text:
namespace Envoy {

// A filter that only allows decodeData() to be called once with fixed data length.
class DecodeDynamicMetadataFilter : public Http::PassThroughFilter {
public:
  constexpr static char name[] = "decode-dynamic-metadata-filter";

  Http::FilterHeadersStatus decodeHeaders(Http::RequestHeaderMap& header_map, bool) override {
    for (auto const& [filter, kvs] :
         decoder_callbacks_->connection()->streamInfo().dynamicMetadata().filter_metadata()) {
      for (auto const& [k, v] : kvs.fields()) {
        std::string value;
        switch (v.kind_case()) {
        case ProtobufWkt::Value::kNumberValue:
          value = fmt::format("{:g}", v.number_value());
          break;
        case ProtobufWkt::Value::kStringValue:
          value = v.string_value();
          break;
        case ProtobufWkt::Value::kBoolValue:
          value = v.bool_value() ? "true" : "false";
          break;
        default:
          // Unsupported type or null value.
          break;
        }
        std::string key = filter + "." + k;
        header_map.addCopy(Http::LowerCaseString(key), value);
      }
    }
    return Http::FilterHeadersStatus::Continue;
  }
};

constexpr char DecodeDynamicMetadataFilter::name[];
static Registry::RegisterFactory<SimpleFilterConfig<DecodeDynamicMetadataFilter>,
                                 Server::Configuration::NamedHttpFilterConfigFactory>
    register_;

} // namespace Envoy

redpajama_set_name: RedPajamaGithub


Start by booking your free intro session now.
Our 1,600-square-foot box isn't fancy. We don't need to flex a Paleo snack bar or in-house sauna to look cool. It's our people that make us great, not bricks and mortar and stuff.
What we've got is a blank space for you to write your new fitness story in. You know, the one where you get in the best shape of your life, make a bunch of lifelong friends, and just get better every day.
We've got all the famous CrossFit tools you love (and sometimes love to hate), but seriously, the most powerful machine we have in our gym is you.
Our coaches are powered by passion. Their commitment to compassionate coaching makes both newbies and experienced CrossFitters feel right at home as soon as they walk in the door.
SWEAT IS MAGIC. COVER YOURSELF IN IT DAILY.


Windows 10 Build 16299 has been confirmed as the final version of Windows 10 Fall Creators Update. Microsoft has just started rolling out the Windows 10 Fall Creators Update to the public.... Despite adopting a conservative, phased roll out strategy with its latest Windows 10 version, Microsoft's Fall Creators Update is off to a quicker start when compared to earlier versions.
Windows 10 Fall Update Problems: Low Disk Space After Upgrade Just like the Windows 8.1 to Windows 10 upgrade, the upgrade process leaves a windows.old folder on your Surface's hard drive so you can roll back to the RTM version if you want.
Fixed it by locking the computer and using the power button icon in the bottom right to restart while holding shift key. From there, I found an option to revert to a previous version of windows.
While upgrading to Windows 10 v1709, one of the Citrix driver files "CtxMcsWbc" is preventing write operations that causes the update to roll back. Solution This issue is fixed with the Windows 10 update released by Microsoft on 14th November 2017.


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Vancouver International Mountain Film Festival Touches Environmental, Indigenous And Mental Health Topics
Sam Danniels, a multi-sport professional athlete in three para-skiing disciplines, is subject of Beyond The Break — photo credit: screenshot
The 24th annual Vancouver International Mountain Film Festival (VIMFF) will be held from Feb. 19 to 28, continuing its mission to celebrate outdoor adventure and mountain culture, and there's a range of topics from para-athete Sam Danniels surf doc to recovering addict Harvey Wright who uses rock climbing as therapeutic tool.
VIMFF connects the global outdoor community with international filmmakers, creators and speakers through mountain film screenings, live multimedia presentations, photography exhibitions, workshops, seminars and other special events. These offerings aim to illustrate experiences and cultures from around the world to bring communities together to promote positive values and active lifestyles.
VIMFF has adapted its shows to a virtual setting due to COVID-19, allowing it to connect with audiences in their homes while increasing its global reach. It has expanded its programming to provide regular online content throughout the year.
Individual tickets cost $9 for films and $17 for shows and workshops. A film-only festival pass costs $85 and an all-access pass costs $105.
While the VIMFF programs high-impact environmental content, last year it also established a board-level committee to build a sustainability baseline and set strategic objectives. It has committed to making improvements in areas such as: being more proactive as a community ecological steward with local schools and organizations; procurement; printing; travel and local transportation; waste management; food and beverage selection and service; and venue considerations, such as convenience of location and energy usage.
VIMFF's Tim Jones Community Achievement Award is given each year to a community member who has made an outstanding contribution to Vancouver's North Shore outdoor or sports community. It's presented in memory of Tim Jones, a paramedic and chief of North Shore Rescue for more than 24 years. The award's mission is to educate and share passion for nature and local mountains. The winner will be announced during the festival.
Here are some of the films and related virtual panel discussions that will be shown at this year's VIMFF:
Beyond the Break is a documentary making its world premiere about Sam Danniels, a multi-sport professional athlete in three para-skiing disciplines, as well as cycling, snowmobiling and paragliding. He refuses to let his life-changing spinal cord injury become a barrier to the many outdoor sports that he loves and has designed and built a new surfboard to tackle the unpredictable waves of the Pacific Northwest (watch trailer below).
Crux: The Climb Towards Mental Health follows a recovering addict who uses rock-climbing to work through his ongoing struggle with mental health.
Water Flows Together acknowledges the importance of Indigenous land. It provides a glimpse into native views on issues of water resource management, which are often missing from larger discussions of water challenges.
The short film The Mystery of Now focuses on artist and Apache Skateboards founder Douglas Miles, who provides the socio-political context that led to life on the San Carlos Apache reservation while providing advice on cultivating resilience, creativity and joy in a time that for many feels uncertain, polarizing and divisive.
Panelists will share Indigenous perspectives and experiences while delving into how identity can be inseparable from land on Feb. 25 at 6 p.m. PST.
Leuser: The Last Place on Earth will have its world premiere at VIMFF. The film shares the story of the most biodiverse ecosystem ever documented by science in Sumatra, Indonesia, which is facing the looming threat of the expansion of large-scale illegal palm oil processing and exporting.
Maybe Tomorrow, which makes its North American premiere at VIMFF, looks at the impact of vanishing sea ice in northwestern Greenland.
Falling Mountains is also making its North American premiere at VIMFF. It looks at how the last three years have been the warmest on record in the European Alps, causing glaciers to recede at an alarming rate and mountains to crumble, and how communities can adapt their economies to keep pace with these changes.
Climate change is also in the spotlight in When Glaciers Go, which examines glacial water shortages in the remote Mustang region of Nepal.
Viewers will be invited to join a discussion on Feb. 23 at 6 p.m. PST (9 p.m. EST) where panelists will share their research and personal experience as witnesses of climate change.
A panel discussion on personal struggles and the positive effects the outdoors can have on mental health will be held on Feb. 19 at 6 p.m. PST (9 p.m. EST)
Watch trailer for Beyond The Break: The Sam Danniels Story:
Andy Kim Christmas Concert To Benefit CAMH Lineup Revealed
Geddy Lee's Acceptance Speech at Artists For Peace and Justice
Soul Asylum's "Runaway Train" Reimagined For 25th Anniversary To Help Find Missing Children
WATCH: Myles Goodwyn Song and Video About Canada's Residential School System
Unison Benevolent Fund COVID-19 Relief Program Surpasses $2 Million Raised
Susan Sarandon Q&A: Actress Talks Transgender Issues and Nepal Visit
Stripping For Better Living
Q&A: An Update From The Karma Box Co.'s Erin McDonald
Rarities CD For Mental Illness: inc. Glass Tiger's Alan Frew, The Spoons, ex Crowded House
Musician Rich Aucoin Touring U.S. by Bicycle to Benefit Mental Health
Helping Hands Jamaica Foundation To Build School In Honour of Denise Jones

redpajama_set_name: RedPajamaCommonCrawl


Animal Law Archives - Dear Esq.
Am I Liable For Running Over An Unleashed Dog?
Can I Sue My Neighbor For His Cat Damaging My Pool Liner?
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How Can I Legally Get My Cat Back?


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How Do You Carry Yours?
Eilidh and Leigh's Story: 'Who Knows If the Moon's A Balloon' Friday, 26 February 2010
Posted by edincityoflit in Stories.
Tags: e e cummings
Hello we are Eilidh and Leigh from Queensferry High School and the poem we are carrying this week is "Who knows if the moon's a balloon" by E.E Cummings.
Our favourite lines in this poem are:
who knows if the moon's a balloon coming out of a keen city in the sky.
than houses and steeples and clouds go sailing.
We like these lines because they have a good description of what it would be like if the moon really was a balloon. There are many more sentences like this but we piked the sentences above because they have a good description to them. If you read between the lines you can see it has a love story.
Poetry Pocketcards – In Detail Still Monday, 22 February 2010
Tags: Adrian Mitchell, e e cummings, Edward Lear, James Hogg, Lewis Carroll, Robert Burns, Rudyard Kipling, T S Eliot, W B Yeats, William Shakespeare
Here is your second batch of poetry pocketcards:
William Butler Yeats was an Irish poet and dramatist, and one of the foremost figures of 20th century literature. In 1923, he was the first Irishman to be awarded the Nobel Prize in Literature.
Edward Estlin Cummings was an American poet, painter, essayist, author, and playwright. His body of work encompasses approximately 2,900 poems, two autobiographical novels, four plays and several essays, as well as numerous drawings and paintings.
Charles Lutwidge Dodgson, better known by the pseudonym Lewis Carroll, was an English author, mathematician, logician, Anglican deacon and a photographer. His most famous writings are Alice's Adventures in Wonderland and its sequel Through the Looking-Glass, as well as the poems "The Hunting of the Snark" and "Jabberwocky", all examples of the genre of literary nonsense.
Rudyard Kipling was a British author and poet, born in Bombay in 1865. His children's books are enduring classics of children's literature, and his poetry exceptionally popular. In 1907, he was the first English language writer to be awarded the Nobel Prize in Literature, and to date he remains its youngest recipient. He declined both the Poet Laureateship and a knighthood.
James Hogg was born near Ettrick in Scotland in 1770 and is often referred to as 'The Ettrick Shepherd'. His employer introduced him to Sir Walter Scott, who asked him to help with a publication entitled The Minstrelsy of the Scottish Border. Eventually becoming a well-known literary figure in Edinburgh, he was recruited by William Blackwood for Blackwood's Magazine, and went on to publish The Private Memoirs and Confessions of A Justified Sinner, now his most widely recognised work, and cited as an influential work by many modern Scottish writers.
Edward Lear was an English artist, illustrator, author, and poet, renowned today primarily for his literary nonsense, in poetry and prose, and especially his limericks, a form that he popularised.
Adrian Mitchell was a London-born poet, novelist and playwright. A former journalist, he became a noted figure on the British anti-authoritarian Left and for almost half a century he was the foremost poet of the country's anti-Bomb movement. He died in 2008, and is survived by his wife, Celia, and five children.
Robert Burns was born in Ayrshire in 1759 and while he contemplated emigration to the West Indies, his collection of Poems, Chiefly in the Scottish Dialect was published by John Wilson of Kilmarnock, and its unexpected success led him to reconsider. Instead, he moved to Edinburgh where he was fêted. During the last years of his life, Burns wrote some of his great poetic masterpieces, including 'Tam o'Shanter' and 'A red, red rose'. He died in aged 37, of heart disease.
Every year, on 25 January, the anniversary of his birth, Scots celebrate Burns Night with a Burns Supper, a traditional celebration consisting of speeches, music and song dedicated to the poet's life and work.
Thomas Stearns Eliot was an American-born English poet, playwright, and literary critic. His first notable publication, The Love Song of J. Alfred Prufrock, is regarded as a masterpiece of the modernist movement. It was followed by some of the best-known poems in the English language, including The Waste Land, Old Possum's Book of Practical Cats, and Four Quartets. He is also known for his seven plays, particularly Murder in the Cathedral and The Cocktail Party. He was awarded the Nobel Prize in Literature and the Order of Merit in 1948.
William Shakespeare was an English poet and playwright, widely regarded as the greatest writer in the English language and the world's pre-eminent dramatist. He is often called England's national poet and the "Bard of Avon".
So, there you have them – our poetry pocketcards. Which do you like best?
@NadineK's Story: 'I Carry Your Heart' Wednesday, 27 January 2010
I carry the last part of "I carry your heart with me (i carry it in" by E.E. Cummings handwritten on the back of a pic I cherish in my purse. Every person interprets a poem the way he/she carries it in his/her own heart. Every time I miss my love, I reach out for this last part; e.e.cummings' wording is so delicate that you could almost feel him carrying a small heart in his hands; and then you can't help but fall in love with his finale.
Simply the most beautiful expressive metaphor of love in the world …
Marsha's stories Tuesday, 19 January 2010
Posted by carryapoem in Stories.
Tags: e e cummings, Elizabeth Bishop, William Shakespeare
I used to carry E.E. Cummings' poem "somewhere i have never travelled, gladly beyond any experience, your eyes have their silence…" in its entirety, in my head. Alas, I've lost bits of it. That brings to mind the fact that I also carried Elizabeth Bishop's 'One Art' in its entirety. Bits are gone but since "The art of losing isn't hard to master; so many things seem filled with the intent to be lost that their loss is no disaster…" I don't feel so badly about the loss of some of Cummings. After all, I am comforted by what I do recall and can always look them up. Similarly I have lost a few bits of Shakespeare's Sonnet 73, "That time of year thou mayst in me behold/When yellow leaves, or none, or few, do hang/Upon those boughs which shake against the cold,/Bare ruined choirs, where late the sweet birds sang." I think that last may explain something about my problem. Still, as I said, better to have those pieces than no poetry at all!
Marsha is the Poetry in The Branches Coordinator for Poets House in New York and retired Coordinator of Adult Services for The New York Public Library.
BIOGRAPHY – E. E. CUMMINGS Wednesday, 6 January 2010
Posted by edincityoflit in Poets.
E. E. Cummings was born in Cambridge, Massachusetts in 1894. He attended Harvard University and served as an ambulance driver in World War I. His first collection of poetry, Tulips and Chimneys, came out in 1923, displaying the inventive use of typography and grammar which would mark him throughout his career.
While E. E. Cummings won numerous awards throughout his life, critical opinion was generally divided on his output. Despite this, Cummings was, and still is, one of the most popular American poets and an influential figure of 20th century poetry. Cummings died in 1962.
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A E Housman Alan Spence Alastair Reid Alfred Lord Tennyson andrew fusek peters Angela Blacklock Brown anon Carol Ann Duffy Christopher Logue Denise Levertov Diana Hendry Dinah Hawken Donald MacAulay Don Paterson Douglas Dunn Dylan Thomas Edwin Morgan e e cummings Elizabeth Lincoln Otis Emily Dickinson Fleur Adcock Found poetry George Mackay Brown Gerald Manley Hopkins Gerard Manley Hopkins Hans Magnus Enzensberger Henry Vaughan Herta Müller Hilarie Belloc Hugh MacDiarmid issac Ewan Jackie Kay Jack Pretsky James Copeland John Betjeman John Donne John Hegley John M Caie Kathleen Jamie Lewis Carroll Mary Oliver Michael Longley Mòr Bean Nill Norman MacCaig Philip Larkin Rainer Maria Rilke Raymond Carver Robert Browning Robert Burns Robert Frost Robert Louis Stevenson Roger McGough R S Thomas Rudyard Kipling Sean O'Brien Sheenagh Pugh Simon Armitage Sophie Hannah Sorley MacLean Susie Maguire Ted Hughes Tom Leonard Tony Harrison T S Eliot Vachel Lindsay Walt Whitman W B Yeats Wendy Cope W H Auden Wilfred Owen William Blake William Carlos Williams William Shakespeare William Wordsworth Yehuda Amichai
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@chrisdonia Do you, now. 7 years ago
We're celebrating all that's great in songwriting and lyrics for @LetsGetLyrical. Which lyric do you love? http://letsgetlyrical.com 8 years ago
RT @LetsGetLyrical: Our event with spectacular poet Robin Robertson & brilliant musician Alasdair Roberts is next Friday 25th. Book earl ... 8 years ago
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Subscribe now. "Risk factors for the development of Barrett's esophagus include being a white male over 50 years of age, GERD symptoms at least once a week for five or more years, presence of a hiatal upper stomach hernia and obesity,".
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Henry is survived by his loving wife Miriam Kessler Warshow, as well as his 5 children, Michal Warshow (Joel Bluestein), Douglas Warshow, Becki Warshow, Margaret Hayward, and Elaine Kates, as well as his 7 grandchildren, Sarah and.
Gerd Kessler has 74 books on Goodreads. Sign in to Goodreads to learn more about Gerd Kessler.
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Feb 5, 2016. Gastroesophageal reflux disease (GERD), also known as reflux, is a common digestive disorder that occurs when a muscle at the end of your esophagus does not close properly. This allows the contents of the stomach to leak back, or reflux, into the esophagus and irritate it. Characterized by a burning in.
Explore historical records and family tree profiles about Gerd Kessler on MyHeritage, the world's family history network.
Gerd A Kessler age 78 Also known as: Gerda Kessler From: Santa Fe, NM 4 Spur Cross Pl,Santa Fe, NM 87508 (505) 471-4226 Previous Addresses: 2491 Sawmill Rd #1508.
Directed by Walter Boos, Ernst Hofbauer. With Puppa Armbruster, Ekkehardt Belle, Erika Blumberger, Marina Blümel. Six more first-hand accounts of sexual awakening.
Discover the little-known cause of heartburn and GERD (it's not what your doctor is telling you. Experience Chris Kresser's unique evidence-based approach as a.
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Nov 7, 2017. And did you know treating acid reflux can help with asthma, too? What is acid reflux? CEENTA Otolaryngologist Chad Kessler, MD. Acid reflux is when stomach acid reverses direction out of the stomach and into the esophagus and possibly the throat and upper airway. GERD – or gastroesophageal reflux.
View the profiles of people named Gerd Keßler. Join Facebook to connect with Gerd Keßler and others you may know. Facebook gives people the power to.
Ask any mom about her baby's birth stats and chances are, she remembers the date, time and day of the week she gave birth on. I have six kids and can name all of these details off, including what the weather was like that day, as well as.
Wolfsburg's Germany midfielder Nadine Kessler was voted female player of the year. "I am a bit disappointed for Manuel," Loew told reporters. "Because at the World Cup Manuel showed a completely different goalkeeping game and that is.
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Acid reflux from our stomach can cause esophagitis, even ulceration. The cause is much more complicated than just excessive acid.
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Dr. h.c. Gerd Gudehus. Dipl.-Geophys. Dr.-Ing. habil. Jürgen Keßler ([email protected] Der Begriff Setzungsfließen bezeichnet eine Rutschung von.
Wir beginnen diese Reihe mit mehreren Beiträgen von Gerd Kessler zur Geschichte des Rheinischen Steinzeugs. Kenntnisstand im 19. Jahrhundert. Die Forscher und Sammler Dombusch, Schmitz und Zais. Als zu Beginn des 19. Jahrhunderts kunstsinnige Kreise in den. Niederlanden und England anfingen Keramiken.
22. Febr. 2017. WESTERWÄLDER STEINZEUG – ein Material macht Karriere ( Gerd Kessler) Das Töpferhandwerk im Mittelalter war im Wesentlichen ein ländliches Gewerbe. Naturgemäß haben sich Töpfer in der Nähe von Tonvorkommen niedergelassen. Ebenfalls musste ausreichend Wald vorhanden sein, um den.
Deposit (11-1, 5-0): Alea Tiffany 2-1, MaKayla Smith 1-0, Emily Raymond 1-0, Kyra Martin 1-0, Kate Tiffany 0-1, Meranda Vandermark 0-1. Walton (2-9, 1-4): Kiley Lamoreaux 1-0, Kylie Coviello 0-1. Shots-corner kicks: D 19-7; W 4-5. Goalies:.
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13. Okt. 2015. Lachen im Theater – gut und schön, findet Gerd Kessler. Doch gegen Klamauk hat er was. Ihm ist Qualität wichtiger. Auch wenn das auf Kosten der Zu.
Heartburn & GERD. If you ask the average Joe on the street what causes heartburn, he'll tell you "too much stomach acid." So, when I explain to patients that.
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Visit Healthgrades for information on Dr. Victor Kessler, MD Find Phone & Address information, medical practice history, affiliated hospitals and more.
Caspar Berens (* 24. April 1836 in Kruberg; † 16. Mai 1912 in Rumbeck) war ein katholischer Geistlicher Rat, Schriftsteller, Dichter des Kolpingliedes und Präses des Kolpingvereines. Er war maßgeblich an der Ansiedlung des Klosters Oventrop in seinem Sprengel beteiligt.
Small clusters have a range of unique physical and chemical phenomena that are strongly size dependent. However, analysis of these phenomena often assumes that thermodynamic equilibrium conditions prevail. We compare.
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Stadtarchiv Wiesbaden, Dr. Udo Zais: "Zais, Beiträge zur Familiengeschichte, Historisches, Familiäres, Persönliches"; Brigitte Klesse: "Ernst Ludwig Ferdinand Daniel Friedrich Zais" in "Die großen Stifter des Kunstgewerbemuseums Köln", 1981, S.28-29:5 III; Gerd Kessler: "Ernst Zais: Hochverdient und doch fast vergessen".
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Just south of California, there is a beautiful Mexican state called Baja California. In that place there is an area called the San Quintin Valley, and in that valley, many of us in Live Different have made a whole lot of memories and have been transformed by our experiences. San Quintin is an irrigated agricultural area surrounded by beautiful desert only four hours south of San Diego.
The Live Different base is located on the west side of the peninsula, just a couple of miles from the Pacific Ocean. The cool breeze coming off the ocean moderates the temperature, but in our part of Mexico, the days are warm, the nights are cool, the food is amazing, and the people will capture your heart!
While Mexico has experienced some gains in the past decades and is no longer considered a developing country by the international community, once you arrive, you will see that there are still many people who are living and working in incredibly difficult conditions. Many of the people living in the San Quintin Valley have moved to the peninsula from mainland Mexico, most commonly from the southern state of Oaxaca, in search of work in the fields of vegetables and fruit. Many of them arrive with no savings, sometimes only speaking their indigenous languages, unable to read or write Spanish, and without birth certificates, which in turn limits access to health care and education. Despite all this, we have come to realize that our friends here are resilient, creative, and generous with the little resources they have.
As a result of the need we saw in the town of Vicente Guerrero and the surrounding San Quintin Valley communities, Live Different started working in Mexico in 2005. Many of the migrant families living here are forced to construct their small homes out of whatever they can find: scraps of wood, cardboard, and plastic. Thanks to the help of Live Different volunteers such as yourself, we have been able to build many homes, schools, and clinics in various communities in the area – and we have each been changed in the process.
The structures that we build are simple by our standards, but each home, school, and clinic is so much more – it is a beacon of hope for a better future, a reminder of the solidarity of friends from different cultures, a place of security and refuge after a long day of work, shelter from the dust and rain, and a place for celebrating the big and small joys in life.
Follow J.R. Alli's life changing experience in Mexico.
This is a sample itinerary for Mexico, your trip itinerary may be slightly different than this.
Time to purchase gifts for the families' home.
House Dedication. Have you ever wondered what it would be like to hand over the keys to a brand new home and give the hope of warmth, security, and a brighter future to a family? This gift and moment will be etched in your memory for many years to come.
Preparation for what is next – Your Live Different Build is going to be one of the most intense and life-changing experiences you will ever have. Because we believe that this is just the beginning of something for you, we want to help prepare you to return home and integrate this experience and the lessons learned. On the final day of our trip we will have a final debriefing that will help you to take this experience and help others understand how we can make a difference in our global community.
Today is an opportunity to explore some of the beauty the Baja has to offer.
Drive up to San Diego, California.
Dorm style accommodations will be provided, location depends on the size of the group.
While in Mexico you will experience a wide variety of food. We serve a balance of familiar North American food along with a cultural experience of some special Mexican meals and treats! All meals are carefully prepared and are full of nutrition. We do our best to cater to specific dietary restrictions, so please inform us of any restrictions you have at your time of registration.
This Live Different Build has benefited me in ways that I never thought possible. It truly was a cleanse for the soul and I can honestly say that it will always be one of the most important things I have ever done in my life. The impact it had on me as a person is incredible and I would not trade this feeling of fulfillment for anything. It opened my eyes to what truly is important in this world and for that I am thankful. I promise that if you do decide to go on this trip, you will not regret it. I went on this trip on my own and came out with a close family. Live Different Builds are definitely what this world needs more of. Also, always remember that change starts with you.
Questions about our work in Mexico?


text:
TAPOL Coordinator vacancy
Based: London
Status: 28 Hours a week (4 days) with potential to build to full-time as a result of successful fundraising.
Remuneration package: £ 30,000 - -34,056 pro rata (depending on skills and experience)
Closing Date: 5.00pm, 28th March 2014
Interviews: Week of 4th / 11th April
Applications: By CV and covering letter explaining how your skills and experience fit the role/person specification. Send an email to barbara.patilla@tapol.org for the job description and further information.
We are looking for a highly motivated and resourceful individual with a genuine commitment to human rights and democracy in Indonesia, seeking to lead this well known and respected human rights campaign. The post-holder will be responsible for the management and strategic development of Tapol's human rights work, ensuring timely delivery of its programmes, exploring new opportunities and taking the organisation on to the next level as Indonesia changes government and continues to develop politically and economically. S/he will have a pivotal role in defining priority areas for Tapol's work, collaborating closely with partners in Indonesia, as well as with UK and European activist networks, and other stakeholders. This crucial role calls for experience of working in international advocacy, good knowledge of human rights in Indonesia, a track record of influencing policy, and first rate project design and fund-raising skills. In addition to international advocacy expertise s/he will be a proven project manager, used to managing budgets, presenting to key stakeholders and building relationships with a wide range of stakeholders. We also require a willingness to travel internationally.
Coordinator Job Ad.pdf
Tagged: TAPOL


text:
Ecins History, Family Crest & Coats of Arms
An ancient Strathclyde-Briton family from the Scottish/English Borderlands were the first to use the name Ecins. They lived in Lanarkshire.
Early Origins of the Ecins family
The surname Ecins was first found in Lanarkshire (Gaelic: Siorrachd Lannraig) a former county in the central Strathclyde region of Scotland, now divided into the Council Areas of North Lanarkshire, South Lanarkshire, and the City of Glasgow, where they originated in the old barony of Akyne. Some of the first records of the name were Atkyn de Barr in 1340 [1] and later in 1405, "John of Akyne, a Scottish merchant petitioned for the return of his ship and goods illegally seized in England." [2] The name and all it's variants are double diminutives of Adam, formed from 'Ad,' the diminutive of Adam + 'kin' [2]
Early History of the Ecins family
This web page shows only a small excerpt of our Ecins research. Another 183 words (13 lines of text) covering the years 1405, 1482, 1497, 1520, 1744, 1773, 1613, 1687, 1676, 1680, 1687, 1613, 1654, 1613, 1642 and 1676 are included under the topic Early Ecins History in all our PDF Extended History products and printed products wherever possible.
Ecins Spelling Variations
Before the printing press standardized spelling in the last few hundred years, no general rules existed in the English language. Spelling variations in Scottish names from the Middle Ages are common even within a single document. Ecins has been spelled Aitken, Aiken, Atkin, Atkins and others.
Early Notables of the Ecins family (pre 1700)
Another 40 words (3 lines of text) are included under the topic Early Ecins Notables in all our PDF Extended History products and printed products wherever possible.
Migration of the Ecins family to Ireland
Some of the Ecins family moved to Ireland, but this topic is not covered in this excerpt.
Another 173 words (12 lines of text) about their life in Ireland is included in all our PDF Extended History products and printed products wherever possible.
Migration of the Ecins family
For Scottish immigrants, the great expense of travel to North America did not seem such a problem in those unstable times. Acres of land awaited them and many got the chance to fight for their freedom in the American War of Independence. These Scots and their ancestors went on to play important roles in the forging of the great nations of the United States and Canada. Among them: Ann and Daniel Aiken who settled in New York State in 1811; David, Henry and Hugh Aiken settled in Philadelphia, Pennsylvania between 1868 and 1880; John Aikens settled in New Orleans La. in 1821.
The Ecins Motto +
Motto: Robore et vigilantia
Motto Translation: Strength and vigilance.
^ Reaney, P.H and R.M. Wilson, A Dictionary of English Surnames. London: Routledge, 1991. Print. (ISBN 0-415-05737-X)
Ecins (Scottish)


text:
\section{Introduction}
In this paper, we consider the self-avoiding walk on fractal graphs called the $(u,v)$-flower.
The self-avoiding walk is important both in graph theory and statistical mechanics.
In graph theory, a self-avoiding walk is usually called a path.
Enumeration of paths is a classical problem in computer science~\cite{knuth11} and enumeration algorithms of all paths connecting two nodes ($s$-$t$ paths) have been actively studied~\cite{Bousquet05}.
Furthermore, paths appear in many graph algorithms such as the depth-first search~\cite{cormen09}.
On the other hand, the self-avoiding walk in the Euclidian spaces is one of the simplest models of a polymer and its scaling properties have been of statistical physicists' interest~\cite{deGennes79}.
This model of a polymer can be mapped to the $N\to 0$ limit of the $N$-vector model as de Gennes pointed out~\cite{deGennes72,deGennes79};
the connection enabled us to understand the model from the viewpoint of critical phenomena of usual spin systems.

The properties of the self-avoiding walk is poorly understood in the Euclidian dimensions, in particular in two, three, and four dimensions.
For the problems of the self-avoiding walk on fractals embedded in the Euclidian space,
analysis becomes easier and we can obtain  exact solutions on some fractals, $e.g.$, the Sierpinski gasket~\cite{rammal84, dhar78}.
Such exact solutions have helped us deepen our understanding of the self-avoiding walk.
However, fractals on which the model is exactly solvable in arbitrary fractal dimensions have not been obtained to the author's knowledge.
In the present paper, generalizing the problem to the self-avoiding walk on fractals $graphs$,
we obtain exact results in arbitrary fractal dimensions.
We thereby verify that critical exponents in fractal graphs are not solely determined by  the fractal dimension.
This fact was conjectured in the 1980s~\cite{rammal84, havlin87,aharony89}, but has never been proved because of the
lack of  exactly solvable models in arbitrary fractal dimensions.

Song \textit{et al.} found that a few graphs in real networks are indeed fractal~\cite{song05, gallos07a}.
They noticed that complex networks thad had been studied many times were fractal, \textit{e.g.}, the WWW network, actors' collaboration network, and biological networks of protein-protein interactions.
After the discovery in the real networks, several artificial fractal complex networks have been devised~\cite{song06}.
One of such networks is the $(u,v)$-flower~\cite{rozenfeld07_1}.
As deterministic fractals such as the Sierpinski gasket and the Cantor set helped us understand real fractals in the Euclidian spaces,
deterministic fractal complex networks can deepen our understanding of dynamics on fractal complex networks in the real world.

Is it possible to understand the scaling properties of paths on graphs in terms of critical phenomena?
In this paper, through the mapping to the $N$-vector model,
we extend the theory of the self-avoiding walk on regular lattices to that on graphs
by using the shortest distance as a  distance rather than the Euclidian distance.
We perform an exact renormalization-group analysis on the self-avoiding walk on the $(u,v)$-flower in order to obtain the effective coordination number of a walker (namely, the connective constant) and a critical exponent of the mapped $N$-vector model in the limit $N\to 0$, namely the zero-component ferromagnet.
We thereby answer the questions as to (i) how the number of paths with a fixed length and a fixed starting point increases
and (ii) how the mean shortest distance between the two end points grows as the path length increases.

This paper is organized as follows.
In Sec.~\ref{sec:ensemble}, we define an ensemble of fixed length paths, the connective constant and the displacement exponent of the self-avoiding walk on a graph.
In Sec.~\ref{sec:model}, we review the $(u,v)$-flower.
We see that the $(u,v)$-flower has several properties which many real networks possess, \textit{i.e.,} a fat-tailed degree distribution~\cite{barabasi99}, hubs, and fractality~\cite{albert02}.

In Sec.~\ref{sec:RG}, we extend the theory of the self-avoiding walk in the Euclidian spaces~\cite{ shapiro78, dhar78,rammal84} to the graphs of the $(u,v)$-flower, on which the shortest distance is used as a distance instead of the Euclidian distance.
By conducting a renormalization-group analysis,
we calculate the connective constant $\mu$ and the critical exponent $\nu$, which is associated with the correlation length of the zero-component ferromagnet on the $(u,v)$-flowers with $\forall u,v\ge 2$.
We thereby  write down the critical exponent $\nu$  in \textit{arbitrary} fractal dimensions greater than unity.
We also compare the results with a tree approximation, which is usually referred to as a mean-field approximation in the context of the study of complex networks.

In Sec.~\ref{sec:exactSol}, we exactly obtain the two-point function for the $(u,u)$-flower and
prove that $\nu=1$ regardless of the fractal dimension  between one and two.

In Sec.~\ref{sec:simulation}, we conduct numerical simulations of the self-avoiding walk
and observe that the number of paths starting from a hub $s$ behaves as in $C_{k}^{(s)} \propto \mu^k k^{\gamma-1}$ and that the mean shortest distance between the starting point and the end point increases as $\overline{d_{k}^{(s)}} \approx k^{\nu}$, where $k$ is the length of a path and  $\gamma$ is the critical exponent associated with the susceptibility of the mapped zero-component ferromagnet.

\section{Ensemble of fixed length paths \label{sec:ensemble}}
In the model of the self-avoiding walk, all the paths of the same length starting from a fixed node  without self-intersection  appear with the same probability.
In order to describe this accurately,
let us define an ensemble.
Let $G=(V,E)$ be a connected finite graph.
A path of length $k$ is defined as
\begin{align}
&\omega = (\omega_0, \omega_1,\cdots, \omega_k),~~~\omega_i \in V,\\
&\omega_i\neq\omega_j \text{~for~} i\neq j,\\
&(\omega_i,\omega_{i+1})\in E  .
\end{align}
Let us denote by $\Omega_{k}^{(s)} $ the set of the paths of length $k$ for a fixed starting node and a free end node.

In order to consider the typical end-to-end distance, we define a probability distribution.
Fixing a path length $k$ and a starting node $s$, we introduce a uniform measure such that
\begin{align}
P(\omega) = \frac{1}{\#\Omega_{k}^{(s)}},~~~~\forall \omega \in \Omega_{k}^{(s)}  . \label{eq:uniformMeasure}
\end{align}
Though this is not a serious problem, note that when the graph is too small, it may not contain a path of length $k$ and hence $\#\Omega_{k}^{(s)}=0$.

In order to discuss the speed of diffusion of a graph,  we next define a distance on a graph. For any nodes $v_1,v_2\in V$,
we let $d(v_1,v_2)$ denote the shortest distance (the length of the shortest path(s)) between the nodes $v_1$ and $v_2$.
The mean shortest distance between the ends of paths whose length is $k$ and which start from node $s$ is then given by
\begin{align}
\overline{d_{k}^{(s)}}:=\frac{ \sum_{(\omega_0,\omega_1,\cdots,\omega_k)\in\Omega_{k}^{(s)} }d(\omega_0,\omega_k) }{\#\Omega_{k}^{(s)}}   , \label{eq:MSD}
\end{align}
where we took the average over the uniform distribution \eqref{eq:uniformMeasure}.
We define the connective constant $\mu$ and the displacement exponent $\nu$ as
\begin{align}
\mu &:= \lim_{k\to\infty}\left( \#\Omega_{k}^{(s)} \right)^{1/k}, \label{eq:muDef} \\
\nu &:= \lim_{k\to\infty} \ln \overline{d_{k}^{(s)}} / \ln k   .  \label{eq:nuPrimeDef}
\end{align}
Here we assumed that $\#\Omega_{k}^{(s)}$ increases as the product of an exponential $\mu^{k}$ and a power function $k^{\nu}$ and that $\overline{d_{k}^{(s)}}$ increases as a power function $k^{\nu}$ in the same form as for  the self-avoiding walk in $\mathbb{R}^{n}$.
Thus, by obtaining $\mu$ and $\nu$, we can tell the number of paths on the graph and the typical distance from the starting point.
The goal of this paper is to calculate these two quantities on graphs in  arbitrary fractal dimensions.

\section{Model of fractal complex network: The $(u,v)$-flower\label{sec:model}}
The fractal graph that we consider here is the $(u,v)$-flower, which was devised by Dorogovtsev \textit{et al.} and Rozenfeld \textit{et al.}~\cite{dorogovtsev02_2, rozenfeld07_1}.
The $(u, v)$-flower is defined in the following way. First, we prepare a cycle of length $u+v$ as the first generation. Second, given a graph of generation $n$, we obtain the $(n+1)$th generation by replacing each link by two parallel paths of length $u$ and $v$ (Fig.~\ref{fig:uv_flower}). We can assume $1\le u\le v$ without losing generality.

\begin{figure}
\includegraphics[width=13cm,clip]{2_2_Flower_2_3_Flower}
\centering
\caption{The $(2,2)$-flower and the $(2,3)$-flower in the first, second and third generations. Each line is replaced by parallel lines of length $u$ and $v$ in construction of the next generation.
}
\label{fig:uv_flower}
\end{figure}

Let $M_{n}$ and $N_n$ be the number of edges and nodes, respectively. From the definition of the $(u,v)$-flower, it straightforwardly follows that
\begin{align}
M_{n} &= w^{n},\\
N_n &= w N_{n-1} - w = \cdots = \frac{w-2}{w-1}\times w^n + \frac{w}{w-1} ,
\end{align}
where
\begin{align}
w&=u+v .
\end{align}
The $(u,v)$-flowers  have only nodes of degree $k=2^{m}$, where $m=1,2,\cdots,n$. Let $N_{n}(m)$ be the number of nodes of degree $2^{m}$ in the $n$th generation.
We thereby have
\begin{align}
N_{n}(m) =
	\begin{cases}
	N_{n-1}(m-1) &\text{for~} m>1,\\
	(w-2)w^{n-1} &\text{for~} m=1.
	\end{cases}
\end{align}
Solving this recurrence relation under the initial condition $N_1(1)=w$, we have
\begin{equation}
N_n(m) =
\begin{cases}
	(w-2)w^{n-m} &\text{for~} m<n,\\
	w     &\text{for~}m=n ,
\end{cases}
\end{equation}
which is related to the degree distribution $P(k)$ in the form $|N_n(m)dm| = |P(k)dk|$.
We therefore have the degree distribution of the $(u,v)$-flower with $u,v\ge 1$ as
\begin{equation}
P(k)\propto k^{-\gamma}~~\text{with}~\gamma=1+\frac{\ln(u+v)}{\ln 2} .
\end{equation}
This means that the $(u,v)$-flower is scale-free as many real networks are~\cite{song05, gallos07a}.

The dimensionality of the $(u,v)$-flowers is totally different for $u=1$ and $u>1$. When $u=1$ the diameter $d_n$ of the $n$th generation is proportional to the generation $n$, while the diameter $d_n$ is a power of $u$ when $u>1$:
\begin{equation}
d_n \sim
\begin{cases}
	(v-1)n &\text{~for~} u=1 ,\\
	u^n    &\text{~for~} u>1 .
\end{cases} \label{eq:dnun}
\end{equation}
Since $N_n\sim w^n$, we can transform Eq.~\eqref{eq:dnun} to
\begin{equation}
d_n\sim
\begin{cases}
	\ln N_n &\text{~for~} u=1, \\
	N_n^{\ln u/\ln(u+v)} &\text{~for~}u>1 .
\end{cases}
\end{equation}
This means that the $(u,v)$-flowers have a small-world property~\cite{watts98} only when $u=1$, while the flowers have finite fractal dimensions for $u>1$.
When $u>1$, it is clear from the construction of flowers that the fractal dimension (the similarity dimension)~\cite{falconer07} of  the $(u,v)$-flower is
\begin{equation}
d_{f} = \frac{\ln(u+v)}{\ln u} \text{~for~} u>1   .
\end{equation}

\section{Exact Renormalization-Group Analysis of the general $(u,v)$-flowers\label{sec:RG}}
The $(u,v)$-flower is a fractal when $u,v\ge 2$ as we mentioned in the previous section.
We always assume that $v\ge u\ge 2$ from now on,
 because the target of this paper is the self-avoiding walk on fractals.
In this section, we define a two-point function and apply an exact renormalization to it.
We thus obtain the connective constant $\mu$ and the critical exponent $\nu$ of the zero-component ferromagnet.
Next we consider the mean-field theory of the self-avoiding walk and compare the result with the prediction from the exact renormalization.

 \subsection{Generating function}
Let $O$  and $R$ be nodes which are separated by a distance $u$ in the first generation and $r_{n}$ be the shortest distance between $O$ and $R$ in the $n$th generation.
The nodes $O$ and $R$ have the largest degree and hence are called hubs.
Because each edge is replaced by two parallel lines of length $u$ and $v$ in the construction,
the shortest distance $r_{n}$ increases as
\begin{align}
r_{n} = r_{n-1}\times u = \cdots = u^{n-1}r_{1} = u^{n} .
\end{align}

Defining $C_{k}^{(n)}(R)$ as the number of self-avoiding paths of length $k$ starting from the node $O$ and ending at the node $R$ in the $n$th generation,
we can construct the two-point function as
\begin{equation}
G_{n}(x) = \sum_{k=1} C_{k}^{(n)}(R) x^{k}   .\label{eq:genFunc}
\end{equation}
The correspondence between the self-avoiding walk and the $N$-vector model~\cite{madras96} tells us that $x$ corresponds to the inverse temperature $\beta$ of the ferromagnet and that the two-point function is the correlation function of the $N$-component spins placed at $O$ and $R$ in the limit of $N\to 0$:
\begin{align}
\lim_{N\to0}\langle S_{i}^{(O)} S_{j}^{(R)}\rangle = \delta_{ij} G_{n}( \beta),
\end{align}
where $S_{i}^{(v)}$ denotes the $i$th component of the spin at a node $v$.

This suggests that the two-point function becomes in the thermodynamic limit
\begin{align}
G_{n}(x) &\sim \exp(-r_{n}/ \xi(x)) \text{~~as~~}n\to\infty, \label{eq:Gassumption}
\intertext{where $\xi(x)$ is the correlation length, which should behave as}
\xi(x)&\sim (x_{c}-x)^{-\nu} \text{~~as~~} x \nearrow x_{c}  .  \label{eq:nuDef}
\end{align}
As we noted above, the  exponent $\nu$ defined here should be equal to  the one in Eq.~\eqref{eq:nuPrimeDef}.
We will see this in Sec.~\ref{subsec:simDisplExp}.

Let us assume that $C_{k}^{(n)}(R)$ in Eq.~\eqref{eq:genFunc} behaves asymptotically as
\begin{equation}
C_{k}^{(n)}(R)^{1/k}\sim \mu,  \label{eq:numOfPathExp}
\end{equation}
because at each step a walker has $\mu$ options to go next on average.
Then the convergence disk of (\ref{eq:genFunc}) is $|x|<1/\mu=:x_{c}$, where $x_{c}$ is a critical point.
The critical point $x_{c}$ is therefore equal to the ferromagnetic transition temperature $\beta_{c}$.
In the Euclidian spaces, it is believed that the critical temperature $\mu=1/\beta_{c}$ and the critical exponent $\nu$ associated with the correlation length of the zero-component ferromagnet are identical with the ones defined in Eqs.~\eqref{eq:muDef} and \eqref{eq:nuPrimeDef} when the shortest distance $d(\cdot, \cdot)$ is replaced by the Euclidian distance~\cite{madras96}.
We assume that $\mu$ and $\nu$ defined in the two different ways are equal on the $(u,v)$-flower too.
We will check the validity of this assumption in Sec.~\ref{sec:simulation}.

We can calculate the two-point function in the following way.
The two-point function of the first generation is
\begin{align}
G_{1}(x) = x^{u} + x^{v}
\end{align}
by definition.
Since the $(n+1)$th generation can be regarded as a cycle of $(u+v)$ pieces of the $n$th generation graphs,
\begin{align}
G_{n+1}( x)=G_{n}( x)^{u} + G_{n}( x)^{v}  .\label{eq:recursionG_n}
\end{align}
The diagrammatic representation of Eq.~\eqref{eq:recursionG_n} is shown in Fig.~\ref{fig:diagram}.
Therefore, we have
\begin{align}
G_{n+1}( x) = G_{1}( G_{n}( x)) .
\end{align}
Repeated use of this relation yields
\begin{align}
G_{n}(x) = \underbrace{G_{1}\circ G_{1}\circ\cdots \circ G_{1}}_{n} (x)  .\label{eq:G_1ntimes}
\end{align}

\begin{figure}
\includegraphics[width=13cm,clip]{diagram}
\centering
\caption{Diagrammatic representations of the two-point function $G_{n}(x)$.
The $(n+1)$th generation can be regarded as a cycle of $(u+v)$ pieces of graphs in the $n$th generation.
}
\label{fig:diagram}
\end{figure}

\subsection{Renormalization-group analysis}
We define a renormalization procedure for the $(u,v)$-flower as the inverse transformation of the constructing procedure of the flower (Fig.~$\ref{fig:RG_flow_2}$).
When the $(n+1)$th generation is given, we coarse-grain the minute structure and obtain the $n$th generation. Every cycle of length $(u+v)$ is therefore replaced by a single edge.
Renormalization of self-avoiding paths is also defined in a similar way.

\begin{figure}
\includegraphics[width=13cm,clip]{RG_flow_2}
\centering
\caption{An example of renormalization of a self-avoiding path on the $(2,2)$-flower. The decimation is carried out by erasing a smaller structure. }
\label{fig:RG_flow_2}
\end{figure}

\begin{figure}
\includegraphics[width=10cm,clip]{RG_flow_1}
\centering
\caption{The renormalization-group flow. The top figure illustrates how $G_{n}(x)$ changes as the generation $n$ gets larger with $x$ fixed. The bottom figure shows the flow of the scaling variable $x$. Here, $x_{n+1}$ is the scaling variable in the $(n+1)$th flower and $x_{n}$ is the one in a coarse-grained flower.
 }
 \label{fig:RG_flow_1}
\end{figure}

Let $\epsilon$ be a sufficiently small positive number. We define the variable $x_{n}$ such that
\begin{equation}
G_{n}(x_{n}) := \epsilon  ~~\text{for all~}n.  \label{eq:defOfx_n}
\end{equation}
The variable $x_{n}$ is the scaling variable of our theory; we observe how it transforms under
the renormalization transformation (Fig.~\ref{fig:RG_flow_1}).
We will prove in Sec.~\ref{subsec:existenceAndUniqueness} the unique existence of $x_{n}$ which satisfies Eq.~\eqref{eq:defOfx_n}.

The two-point function of the $(n+1)$th generation and that of the $n$th generation are related as
\begin{equation}
G_{n+1}(x_{n+1}) = \epsilon = G_{n}(x_{n})   .\label{eq:G_np1G_n}
\end{equation}
This specifies how the scaling variable $x$ is renormalized.
From Eqs.~(\ref{eq:G_1ntimes}) and (\ref{eq:G_np1G_n}), we obtain
\begin{align}
G_{n}(x_{n}) = G_{n+1}(x_{n+1}) = G_{n}( G_{1}( x_{n+1}) ) = G_{n}( x_{n+1}^{u} + x_{n+1}^{v})  . \label{eq:GnAndGnp1}
\end{align}
The scaling variable therefore changes under the renormalization transformation as
\begin{align}
x_{n} = x_{n+1}^{u} + x_{n+1}^{v}   .\label{eq:RG_flow}
\end{align}
We will  show in Sec.~\ref{subsec:existenceAndUniqueness} that the scaling variable $x_{n}$ changes as shown in Fig.~\ref{fig:RG_flow_1}.

Next, we obtain the critical exponent $\nu$ by studying $\xi(x)$
near the fixed point $x_{c}$.
From Eqs.~\eqref{eq:Gassumption} and \eqref{eq:GnAndGnp1} we should have
\begin{align}
 \frac{r_{n+1}}{\xi(x_{n+1})} &= \frac{r_{n}}{\xi(x_{n})} ,
\end{align}
and hence
\begin{align}
(x_{c} -x_{n+1} )^{-\nu}& \sim \frac{r_{n+1}}{r_{n}} (x_{c} -x_{n} )^{-\nu} = u (x_{c} -x_{n} )^{-\nu}
\end{align}
in the limit $n\to\infty$.
The critical exponent $\nu$ is therefore expressed as
\begin{align}
\nu = \frac{\ln(u)}{\ln\left( \frac{x_{c} - x_{n}}{x_{c}-x_{n+1}}\right)} = \frac{\ln(u)}{\ln\left( \frac{x_{n} - x_{c}}{x_{n+1}-x_{c}}\right)}   . \label{eq:nuTwoGen}
\end{align}
The Taylor expansion around the nontrivial fixed point enables us to express $\nu$ in terms of $x_{c}$:
\begin{align}
x_{n} - x_{c} &= x_{n+1}^{u} + x_{n+1}^{v} - x_{c} \notag\\
&\approx x_{c}^{u} + u x_{c}^{u-1}(x_{n+1}-x_{c}) + x_{c}^{v} + v x_{c}^{v-1} (x_{n+1}-x_{c}) - x_{c} \notag \\
&= ( ux_{c}^{u-1} + v x_{c}^{v-1} )(x_{n+1}-x_{c})
\intertext{with}
x_{c}&=x_{c}^{u} + x_{c}^{v}   .\label{eq:fixedPointEq}
\intertext{Feeding this equation into Eq.~\eqref{eq:nuTwoGen}, we obtain the final expression as}
\nu &= \frac{\ln(u)}{\ln\left( u x_{c}^{u-1} + v x_{c}^{v-1}\right)}. \label{eq:nuRG_prediction}
\end{align}
Equation (\ref{eq:fixedPointEq}) cannot be solved by hand in general, and hence we will rely on a numerical solver
when we compare this result with the value of numerical simulation in Sec.~\ref{sec:simulation}.

\subsection{Existence and uniqueness of a nontrivial fixed point \label{subsec:existenceAndUniqueness}}
In the above argument, we assumed the existence of a positive fixed point $x_{c}$ satisfying Eq.~\eqref{eq:fixedPointEq} and the solution $x_{n}$ which meets Eq.~(\ref{eq:defOfx_n}).
We prove the existence and the uniqueness of $x_{c}>0$ and that of $x_{n}$ as follows.

Let us study how the scaling variable $x$ changes under the renormalization-group equation~\eqref{eq:RG_flow}. We define the difference of a scaling variable in the original system and a coarse-grained system as
\begin{align}
f(x):=x^u + x^v -x   .
\end{align}
Because $2\le u \le v$,
\begin{align}
f(0) &= 0,~~~f(1)=1,~~~f'(0)<0,\\
f''(x) &= u(u-1)x^{u-2} + v(v-1)x^{v-2} > 0 \text{~~~for~~~}x>0   .
\end{align}
\begin{figure}
\includegraphics[width=5cm,clip]{fx}
\centering
\caption{The function $f(x)=x^u+x^v-x$, which has a zero point between $0$ and $1$.}
\label{fig:fx}
\end{figure}
Therefore, there exists exactly one positive number $x_{c}$ which satisfies $0<x_c<1$ and $f(x_c)=0$ (Fig.~$\ref{fig:fx}$). In other words, the renormalization-group equation of the self-avoiding walk on the $(u,v)$-flower has exactly one nontrivial fixed point for $2\le u,v$.
It straightforwardly follows that
\begin{align}
\mu = \frac{1}{x_c} > 1  .
\end{align}
This result is natural because $\mu$ means the effective coordination number. If $\mu$ were smaller than unity, a walker would quickly come to a dead end and a path could not spread out.\\

Next, we show  using mathematical induction that $G_{n}(x)$ is a monotonically increasing function of x in $x>0$ for $\forall n\in \mathbb{N}$ and that $G_{n}(x)$ satisfies $G_{n}(0)=0$ and $G_{n}(x_{c})=x_{c}$.
\begin{enumerate}[(i)]
\item For $n=1$,\\
We have
\begin{align}
\frac{dG_{1}}{dx}(x) &= ux^{u-1} + vx^{v-1} > 0 \text{~for~} x>0,\\
G_{1}(x_{c}) &= x_{c}^{u} + x_{c}^{v} = x_{c} ,\\
G_{1}(0 ) &= 0  .
\end{align}
Therefore, the statement is true for $n=1$.

\item Suppose that the statement is true for $G_{n}(x)$. We first prove the monotonicity of $G_{n+1}(x)$, which is given by
\begin{align}
G_{n+1}(x) = G_{n}(G_{1}(x))  .
\end{align}
Since both $G_{1}$ and $G_{n}$ are monotonically increasing functions,
the composition of $G_{n}$ and $G_{1}$ is also a monotonically increasing function. Furthermore, we have
\begin{align}
G_{n+1}(x_{c}) &= G_{n}( G_{1}(x_{c})) = G_{n}(x_{c}) = x_{c},\\
G_{n+1}(0)     &= G_{n}( G_{1}(0    )) = G_{n}(0) = 0.
\end{align}
Therefore, the statement is also satisfied for $G_{n+1}$.
\end{enumerate}

Together with the continuity of $G_{n}(x)$, we have now proved the unique existence of $x_{n}\in (0,x_{c})$ which satisfies Eq.~(\ref{eq:defOfx_n}) for an arbitrary constant $\epsilon \in (0,x_{c})$.

\subsection{\texorpdfstring{Range of $\nu$}{Range of nu}}
We can study the range of the critical exponent $\nu$ in  Eq.~\eqref{eq:nuRG_prediction} by using inequalities.
We define $x_c$ as the unique positive solution of Eq.~(\ref{eq:fixedPointEq}) from now on:
\begin{align}
x_c^{u-1} + x_c^{v-1}=1,~~~2\le u \le v .
\end{align}
First, we can obtain the upper bound of $\nu$ as
\begin{align}
\nu = \frac{\ln(u)}{\ln(ux_{c}^{u-1} + vx_{c}^{v-1}) }
\le \frac{\ln(u)}{\ln(ux_{c}^{u-1} + ux_{c}^{v-1}) }
= \frac{\ln(u)}{\ln \left(u \left(x_{c}^{u-1} + x_{c}^{v-1}\right) \right)}=1.
\end{align}
The equality holds iif $u=v$.

We next bound $\nu$ from below. Since $0<x_c<1$ and $u\le v$, we have
\begin{align}
\nu\ge \frac{\ln(u)}{\ln(ux_{c}^{u-1} + vx_{c}^{u-1}) }
= \frac{\ln(u)} {\ln(u+v) + (u-1)\ln(x_c)} > \frac{\ln(u)}{\ln(u+v)} > 0 .
\end{align}
Furthermore, by setting $x_c = y_{c}^{1/(v-1)}$, we have
\begin{align}
& y_c < 1,\\
& y_{c}^{\frac{u-1}{v-1}} + y_c = 1,\\
& \lim_{\substack{v\to\infty \\ u:\text{~fixed}}  } y_c = 1,\\
& \lim_{\substack{v\to\infty \\ u:\text{~fixed}}  } y_{c}^{\frac{1}{v-1}} = 1^0 = 1,\\
\intertext{and therefore}
\lim_{\substack{v\to\infty \\ u:\text{~fixed}}  }x_c &= 1.
\end{align}
\begin{equation}
\lim_{\substack{v\to\infty \\ u:\text{~fixed}} } \nu =
\lim_{\substack{v\to\infty \\ u:\text{~fixed}}  } \frac{\ln(u)}{\ln(ux_{c}^{u-1} + vx_{c}^{v-1}) } = 0   .
\end{equation}
According to its definition, the exponent $\nu$ should satisfy $0\le \nu\le 1$,
which is consistent with the prediction of the renormalization-group analysis above.
We can interpret the limit $v\to \infty$ with $u$ being fixed as follows.
When $v\gg u$, the distance between the starting point and the end point increases slowly, because the lines of length $u$ serve as shortcuts.
Therefore, $\nu$ takes a small value.

In conclusion, the range of $\nu$ is $0 < \nu \le 1$. The equality $\nu=1$ holds true iif $u=v$, while $\nu$ can become arbitrarily close to $0$ for $u\neq v$.

\subsection{Exact results \label{subsec:exactResult}}
As we noted previously, the solution of Eq.~(\ref{eq:fixedPointEq}) cannot be written down explicitly in general.
There are, however, exceptional cases where we can obtain $x_c$, $\mu$, and $\nu$ explicitly.

First for the $(u,u)$-flower,
Eq.~(\ref{eq:fixedPointEq}) reduces to
\begin{align}
x_c = 2 x_{c}^u \iff x_c = 2^{-\frac{1}{u-1} },
\end{align}
from which we obtain
\begin{align}
\mu &= 2^{\frac{1}{u-1} } ,\label{eq:mu_RG_u_u} \\
\nu &= \frac{\ln(u)}{\ln(u)} = 1 \label{eq:nu_RG_u_u}  .
\end{align}
We will see in Sec.\ref{sec:exactSol} that this result coincides with the exact solution which we will derive without using the renormalization-group analysis.

Next for the $(u,2u-1)$-flower,
by setting $y = x_{c}^{u-1}$, we can reduce Eq.~(\ref{eq:fixedPointEq}) to the quadratic equation
\begin{align}
& y^2 + y - 1 = 0, \\
\intertext{which yields}
& y = \frac{-1 + \sqrt{5}}{2} \\
\intertext{because $y>0$, and then}
& x_c = \left( \frac{-1 + \sqrt{5}}{2}  \right)^{\frac{1}{u-1}}  .
\end{align}
We thereby obtain
\begin{align}
& \mu = \frac{1}{x_c} = \left( \frac{-1 + \sqrt{5}}{2}  \right)^{\frac{-1}{u-1}} ,\label{eq:mu_RG_u_2um1} \\
& \nu = \frac{\ln(u)}{ \ln\left( \frac{5-\sqrt{5}}{2}u + \frac{-3 + \sqrt{5}}{2} \right)}  .
\end{align}
In this case, $\nu$ is a monotonically increasing function of $u$ and converges to unity in the limit of $u\to\infty$.

\subsection{Comparison to the mean-field theory}
Let us compare our analytic expressions with  mean-field theory.
A tree approximation is usually referred to as a mean-field theory when we discuss stochastic processes on complex networks.
Under the mean-field approximation, the $(u,v)$-flower is approximated to a tree whose nodes have the same degree as the mean degree of the original flower.

The self-avoiding walk on this tree is identical with the random walk with an immediate return being forbidden (namely, the non-reversal random walk)~\cite{herrero03,herrero05}. Since the connective constant $\mu$ is the effective coordination number,
the tree approximation gives
\begin{align}
\mu_{\mathrm{MF}} = \langle k\rangle - 1 = \frac{2M_n}{N_n} - 1 \xrightarrow{n\to\infty}  \frac{u+v}{u+v-2}  .\label{eq:mu_tree}
\end{align}
Since we have neglected loops, the expression in Eq.~\eqref{eq:mu_tree} is expected to overestimate the value of $\mu$; a walker may encounter a visited site on a graph with loops, and hence the effective coordination number $\mu$ should be  smaller compared to a tree with the same average degree.  We confirm that our expectation is correct both analytically and numerically. In this section, we first show analytic results (Fig.~$\ref{fig:compareRGMF_2figs}$).
We will explain our numerical simulation in Sec.~\ref{sec:simulation}.

First for the $(u,u)$-flower,
we obtain from Eqs.~(\ref{eq:mu_RG_u_u}) and (\ref{eq:mu_tree})
\begin{align}
\mu &= 2^{\frac{1}{u-1}},\\
\mu_{\mathrm{MF}} &= \lim_{n\to\infty} \langle k \rangle - 1=\lim_{n\to\infty} \frac{2M_n}{N_n} - 1 = 1 + \frac{1}{u-1},
\intertext{which means}
\mu_{\mathrm{MF}}& \ge \mu .
\end{align}
Second for the $(u,2u-1)$-flower,
we obtain from Eqs.~(\ref{eq:mu_RG_u_2um1}) and (\ref{eq:mu_tree}) the following:
\begin{align}
\mu &= \left( \frac{\sqrt{5}+1}{2} \right) ^{\frac{1}{u-1}},\\
\mu_{\mathrm{MF}} &= 1 + \frac{2}{3u-3}  .
\end{align}
We can show $\mu_{\mathrm{MF}} > \mu$ by setting $z = 1/(u-1)$ with $0<z\le 1$.

\begin{figure}
\includegraphics[width=15cm,clip]{compareRGMF_2figs}
\centering
\caption{Comparison of the connective constants in the mean-field theory and the renormalization-group. The mean-field estimate $\mu_{\mathrm{MF}}$ always overestimates the true connective constant $\mu$.}
\label{fig:compareRGMF_2figs}
\end{figure}

\section{Exact solution of the $(u,u)$-flower\label{sec:exactSol}}
We can indeed obtain the exact solution for the $(u,u)$-flower without relying on the renormalization-group analysis  in Sec.~\ref{sec:RG}.
Using Eq.~(\ref{eq:recursionG_n}) repeatedly, we obtain
\begin{align}
G_1(x) &= x^u + x^u = 2x^u ,\\
G_2(x) &= G_1(x) ^u + G_1(x) ^u = 2 G_1(x) ^u = 2 (2x^u)^u \nonumber \\
           &= 2^{u+1}x^{u^2} ,\\
G_3(x) &= G_2(x) ^u + G_2(x) ^u = 2 G_2(x) ^u = 2 ( 2^{u+1}x^{u^2} )^u \nonumber\\
           &= 2^{u^2 + u+1}x^{u^3} ,\\
\cdots\\
G_n(x) &= 2^{u^{n-1} + u^{n-2}+\cdots + 1} = 2^{\frac{u^n-1}{u-1} }x^{u^n} ,
\end{align}
which are cast into the form
\begin{align}
\exp\left( -\frac{r_n}{\xi(x)} \right) &= G_n(r_n,x) = 2^{\frac{u^n-1}{u-1} }x^{u^n},
\intertext{with}
\xi(x) &= -\frac{r_n}{\ln\left( 2^{\frac{u^n-1}{u-1} }x^{u^n} \right)} = -\frac{u^n}{\ln\left( 2^{\frac{u^n-1}{u-1} }x^{u^n} \right)}.
\end{align}
Let $x_{c}^{(n)}$ be
\begin{align}
x_{c}^{(n)}:=2^{\frac{-1+u^{-n}}{u-1}}  .
\end{align}
We then have $0<\xi(x) < \infty$ when $0<x<x_{c}^{(n)}$ and $\xi(x)$ diverges as $x\nearrow x_{c}^{(n)}$.
The Taylor expansion around $x_{c}^{(n)}$ gives
\begin{align}
\xi(x) = \frac{2^{ \frac{-1+u^{-n}}{u-1} }}{x_{c}^{(n)} - x + O((x_{c}^{(n)} - x)^2)}.
\end{align}
In the thermodynamic limit $n\to\infty$, we arrive at
\begin{align}
&\lim_{n\to\infty}x_{c}^{(n)} = 2^{\frac{-1}{u-1}}=:x_c ,\\
&\xi(x)\xrightarrow{n\to\infty} = \frac{2^{\frac{-1}{u-1}}}{x_c - x + O((x_c-x)^2)} .
\end{align}
Therefore,
\begin{align}
\mu &= 2^{1/(u-1)},\\
\nu &= 1,
\end{align}
which agree with Eqs.~\eqref{eq:mu_RG_u_u} and \eqref{eq:nu_RG_u_u}.
The critical point $x_{c}^{(n)}$ is shifted from $x_{c}$ because of a finite-size effect. This effect disappears when the system size becomes infinite and the critical point reaches the correct value in the thermodynamic limit.

In this section, we have  proved that
\textit{the critical exponent $\nu$ of the self-avoiding walk on the $(u,u)$-flower is $\nu=1$ for $\forall u>1$.}
On the other hand, the fractal dimension of the $(u,u)$-flower is $d_{\mathrm{f}} = \ln (2u) / \ln(u)$,
 which takes a value in the range $1<d_{\mathrm{f}}\le 2$. We therefore confirm that
\textit{there is no one-to-one correspondence between the fractal dimension and the critical exponent $\nu$.}

The critical exponents of the self-avoiding walk in the Euclidian space are considered to be determined only by the dimensionality.
It is indeed conjectured that $\nu = 3/4$ in $\mathbb{R}^2$~\cite{madras96}.
Extension of the self-avoiding walk from the Euclidian space to fractals  makes an infinite number of universality classes.

\section{Numerical Simulations\label{sec:simulation}}
In Sec.~\ref{sec:RG}, we used some hypotheses to derive the connective constant $\mu$ and the critical exponent $\nu$.
In order to confirm the hypotheses, we here present our numerical simulations.
Only in this section and Appendix \ref{chap:MCAnnal}, we write the displacement exponent $\nu$ defined in Eq.~\eqref{eq:nuPrimeDef} as $\nu'$ so as to distinguish it from the critical exponent $\nu$ defined in the other way, Eq.~\eqref{eq:nuDef}.

\subsection{The number of paths\label{subsec:numOfPaths}}
We hypothesized that the number of paths of length $k$ increases exponentially in Eq.~\eqref{eq:numOfPathExp}.
In order to check the validity of this assumption,
we counted up the number of paths of length $k$ which start from a hub and have a \textit{free end point}, using the depth-first search algorithm~\cite{cormen09}.
Note that the end point was fixed in Eq.~\eqref{eq:numOfPathExp}, but we adapt a free end point here.
This is because we can expect the leading term of the asymptotic form the number of paths does not depend on whether
the end point is fixed or free as in the self-avoiding walk in the Euclidian space.

We carry out the depth-first search  in the following way~\cite{cormen09}. .
We first define a tree of height $k_{\mathrm{max}}$, whose node represents a self-avoiding path, and next explore the tree by a depth-first manner. Nodes of depth $k$ consist of all self-avoiding paths of length $k$ starting from a node $s$. Two nodes are connected if the path of the child node can be generated by appending an edge to that of the parent node.

Drawing an analogy to the self-avoiding walk  in the Euclidian spaces, we assume that the number of paths of length $k$ starting from a node $s$ with a free end point behaves as
\begin{align}
C_{k}^{(s)} = A^{(s)} \mu^k k^{\gamma-1}  ,  \label{eq:C_k}
\end{align}
where $\gamma$ is the critical exponent associated with the susceptibility.
Because $C_{k}^{(s)}$ increases exponentially, it is easy to acquire the value of $\mu$, but  $\gamma$, which is of more interest from the perspective of critical phenomena, is difficult to obtain accurately.

Choosing a node with the largest degree, namely a hub, as a starting point $s$, we computed $C_{k}^{(s)}$ for $n=4,2\le u\le v\le 10,$ and $1\le k\le 30$ and fitted the series $C_{k}^{(s)}$ to
\begin{align}
\ln C_{k}^{(s)} = A' + k\ln\mu + (\gamma -1)\ln k  .  \label{eq:fitting_mu}
\end{align}
We obtained only $\mu$ in high precision (Fig.~\ref{fig:compare_mu}).
The value of $\mu$ of the simulation agrees well with the one of the renormalization-group analysis, while
the tree approximation overestimate $\mu$  because the existence of loops is not taken into consideration.
This figure supports the plausibility of Eq.~\eqref{eq:numOfPathExp}.
The upper-right points correspond to the $(2,2)$-flower.
These points are off the line $x=y$ because the finite site effect appears  most strongly for the smallest flower, \textit{i.e.}, the $(2,2)$-flower.

\begin{figure}
\includegraphics[width=13cm,clip]{compare_mu}
\centering
\caption{Comparison of the connective constant $\mu$ obtained by three different methods for various values of $u$ and $v$. The horizontal axis denotes the estimate of $\mu$ in simulation with the fitting in Eq.~(\ref{eq:fitting_mu}), while the vertical axis denotes that of the renormalization-group analysis and the tree approximation (mean-field theory with the common values of $u$ and $v$). The simulation condition is $n=4$, $2\le u\le v\le 10,\text{~and~}1\le k\le 30$. A hub was chosen as the starting point.}
\label{fig:compare_mu}
\end{figure}

\subsection{The displacement exponent\label{subsec:simDisplExp}}
We hypothesized in Eq.~\eqref{eq:nuPrimeDef} that the mean shortest distance from the starting point increases as a power function of the path length with the displacement exponent $\nu'$.
We here confirm it by the depth-first search algorithm~\cite{cormen09}.
Choosing a node with the largest degree, namely a hub, as a starting point $s$, we computed $\ln \overline{ d_{k}^{(s)} }$ for $n=4,2\le u\le v\le 10,$ and $1\le k\le 30$ by enumerating all the paths of length $k$.
We found that $\ln \overline{ d_{k}^{(s)} }$ fluctuates around an asymptotic line and the amplitude of the fluctuation gets smaller as $k$ becomes larger,
approaching to the line;
see Fig.~\ref{fig:MeanShortestDistance_k} for $(u,v,n)=(3,5,5)$ for example.
The figure supports our assumption of the form $\overline{d_{k}^{(s)}}\propto k^{\nu'}$.

\begin{figure}
\includegraphics[width=10cm,clip]{MeanShortestDistance_k}
\centering
\caption{The mean shortest distance $\overline{d_{k}^{(s)}}$ against the path length $k$. The series of $\overline{d_{k}^{(s)}}$ computed by the depth-first search is fitted to $\ln\overline{d_{k}^{(s)}} = A + \nu' \ln k$. We chose a hub as the starting node $s$. We counted all the paths of $k\le 87$ for $(u,v,n)=(3,5,5)$. $\ln \overline{ d_{k}^{(s)} }$ fluctuates around an asymptotic line and the amplitude of the fluctuation gets smaller as $k$ becomes larger}
\label{fig:MeanShortestDistance_k}
\end{figure}

Next, we also hypothesized that the critical exponent $\nu$, which is defined through the two-point function by Eq.~(\ref{eq:nuDef}), is equal to the displacement exponent $\nu'$ in Eq.~(\ref{eq:nuPrimeDef}): $\nu=\nu'$.
We conducted a Monte-Carlo simulation in order to check the validity of this assumption (Fig.~$\ref{fig:nu_nu_MC_bin}$).
We need to evaluate long paths to obtain $\nu'$ in high precision.
Because the number of paths grows exponentially, we cannot use the depth-first search algorithm, which enumerates all the paths.
We therefore adapted the biased sampling algorithm~\cite{binder10}, which is a kind of Monte-Carlo algorithm, to generate long paths.
In the biased sampling algorithm, we make a walker select the next site randomly among adjacent unvisited sites,
and thereby define $P'(\omega)$ as a distribution that the trajectory of the walker follows.
Let $l_i$ be the number of sites to which a walker can go next in the step $i$. Then a path appears with a probability proportional to $1/\prod_i l_i$.
We can express the average of any quantity $X$ in the form
\begin{align}
\langle X\rangle &= \frac{\int_{\Omega_{k}^{(s)}} X(\omega)\prod_{i=0}^{k-1}l_i(\omega) d\mu'}{\int_{\Omega_{k}^{(s)}} \prod_{i=0}^{k-1}l_i(\omega) d\mu'} \\
&\approx \frac{ X(\omega^{(1)})\prod_{i=0}^{k-1}l_i(\omega^{(1)})  +   \cdots + X(\omega^{(M)})\prod_{i=0}^{k-1}l_i(\omega^{(M)})}{\prod_{i=0}^{k-1}l_i(\omega^{(1)})  + \cdots + \prod_{i=0}^{k-1}l_i(\omega^{(M)})}  .  \label{eq:averageA_BS}
\end{align}
Here $\omega^{(i)}$ for $1\le i\le M$ is a random variable (path) which follows the distribution $P'(\omega)$.

The simulation condition is $2\le u\le 5$ and $2\le v\le 10$.
We computed the average $\overline{d_{k}^{(s)}}$ over $10,000$ configurations of paths, using Eq.~\eqref{eq:averageA_BS} for various values of $u$ and $v$.
We used a hub as the starting node $s$.
Assuming the relation $\eqref{eq:nuPrimeDef}$, we fitted the estimate of the obtained mean shortest distance $\overline{d_{k}^{(s)}}$ to
\begin{align}
\ln  \overline{d_{k}^{(s)}}  = A + \nu' \ln k  .   \label{eq:nuPrimeModel}
\end{align}
We rejected the data point for $(u,v)=(2,2)$ because the finite size effect appeared so strongly that fitting could not be done.
Detail of analysis is written in Appendix \ref{chap:MCAnnal}.
Figure~$\ref{fig:nu_nu_MC_bin}$ supports our assumption that the exponents defined in the two ways are indeed equal to each other: $\nu=\nu'$.

\begin{figure}
\includegraphics[width=15cm,clip]{nu_nu_MC_bin}
\centering
\caption{The critical exponent $\nu$ of the zero-component ferromagnet and the displacement exponent $\nu'$ defined in terms of the end-to-end shortest distance  estimated by simulations for various values of $u$ and $v$.
We estimate the critical exponent $\nu$ by the renormalization-group analysis and computed the displacement exponent $\nu'$ by the biased sampling algorithm followed by curve fitting exemplified in Fig.~\ref{fig:MeanShortestDistance_k_MC} in Appendix \ref{chap:MCAnnal}. We chose a hub as the starting point $s$.
The simulation condition was $n=4,~2\le u\le 5,$ and $2\le v\le 10$.
}
\label{fig:nu_nu_MC_bin}
\end{figure}

\section{conclusion}
We studied the scaling properties of the self-avoiding walk on the $(u,v)$-flower.
By obtaining the connective constant $\mu$ and the critical exponent $\nu$,
we studied that (i) how the number of paths with a fixed length and a fixed starting point increases
and (ii) how the mean shortest distance between the two end points grows as the path length increases.

In the Euclidian space, it is widely believed that the critical exponents of the self-avoiding walk depends  only on the Euclidian dimension. In contrast, for the generalized  problem on fractals, it has been conjectured since the 1980s~\cite{rammal84, havlin87,aharony89} that
critical exponents of the self-avoiding walk are not determined only by the similarity dimension.
Critical exponents are difficult to obtain exactly except for a few cases in the Euclidian spaces~\cite{dhar78, rammal84}
and hence the direct verification of the conjecture had never been done.
Adaptation of the $(u,v)$-flowers, on which we can easily carry out the renormalization-group analysis, enabled us to confirm this conjecture directly.
We expect that fractal complex networks are useful in understanding scaling of other stochastic models in fractals as well.

In contrast to scaling theories for Markovian processes on complex networks~\cite{barrat08, condamin07, gallos07b, condamin08},
those for non-Markovian processes such as the self-avoiding walk are poorly understood.
The present methodology of the renormalization group, however, is also applicable to non-Markovian dynamics on graphs as well as Markovian processes.
We believe that this direction of research will deepen our understanding of non-Markovian dynamics on complex networks.

It will be interesting to consider the extension of Flory's approximation of $\nu$ to fractal graphs.
Flory's approximation is to approximate $\nu$ by the Euclidian dimension: $\nu=3/(2+d)$.
Extension of this formula to fractals embedded in the Euclidian space has been studied~\cite{rammal84, havlin87, aharony89}.
It is impossible to apply the renormalization-group analysis used in the present paper to real complex networks
because graphs for which the exact renormalization can be applied are limited;
this is the fundamental limit of the present renormalization-group analysis.
We, however, expect that the scaling properties of paths on networks are determined only by a few parameters including  not only the similarity dimension but also other parameters.
Our exact results will serve as a basic model to develop a scaling theory which is generally applicable.
For example, we found that the speed of the increase of the mean shortest distance between end-to-end points is related with the critical exponent of the zero-component ferromagnet on the $(u,v)$-flower.
If $\nu$ can be expressed as a function of a few parameters,
we can predict the number of the $s$-$t$ paths and the mean shortest end-to-end distance.
It is also of interest to study whether the critical exponent $\nu$ of the $N$-vector model in the limit $N\to 0$ is the same  on other fractal networks as that of the displacement exponent $\nu$, which
is defined by $\overline{d_{k}^{(s)}} \approx k^{\nu}$.

\begin{acknowledgments}
I wish to thank my supervisor Naomichi Hatano for advice and reading this manuscript.
I am also grateful to Tatsuro Kawamoto and Tomotaka Kuwahara for useful discussion.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


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Jesuto found 16 bible verses related to Equal
Similar Terms - Equality, Equally
Revelation 21:16 (WEB) - The city lies foursquare, and its length is as great as its breadth. He measured the city with the reed, Twelve thousand twelve stadia. Its length, breadth, and height are equal.
Colossians 4:1 (WEB) - Masters, give to your servants that which is just and equal, knowing that you also have a Master in heaven.
John 5:18 (WEB) - For this cause therefore the Jews sought all the more to kill him, because he not only broke the Sabbath, but also called God his own Father, making himself equal with God.
Mark 12:42 (WEB) - A poor widow came, and she cast in two small brass coins, which equal a quadrans coin.
Matthew 20:12 (WEB) - saying, 'These last have spent one hour, and you have made them equal to us, who have borne the burden of the day and the scorching heat!'
Ezekiel 33:20 (WEB) - Yet you say, The way of the Lord is not equal. House of Israel, I will judge every one of you after his ways.
Ezekiel 33:17 (WEB) - Yet the children of your people say, The way of the Lord is not equal: but as for them, their way is not equal.
Ezekiel 18:29 (WEB) - Yet says the house of Israel, The way of the Lord is not equal. house of Israel, are not my ways equal? Aren't your ways unequal?
Ezekiel 18:25 (WEB) - Yet you say, The way of the Lord is not equal. Hear now, house of Israel: Is my way not equal? Aren't your ways unequal?
Isaiah 46:5 (WEB) - To whom will you liken me, and make me equal, and compare me, that we may be like?
Isaiah 40:25 (WEB) - To whom then will you liken me? Who is my equal? says the Holy One.
Job 41:33 (WEB) - On earth there is not his equal, that is made without fear.
Job 28:19 (WEB) - The topaz of Ethiopia shall not equal it, Neither shall it be valued with pure gold.
Job 28:17 (WEB) - Gold and glass can't equal it, neither shall it be exchanged for jewels of fine gold.
1 Chronicles 12:14 (WEB) - These of the sons of Gad were captains of the army: he who was least was equal to one hundred, and the greatest to one thousand.
Exodus 30:34 (WEB) - Yahweh said to Moses, Take to yourself sweet spices, gum resin, and onycha, and galbanum; sweet spices with pure frankincense: of each shall there be an equal weight;


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The Effects of Different Types of Feedback on Revision
Chiharu Nakanishi
The purpose of the present study is to examine the effects of feedback and revision on the writing of Japanese EFL learners. The students were divided into four groups, depending on from whom they were given feedback. Forty students participated in this study. The participants were trained to give both self-feedback and peer-feedback in class. After writing first drafts, the students were given feedback in one of the four forms of feedback. (Group A: required to revise after self-feedback, Group B: required to revise after peer-feedback, Group C: required to revise after teacher-feedback, Group D: required to revise after peer & teacher-feedback). The result was that the scores of all groups became higher after each type of feedback, and there was no significant difference according to feedback types. However, the questionnaire indicated that the peer and teacher feedback group most often reported that the comments were useful in revising their drafts.
Keywords: writing, self-feedback, peer-feedback, teacher-feedback, revision


"It's just remarkable how quickly he resumed being a normal teenager," said his mother, Elizabeth.
That's because last fall Camden, who's 15, suddenly went from a dedicated, promising athlete to a heart patient who was facing surgery that threatened to bench him for good. A fortuitous screening, an innovative robotic procedure and unwavering determination put Camden back on the field in remarkable time.
Camden grew up near Denton, 40 miles north of Dallas, a natural athlete who never met a sport he didn't love. Last August his freshman football team at Guyer High School underwent heart screenings as part of a program sponsored that sponsors free or low-cost screenings for young athletes in North Texas and arranges donations of automated external defibrillators to area organizations. The organization, Living for Zachary, was founded by the family of Zachary Schrah, a 16-year-old football player who collapsed and died in 2009 on a practice field in Plano, Texas, from sudden cardiac arrest.
Camden's screening revealed an isolated cleft of the mitral valve, a congenital heart defect that allowed blood leaving his heart to leak back in. Over time the condition can cause an enlarged heart, arrhythmias and heart failure.
He'd never had a symptom or a problem. He didn't go back to practice.
Steven Mottl, M.D., a Denton cardiologist, said that nowadays, a congenital mitral valve problem is usually detected prenatally or early in life.
The American Heart Association and the American College of Cardiology recommend a 14-point checklist for screening young people for heart disease that does not include an electrocardiagram unless initial tests indicate it is necessary. Their joint scientific statement concludes that athletes are no more likely to have genetic heart diseases than the general population, and that current evidence does not show that universal ECGs would save lives.
Once Camden's mitral valve problem was diagnosed, the initial recommendation was to perform a sternotomy, where surgeons split the breastbone to access the heart and repair the valve. But that would have meant a long, painful recovery – and no contact sports.
Mottl and Dr. Robert Smith, a cardiac surgeon in Plano, had another idea. Robotic surgery – in which the surgeon guides small instruments through the body to perform the procedure – would require only small incisions on the side of the ribcage and avoid a sternotomy.
Just a few days before the scheduled surgery, the Thrailkills decided to try the robotic method. "We figured if this is curable, let's do it in a way where he can return to the life he loves," Elizabeth said.
Smith performed the surgery at The Heart Hospital Baylor Plano on Oct. 6, and three days later Camden went home. Three weeks later he was back in school. By December he was working out. He was at tryouts in January for the freshman baseball team, earning the starting centerfield job.
The AHA and ACC have a lengthy set of guidelines to help doctors determine whether people with heart issues – from hypertension to transplants – can continue participating in sports. They encompass factors such as genetics, the nature of the problem and likelihood of recurrence, and stress the need for follow-up care and the availability of automatic external defibrillators and CPR-trained coaches at athletic events.
The young athlete's story has thrust him somewhat into the spotlight, where he's not entirely comfortable.


On Aug. 29, the Detroit Public Schools Community District announced drinking water at all of its schools will be shut off, following test results that showed elevated levels of lead or copper in 16 of 24 schools recently tested. The district set out to test all 106 school buildings this spring and previously had shut off drinking water in 18 schools due to high levels of heavy metals, as reported by USA Today.
While not all the schools have completed testing yet, nearly a third of the city's school buildings have tested positive for excessive lead and copper levels. As a results, all water fountains and drinking water sources at all Detroit public schools will be shut off before the school year begins and students will be provided bottled water. Superintendent Nikolai Vitti said that the decision to shut off drinking water sources at all schools was made out of caution.
"Although we have no evidence that there are elevated levels of copper or lead in our other schools where we are awaiting test results, out of an abundance of caution and concern for the safety of our students and employees I am turning off all drinking water in our schools until a deeper and broader analysis can be conducted to determine the long-term solutions for all schools," Vitti said.
While the decision to shut off drinking water sources and provide bottled water while the district waits for the arrival of water coolers will be costly, Detroit Mayor Mike Duggan has been supportive of the decision. Duggan announced his intent to reach out to charter school operators to conduct similar water quality testing.
"Aging school infrastructure (plumbing) is the reason for the precautionary measure of providing bottled water. The treated drinking water provided by GLWA (Great Lakes Water Authority) and distributed by DWSD (Detroit Water and Sewerage Department) not only meets, but surpasses all federal and state Safe Drinking Water Act regulations," GLWA and DWSD responded in a joint-statement.


You're probably more familiar with parsley as a green herb used to bring flavor to your dishes and garnish your salads than as a medicine herb.
The benefits of parsley are numerous and as a tea, it may help to cleanse your system as well as it may be the solution for irregular menstruation and cramps.
There are numerous psychiatric and neurologic disorders that could be caused by neurotoxicity. Symptoms may include memory loss, reaction time, sleep disruption, confusion, fatigue, numbness in hands or feet and even depression. Our nervous system being a vital system to our well being, benefits from parsley tea as a preventative measure of neurotoxicity, and effective treatment of damage.
Parsley has been found to be effective for all kidney and urinary conditions except severe kidney inflammation. Drinking parsley tea helps to prevent salt from being reabsorbed into the body tissues. In other words, parsley literally forces debris out of the kidneys, liver and bladder. It helps improve edema and general water retention, fatigue and scanty or painful urination.
Add the parsley and lemon into a cup and put the boiled water into it. Let it steep for 5 minutes. Then, remove the parsley and the lemon, and add the honey.


The use of solar power for electricity generation is deemed a non- consumptive use of natural resources and produces zero greenhouse gas emissions. Solar-generated electricity is set to play a significant role in reaching the South African government's renewable energy target of 10GWh of renewable energy by 2013.
Feed-in tariffs guarantee prices for developers, but there is a lack of certainty on the amount of renewable electricity such laws would deliver under local conditions. Portfolio standards set a fixed quantity, which would guarantee diversity of supply. Power purchase agreements, access to the grid and creating markets for green electricity and some supporting activities are key sector support policy options.