical regime where
the connectivity between the anchor points mainly occurs.

In \cite{SimmonsZiffKleban09,DelfinoViti10} the following ratio was considered:
\begin{equation}
\rev{R(p)} = \frac{P(r_1,r_2,r_3)}{\sqrt{P(r_1,r_2) P(r_1,r_3) P(r_2,r_3)}}
\label{eq:Rratio}
\end{equation}
where $r_1$, $r_2$ and $r_3$ are three points in the system, $P(r_i,r_j)$ is the probability that points $r_i$ and $r_j$ connect, and $P(r_1,r_2,r_3)$ is the probability that all three points connect.

\begin{figure}[htbp]
   \centering
   \includegraphics[width=3 in]{MannaFigRratio}
  \caption{\rev{(color online) Scaling plot of $R(p)$ vs.\ $(p-p_c) L^{1/\nu}$ where $R(p)$ is given in Eq.\ (\ref{eq:Rratio}), for three points at positions ($0,0$), ($0,L/n$), and ($L/n,0$), for $n = 2$ (red, the  curve with the highest peak), $n = 4$, (green, the curve with the second-highest peak), $n = 8$ (blue, the curve with the third-highest peak), and $n = 16$ (black, the curve that does not reach a peak in this interval), for $L = 64$, 128, 256, and 512 respectively. Other runs show that there is a small  $L$-dependence on the results, but the main variation is due to $n$.  At $p = p_c = 1/2$, the value of $R(p_c)$ approaches the theoretical value $C_1 = 1.022$  \cite{SimmonsZiffKleban09,DelfinoViti10} as $n$ gets large, in which case the three points are close together compared to the size of the system.  The meaning of the crossing point for $(p-p_c)L^{1/\nu} \approx -0.2$ is unclear, and may not be maintained for larger systems.}}
 \label{fig:Rratio}
\end{figure}

      This ratio has previously been studied, to our knowledge, only at $p = p_c$, where the value of $R(p_c)$ approaches the value $C_1 = 1.0220$
   when the three points are far separated and the system size is infinite.  This value of $C_1$ was first observed numerically in
   \cite{SimmonsZiffKleban09} and then derived analytically from conformal field theory in \cite{DelfinoViti10}. The fact that this ratio is
   unequal to 1 implies a correlation between the three points in the system.   \rev{If we make the assumption that $P(r_i,r_j) =
   P_\infty(p)^2$ and $P(r_1,r_2,r_3) = P_\infty(p)^3$, which we expect to be the case for $p > p_c$, then we would have $R = 1$.} At $p_c$, where
   the infinite cluster does not span throughout the system, one would not expect this to be valid and indeed $R(p) \ne 1$, although \rev{it turns out quite close to 1.}

      Here we consider the three points in a right triangle, ($0,0$), ($0,L/n$), and ($L/n,0$), in an $L \times L$ periodic system, for $n = 2,$ 4 and 8 . As $n$ increases
  for large $L$ (that is, as the separation of the three points is small compared to the size of the system), $R(p_c)$ approaches the value
   $C_1$. Using the NZ method, we were able to calculate $R(p)$ as a function of $p$ after executing a microcanonical simulation where we found the
   $P(r_i,r_j)$ and $P(r_1,r_2,r_3)$ as a function of the number of bonds added.  We then carried out the convolution to the canonical ($p$-dependent) functions for all $P$'s
   separately, and  calculated $R(p)$ according to Eq.\ (\ref{eq:Rratio}).  The results are shown in Fig.\ \ref{fig:Rratio}.

      As can be seen, at $p = p_c$, $R(p_c)$ approaches $C_1$ as $n$ increases (in which case the points get closer together compared to the size of the system).
In the limit that $L \to \infty$, $R(p)$  \rev{evidently} becomes a discontinuous function \rev{of $p$}, with $R(p_c)=C_1$ for
   $p = p_c$, and $R(p)=1$ for $p>p_c$.  \rev{The behavior for $p < p_c$ is not clear.}  Notice in Fig.\ \ref{fig:Rratio} that there is a maximum for $R(p)$ in finite systems at $z = (p-p_c) L^{1/\nu}
   \approx -0.5$, meaning for some values of $p < p_c$, $R(p)$ is greater than the value at $p_c$. However, it is not clear what the behavior is as
   $n\to \infty$ (for large $L$); it is possible that the peak for negative $z$ disappears and the peak occurs only at $z = 0$ or $p = p_c$.  \rev{The behavior for $p<p_c$ needs further investigation.}

      At the point $p_{c3} \approx 0.5445$ where three points first connect, it can be seen that $R(p)$ approaches 1, since that would correspond to $(p-p_c) L^{1/\nu}$ going
   to infinity as $L$ goes to infinity. This result reiterates that at the places where multiple points connect, there are no correlations among
   connections between different pairs of \rev{widely separated} points.

\begin {table}[t]
\caption{
         Our best estimates for the extrapolated values of the average percolation thresholds
         $\overline p_{ck}$ from direct measurements (second column) and from $P_\infty$
         via Eqs.\ (\ref{eq:pck}) and  (\ref{eq:pckalt}) for different values of $k$.  The averages
         of these values are quoted in the abstract.
         }
\begin{tabular}{llll} \\ \hline
$k$   \hspace*{1.0 cm}& $\overline p_{ck}$ measured     \hspace*{1.0 cm}& Eq.\ (\ref{eq:pck})   \hspace*{1.0 cm}& Eq.\ (\ref{eq:pckalt})    \\ \hline
1    & 0.51749(5)   & 0.51761(3)  & 0.51755(3)    \\
2    & 0.53212(5)   & 0.53220(3)  & 0.53226(3)    \\
3    & 0.54450(5)   & 0.54458(3)  & 0.54461(3)    \\
4    & 0.55520(5)   & 0.55530(3)  & 0.55531(3)    \\ \hline
\end{tabular}
\label {tab:01}
\end {table}

\section{Discussion}
\label{sec:discussion}

      We have shown that exploring the average value of the probability $p$ of bond occupation at which a certain number of
   separated points first connect leads to a new set of average thresholds. The distribution of
   the values of $p$ is broad, so that this threshold is not sharp as in the
   usual case of thresholds in percolation. For example, the median rather than the mean
   of the distribution would give a different value. We have shown that the values can
   be related to $P_\infty(p)$, and confirm this relation by simulation. From this theory
   it is apparent that while the percolation thresholds $\overline p_{ck}$ indeed depend on
   the number $k$ of points, their values are robust with respect to the actual spatial
   distribution of the $k$ points. For example, the $k$ points may either be symmetrically
   placed on the lattice or, they can be randomly distributed (for $L \to \infty$).

      This work suggests further research in a variety of areas. It might be interesting
   to study these thresholds in higher dimensions, where the relations to $P_\infty(p)$
   in Eqs.\ (\ref{eq:pck}) and (\ref{eq:pckalt}), and the scaling in (\ref{eq:nuk})
   (but with $\nu$ and $\beta$ being the three-dimensional result) should still hold,
   for connections to points as we considered here. Furthermore, connections between
   higher-dimensional objects (lines, surfaces, ...) can also be considered. One question
   to consider is whether the thresholds continue to have broad distributions as found
   here, and how those thresholds scale with $L$.

      With respect to the correlations $R(p)$, one can consider a point in the center of a
  \rev{surface of }a cylinder (that is, the center of a square with periodic b.c.\ in one direction), and find the
   probability of connecting the center to one boundary or to both boundaries of the
   cylinder. At $p_c$, the corresponding $R(p)$  should go to the value  $C_0 =  2^{7/2}
   3^{-3/4} \pi^{5/2} \Gamma(1/3)^{-9/2} = 1.029 9268\ldots$ \cite{SimmonsZiffKleban09}
   while the behavior away from $p_c$ has not been studied before. Likewise, similar
   correlations in higher dimensions have not been studied. Many aspects of correlations
   in percolation are yet to be explored.

   \section{Acknowledgment} The authors would like to thank Deepak Dhar for a careful reading
   and  constructive comments on the paper.

\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


text:
The CERN asset management challenge
I have written before about the massive Hadron Collider at CERN and more recently about the Higgs Particle excitement there. So, when my friends at Infor told me their Asset Management software helps with that complex, I had all kinds of questions.
Works Management describes the scope of the challenge below. Complex is the appropriate word.
"With more than one million pieces of equipment to manage, in addition to its internal personnel, CERN uses about 50 external service providers, with a range of service agreements, including fixed-fee contracts, performance-based contracts, task and component based agreements etc. Hence, says Martel, the requirement for a flexible management system, so that every equipment item and maintenance task can be traced – so helping to anticipate malfunctions and maintain uptime for CERN's scientific research programmes.
Today, a large part of CERN's infrastructure maintenance activities, such as caretaking, roads, heating and cooling, security etc, as well as part of its scientific instrumentation activity, are managed using Infor10 EAM, he says. The system generates more than 180,000 work orders per year, schedules preventative maintenance tasks, provides stock control functionality and organises maintenance and inspection programmes.
For the scientific instruments, a manufacturing control system has also been set up. With about 200,000 in-scope equipment items identified, Infor10 EAM has become the heart of this system. "
Photo Credit: Boston.com
July 31, 2012 in Enterprise software | Permalink | Comments (0) | TrackBack (0)
The Digital Swiss Army Knife
It is a AM/FM radio. A NOAA Weather radio. A LED flashlight. An USB outlet to charge your electronics. It can be powered via its manual crank. Via solar. Or DC power. Portable at a little over a pound. The American Red Cross FRX3 made by Etón.
July 31, 2012 in Alternative Fuels, Mobile applications and commerce | Permalink | Comments (0) | TrackBack (0)
Retail Trends for VARs
Business Solutions magazine which is aimed at VARs has a summary of macro technology trends in Retail – Mobile POS, innovations in video surveillance and receipt printers and moving vertical apps to the cloud.
July 31, 2012 | Permalink | Comments (0) | TrackBack (0)
The "Fast Pool" at the London Aquatic Centre
The physics and technology that Michael Phelps, Missy Franklin and other Olympic swimmers are enjoying
"You Talk. We Draw"
Fascinating Concept from Ink Factory Studio
"By actively listening and synthesizing your discussion, brainstorm or keynote speech, we transcribe your words into real-time, hand drawn visuals. These visuals are the combination of written text and images that represent thoughts, concepts, key messages, strategic visions or just a simple summary of your conversation."
July 30, 2012 in Creativity in Product Design | Permalink | Comments (0) | TrackBack (0)
The Amazing Olympic Cauldron
"Our very first briefing from the technical team ... was please can you come up with a design for the cauldron, and whatever you do, make sure there's no moving parts," designer Thomas Heatherwick told reporters after Friday's ceremony.
"And we were 'how are we going to persuade them, they are never to go for this'.
"It's the most moving parts that's humanly possible to have in a cauldron."
"The cauldron is made up of the "polished copper objects" which are in the shape of flower petals about a foot long.
There are 204 of them, representing each of the countries taking part in the Olympics, and they are attached to steel pipes, each of them about 28 feet high, which contain a gas pipe connected to the mains supply.
The pipes are made of a special type of steel with a heat and acid chemical treatment that give them a colour called 'bad black'. Each petal is individually made and each had to be clicked into place into a specific rod. At the end of the Games the cauldron will be dismantled and the petals scattered to the 204 nations that took part in the opening ceremony. "
The petals were constructed by "Stage One, a metalworking firm based in Towkwith, North Yorks, which is one of the few companies in Britain with the expertise for the task."
Photo credit above of the petals at ground level as they were lit by the 7 athletes given the honor, and below after they were raised and came together
Innovative Fruit
New Zealand is known for its wonderful dairy products. But they also have the perfect complement for cheese – fruit paste you can cut into chunks. My wife recently brought home some from Rutherford & Meyer. In fact, they say the pastes "are designed to be sliced not spread". Also, they come in exotic flavors - Quince, Fig, Plum, Pear, and Apricot.
So, fruit in exotic shapes, texture and flavors. Innovative enough?
64,000,000 points of light
8,000 holes in each of the 8,000 torches used to bring the Olympic flame to the stadium.
From Welding and Gases today
"Arguably the most iconic symbol of the Olympics, this year's Olympic torch is made from a special aluminum alloy originally developed for the aerospace and automotive industry. The alloy's characteristics make it heat resistant, lightweight and strong.
The torch has a unique triangular design (symbolic of 3 Olympics in London) incorporating a complex pattern of 8,000 holes (representing the 8,000 people who carried the torch on its journey from Olympia, Greece, to London).
Along with their symbolic representation, the holes are functional. One of the torch's designers, Jay Osgerby , says, "The wind moves through the torch, the perforations allow the metal to cool, and so the torch never gets hot."
In creating the torch, the holes are cut from the alloy using a numerically controlled 2D laser cutting machine.
After this, the manufacturer uses 3D laser technology to weld the parts of the torch together in a smooth, seamless joint and cut additional holes in the welded areas.
As for the actual flame, the 2012 torch uses a gas mix including two-thirds propane and one-third butane.
Each of the 8,000 torches used this year (yes, they use a separate torch for every runner) has enough gas to burn for 13-14 minutes, although it only takes 3-6 minutes for each carrier to travel the 300 meters (328 yards) of each leg."
Technology at the London Opening Ceremony
This slideshow goes into some of the jaw dropping, technology enabled scenes from last night.
They included LED lights at every seat, David Beckham's speed boat "Max Power", the AgastaWestland AW101 helicopter from which the Queen and James Bond skydive , amber light emitting diodes which created the image of flowing liquid steel accompanied with piped sulfur smell during the Industrial Revolution segment, flying bicycles and the synchronized fireworks.
Oh and btw, the event also honored Tim Berners-Lee, father of the WWW.
The "Made for Home" Olympics Opening Ceremony
Confession – all week long as my wife and son have reported the festive mood in London (and Oxford and Cambridge) I wished I was there. As I have cataloged 15 different posts on various innovations inspired by the Olympics, I had wanted to be at the Opening Ceremony.
But watching it on TV last night, laptop and smartphone nearby, I was perfectly content I was on my chair and exercise bike. I got in the mood by listening to Led Zeppelin's Stairway to Heaven. I knew Danny Boyle's production planned to have plenty of Britain's countryside and the song always takes me rural with its lyrics which include brook, whispering wind and hedgerow. I then watched a replay of the Beijing's Opening Ceremony on the NBC Olympics site (which is also best place to catch all the 302 events live and free if you register with your cable account) – feeling a bit sorry for what Danny had to benchmark against.
I need not have worried for Danny. He clearly learned a thing or two from Bollywood and Slumdog Millionaire. What a spectacle! The best and the most eccentric of what the British have to offer.
There were many segments I can argue looked better at home. The Queen/James Bond/Corgis (how can you forget them?) segment, David Beckham powerboating with the torch on the Thames, the close up of Rowan Atkinson during the Chariots of Fire segment, the parade of the athletes (NBC jammed in many commercials during the parade, and so thankfully edited the time for each country) and not needing binoculars to focus on the smiles and colorful costumes.
And at home, I could join many of my friends (Andrew McCarthy, Chris Selland, Bob Egan) virtually over Twitter and cheer and jeer. I have done so now for the SuperBowl in 2011, the Academy Awards earlier this year. If you do a little research before the event, and if you have handy Google and Wikipedia, it makes for a much richer experience without having to fight traffic or security.
Besides, I doubt very much I could have ordered a Blue Moon Summer Honey Wheat at the Games. And raise a toast to Consumerization of Technology.
July 28, 2012 in Smart Autos, Homes, Sports, Restaurants... | Permalink | Comments (0) | TrackBack (0)


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