So, what's a truffle farmer to do while we wait the 5-8 years for truffles to appear? Plenty!
First, you need to make sure there's plenty of water for those dry hot summers we're becoming famous for this part of North Carolina. We have installed the micro-sprinkler system attached to the well we use for our principal water source. While it delivers water to the area around the tree quite efficiently, it can spring leaks underground.
And last, but certainly not least, is the tilling. Till between the rows the top 1-1.5 inch of soil in the spring. This is extremely important for the aeration of the soil and to promote root growth. This introduces one of the most challenging and interesting elements of our pioneering adventure. We agreed that having an old red belly tractor would be "neat." Well, it looked neat but it started shedding small parts as soon as it arrived. Eventually we found someone who thrilled to the challenge of restoration and waved good-bye as it left for its new home. Next came the tractor too wide to navigate the rows (remember when I said we should have spaced them farther apart?) Finally, tractor number 3 which serves the purpose very nicely and remains with us to this day performing all kinds of farm-type work.
In addition to these activities, there's the weeding. We learned early on that ours wouldn't be an organic operation. Chemical weed control was regrettably necessary. With both of us still working full time jobs to support our farming habit, time was of the essence. Determined to manage the orchard ourselves, we did what we had to do to keep it up. It was enough to do in a week-end, just managing things as they were and with only 125 trees. We should have begun pruning early to keep the seedlings shaped like upside down umbrellas with the center open for the sun to shine in. Isn't hindsight great? We got to do lots of that later when the branches were MUCH bigger. Oh well, ignorance is bliss and we congratulated ourselves for becoming week-end farming warriors and, after all, we were keeping our eye on the prize. We knew the best was yet to come.


text:
Q: Polymorphism and shared_ptr passed by reference I try to send to function a shared_ptr with polymorphic class.
My objective is to find a best way to send my shared_ptr
without increase ref_count.
EDIT: I don't search solution where my shared_ptr is replaced because I want to call shared_ptr.reset() for example.
Currently, void doGenericTemplate(std::shared_ptr<CLASS>& ptr) is what I want in result BUT I prefer a single function in program.

*

*Do you have another solution ?

Moreover, I don't understand why the function void doGeneric(std::shared_ptr<Base>& ptr) doesn't compile (equivalent without shared_ptr work fine: please check doClassic in complete code).

*Do you have an explain ?

Thanks you !
Partial code
#include <iostream>
#include <memory>

class Base
{
    public:
        Base() = default;
        virtual ~Base() = default;
        virtual void run() = 0;
};

class Derived1: public Base
{
    public:
        Derived1() = default;
        virtual ~Derived1() = default;
        void run()
        {
            std::cout << "  Derived1";
        }
};

class Derived2: public Base
{
    public:
        Derived2() = default;
        virtual ~Derived2() = default;
        void run()
        {
            std::cout << "  Derived2";
        }
};

// This function works but increase count
void doGenericCopy(std::shared_ptr<Base> ptr)
{
    ptr->run();
    std::cout << "  Ref count: " << ptr.use_count() << std::endl;
}

// This function works without increase count = OK !
void doSpecificD1(std::shared_ptr<Derived1>& ptr)
{
    ptr->run();
    std::cout << "  Ref count: " << ptr.use_count() << std::endl;
}

// Compilation error = FAILED !
void doGeneric(std::shared_ptr<Base>& ptr)
{
    ptr->run();
    std::cout << "  Ref count: " << ptr.use_count() << std::endl;
}

// Working fine for all Derivate = OK !
template<typename CLASS>
void doGenericTemplate(std::shared_ptr<CLASS>& ptr)
{
    ptr->run();
    std::cout << "  Ref count: " << ptr.use_count() << std::endl;
}

int main()
{
    auto d1 = std::make_shared<Derived1>();
    auto d2 = std::make_shared<Derived2>();

    std::cout << "With copy: " << std::endl;
    doGenericCopy(d1);
    doGenericCopy(d2);

    std::cout << "Specific: " << std::endl;
    doSpecificD1(d1);

    std::cout << "Template: " << std::endl;
    doGenericTemplate(d1);
    doGenericTemplate(d2);

    // Compilation issue
    //doGeneric(d1);
}

Complete code
https://ideone.com/ZL0v7z
Conclusion
Currently in c++, shared_ptr has not in language a specific tools to use polymorphism of class inside template.
The best way is to refactor my code and avoids to manage shared_ptr (ref_count, reset).
Thanks guys !

A:

*

*Do you have another solution ?

Pass object by reference or const reference instead of shared_ptr.
void doGeneric(Base& r)
{
    r.run();
}

Firstly - this shows explicitly that you do not store or cache pointer somwhere. Secondly - you avoid ambiguities like the one you presented here.

*Do you have an explain ?

Passing shared_ptr<Derived> to function causes implicit cast to shared_ptr<Base>. This new shared_ptr<Base> is temporary, so it can not be cast to shared_ptr<Base> &. This implicit cast would increase ref count even if you could pass it.

A: A shared_ptr<Base> and shared_ptr<Derived> are unrelated types, except you can implicitly create a shared_ptr<Base> from a shared_ptr<Derived>.
This creation adds a reference count.
If you really, really want to avoid that reference count...
template<class T>
struct shared_ptr_view {
  template<class D>
  shared_ptr_view( std::shared_ptr<D>& sptr ):
    vtable( get_vtable<D>() ),
    ptr( std::addressof(sptr) )
  {}
  shared_ptr_view( shared_ptr_view const& ) = default;
  shared_ptr_view() = default;
  shared_ptr_view& operator=( shared_ptr_view const& ) = delete;
  T* get() const { if(vtable) return vtable->get(ptr); return nullptr; }
  void clear() const { if(vtable) vtable->clear(ptr); }
  std::shared_ptr<T> copy() const { if(vtable) return vtable->copy(ptr); return {} }
  operator std::shared_ptr<T>() const { return copy(); }
  T* operator->() const { return get(); }
  T& operator*() const { return *get(); }
  explicit operator bool() const { return get(); }
  std::size_t use_count() const { if (vtable) return vtable->use_count(ptr); return 0; }
private:
  struct vtable_t {
    T*(*get)(void*) = 0;
    std::shared_ptr<T>(*copy)(void*) = 0;
    void(*clear)(void*) = 0;
    std::size_t(*use_count)(void*) = 0;
  };
  vtable_t const* vtable = 0;
  void* ptr = 0;
  template<class D>
  static vtable_t create_vtable() {
    return {
      [](void* ptr)->T*{ return static_cast<std::shared_ptr<D>*>(ptr)->get(); },
      [](void* ptr)->std::shared_ptr<T>{ return *static_cast<std::shared_ptr<D>*>(ptr); },
      [](void* ptr){ static_cast<std::shared_ptr<D>*>(ptr)->reset(); },
      [](void* ptr){ return static_cast<std::shared_ptr<D>*>(ptr)->use_count(); }
    };
  }
  template<class D>
  static vtable_t const* get_vtable() {
    static const auto vtable = create_vtable<D>();
    return &vtable;
  }
};

then
void doGeneric( shared_ptr_view<Base> ptr ) {
  ptr->run();
  std::cout << "  Ref count: " << ptr.use_count() << std::endl;
}

does not increase the reference count.  I think it is raw insanity.
shared_ptr_view.clear() works, but shared_ptr_view.reset(T*) cannot: a shared_ptr_view<Derived> cannot be reset to point to a Base*.

redpajama_set_name: RedPajamaStackExchange


text:
Shadows Over an African Heart
Shadows Along the Zambezi
Lumpy The Elephant
Mom's Cat Stories
Romantic suspense novels
Hawkins' Novels & Publications
Diana M. Hawkins writes romantic suspense novels, children's books, and other works from her location in Lawrenceville, Georgia. Below are her major published works, along with a brief synopsis outlining each one.
In 2008, Zimbabwe is a particularly dangerous place. Corruption, violence, rape, murder, and inhuman levels of greed and brutality rule the land as lawless political factions battle for power. Pieter Van Rooyen, a commercial farmer-turned-environmentalist, has felt the terror firsthand. Seven years earlier, his family was brutally murdered and his farm seized during Zimbabwe's violent land distribution scheme. The experience changed his life and priorities; now he is dedicating his life to honoring life.
He joins forces with Jessica Brennan, an American wildlife biologist, to protect Zimbabwe's most threatened treasure, its elephants that are being slaughtered by poachers and corrupt government officials alike—under the guise of conservation. While conducting a study of Zimbabwe's elephants in the eastern Zambezi Valley, Jessica witnesses many of the threats they face, including habitat encroachment, floods, droughts, mismanagement of wildlife areas and their slaughter for ivory.
Jessica and Pieter are joined by his former neighbor, Angus McLaren, another dispossessed farmer who narrowly escapes with his life when his farm is stolen by the so-called veterans of the independence war. Together, the trio wins over the local National Park Service chief, Hector Kaminjolo, and professional hunter Blair Nisbet.
Despite the terror and sadness that surround them, Jessica and Pieter are reminded of the best of human nature as they discover love. Against a backdrop of kidnappings, murders, and international intrigue, a healing romance emerges, proving that love truly can conquer all.
The African Elephant LATEST NEWS
Today, experts fear that at current poaching rates the African elephant could be extinct in the wild in less than three generations.
In 1979, there were an estimated 1.3 million elephants scattered across the plains, deserts, and rainforests of Africa. In 2007, just 28 years later, that number had has been slashed to approximately 500,000.
JUST DO THE MATH—it means that some 800,000 elephants were slaughtered during that period, at an unbelievable rate of more than 28,000 per year. See the hot spots on National Geographic's map at: http://ngm.nationalgeographic.com/2012/10/ivory/elephant-ivory-poaching-graphic
Despite the dire predictions being made by experts and the tireless efforts of celebrities including Prince Harry of Great Britain and others (http://www.onegreenplanet.org/animalsandnature/celebrities-speaking-up-for-elephants/) who donate their millions, time, and voices to inspire the world to conserve wildlife, particularly elephants, the situation is becoming increasingly grim.
According to a new study that provides the first reliable, continent-wide estimates of illegal kills, records show that in just three years—from 2010 until 2012—ivory poachers have slaughtered 100,000 African elephants. Now we await, with baited breath, the results of a continent-wide aerial survey, the Great Elephant Census that is currently underway. Its results were expected in mid-2015, and as soon as I get them, I'll post them on this web site. For more details, see http://news.nationalgeographic.com/news/2014/08/140818-elephants-africa-poaching-cites-census/
Wildlife biologists fear that these huge losses could reduce the genetic diversity of the African elephant to the point where healthy and robust populations become dangerously weakened.
Elephants are vital to the web of life in Africa.
They are a keystone species, that helps balance all the others in their ecosystem. They open up forest land to create firebreaks and grasslands. Their digging creates water access for other animals, leaving nutrients in their wake. Sometimes called the "megagardeners of the forest," elephants are essential to the dispersal of seeds that maintain tree diversity.
Her Specialties:
© 2016 Diana M Hawkins. All Rights Reserved.

redpajama_set_name: RedPajamaCommonCrawl


I know this is a very touchy topic and I hope I do not offend God and man by the views I will share in this blogpost. However, I have carried the thoughts in mind for about a month now and I feel the need to let them all out this evening.
Two things happened in the month of February that led me to this reasoning. Firstly, I had cause to attend a Sunday service at a branch of a very popular Nigerian Pentecostal church in East London; secondly, I attended an International Corporate Social Responsibility (CSR) conference in Lagos, a week after.
I will begin with the church service. As I walked into the auditorium that fateful Sunday, I expected to see a mammoth crowd as you would usually see if you visited the church's headquarters here in Lagos. Surprisingly, that wasn't the case. The pews were largely empty and the aisle clear. I however got seated but what was more interesting to me was the Pastor's message.
She enjoined the congregation to pray without ceasing stating that we wrestle against principalities and powers, and thereafter began to highlight instances during which we need to pray, but they seemed a bit mundane to me. For instance, she said – 'if you are a woman whose pot of food constantly gets burnt, then you need to pray'.
On our way home, my BFF with whom I went to church and I reviewed the message and laughed. The message was awkward to us because in Nigeria, we are used to praying about getting jobs, spouses, financial breakthroughs, visas, protection from armed robbers etc.
Few days after I returned to Lagos, I attended an international CSR conference and the keynote speaker stated that what is considered as CSR would differ from one country to another based on the local socio-cultural influences. His classic example was the health care system in the UK and US. He said that while corporations who invest heavily in health insurance for their employees in the US pride themselves as being socially responsible, that practice cannot be considered CSR in the UK because the British government has a robust healthcare system under the NHS which caters to the well-being of the populace.
This analogy got me thinking about the preaching I received in the UK, and as I pondered, I came to a conclusion that perhaps socio-cultural influences also play a role in the way Christianity is received and practised.
In a developed society where good largely thrives over evil, corruption is minimised, truth and justice prevail, people get jobs and appointments on merit, visas are obtained if you meet the stipulated requirements, food is affordable, there is security, healthcare is subsidised and the common man can secure a mortgage to purchase a home, then perhaps all you may need to pray about could be - how to be a better cook. Furthermore, I came to a realisation that those who were seated in the congregation were individuals who genuinely wanted a fellowship with God.
This again brings me back home. Would the corrupt politician who occupies a front seat in church be in church if we have a system that effectively checks corruption? Would the young school leaver be in church if he was certain that without prayers or breaking a sweat he would get a job? Would the average worker be in church if he knew he would get a promotion when it falls due? Would the mums be in church if our men were more disciplined? Would the spinsters be in church if our society did not stigmatize young unmarried ladies; and so on and so forth.
The answers to these questions will be helpful in ascertaining if we genuinely love God, or if we are just a religious people seeking miracles.


text:
A viza (Huso huso) a csontos halak (Osteichthyes) főosztályának a sugarasúszójú halak (Actinopterygii) osztályába, ezen belül a tokalakúak (Acipenseriformes) rendjébe és a valódi tokfélék (Acipenseridae) családjába tartozó faj.

A többi tokfélénél jóval nagyobbra növő és sokáig élő halfaj, hiszen életkilátása a száz évet is meghaladhatja. Európa legnagyobb édesvízi hala endemikus élőlény a Kaszpi- és Fekete-tengeri medencében, és kisebb állománya megtalálható az Adriai-tenger vízrendszerében.

Intenzív halászata és az ikrájából készített nagyon értékes beluga- vagy fekete kaviár miatti túlhalászás, és az orvhorgászat következtében állománya jelentős mértékben lecsökkent. Az élettere is jelentősen beszűkült, hiszen a folyószabályozások során épített vízlépcsőkön elakad, és nem tud a folyók felsőbb részébe jutni.

Magyarországon a korábban nagy jelentőségű vizafogás, amely egykor a halászat meghatározó jelentőségű ágazata volt, mára teljesen ellehetetlenedett. Horgászata nagyobb mértékben csak a tengerparti országokban lehetséges, de az állománya olyan mértékben megritkult, hogy a washingtoni egyezmény döntése értelmében hivatalosan csak a tenyésztett halak ikráját lehet nemzetközi kereskedelmi forgalomba hozni.

Elnevezései
A magyar halászok körében régen nagy népszerűségnek örvendő viza több népnyelvi elnevezést is kapott. Ilyenek például a fajtok, az orhal, a szinviza, a vizahal és a viza-tok. Tudományos nevét: Huso huso az etimológia a görög eredetű hus szóból vezeti le, mely magyarul disznót jelent.

Más nyelvekben is visszaköszön orosz elnevezése a «белуга» (beluga), amely a «белый» (fehér) szóból eredeztethető. Magyarországon is számon tartják az ínyencek a nagyon finomnak tartott és rendkívül drága beluga kaviárt, mely a viza ikrájából is készül. Az általánosnak mondható 113,6 grammos beluga viza-kaviár ára  forint.

Előfordulása
A Fekete-tengerben és a Kaszpi-tengerben, valamint ritkábban az Adriai-tengerben és a vízrendszerükhöz tartozó folyóvizekben honos. Ívásakor a tengerbe ömlő folyókba vonul. Korábban a folyóvíz szabályozások előtti időkben egészen messzire felhatolt. Bécsben vizamészárszékek működtek és onnan szállították tovább szekéren a halat a francia és a lengyel piacokra. Napjainkban a vízlépcsők megépítése miatt ez a távolság jelentősen lecsökkent és eltűnt a hal sok folyószakaszról.

Megjelenése
Rendkívül lassan, de óriásira növő anadrom faj. A legnagyobb, rekord méretű példány 7,2 méter hosszú és 1571 kilogramm tömegű volt. A vizák (Huso nemzetség) a világ legnagyobb édesvízi halai. A csontos halak főosztályába tartoznak, de a vázuk porcos, ezért egyfajta porcos ganoidnak tekinthető.

Teste többé-kevésbé csupasz, rajta 5 sorban elhelyezkedő csontvértek és elszórva csontszemcsék vagy más néven vértpikkelyek (ganoid pikkelyek) fedik. A fején csontos pajzsok találhatók. Négy bajuszszála az alsóállású száj előtt helyezkedik el. Állkapcsa előretolható. Orra tompa, bajuszszálai hengeresek és rojtosak. Szája nagy, alulról eléri a fej két szélét. Alsó ajka középen megszakított, ellentétben a sima tokkal.

Alfajai
A vizának négy alfaja van:
Huso huso huso – a Fekete-tenger nyugati fele, Adriai-tenger
Huso huso orientalis – a Fekete-tenger keleti fele
Huso huso maeoticus / Acipenser huso Linnaeus (beluga) – Azovi-tenger
Huso huso caspicus – Kaszpi-tenger

Hasonló fajok
Legjobban közeli rokonaihoz a valódi tokfélékhez hasonlít, de markáns nagy méretével eltér tőlük. Különböznek továbbá, hogy a vágó toknak nemcsak az alsó ajka megszakított, hanem a felső is két félre osztott. A sima toknak az ajka nincs megszakítva és a bajuszszálai rojtozottak. A sőregtok orra feltűnően hosszú és vékonyabb. A szibériai tok szája kisebb, bajuszszálai közelebb állnak az orrcsúcsához, mint a szájhoz. A kecsege szája kicsi és a bajuszszálai rojtozottak.

Életmódja

A viza mozgása kissé nehézkes. Életének egy részét a tengerben, másik részét a folyókban tölti. A fiatal állat a homokban keresgéli férgekből, lárvákból, csigákból és kagylókból álló táplálékát, idősebb korában kisebb halakat is fogyaszt.

Szaporodása
Ivarérettségét csak 12–18 éves korában éri el, de 100 évig is élhet. A vizák évente két hullámban úsznak fel a tengerről ívásra, a folyók sekélyebb vizeire. Az állomány egy része ősszel úszik fel a folyókon, ahol a víz fenekén egy-egy mélyedésben vagy gödörben áttelelnek. A másik részük csak tavasszal kezdi meg a vándorlást.

Az ívásra március és május körül kerül sor, a folyók sóderes, köves aljzata fölött. Egy nőstény több százezer, de akár hétmillió(!), 2,5-3 milliméteres átmérőjű ikrát rak le. A körülbelül 8 nap alatt kikelő lárvák további 9 nap után kezdik meg önálló táplálkozásukat. A szülők az ívás után azonnal visszatérnek a tengerbe. Az ivadék sem időz az édesvízben, hanem a folyók deltavidékének félsós vizébe, majd néhány év után a nyílt tengerbe vándorol.

Kárpát-medencei előfordulása

Magyarországi folyóvizekben a halászok körében korábban oly nagyra tartott állománya, mind a Dunán, mind a Tiszán a Vaskapu-szorosnál épített erőműveknek és a vízszennyezettség fokozódásának hatására drasztikusan lecsökkent. Az utóbbi évszázad második felében feljegyzett vizafogások a Duna magyar szakaszán már eseményszámba mentek. Ezzel szemben 1554-1555-ből származó források szerint több mint 160 vizát fogtak a halászok a vizafogókban.

A magyar történelemben említések a vizákról
A Képes krónika leírja, hogy 1053-ban I. András a Győr alatt állomásozó III. Henrik német-római császár éhező seregének megsegítéséül küldött többek között ötven vizát. Egy 1230-as oklevél alapján IV. Béla, ekkor még ifjabb király a heiligenkreuzi cisztercita kolostornak 200 vizát (husones - wizahal) ajándékoz évente. 1318-ban István veszprémi püspök egy váci dunai Tanya viza-halászóhelyet és más birtokokat elcserél Károly Róberttel. 1338-ban Fejér vármegyei Tolve melletti dunai viza-fogókat említenek egy birtokátadás kapcsán. 1423-ban György passaui püspök személyesen győződött meg az esztergomi érsekség vizahalászatának gazdagságáról. 1434-ben a nyúlszigeti apácák perében wyzafolowgy-at említenek. Állítólag 1447-ben Beatrix királyné 105 dukátért 21 vizát vásárolt a gútai halászoktól. Az adat hitelessége Beatrix születési évének ismeretében, erősen megkérdőjelezhető. A 15. század végén a vizahalászat (eladás) bevétele külön jövedelmi tétel volt az esztergomi érsekség számadáskönyveiben (például Gútáról, Naszvadról), melyből a legtöbbet a királyné vásárolt. Valamikor 1498-1511 között gróf Szentgyörgyi Farkas vizafogót építtetett a Dunán. Ennek gátját a komáromi várnagy Korlátkövi Osvát széthányatta, amiből per kerekedett, de végül II. Ulászló közbelépett s magára vállalta a per folytatását. Oláh Miklós humanista beszámolójában arról tudósít, hogy az 1537. esztendőben különösen eredményes dunai halászat alkalmával sikerült mintegy ezer vizát fogni. Az 1592-es urbárium is említi a komáromi vizafogókat. A viza kereskedelméhez a komáromi jegyzőkönyvekben is találni adatokat a 16. század végéről.

A 18. század elején Bél Mátyás így írt a dunai tokhalászatról:

Károli János 1877-ben már ritkaságként említette a dunai tokféléket, és fogyatkozásukról így vélekedett:

Az 1950-es évekig még megtalálható volt a Duna és a Tisza vízrendszerében. A Dunán a viza számított a legnagyobb és a legértékesebb mindennapos halnak. Gyakran óriási (100–500 kg-os) példányai is előfordultak a halászzsákmányokban. Budapest XIII. kerületének középső részét máig Vizafogónak nevezik. Egykor minden nagyobb folyónkból halászták; a Drávából, a Tiszából, a Marosból és a Körösökből is. A Tiszából 1920-ban Vásárosnaménynál, 1933-ban Tiszafürednél, 1953-ban Tiszakécskénél még fogtak, később azonban már csak a Dunából, elvétve egy-egy példányt. A legutóbbi hármat is a Dunából fogták: 1957-ben Paksnál egy 2,7 méterest, 1972-ben Ercsinél egy 120 kilóst, majd ismét Paksnál, 1986-ban egy 3 méteres, 180 kilós példányt. Sajnálatos módon a Kárpát-medencében a többi anadrom tokféle az Acipenser güldenstaedti – vágó tok, az Acipenser nudiventris – sima tok, és az Acipenser stellatus – sőregtok is a kihalás szélére került.

Mesterséges tenyésztése
Az 1970-es években Magyarországon sikeres kísérleteket folytattak a kecsege és a viza keresztezésével. A hibridet "vicsegének" nevezték el. Később azonban a tenyészanyag fenntartási nehézségei miatt, az ilyen programok megszűntek. A magyarországi toktenyésztésnek a VIZA 2020 program ad új lehetőséget. Ez a program a fajok mesterséges szaporítását, telepítését és a még megmaradt élőhelyek rekonstruálását is magában foglalja. Például 2010 szeptemberében visszatelepítési program keretében 100 kishalat engedtek a Dunába. A 2010 novemberében az Ercsinél a Dunába engedett jelölt vizaivadékok közül a Vaskapunál már ki is fogtak példányt román halászok. A hal 10 nap alatt több mint 650 kilométert tett meg. A kifogott vizát lefotózták, videófelvételt készítettek róla, és visszahelyezték a Dunába, hogy folytatni tudja útját a Fekete-tenger felé. Később a No.10998 jelű viza el is érte a Duna deltát, ezáltal bizonyossá vált, hogy a Duna felső szakaszáról a halak valóban eljutnak tengeri élőhelyükig.

Dunai halászata

Ősszel a téli szállást kereső halak a víz felszínén lomhán úszkáltak, csak kelepcébe kellett csalni az úgynevezett "vizafogó tanyán".
A vizafogó tanyát a halászoknak időben elő kellett készíteni. Cégével karókat vertek le a vízbe a varsa számára. A viza beúszott a varsába, és bennrekedt.

Ha még jégolvadás előtt történt a halászat, szigonyt vágtak a hal hasába.
Az ívásra vonuló vizákat két hajó közé kifeszített hálóval halászták a zátonyos, gázlós folyószakaszokon.

Védettsége
Magyarországon védett faj, természetvédelmi értéke tízezer forint.

Galéria

Jegyzetek

További információk

 Vizafogó blog: hazai viza fogások gyűjteménye

Internetes leírások a vizáról

Ajánlott magyar nyelvű könyvek
 Dudich, E., Loksa, I. (1987): Állatrendszertan – Tankönyvkiadó, Budapest
 Papp, L.(1996): Zootaxonómia – egységes jegyzet – Állatorvostudományi Egyetem, Budapest
 Deckert, K. et al (1974): Uránia Állatvilág: halak, kétéltűek, hüllők – Gondolat Kiadó, Budapest

Valódi tokfélék
Halfajok
A Földközi-tenger halai
A Fekete-tenger halai
A Kaszpi-tenger halai
A Kárpát-medence halai
Magyarország halai
Románia halai

redpajama_set_name: RedPajamaWikipedia


text:
LISTMANIA 2016: WIL CIFER'S TOP 10 PROGRESSIVE METAL ALBUMS OF 2016 OUR LIST OF 2016'S MOST INFECTIOUS EXTREME METAL SONGS (PART 1): HARAKIRI FOR THE SKY AND ANAAL NATHRAKH
AN NCS ALBUM PREMIERE: INSULTERS — "METAL STILL MEANS DANGER"
Album Reviews, Premieres Add comments
The Spanish band Insulters named their new album Metal Still Means Danger. It includes songs named "Bang Your Fucking Skull", "Here Falls the Hammer", and of course "Metal Still Means Danger". When you openly brandish so many over-the-top heavy metal tropes, you run some risks — and you'd better be able to back it up with something more than bullet belts, pentagrams, and even the right kind of spirit. Insulters definitely back it up, as you're about to find out.
Metal Still Means Danger was officially released on January 1, 2017, by Unholy Prophecies and Equinox Discos, and we're helping spread the word through the premiere of a full album stream. It's a nasty nine-track hellride that will punch a lot of primal metalhead buttons, and yes, it is likely to cause an orgy of headbanging.
In genre terms, the core of Insulters' sound is black thrash, but they rely more on the rhythms of d-beat punk than you might be expecting; you don't get a burst of blast-beats until the third track, and they're used sparingly after that. And while the tempo runs high and hot for the most part, Insulters do ease off the throttle here and there, to change the atmosphere from fiendishly alive and dangerous to ghoulishly dead and dangerous, like reanimated corpses.
The riffs, of course, are the critical ingredient in this kind of music, and Insulters have packed the album with highly addictive ones — and they also give the music a poisonous, morbid, satanic air. This is definitely the devil's rock 'n' roll. And in addition to arming themselves with a big array of filthy riffs, Insulters also pull the trigger on some very tasty solos, some of them slithering and serpentine, some of them psychedelic, some of them fiery enough to melt the frets.
The music is damned fun. Even if you go into the album with a jaded perspective, it really has a way of getting its hooks in, and it sinks them more and more deeply into the skull as the album races along.
But as much fun as the songs are, they're still undeniably vicious, and a lot of their barbaric mien is attributable to the vocals — which are a scalding mix of high goblin snarls and shrieks, raw yells, volcanic spews of vomit, visceral grunts, and in general the kind of bestiality that wants to rip open your jugular vein with its teeth, just for the pleasure of being bathed in a warm blood spray.
So yeah, Insulters can get away with calling their album Metal Still Means Danger. You'll get a good sense of where Insulters are coming from regardless of which song you might pick as a test, but my own favorites are "Icons & Symbols", "Forged In Hell's Fire", "Burn With the Witch", and the title track.
Metal Still Means Danger was mixed and mastered by Javi Felez (Graveyard, Körgull) at his Moontower Studios. It was officially released by Unholy Prophecies and Equinox Discos on January 1, 2017, and you can pick it up in a large 7″ four-panel digipack format here. A gatefold vinyl edition will follow later this year.
http://www.unholyprophecies.com
https://unholyprophecies.bandcamp.com/
https://www.facebook.com/unholyprophecies666
https://www.facebook.com/insulters666
https://www.insulters.bandcamp.com
Metal Still Means Danger (CD Giant Digipak) by INSULTERS
Posted by Islander at 11:24 am Tagged with: Insulters
One Response to "AN NCS ALBUM PREMIERE: INSULTERS — "METAL STILL MEANS DANGER""
Derek/Godless Angel says:
Damn, there's some serious rippers on here 🙂


Super Shards! This set of German Super Shards Glass Glitter (40 Grit) from Meyer Imports provides a beautiful grouping of the colors that every crafter needs. In this corked glass bottle set you get 6 bottles, each filled with 1/2 oz of different Super Shard Glitters.


text:
Curtiss-Wright Corporation
Curtiss-Wright Corporation - Find Remote Work From Home or Flexible Jobs
About Curtiss-Wright Corporation
A multinational product manufacturer, the Curtiss-Wright Corporation is a public company that supplies some of the largest, critical global industries with essential components and services. The Curtiss-Wright Corporation's history dates back to 1929 when aviation leaders Orville and Wilbur Wright of the Wright Aeronautical Corporation and Mr. Glen Curtiss of the Curtiss Aeroplane and Motor Company merged to form the largest aircraft company in existence in the early 20th century. Glen Curtiss is deemed "the father of naval aviation," while the Wright brothers are lauded as "the fathers of flight."
Headquartered in Charlotte, North Carolina, the Curtiss-Wright Corporation maintains offices and divisions across the United States, China, Germany, India, Singapore, the United Kingdom, Korea, and the Netherlands, among others. The company's divisions are broken into three core segments: commercial and industrial, defense, and power, which include industrial, sensors and controls, surface technologies, defense solutions, EMS, and nuclear divisions. Clients from the commercial aerospace, defense, industrial, and power-generation markets worldwide rely on Curtiss-Wright's products and services, which include joystick controls, sensors, control valves, gearboxes, flight controls, instrumentation, and much more.
As an employer, the Curtiss-Wright Corporation understands that its success is only achievable thanks to the contributions and commitment of its dedicated team. Employees rise to new challenges on a daily basis and share values rooted in excellence and integrity. The company's culture is marked by an entrepreneurial spirit, diversity, innovative technology, and a history of steady growth. Careers with Curtiss-Wright entail creative challenges and opportunities to work in a global environment. In the past, the Curtiss-Wright Corporation has offered abundant full-time positions, many of which feature freelance, temporary, and telecommuting opportunities. Past vacancies have been offered to applicants in cities throughout North America, from Webster, Texas, to Mississauga, Ontario, Canada.
Visit Curtiss-Wright Corporation's website
For Research: Past Remote and Flexible Jobs at Curtiss-Wright Corporation
We include these past jobs as a way for you to explore what kinds of remote and flexible jobs Curtiss-Wright Corporation has hired for in the past and might be likely to hire for again in the future.
Charlotte, NC Candidates need to be able to work in the City or State specified
Develop account strategies, build relationships with C-Level personnel, and drive sales growth within the market. Must have a bachelor's degree, strong communication skills, and 10+ years' technical sales experience. Some telecommuting with travel.
Cincinnati, OH Candidates need to be able to work in the City or State specified
Prepare quotes, follow-up on leads, do market research, and perform prototyping. Promote and sell products and services and meet sales targets. A bachelors degree in engineering and 4-6 yrs of relevant exp. are required. Remote-based with travel.
Gothenburg, Sweden Candidates need to be able to work in the City or State specified
Sales Account Manager is needed for a full-time remote opportunity. Candidate will grow sales and manage defined key accounts. Must be able to meet or exceed sales targets. Prior sales experience is required. Fluency in English/Swedish also required.
Temporary Job Full-Time
Full-time IT technician needed for a short-term temporary opportunity. Will be responsible for analyzing and resolving issues and installing software. Completion of technical or trade schooling in related field and two years' experience required.
Freelance Job Full-Time
Shelby, NC Candidates need to be able to work in the City or State specified
Drafter sought for a short-term temporary full-time contract opportunity. Create engineering drawings and layouts for various assemblies. A high school diploma or equivalent, 2+ yrs.' related exp., and proficiency with Siemens NX Version 10 needed.
Quality Inspector
Mississauga, ON, Canada Candidates need to be able to work in the City or State specified
Quality inspector needed for a short-term temporary opportunity. This is a full-time position. Will be responsible for interpreting schematics and engineering drawings. Bachelor's degree or equivalent and seven years of experience required.
Webster, TX Candidates need to be able to work in the City or State specified
Seeking a Regional Sales Manager for a remote opportunity. Candidate will plan, organize, and develop assigned territory's market. Must be able to negotiate and close contracts with customers. Bachelor's degree and prior related experience required.
NY, NJ, PA, OH, MI, WV, or Northeast Candidates need to be able to work in the City or State specified
Use strong relationship development skills within current customer base to drive sales of variety of system solutions. Must have sales experience in military, avionics or aerospace industries. Home office in Northeastern United States.
Export Compliance Administrator (Charlotte, NC; Los Angeles,CA; Boston, MA)
Charlotte, NC, Washington, DC, Los Angeles, CA, Phoenix, AZ, Boston, MA Candidates need to be able to work in the City or State specified
Manage export-related issues & ensure compliance with federal regulations. May work on site or telecommute from these company locations: Los Angeles, Boston, Phoenix, DC.


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Home/Latest/Why Biden should collaborate with Africa to fight climate change
Why Biden should collaborate with Africa to fight climate change
Mason Witzler Send an email February 17, 2021
Since becoming President on January 20, Joseph R. Biden Jr. has not held back in demonstrating a prideful and passionate vision for addressing the climate crisis. Biden wants America to lead the world in creating the first Clean Energy Revolution.
In the State Dining room of the White House on January 27, Biden announced a preamble to signing the executive order that would spark American direction towards a future of sustainable development that addresses the climate change crisis as both a moral obligation and economic imperative.
"It's a future of enormous hope and opportunity. It's about coming to the moment to deal with this maximum threat that we-that's now facing us- climate change – with a greater sense of urgency. In my view, we've already waited too long to deal with this climate crisis and we can't wait any longer. We see it with our own eyes, we feel it, we know it in our bones, and it's time to act," the president said.
In signing the new executive order titled " Tackling the Climate Crisis at Home and Abroad", Biden put into place several initiatives that demonstrate U.S ambition, empowerment, innovation, accountability, and leadership.
The president has said his administration will put the climate crisis at the center of United States Foreign Policy and National security. In doing so, the united states will work with other countries and partners, both bilaterally and multilaterally, to put the world on a sustainable climate pathway. This means rejoining the Paris Agreement and building upon its three overarching objectives – a safe global temperature, increased climate resilience, and financial flows aligned with a pathway toward low greenhouse gas emissions and climate resilient development.
The Biden White House will also take a government wide approach to the climate crisis such as the establishment of the White House office of Domestic Climate Policy and the National Climate task force. The task force will facilitate planning and implementation of the key Federal actions to reduce climate pollution; increase resilience to the impacts of climate change; protect public health; conserve our lands, waters, oceans, and biodiversity; deliver environmental justice; and spur well-paying union jobs and economic growth. They will engage on these matters with State, Local, Tribal, and territorial governments; workers and communities; and leaders across various sectors of the economy.
Biden's vision for the domestic clean energy revolution is ambitious, articulate, and innovative. His direction for America appears clear and effective. However, he must follow through on his Foreign Policy promises and extend this vision to solving the most challenging climate issues in the world.
United States announces $37 million contribution to 'Education Cannot Wait', global fund for education in emergencies
U.S. deputy special envoy for climate Jonathan Pershing to travel to South Africa, Namibia, Congo, DR Congo and Senegal to discuss crisis ahead of COP26
Africa as a whole faces a greater threat than other regions in terms of growing climate change risk. The State of the Climate in Africa 2019 report by the World Meteorological Organization has highlighted the severity of the issues.
Africa faces significant challenges in addressing the climate change risks, including increasing temperature, changing precipitation patterns, rising sea levels and more frequent extreme weather and climate events such as heat and drought.
These issues have a pronounced effect on the Agriculture sector which acts as the backbone of Africa's economy. People depend on agriculture for their livelihoods and food security.
Climate change also has a debilitating effect on the public health, impacting both environmental and social determinants. Africa is uniquely at risk for health effects of climate change because it has high burdens of climate sensitive diseases and low preparedness and adaptive response capacity.
Given these risks about the state of African Climate change risk, Biden should demonstrate his true climate change leadership and collaborate with Africa to begin their very own Clean Energy revolution.


Here is a biography whose eccentric genius perfectly matches that of its subjects. Penelope Fitzgerald tells the lives of four extraordinary Englishmen-her father and his brothers-with style and wit. Here is the story of a deeply fascinating family mind, shared by four brothers and passed along to their remarkable biographer.
Penelope Fitzgerald (1918-2000) is the author of 9 novels, 3 works of biography, and a posthumously published collection of short fiction. The Blue Flower won the NBCC Award for Fiction and was chosen by the editors of The New York Times Book Review as one of the eleven best books of 1997. Offshore won the Booker Prize, and three of her other novels have made the Booker short list. For almost all her life she lived in London.


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text:
Outstanding Individual
Best-Non-English-Language
Outstanding Outfit
Commercial Project
Outstanding Team
Most Beautiful
Arts, Entertainment & Culture
Leisure, Games & Sport
Maps, Places & Spaces
People, Language & Identity
Politics & Global
Visualization & Information Design
Internal Business Project
Paid tool
Dataviz Website
Dataviz Project
Mini Visualization
Dataviz Tool
Star Wars - Screen Time Analysis
An analysis of the Star Wars Movie Franchise. How much time on screen is dedicated to light side vs dark side? Which characters spend the most time on screen? Which movie did R2-D2 have the most...
public.tableau.com
Did people listen to Baz Luhrmann?
Driving to work recently I heard Baz Luhrmann's infamous 'Everybody's free to wear sunscreen'. Great song, big hit in the UK, but it got me thinking - did anybody listen to him?
www.thedatathing.com
Magic Wands of Every Harry Potter Character
Ron had a wand of ash wood and a core of unicorn hair— before he broke it after a nasty encounter with the Whomping Willow, of course. In celebration of the 20th anniversary of the first ever...
designtaxi.com
The Colors of Bob Dylan
Each piece of music has a key: the note on which the whole harmonic composition is built. How can we use this information to visually represent the complexity of a musician's production over...
www.behance.net
Topography Of Horror
This is an infographic narrative execution of Francis Ford Coppola's film Apocalypse Now. It details Captain Willard's journey to meet Colonel Kurtz. Done for no other reason than the pleasure...
Films Around the Clock Under the Midnight Sun
"Films Around the Clock Under the Midnight Sun" explores the schedule of the Midnight Sun Film Festival organised in 2018. Data for this visualisation consists of the last published schedule of the...
All Flights from Dragon Ball Z
Based on the manga by Akira Toriyama, the first episode of Dragon Ball Z aired in Japan on April 26, 1989. Even after more than 25 years, the anime is still extremely popular, with a filler-free...
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Voices that care
This visualization on charity songs was created on invitation by Datasketch.es (Shirley Wu and Nadieh Bremer). While the subject was "community", I chose to visualize the (top contributing) charity...
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The 'Game of Thrones' Social Network
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news.northeastern.edu
Love and Happiness in Anna Karenina
Anna Karenina has one of the greatest opening lines in all of literature: "Happy families are all alike; every unhappy family is unhappy in its own way." This project investigates the connection...
rockthevizcomm.com
David Bowie's 50-year Creative Output at a Glance
As the last songs Bowie recorded are released as part of an album accompanying the Lazarus stage show, we look into the extraordinary breadth and depth of his creative endeavours in music, film and...
www.theguardian.com
Artists with Multiple Songs in Spotify's Top 100 - 2017
Visualizing the lyrics and audio features for artists with multiple songs in Spotify's 2017 Top 100.
The Cricket Cage
China's Forbidden City in Beijing, remodelled today as the Palace Museum, is a mystical place full of wonderful stories. This full-page infographic uses data to visualise one such tale. According...
multimedia.scmp.com
The Shape of Shakespeare's Sonnets
All 154 of Shakespeare's sonnets were run through sentiment analysis to produce word and overall line sentiment (positive, negative, neutral). This was then visualized in large interactive format...
Kimchee Infographic
infographicslab203.com
Drawing Feelings
"Drawing Feelings" is a personal journey of finding my inside and outside worlds through daily drawings of objects that represent my feelings. World Inside represents how we feel in society...
www.drawingfeelings.com
Emotion Park
Emotion Park is an experimental data visualization project to see how well machines can analyze song lyrics. The visualization tries to capture the emotion of the song lyrics in the form of a...
mustafasaifee.com
Film Trends
This is a story about how film plots mirror (or shape) historical events. For example, how early did the film industry portray the AIDS epidemic? Has movie representation of Islam changed with...
pudding.cool
Film or Digital? Breaking Down Hollywood's Choice of Shooting Medium
In 2017, there are still directors who shoot on film (sometimes exclusively). Others use both film and digital when it serves a purpose. In this project, I explore the filmmaker's choices. When we...
A Visual Guide to 'The Big Lebowski'
In the twenty years since its 1998 release, Joel and Ethan Coen's neo-noir buddy comedy 'The Big Lebowski' has emerged as a cult sensation. A yearly festival is devoted to the film and its...
www.stevengbraun.com
Shortlist	Longlist
Interactive Elvis Presley Jukebox
The 'interactive Elvis Presley Jukebox' is a visual analysis of the tempo of close to 400 Elvis Presley songs. Each facial grid is a song. A brighter blue indicates a faster tempo & a lighter...
gramener.com
Tibetan Opera
Tibetan Opera is called "Gillam", which means "fairy sister". According to legend, Tibetan opera was first performed by seven sisters, and the contents of the opera were mostly myths and stories in...
The interesting regularity of graphene was discovered by studying pencils, and a series of posters and sculptures were made. Lead in the pencil containing graphene with electrical conductivity and...
www.zcool.com.cn
The Overseas Delivery of "The Infinite Challenge"
In this period of overseas planning, the members of "The Infinite Challenge" received applications from all over the world , and some of them are selected for distribution. This process diagram is...
my.zcool.com.cn
What are the most favorite pets in the world?
Fish are more popular in China than elsewhere, while the cat is the favorite domestic animal of the French.
www.courrierinternational.com
Book Binding in China
Presented in the form of timeline: Decorative art of book in China which are classified according to different materials and forms, Binding styles of Chinese ancient books mainly include oracle...
Creation of a Thangka
Thangka is the unique fabric-painting art of Tibet, and few modern people know the origins and production processes of Thangka. I used the form of the temple city to explain the production process...
Best-Non-English-Language	Winners	Bronze	Shortlist	Longlist
K-Pop Artists
One of the strongest Korean trends is K-Pop. This visualizes the K-Pop industry, giving a bird's-eye view of the top four agencies and their artists. YouTube data shows their emotions and...
Discussions in The Hobbit
I wanted to explore the discussions in The Hobbit by J.R.R. Tolkien. Only those words the characters say aloud are visualised. The visualisation shows the amount of discussion in each chapter as...
Envious!
This is a project that worked on a digital remix of Stephanie Posavec and Giorga Lupi's acclaimed "Dear Data" project, drawing inspiration from the analog data graphics to develop novel dynamic and...
4trees.github.io


Oh Magoo, you've done it again! I read Rip Van Winkle when I was a kid at some point in time, and yet I remembered it best from the Mr. Magoo animated version.
Perhaps basing your knowledge of literature on a super-condensed, 20 minute version of a novel hundreds of pages long isn't a sound idea, but in the case of the quite short Rip Van Winkle it actually was just fine. Having reread it and matching it up with my recollection of the cartoon, which admittedly I haven't seen in about 30 years, I think it holds up well.
Hahaha...wouldn't Washington Irving be proud to be reading this review if he could? To have his enduring work reduced to its questioned quality in condensed cartoon form; "My god," I imagine him saying, "what an honor!"
This story of a wastrel (quite familiar to me in the form of folks I've known) gone off the reservation only to return bewildered to an unfamiliar home is a great piece of European folklore carried over to America. Bewitching beings beyond the fringe (yes, I'm stealing the phrase from Cook & Dudley) played a big role in the faerie stories of "the old country". It's nice to see them transplant so well to the wooded reaches of colonial (on the cusp of post) America.


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\section{Introduction}

In this paper we present a combinatorial proof of a relation between
the generating functions of unicellular and bicellular maps,
${\bf C}_{g}(z)$ and ${\bf C}_{g}^{[2]}(z)$:
\begin{equation}\label{E:1}
\sum_{g_1=0}^{g+1}\,{\bf C}_{g_1}(z){\bf C}_{g+1-g_1}(z)
+{\bf C}_{g}^{[2]}(z)= {\bf C}_{g+1}(z)/z.
\end{equation}

Eq.~(\ref{E:1}) is a consequence of the Schwinger-Dyson equation of
matrix theory \cite{Dyson,Schwinger}. It can also be proved by extending
the representation theoretic framework of Zagier \cite{Zagier}. To the best
of our knowledge, our bijection represents the first combinatorial proof of
eq.~(\ref{E:1}).

The motivation for this paper stems from the algorithmic folding problem
of RNA-pseudoknot structures over one and two backbones \cite{gfold,fenix2bb}.
The folding of RNA molecules means to identify some minimum energy
configuration of a given sequence. These configurations are subject to
certain constraints on how two nucleotides can bond
\cite{gfold,fenix2bb,Fenix:08}.
RNA structures over two backbones are called RNA-RNA interaction structures
\cite{rip1, rip2} and of importance in the context of many biochemical,
regulatory activities.

Theorem~\ref{T:thm1} provides a rewiring algorithm transforming bicellular
maps into certain unicellular maps. It thus allows to reduce the folding
problem of RNA-RNA interaction structures to that of
RNA-pseudoknot structures over one backbone, see Fig.~\ref{F:2b-1b}.
This rewiring is of practical interest, since the time
complexity of folding the rewired interaction structure is given by
$O((n+m)^5)$, where $n,m$ are the lengths of the respective backbones.
The direct folding of the interaction structure however has a time
complexity of $O(n^6)$ where $n$ is the length of the longer sequence.
Since there exist an abundance of ``small RNA'' interactions between
a large and a very small RNA structure, the $O((n+m)^5)$ time complexity
is oftentimes much smaller than $O(n^6)$ \cite{fenix2bb}.

\begin{figure}[ht]
\begin{center}
\includegraphics[width=0.9\columnwidth]{2b-1b.eps}
\end{center}
\caption{\small Rewriting diagram over 2 backbones into diagrams over one
backbone. A diagram over 2 backbones $(a)$, its bicellular map $(b)$
and its corresponding unicellular map $(c)$ and its diagram over one backbone
$(d)$.}\label{F:2b-1b}
\end{figure}

The paper is organized as follows: first we recall some basic facts
about diagrams, fatgraphs, unicellular and bicellular maps. We shall work
with planted unicellular and double planted bicellular maps. These plants
are additional vertices of degree one and emerge naturally in the context
of RNA as there is a $5^{'}$ to $3^{'}$ orientation of the molecular backbone.
Modulo Poincar\'{e}-duality the plant ``marks'' the beginning and ending of
the backbone. Interestingly, the plants themselves play a key role in the
combinatorial construction.

Second we dissect the bijection into three separate maps by introducing a certain
partition of the set of unicellular maps of fixed topological genus. Then we
prove our two main lemmas. These show that, with respect to the above mentioned
partition, a unicellular map either corresponds uniquely to a pair of unicellular
maps of lower genus (Lemma~\ref{L:lem1}) or to a unique bicellular map of lower genus
(Lemma~\ref{L:lem2}).

We third prove the main result, Theorem~\ref{T:thm1}, by combining the two
lemmas and give eq.~(\ref{E:1}) as an enumerative corollary.

\section{Some basic facts}

\subsection{Unicellular maps and bicellular maps}

\begin{definition}
A unicellular map, $u$ with $n$ edges is a triple $u=([2n],\alpha,\sigma)$, where
$\alpha$ is an involution of $[2n]$ without fixed points and $\sigma$ is a
permutation of $[2n]$ such that $\gamma=\alpha\circ\sigma $ has only one cycle.
The elements of $[2n]$ are called half-edges of $u$. The cycles of $\alpha$ and
$\sigma$ are called the edges and the vertices of $u$, respectively. The
permutation $\gamma$ is called the face or boundary component of $u$.
\end{definition}

Given a unicellular map $u=([2n], \alpha, \sigma)$, its associated graph $G$ is
the graph whose edges are given by the cycles of $\alpha$, vertices by the cycles
of $\sigma$.
We can consider a $G$-edge as a ribbon whose two sides are labeled by the
half-edges as follows:
if a half-edge $h$ belongs to a cycle $e$ of $\alpha$ and a certain $v$ of
$\sigma$, then $h$ is the right-hand side of the ribbon corresponding to $e$,
when entering $v$.

We draw the graph $G$ in such a way that around each vertex $v$, the counterclockwise
ordering of the half-edges belonging to the cycle $v$ is given by the cycle $v$. This
ordering of half-edges enriches the combinatorial graph $G$ to a ribbon graph or fat
graph $\mathbb{G}$. Clearly, a fat graph $\mathbb{G}$ with one boundary component is
tantamount to the unicellular map $u$, see Fig.~\ref{F:unicellular}(a).
$\gamma=\alpha\circ\sigma $ is interpreted as the cycle of half-edges visited
when making the tour of the graph, keeping the graph on its left.

\begin{definition}
A planted unicellular map having $n$ edges is a unicellular map
$u=([2n+2],\alpha,\sigma)$, such that $(1,2n+2)$ is a cycle of
$\alpha$. We shall label the face of $u$ as
$$
\gamma=[1_R,1, 2, \ldots, 2n, 2n_R]
$$
and denote $(2n_R)$ as $p$, the plant of $u$.
\end{definition}

Given a planted unicellular map $u$ the face $\gamma$ induces a linear order
$<_{u}$ on $H$ via:
$$
1_R <_{u} \gamma(1_R)<_{u} \gamma^2(1_R)<_{u} \ldots <_{u} \gamma^{2n-1}(1_R)
<_{u} \gamma^{2n}(1_R)<\gamma^{2n+1}(1_R)=2n_R.
$$

\begin{figure}[ht]
\begin{center}
\includegraphics[width=0.8\columnwidth]{unicellular.eps}
\end{center}
\caption{\small A unicellular map with one vertex without (left) and with
plant (right).
The half-edges of a vertex are read counterclockwise, i.e.,
$(1_R,3,2,1,4)$. The vertex $(4_R)$ is the plant.
}\label{F:unicellular}
\end{figure}

Suppose $u$ has $J$ vertices, $v_1, v_2, \ldots, v_J$. Then there is a natural
equivalence relation of half-edges, given by $h \sim \alpha(h)$ and in particular,
$1_R \sim 2n_R$.

For each vertex $v_j$, $j \in J$, let $\min_u(v_j)$ denote the first half-edge
where $\gamma$ arrives at $v_j$. We write $v_j$, reading the
$v_j$-half-edges counter clockwise and starting at $h_j^1=\min(v_j)$:
$$
v_j=(h_j^1, \ldots, h_j^{m_j}).
$$
In particular, the vertex containing the half-edge $1_R$ is denoted by $v_1$.
The order $<_u$ induces thus a linear order $<_v$ on the vertices by setting
$v_i<v_j$ iff $\min_u(v_i) < \min_u(v_j)$.

\begin{definition}
A planted bicellular map $b$ having $n$ edges is a triple $b=(L, \beta, \tau)$,
where $L$ is a set of cardinality $(2n+4)$ such that
$$
L=\{1_R, 1, \ldots, m, m_R, (m+1)_R,  m+1, \ldots,  2n,  2n_R\},  \qquad
1< m < 2n-1.
$$
$\beta$ is a fixed-point free involution containing the cycles $(1_R,m_R)$ and
$((m+1)_R, 2n_R)$. $\beta\circ\tau$ consists of the two cycles
$$
\omega_1=(1_R, 1, 2, \ldots, m, m_R), \quad \text{\rm } \quad
\omega_2=((m+1)_R,  m+1,  m+2, \ldots,  2n,  2n_R).
$$
The elements of $[2n]$ are called half-edges of $b$ and there exists some
half-edge $x \in \omega_1$, such that $\beta(x) \in \omega_2$.
\end{definition}
The cycles $\beta \setminus \{(1_R,m_R) \cup ((m+1)_R, 2n_R)\}$ and $\tau \setminus
\{m_R,(2n_R)\}$ are called the {edges} and {vertices} of $b$. $\omega_1$ and
$\omega_2$ are the two {faces} of $b$. The cycles $p_1=(m_R)$ and $p_2=(2n_R)$ are
the two plants, see Fig.\ref{F:bi-example}.
We furthermore assume the following linear order of the half-edges of the two faces
$\omega_1$ and $\omega_2$:
$$
1_R <_{b} \omega_1(1_R)<_{b} \ldots  \omega_1^{m+1}(1_R)=m_R<_{b} (m+1)_R <_{b}
\omega_2((m+1)_R)<_{b} \ldots  \omega_2^{2n-m+1}((m+1)_R)=2n_R.
$$

\begin{figure}[ht]
\centerline{%
\epsfig{file=bicellular-ex.eps,width=0.8 \textwidth}\hskip15pt }
\caption{\small A bicellular map with $2$ edges, $2$ vertices, and genus $0$ as:
(a) ribbon graph; (b) pair of permutations;.
}\label{F:bi-example}
\end{figure}

As in the case of unicellular maps, a bicellular map, $b=(L, \beta, \tau)$, has an
associated connected graph $G^{'}$, whose edges are given by the cycles of
$\beta \setminus\{(1_R,m_R) \cup ((m+1)_R, 2n_R)\}$, vertices by the cycles of
$\tau \setminus\{(m)_R,(2n_R)\}$. $G'$ can also be fattened to $\mathbb{G}'$
and the notion of $\min_b(v_j)$ as well as the linear order $<_{v, b}$ on the vertices of
the bicellular map are defined  analogously.

\subsection{The RNA connection}

RNA molecules are linear biopolymers consisting of the four nucleotides $A$, $U$, $C$,
and $G$ characterized by a sequence endowed with a unique orientation
($5^{'}$ to $3^{'}$).
Each nucleotide can interact (base pair) with at most one other nucleotide by
means of specific hydrogen bonds. Only the Watson-Crick pairs $GC$
and $AU$ as well as the wobble $GU$ are admissible.
RNA structures
can be presented  as {diagrams}, that is a structure with a labeled graph $G$ over the
set $[N]=\{1, 2, \ldots, N \}$  represented  by drawing the vertices
$1, 2, \ldots, N$ on a horizontal line in the natural order and the arcs
$(i, j)$, where $i < j$, in the upper half-plane, see Fig. ~\ref{F:diagramrepre}.
A backbone is a sequence of consecutive integers contained in $[N]$.
A diagram over $b$ backbones is a diagram together with a partition of $[N]$ into $b$
backbones. The cases $b=1$ and $b=2$ are referred to as RNA structures and RNA
interaction structures.
\begin{figure}[ht]
\begin{center}
\includegraphics[width=0.8\columnwidth]{RNA.eps}
\end{center}
\caption{\small An RNA structure as a planar graph and as a
          diagram}\label{F:diagramrepre}
\end{figure}

RNA structures and interaction structures contain more information that just the
set of contacts between nucleotides. Aside form the $5^{'}$ to $3^{'}$ orientation of
the backbone itself there is in addition a fixed ordering of the backbone relative to
the base pairs.
This orientation implies that the contact graph together with the backbone gives rise
to a natural fatgraph structure as shown in Fig.~\ref{F:bc-one}, $\mathbb{G}$
\cite{Loebl:08,Penner:10}. We obtain again the counterclockwise traveling of the
half-edges around each vertex as for unicellular maps. This fattening works
analogously for RNA diagrams over two backbones \cite{Reidys:top1,fenix2bb},
see Fig.~\ref{F:bc-two}.

Euler's characteristic equation shows that, without affecting the topological type
of the fatgraph $\mathbb{G}$, one can collapse each backbone into a single vertex
with the induced fattening. In other words, there is an equivalent fatgraph
representation of RNA-diagrams having a vertex for each respective backbone.
Moreover, we may enrich this representation by adding an arc that labels the
$5^{'}$ to $3^{'}$ end of the backbone. We refer to this arc as rainbow-arc or just
rainbow.

\begin{figure}[ht]
\begin{center}
\includegraphics[width=0.9\columnwidth]{bc-one.eps}
\end{center}
\caption{\small A diagram with $3$ arcs $(a)$ is fattened $(b)$. $\gamma=\alpha \circ \sigma=
(4,2,6)(1,5,3)$ are its two boundary components (red)(blue).}\label{F:bc-one}
\end{figure}

\begin{figure}[ht]
\begin{center}
\includegraphics[width=0.7\columnwidth]{bc-two.eps}
\end{center}
\caption{\small A diagram with $2$ arcs over two backbones $(a)$ and its fattening $(b)$.
$\omega=\beta \circ \tau=(3, 2)(1, 4)$ are its two
boundary components (red) (blue).}\label{F:bc-two}
\end{figure}

Clearly the $n$ arcs of the diagram determine after fattening $2n$ halfedges and
the fatgraph consists of a pair $(\alpha',\sigma')$ together with the additional
rainbow arc. Then, the mapping
$$
(\sigma',\alpha')\mapsto (\alpha'\circ \sigma',\alpha')
$$
is a bijection mapping vertices into boundary components. Topologically this is the
Poincar\'{e} dual, mapping a fatgraph over one-backbone with rainbow into an planted
unicellular map, see Fig.~\ref{F:dual}.

\begin{figure}[ht]
\begin{center}
\includegraphics[width=1.0\columnwidth]{dual.eps}
\end{center}
\caption{\small A fattened diagram over one backbone, backbone collapse and
the resulting planted, unicellular map.}\label{F:dual}
\end{figure}

The scenario is analogus for RNA-diagrams over two backbones, where we insert two
rainbows over the respective backbones. Formation of the Poincar\'{e} dual, as
illustrated in Fig.~\ref{F:dual2} generates a planted bicellular map.

\begin{figure}[ht]
\begin{center}
\includegraphics[width=1.0\columnwidth]{dual2.eps}
\end{center}
\caption{\small A fattened diagram over two backbones, backbone collapse and
the resulting planted, bicellular map. }\label{F:dual2}
\end{figure}

\section{Two lemmas}

Let $U_{g+1,n+1}$ denote the set of unicellular maps of genus $(g+1)$ with $(n+1)$ edges.
We observe that $U_{g+1,n+1}$ partitions into the following three classes
\begin{equation}\label{E:U}
U_{g+1,n+1}=U^I_{g+1,n+1}  \dot\cup\;
U^{II}_{g+1,n+1} \dot\cup \; U^{III}_{g+1,n+1},
\end{equation}
where
\begin{itemize}
\item $U_{g+1,n+1}^{I}$,
      the set of unicellular maps of genus $(g+1)$ in which $1$ and $\alpha(1)$
      are incident to two different vertices, such that
$$
\exists \; k;\  1 <  k < \alpha(1); \qquad  \alpha(1) < \alpha(k).
$$
\item $U_{g+1,n+1}^{II}$,
      the set of unicellular maps of genus $(g+1)$ in which $1$ and
      $\alpha(1)$ belong to the same vertex,
$$
\exists \; k;\  1 <  k < \alpha(1); \qquad  \alpha(1) < \alpha(k).
$$
\item $U_{g+1,n+1}^{III}$,
      the set of unicellular maps of genus $g$ in which $1$ and $\alpha(1)$
      are incident to two different vertices, such that
$$
\forall \;k;\  1 < k <  \alpha(1); \qquad
                          \alpha(k) < \alpha(1).
$$
\end{itemize}

Our first result shows that $U_{g+1,n+1}^{III}$ can be inductively constructed via
unicellular maps of lower genus.
Let $u=(H, \alpha, \sigma)\in U^{III}_{g+1,n+1}$ with boundary component
$\gamma=(1_R, 1, 2, \ldots, 2n+1, 2n+2, 2(n+1)_R )$. We relabel
$$
\gamma=\left(1_{R_{u_2}},1_{R_{u_1}},1_{u_1},\dots,(2k)_{u_1},
        (2k)_{R_{u_1}},
         1_{u_2},\dots,(2(n-k))_{u_2}, (2(n-k))_{R_{u_2}}\right),
$$
where $1_{R_{u_1}}=1$ and $(2k)_{R_{u_1}}=\alpha(1)$.
\begin{lemma}\label{L:lem1}
There is a bijection
$$
\theta \colon \dot\bigcup_{0\le g_1\le g+1,\; 0\le j\le n}\left(U_{g_1,j}\times  U_{g+1-g_1,n-j}\right)
                        \longrightarrow U^{III}_{g+1,n+1}.
$$
\end{lemma}
\begin{proof}
We begin by specifying the argument for $\theta$:
\begin{itemize}
\item $u_1=(H_1, \alpha_1, \sigma_1)$, with
$$
\gamma_1=(1_{R_{u_1}}, 1_{u_1}, \ldots, (2k)_{u_1}, (2k)_{R_{u_1}})
$$
and the $J_1$ vertices
$v_{1,u_1},\ldots, v_{i,u_1}, \ldots, v_{J_1, u_1}$, where
$$
v_{J_1, u_1}=(2k)_{R_{u_1}},\qquad v_{1, u_1}=(h_{1, u_1}^1, h_{1,u_1}^2, \ldots,
h_{1,u_1}^{m_1}),
$$
for some $m_1>0$, and $h_{1, u_1}^1=1_{R_{u_1}}$ and $h_{1, u_1}^{m_1}=(2k)_{u_1}$.
\item $u_2=(H_2, \alpha_2, \sigma_2)$, with boundary component
$$
\gamma_2=
     (1_{R_{u_2}}, 1_{u_2}, \ldots, (2(n-k))_{u_2}, (2(n-k))_{R_{u_2}})
$$
and the $J_2$ vertices, $v_{1, u_2}
      \ldots v_{i, u_2} \ldots v_{J_2, u_2}$, where
$$
v_{J_2, u_2}=(2(n-k))_{R_{u_2}}, \qquad v_{1,u_2}=
      (h_{1,u_2}^{1}, \ldots, h_{1,u_2}^{m_2}),
$$
for some $m_2>0$ and $h_{1,u_2}^{1}=1_{R_{u_2}}$ and $h_{1, u_2}^{m_2}=(2(n-k))_{u_2}$.
\end{itemize}

For $u_1$ $u_2$, consider the two vertices $v_{J_1, u_1}$ (the plant of $u_1$)
and $v_{1,u_2}$. The key operation consists in ``gluing'' $v_{J_1, u_1}$ into
$v_{1,u_2}$, thereby producing the new vertex
$$
w_{1,u_2}=(h_{1,u_2}^1,(2k)_{R_{u_1}}, h_{1,u_2}^2, \ldots, h_{1, u_2}^{m_2}).
$$
By construction, this produces the unicellular map, $\theta(u_1,u_2)$,
with boundary component
$$
\gamma=\left(1_{R_{u_2}},\underbrace{1_{R_{u_1}},1_{u_1},\dots,(2k)_{u_1},
        (2k)_{R_{u_1}}}_{\gamma_1},
         1_{u_2},\dots,(2(n-k))_{u_2}, (2(n-k))_{R_{u_2}}\right)
$$
and vertex set
$$
\{v_{i,u_1} \mid 1\le i <  J_1\}\dot\cup \{w_{1,u_2}\}\dot\cup
\{v_{i,u_2} \mid 2\le i\le J_2\}.
$$
The combinatorial interpretation of this ``gluing''  is illustrated in
Fig.~\ref{F:proof-glue-slice}.

\begin{figure}[ht]
\begin{center}
\includegraphics[width=0.9 \columnwidth]{lemma1.eps}
\end{center}
\caption{\small The "proof" of Lemma~\ref{L:lem1}.}\label{F:proof-glue-slice}
\end{figure}

We next observe that $\theta(u_1,u_2)$ has genus $g_1+g_2=g+1$. Namely, we have
$2-2g_1=(v_{J_1}-1)-k+1$ and $2-2g_2=(v_{J_2}-1)-(n-k)+1$,
i.e.~$2-2(g_1+g_2) = (v_{J_1}+v_{J_2}-2) - (n+1) + 1$. Since the $u_1$-plant
becomes an edge, $\theta(u_1,u_2)$ satisfies
$$
2-2(g+1) = (v_{J_1}+v_{J_2}-2) - (n+1) +1,
$$
whence $\theta(u_1,u_2)$ has genus $g+1=(g_1+g_2)$.
Consequently we have established the mapping
$$
\theta \colon \dot\bigcup_{0\le g_1\le g+1}\left(U_{g_1,j}\times  U_{g+1-g_1,n-j}\right)
\longrightarrow U^{III}_{g+1,n+1}.
$$

We proceed by showing that $\theta$ is bijective by explicitly specifying its inverse.
To this end let $u=(H, \alpha, \sigma)\in U_{n+1,g+1}^{III}$ with the plant
$p$ and face
$$
\gamma=\left(1_{R_{u_2}},1_{R_{u_1}},1_{u_1},\dots,(2k)_{u_1},
        (2k)_{R_{u_1}},
         1_{u_2},\dots,(2(n-k))_{u_2}, (2(n-k))_{R_{u_2}}\right),
$$
where $1_{R_{u_1}}=1$ and $(2k)_{R_{u_1}}=\alpha(1)$, having $J$ cycles $v_1, v_2,
\ldots, v_J$. By assumption, $\{1_{R_{u_1}},\alpha(1_{R_{u_1}})\}$ is incident to
two different vertices, such that
$$
\forall \;k_{u_1};\  1_{R_{u_1}} < k_{u_1} <  \alpha(1_{R_{u_1}}); \qquad
                          \alpha(k_{u_1}) < \alpha(1_{R_{u_1}}).
$$

We set $v_1=(h_{1}^1, h_{1}^2, h_{1}^3, \ldots, h_{1}^{m})$ with $\min(v_1)=h_1^1=1_{R_{u_2}}$ and
$v_2=(h_{2}^1, h_{2}^2, \ldots, h_{2}^{m^{'}})$ for some $m$ and $m^{'}$ with
$\min(v_2)=1_{R_{u_1}}$, see Fig.~\ref{F:relation1}.

\begin{figure}[ht]
\begin{center}
\includegraphics[width=0.5\columnwidth]{relation1.eps}
\end{center}
\caption{\small Constructing the inverse of $\theta$.}\label{F:relation1}
\end{figure}

Then $\alpha(1_{R_{u_1}})=h_{1}^2=(2k)_{R_{u_1}}$, and $\alpha(1_{R_{u_1}})<_u \alpha(h_{1}^3)$.
Since for any $1_{R_{u_1}} < k_{u_1} <\alpha(1_{R_{u_1}})$ we have
$\alpha(k_{u_1}) < \alpha(1_{R_{u_1}})$, the boundary
component $\gamma$ contains a sequence of half-edges
$$
(1_{R_{u_1}},1_{u_1},\dots,(2k)_{u_1},(2k)_{R_{u_1}}).
$$
Let $H_1=\{1_{R_{u_1}},1_{u_1},2_{u_1},\dots,\alpha(1_{R_{u_1}})\}$ and $H_2$ its complement. Then
$\alpha$ induces by restriction two mappings
$$
\alpha|_{H_1} \colon H_1 \longrightarrow  H_1,\qquad
\alpha|_{H_2} \colon H_2 \longrightarrow  H_2.
$$
In particular $\alpha(1_{R_{u_1}})$ is even.

We now introduce the mapping $\psi$ obtained by ``cutting'' the edge
$\{1_{R_{u_1}},\alpha(1_{R_{u_1}})\}$ in $u$.
To this end we introduce the two new vertices
\begin{eqnarray*}
v_{1, u_2}   & = & (h_{1}^1,  h_{1}^3, \ldots, h_{1}^{m}) \\
v_{J_1, u_1} & = & (h_{1}^2).
\end{eqnarray*}

Now, taking the union of $v_{J_1, u_1}$  with all $u$-vertices that are cycles of
half-edges contained in $H_1=\{1_{R_{u_1}},1_{u_1},2_{u_1},\dots,\alpha(1_{R_{u_1}})\}$
and restricting $\alpha$ to $H_1$, generates a new map $u_1$.
$u_1$ is evidently unicellular since $(1_{R_{u_1}},1_{u_1},2_{u_1},\dots,
\alpha(1_{R_{u_1}}))$ is its unique boundary component.

We next replace $v_1$ by $v_{1, u_2}= (h_{1}^1,  h_{1}^3, \ldots, h_{1}^{m})$.
Then the set of all $u$-vertices different from $v_1$ that are contained in
$H_2=H\setminus H_1$ and $v_{1, u_2}$, together with the restriction of $\alpha$ to
$H_2$ form a new map, $u_2$ . The latter is by construction unicellular and
its boundary component is given by
$$
\gamma_2 = (1_{R_{u_2}},1_{u_2},\dots,(2(n-k))_{u_2},(2(n-k))_{R_{u_2}}).
$$
Considering the Euler characteristics we can conclude $(g+1)= g_1+g_2$.

By construction,
$$
\psi\circ \theta=\text{\rm id}_{
\dot\bigcup_{0\le g_1\le g+1,0\le j\le n}\left(U_{g_1,j}\times  U_{g+1-g_1,n-j}\right)}
$$
and
$$
\theta\circ \psi=\text{\rm id}_{U^{III}_{g+1,n+1}},
$$
whence $\theta$ is a bijection.
\end{proof}

The second result relates bicellular maps and unicellular maps of types $I$
and $II$; the key idea is analogous to that in Lemma~\ref{L:lem1}.

Let $B_{g,n}$ denote the set of bicellular map of genus $g$ with $n$ edges.
We observe that $B_{g,n}$ can be written as
$B_{g,n} = B_{g,n}^I\dot\cup\; B_{g,n}^{II}$, where $B_{g,n}^I$ denotes the set of bicellular
maps of genus $g$ with $n$ edges in which the two plants $p_1$ and
$p_2$ are incident to two different vertices and $B_{g,n}^{II}$
denotes its complement.

Furthermore, for $b\in B_{g,n}^I \dot\cup B_{g,n}^{II}$, we have
\begin{equation}\label{E:b1}
\exists \; x \in \omega_1; \ \beta(x)\in \omega_2.
\end{equation}
Let now $u=(H,\alpha,\sigma)$ be a unicellular map of genus $(g+1)$ having $(n+1)$
edges with boundary component
$$
\gamma=(1_R,1,2,\ldots,2n, (2n+1), (2n+2), (2n+2)_R).
$$
We shall relabel $\gamma$ as
$$
\gamma=\left((m+1)_{R_b},1_{R_b},1_b,\dots, m_b, m_{R_b},
(m+1)_b, \dots, (2n)_b, (2n)_{R_b}  \right).
$$
\begin{lemma}\label{L:lem2}
There exists a bijection
$$
\eta \colon B^{I}_{g, n}\dot\cup \; B^{II}_{g, n}
\longrightarrow U^{I}_{g+1,n+1}\dot\cup \; U^{II}_{g+1,n+1},
$$
and $\eta$ induces by restriction the two bijections
$$
\eta_I \colon B^{I}_{g, n} \longrightarrow U^{I}_{g+1,n+1}\quad\text{\rm and}\quad
\eta_{II} \colon B^{II}_{g, n} \longrightarrow U^{II}_{g+1,n+1}.
$$
\end{lemma}

\begin{figure}[ht]
\centerline{%
\epsfig{file=type-b.eps,width=0.9 \textwidth}\hskip15pt }
\caption{\small Lemma~\ref{L:lem2}: gluing and slicing, the case $B^{I}_{g, n+1}$.
}\label{F:type-b}
\end{figure}

\begin{figure}[ht]
\centerline{%
\epsfig{file=type-c.eps,width=0.8 \textwidth}\hskip15pt }
\caption{\small Lemma~\ref{L:lem2}: gluing and slicing, the case $B^{II}_{g, n+1}$.
}\label{F:type-c}
\end{figure}

\begin{proof}
Let $b=(L,\beta,\tau)$ be a planted bicellular map of genus $g$ having $n$ edges with
plants $p_1$ and $p_2$ and tour $\beta \circ \tau=\omega_1\circ \omega_2$. Let
$$
\omega_1=(1_{R_b}, 1_b, \ldots, m_b, m_{R_b}) \quad\text{\rm and}\quad
\omega_2=((m+1)_{R_b}, (m+1)_b, \ldots, 2n_b, 2n_{R_b})
$$
and $v_{i, b}$, for $1\leq i \leq J$ be the set of its vertices.

Consider the two vertices $(m_{R_b})$ and  $v_{p_2, b}$, where $(m_{R_b})$ is
the plant $p_1$ and $v_{p_2, b}$ denote the cycle containing half-edge
$(m+1)_{R_b}$. I.e.~we have
$$
v_{p_2, b}= (h^1_{p_2, b}, h^2_{p_2, b}, \ldots, h^l_{p_2, b}), \quad
\text{for \quad} l > 0.
$$
where $h^1_{p_2, b}=\min v_{p_2, b}$.
Note that if $h^1_{p_2, b}= \min v_{p_2, b} = (m+1)_{R_b}$, then  $v_{p_2, b}$ is
different from $v_{1,b}=(1_{R_b},\dots)$, whence $b \in B_{g,n}^{I}$ and if
$h^1_{p_2, b}= 1_{R_b}$, then $v_{p_2, b}=v_{1,b}$ and consequently $b \in B_{g,n}^{II}$.

The key operation consists in "gluing " $p_1=(m_{R_b})$ into $v_{p_2, b}$. This generates
the unicellular map, $\eta(b)$, with boundary component
\begin{equation}\label{E:bc-eta(b)}
\gamma=\left((m+1)_{R_b},\underbrace{1_{R_b},1_b,\dots, m_b, m_{R_b}}_{\omega_1}, (m+1)_b,
\dots, (2n)_b, (2n)_{R_b}  \right)
\end{equation}
and the new vertex
$$
w_{p_2, b}=(h_{p_2, b}^1,  m_{R_b}, h_{p_2, b}^2, \ldots,
h^l_{p_2, b}) \quad \text{where} \quad h^1_{p_2, b}= (m+1)_{R_b},
$$
obtained by gluing $(m_{R_b})$ into $v_{p_2, b}$. Accordingly, $\eta(b)$ has vertex set
$$
(\{v_{i,b} \mid 1\leq i \leq J\} \dot\cup  \{w_{p_2, b}\})\setminus\{v_{p_2, b}, (m_{R_b})\}.
$$
Note that in case of $v_{1,b} \neq v_{p_2, b}$, the gluing does not merge these
$b$-vertices.

Suppose now $b \in B^{I}_{g, n}$. By definition there exists some
$x \in \omega_1$ such that $\beta(x)\in \omega_2$.
Thus there exists some $1_{R_b}< x < m_{R_b}$, such that $(m+1)_{R_b}<\beta(x)<2n_{R_b}$.
Gluing produces the unicellular map $\eta(b)$ whose boundary component is
given in eq.~\ref{E:bc-eta(b)}. We observe that the half-edges $1_{R_b}$ and $m_{R_b}$
map exactly to the half-edges $1$ and $\alpha(1)$ in $\eta(b)$ and furthermore,
the half-edges $(m+1)_b$ to $2n_{R_b}$ map to $\eta(b)$-halfedges that are all
greater than $\alpha(1)$. Consequently, there exists some $\eta(b)$ half-edge,
$1< x <\alpha(1)$ such that $\alpha(x) >\alpha(1)$, whence $\eta(b) \in U^{I}_{g+1, n+1}$.

The case of $b \in B^{II}_{g, n}$ is analogous. Then there also exists some $1< x
<\alpha(1)$ such that $\alpha(x) >\alpha(1)$ holds, whence $\eta(b) \in U^{II}_{g+1, n+1}$.
In Fig.~\ref{F:type-b} and Fig.~\ref{F:type-c} we depict what happens if
we glue $(m_{R_b})$ into $v_{p_2, b}$ in these respective cases.

We next inspect that $\eta(b)$ has genus $(g+1)$. Indeed, $b$ satisfies
$2-2g=v_{J}-n+2$, i.e.~$2-2(g+1)=v_{J}-(n+1)+1$. Since the gluing transforms
the $p_1$ plant into an edge, the latter equation shows that $\eta(b)$ has genus $(g+1)$.

We have thus shown that there exists a welldefined mapping
$$
\eta \colon B^{I}_{g, n}\dot\cup \; B^{II}_{g, n}
\longrightarrow U^{I}_{g+1,n+1}\dot\cup \; U^{II}_{g+1,n+1},
$$
that induces by restriction the mappings
$$
\eta_I \colon B^{I}_{g, n} \longrightarrow U^{I}_{g+1,n+1}\quad\text{\rm and}\quad
\eta_{II} \colon B^{II}_{g, n} \longrightarrow U^{II}_{g+1,n+1}.
$$

We next construct the inverse of $\eta$.
To this end, let $u=(H, \alpha, \sigma)$ be a unicellular map of genus $g$ having
$(n+1)$ edges with plant $p$ and face
\begin{equation}\label{E:bc-u}
\gamma=\left( (m+1)_{R_b}, 1_{R_b}, 1_b, \dots, m_b, m_{R_b}, (m+1)_b, \dots, (2n)_b, (2n)_{R_b}
       \right),
\end{equation}
where $1_{R_{b}}=1_u$, $\alpha(1_u)= m_{R_b} $ and $\sigma$ having the
$K$ cycles $v_{1, u}, v_{2, u},\ldots, v_{K, u}$.

\begin{figure}[ht]
\begin{center}
\includegraphics[width=0.7\columnwidth]{relation2.eps}
\end{center}
\caption{\small Constructing the inverse of $\eta$.}\label{F:relation2}
\end{figure}

Suppose first $u \in U_{g+1,n+1}^{I}$, then $\{1_{R_{b}},\alpha(1_{R_{b}})\}$ is
incident to two different vertices. We set
$$
v_1=(h_{1}^1, h_{1}^2, h_{1}^3, \ldots, h_{1}^{j})
$$
where $h_1^1=(m+1)_{R_b}$ and
$$
v_{2}=(h_{2}^1, h_{2}^2, \ldots, h_{2}^l),
$$
where by definition $h_{2}^1=1_{R_{b}}$ and $\alpha(1_{R_{b}})=m_{R_b}$.
Consequently, we have
$$
h_1^2=\sigma(h_1^1)= (\alpha \circ \gamma) (h_1^1)= \alpha (1_{R_b})=m_{R_b}.
$$
Second let $u \in U^{II}_{g+1, n+1}$. Then $\{1_{R_{b}},\alpha(1_{R_{b}})\}$
is incident to
$$
v_1=(h_{1}^1, h_{1}^2, h_{1}^3, \ldots, h_{1}^{j}),
$$
such that $h_1^1=(m+1)_{R_{b}}$ and
$$
h_1^2= (\alpha \circ \gamma)(h_1^1 ) = \alpha(1_{R_b}) = m_{R_b}.
$$
Since $\alpha(1_{R_{b}})$ and $1_{R_{b}}$ are incident to the same vertex and
$h_1^2=\alpha(1_{R_b})$, we can conclude that $1_{R_{b}}$ is a half-edge of $v_1$.
In other words, there exist some half-edge $h_{1}^{a}$ (namely $h_{1}^{a}=1_{R_b}$), for
some $1< a <j$, such that $\alpha(h_{1}^a)=m_{R_{b}}$.

We now introduce the mapping $\varsigma$ obtained by ``cutting'' the edge $\{1_{R_b},
\alpha(1_{R_b})\}$ in $u$. That is, $\varsigma$ splices $v_1$ into the two vertices
\begin{eqnarray*}
v_{p_2, b}   & = & (h_{1}^1,  h_{1}^3, \ldots, h_{1}^{j}) \\
p_1 & = & (h_{1}^2).
\end{eqnarray*}
This process generates the new vertex set
$$
\{v_{i} \mid 1< i \leq K \}\cup \{v_{p_2, b}\} \cup \{ p_1\}.
$$
Since $\alpha(1_{R_{b}})=m_{R_b}$, the sequence of half-edges
$$
\omega_1=(1_{R_b},1_b,2_{b},\dots,\alpha(1_{R_{b}}))
$$
and
$$
\omega_2=\left( (m+1)_{R_b}, (m+1)_b, \dots, (2n)_b, (2n)_{R_b}\right),
$$
represent the two boundary components of the new map. \\
Furthermore, since for $u \in U^{I}_{g+1,n+1}\dot\cup \; U^{II}_{g+1,n+1}$,
there exists some $k$, $1 <  k < \alpha(1)$, such that $\alpha(1) < \alpha(k)$.
Since $u$ has the boundary component given in eq.~(\ref{E:bc-u}), we have
$1=1_{R_b}$ and $\alpha(1)=m_b$. Accordingly, there exists some
$1_{R_{b}} <  k < \alpha(1_{R_{b}})$, such that $\alpha(1_{R_{b}}) < \alpha(k)$.

$\varsigma(u)$ has the two new boundary components  $\omega_1$ and $\omega_2$,
i.e.~there exist some $k \in \omega_1$, such that $\beta(k) \in \omega_2$ and
$\varsigma(u)$ is bicellular map. By construction, if $u \in U^{I}_{g+1,n+1}$,
then $\varsigma(u)$ has its two plants incident to two distinct vertices, whence
$ \varsigma(u)\in B^{I}_{g,n}$. In case of $u \in U^{II}_{g+1,n+1}$ then
$\varsigma(u)$ has its two plants incident to one vertex and $\varsigma(u) \in
B^{II}_{g,n}$.

Euler's characteristic formula implies that $g(u) = g(\varsigma(u))+1$.
Furthermore, by construction,
$$
\varsigma\circ \eta =\text{\rm id}_{B_{g,n}} \quad\text{\rm and} \quad
\eta\circ \varsigma =\text{\rm id}_{{U^{I}_{g+1,n+1}} \dot\cup {U^{II}_{g+1,n+1}}}.
$$
Thus $\eta$ is a bijection that induces by construction the bijections
$\eta_I$ and $\eta_{II}$ and the lemma follows.
\end{proof}

\section{The main result}

\begin{theorem}\label{T:thm1}
Let $U_{g,n}$ and $B_{g,n}$ denote the sets of unicellular and bicellular maps
containing $n$ edges and genus $g$. Then there is a bijection
\begin{equation}
\beta\colon \dot\bigcup_{0\le g_1\le g+1,\; 0\le j\le n}\left(U_{g_1,j}\times U_{g+1-g_1,n-j}\right)
\;\dot \cup \; B_{g,n}  \longrightarrow U_{g+1, n+1}.
\end{equation}
\end{theorem}
\begin{proof}
We have shown in Lemma~\ref{L:lem1} and Lemma~\ref{L:lem2} that there are bijections
\begin{eqnarray*}
\theta \colon \dot\bigcup_{0\le g_1\le g+1,\; 0\le j\le n+1}\left(U_{g_1,j}\times
U_{g+1-g_1,n-j}\right) & \longrightarrow &  U^{III}_{g+1,n+1} \\
\eta \colon B_{g, n+1}
 & \longrightarrow & U^{I}_{g+1,n+1}\dot\cup \; U^{II}_{g+1,n+1}.
\end{eqnarray*}
These two bijections determine
$$
\beta\colon \dot\bigcup_{g_1, j}\left(U_{g_1,j}\times  U_{g+1-g_1,n-j}\right)
\;\dot \cup \; B_{g,n}  \longrightarrow U_{g+1, n+1},
$$
whence the theorem.
\end{proof}

An immediate enumerative corollary of this bijection is the following result:

\begin{corollary}\label{C:2to1}
The generating function of unicellular and bicellular maps,
${\bf C}_{g}(z)$ and ${\bf C}_{g}^{[2]}(z)$ satisfy the following equation
\begin{equation}
\sum_{g_1=0}^{g+1}\,{\bf C}_{g_1}(z){\bf C}_{g+1-g_1}(z)
+{\bf C}_{g}^{[2]}(z)= {\bf C}_{g+1}(z)/z,
\end{equation}
which equivalent to the coefficient equation
\begin{equation}\label{E:recursion}
\sum_{g_1=0}^{g+1}\,\sum_{i \geq 0}^n\,{\sf c}_{g_1}(i) {\sf c}_{g+1-g_1}(n-i)
+ {\sf c}_g^{[2]}(n)={\sf c}_{g+1}(n+1)
\end{equation}
\end{corollary}

Corollary~\ref{C:2to1} can be proved using either (a) the matrix model
\cite{Dyson, Schwinger} and in particular the Schwinger-Dyson equation or
(b) representation theory \cite{Sagan,Zagier}.

redpajama_set_name: RedPajamaArXiv


text:
← Moral Exhortation
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Conspiracy?
Posted on March 14, 2008 by david
I don't think I have ever before posted a criticism of another church or church leader here. But I can't leave Bishop Devine's comments on the gay community without comment. I've tried to find the full text of what he said but it doesn't seem to be posted anywhere as yet – so I am relying on reports on the BBC website.
Many things to say – but I come down to this one.
Once you start seeing people and groups who are different from you as a conspiracy, you are at risk of not being able to see them as people and respond to them with openness, love and charity. Once you start to see people and groups who are different from you as a conspiracy, you are at risk of simply seeing them as a threat and being unable to measure, ponder and respond to what they are, what they think and what they say.
I believe that Jesus saw people and loved them as they were. In particular, he responded to people whom others cast out.
This entry was posted in Blog Entry and tagged conspiracy, Devine, gay. Bookmark the permalink.
20 Responses to Conspiracy?
Rev Ruth says:
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glad you spoke up
Miss Dagurreotype says:
I haven't seen the original remarks or the BBC coverage, so I can't comment on what the other Bishop has said or not said.
That said, I really like that last paragraph of your's +David.
Thanks for that +David – couldn't agree more!
David, Bishop Devine's comments are an appalling piece of revisionism: is he suggesting there were no pink triangles in the Nazi death camps?
His attempt to suggest that those whom he dislikes are engaged in some sort of 'conspiracy' smacks of the sort conversation heard in sectarian circles at the height of the Troubles.
Well said, +David. If +Devine believes gay people are not entitled to consider themselves victims, perhaps he would feel differently if a member of his family had been mugged because of his orientation.
Well said. Now if Bishop Devine had a blog, we could share with him….
The position of the Roman Catholic hierarchy in respect of homosexuality is unequivocal, honest and unambiguous in its homophobia and bigotry. But at least one knows where it stands – where does the SEC stand one often wonders.
The SEC is a church in which many voices contribute to a dialogue on this and other issues. As in other churches, those voices rightly express a range of views so it is very difficult for the SEC to express a view with the same clarity as the Roman Catholic Church. Indeed many of us belong in most of the viewpoints at the same time. That is not a lack of principle – more an honesty about the complexity of the issues. That said, I think that the instincts of the SEC tend mainly – but far from exclusively – to lie in the liberal direction. That comes out of history, out of conviction, out of current practice and from statements such as that made by the College of Bishops in March 2005. Inclusiveness may sound like a good standard around which to rally – but the irony is that to include some is to exclude others.
David, you are quite right all should be welcome and none excluded. But there is a major difference in the way that the Church treats those who oppose the inclusion of lesbians and gay men as full and equal members of the Church and the way that it treats lesbians and gay men. The difference is that the Church actively discriminates against lesbians and gay men, and publicly supports such discrimination. How would you feel in +Gene Robinson's position or Jeffery John's? Listen to us when we say that the Church does not include us!
This is difficult. I think you may have missed my point that inclusiveness which doesn't have any boundaries at all simply ends up as a kind of exclusion.
Secondly, you can accuse the church of actively discriminating … but you are choosing not to recognise that the church is deeply divided on this issue. Can you recognise integrity in those who take a view different from your own and claim the authority of scripture in support of it?
David, thank you for engaging in with me in this discussion. I don't think I was suggesting inclusiveness without boundaries, but the points I was trying to make above were that those who support direct discrimination against lesbians and gay men in the Church do so by placing conditions on those such as yourself in positions of authority: "if you treat lesbians and gay men equally we will: leave your church, not pay our quota, not accept your authority" – take your pick of their threats. Whereas lesbians and gay Christians are saying "please treat us equally and we will continue to respect the integrity of those who do not think we should be treated equally – whilst disagreeing with them". No threats – but then we don't have the power to make threats. Secondly they discriminate against us not because of what we believe, but because of what we are, because of what God made us.
Do I understand you to say that if a view is held with integrity it is unchallengeable? Hitler had very strong beliefs held undoubtedly with integrity. Racists have strongly held beliefs supported by the authority of scripture as they interpret it. Supporters of slavery had very strong beliefs supported by the authority of scripture as they understood it. Integrity is no criterion of truth of beliefs. It is the other side who draw the lines to exclude lesbians and gay men. You will probably know the quote: "those who draw a line of exclusion are often surprised to see Jesus on the other side of it."
Thanks for your comment, Phil. You've made me think .. not very successfully, I fear.
I'm not sure that it is fair to suggest that those in leadership like myself act as we do only because we are responding to threat. I hope you think better of us than that!
No I don't think views held with integrity are unchallengeable. Just that I haven't heard you challenge them. Those views are not unchallengeable – the 'scriptural authority' arguments do not trump all others. But neither, in my view, does the discrimination argument – not matter how keenly and justifiably it is felt by people like you.
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I am sorry,David, but I do think that some of those in positions of episcopal authority have responded to threats, perhaps with justification when some dioceses are so fragile, or when the whole Communion is threatened with schism.
That aside, you accuse me of not challenging the arguments of those who actively discriminate against me. I am surprised that you thing that the victimised minority should be made to justify why they should not be victimised, although that is of course the classic position of the oppressor. The problem of course is that, apart from quoting the very few direct references to homosexuality in Scripture, those who support discrimination rarely articulate why they choose to accept a particular interpretation of scripture on this issue and not on other issues.
Perhaps you should start, David, by articulating why you, and the College of Bishops, support continued discrimination against lesbians and gay men within the Church, and yet freely ignore with little demur the Dominical injunction against heterosexual divorce.
Phil. I am sorry but we have passed from a careful and thoughtful discussion which had considerable integrity .. into something which is in danger of recycling. I think we should end it there.
David, you disappoint me. Perhaps you could explain to me how my last comment lacked integrity…and why you have suddenly become so sensitive. I still consider the parallel I made to be very apposite. Perhaps we were getting too close to the truth for your comfort.
Phil, I think +David is right. This conversation was escalating in ways that are not productive.
That is not to say that there isn't a conversation there that is much needed, but once it reaches a point that neither person feels able to respond to what the other is saying, it is time to step back and seek another opportunity to engage more constructively.
Maybe we can address some of the issues at the listening day? (so, on the one hand, Phil's concern that church sometimes denies the full humanity of gay people, and David's concern that no one argument (either a particular view of scripture, or a particular way of expressing issues of justice and inclusion) trump all others without an attempt at mutual understanding.)
Thanks to both Phil and Kimberly. Ok – I'm going to try and do a more positive recycling of this discussion back at the top of the blog, as it were.


text:
Q: Why does OSX fail on parsing the extras_require section of my setup.py file? In my setup.py file, I have the following:
setup(
    ...
    extras_require={
        ':python_version<="2.7"': [
            'pydot>1.0',
            ],
        ':python_version>="3.5"': [
            'pydot3k',
            ],
    ...
)

This works fine on Linux (on Travis CI) and Windows (on AppVeyor) but fails on OSX (also on Travis) with the error message:

error in mypackage setup command: Invalid environment marker: python_version<="2.7"

What is the reason for this failure, and how can I avoid it?

A: The problem was solved by adding - pip install --upgrade setuptools to my .travis.yml file.


The test occurred at 8.56pm EDT (12.56am GMT April 4) and lasted less than a minute. Before its stainless steel Starship could take to the skies, however, its test version needs to make a few hops first. The video featured above was captured by Spadre.com, a website for the South Padre Surf Company on South Padre Island across from SpaceX's facility.
Starhopper marked the first time it ignited its engine, which will be most possibly followed by short hop flights in upcoming months.
United States manufacturer of advanced rockets and spacecrafts, SpaceX has test-fired the onboard engine Raptor of its next-generation spacecraft the Starship's hopper version for the first time. The site posted another look at the hop from outside the road blocks around the facility. A suborbital hop would require all three engines. The Starship is SpaceX's very big passenger spacecraft that the private American aerospace manufacturer is building to send people to Mars and the Moon.
SpaceX initially built the prototype with a nose cone, extending its height to 128ft (39m), however the cone was blown off by powerful winds. Musk later said that the nosecone was unnecessary for continued testing of the prototype.
Starship is the spacecraft SpaceX wants to use for a variety of purposes, from colonising Mars to conduct internal trips around the Earth.
Health Insurance Portability and Accountability Act of 1996) to create specialized skills for healthcare-related services. Amazon will provide its HIPAA-eligible environment to voice app developers to create healthcare skills for Alexa.
It's not clear which committees received letters from Cohen, or what they plan to do in response. The letter was sent to a veritable who's-who of Trump opponents , including Reps.
The duo will take part in the practice round at Augusta National on Friday but did not make the cut to Saturday's final round. Even though she was not the most accurate with her driver, she felt she held an advantage over the field at Augusta National.


text:
Mathematics, 03.08.2020 19:01, nonjabulomabaso8371
The center of a circle is at the origin on a coordinate grid. The vertex of a parabola that opens upward is at (0.9). If the circle intersects the parabola at the parabola's vertex, which statement must be true?
answered: lilxjayyy
The circle has radius = 9 units, and its equation is:
The parabola has equation of the form:
with being a positive number
Given the characteristics of the two figures (circle and parabola) as described,
since the parabola intersects the circle at a single point (it vertex) then the radius of the circle centered at the origin must be 9. that makes the equation of the circle to have the following standard form;
Since there is no other info regarding the parabola, the most one can say about the equation of the parabola, is that in vertex form, the parabola's equation must be of the form:
with being a positive number.
jwjwkwkwkkkdjebd b jdjejdndj he jenej
hunhgunyt7 in u uuuhiuteu
Mathematics, 21.06.2019 14:50, amcdaniel1
Which function has the same domain as y=2x
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Which term best describes the association between variables a and b
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27 is what percent of 108? 27 is % of 108
Mathematics, 21.06.2019 17:10, payshencec21
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) what is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive? (b) what is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) what proportion of bags contains more than 1225 chocolate chips? (d) what is the percentile rank of a bag that contains 1425 chocolate chips?
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Born in Edinburgh. He was the youngest son of William Mossman Senior (1793-1851), sculptor and marble cutter who was born in West Linton, Peebleshire and died in Glasgow. William Mossman Junior trained in the family firm and in the London studios of Marochetti, William Behnes and John Thomas, for whom he produced carving work on the Houses of Parliament. For a short period (1869-71) he taught at Glasgow School of Art. He died in Glasgow and was interred in Sighthill Cemetery.


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PennDOT on Monday announced that traffic deaths in Pennsylvania reached a record low since record keeping began in 1928.
There were 1,188 fatalities on Pennsylvania roads last year, 12 less than 2015.
While the number of highway deaths dropped in many types of crashes, there were significant decreases noted in run-off-the-road, hit-fixed-object, and drinking-driver fatalities. Fatalities in run-off-the-road crashes dropped from 580 in 2015 to 518. Hit-fixed-object fatalities decreased from 459 in 2015 to 401 last year. Deaths attributed to drinking-driver-related crashes declined to 263, down from 306 in 2015.
Fatalities increased in some types of crashes. There were 279 fatalities that occurred at intersections, up from 251 in 2015. Also, pedestrian deaths resulting from crashes increased to 172 up from 153 in 2015.