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Q: Python ImportError I have installed pyqrcode => PyQRCode on Ubuntu 12.04 x86_64.
by running make && sudo make install.
At then end of the successful make/make install, the last line is:
Installed
/usr/local/lib/python2.7/dist-packages/qrcode-0.2.1-py2.7-linux-x86_64.egg
But when I try to import qrcode I get this error:
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "qrcode/__init__.py", line 6, in <module>
from qrcode import _qrcode
ImportError: cannot import name _qrcode
A: sudo pip install qrcode worked just fine for me.
My guess is that after compiling, you started Python up from the source directory, and so it looked in the local qrcode directory -- i.e. pyqrcode-0.2.1/qrcode instead of in the usual Python path. Try running it from another directory. To be specific:
~/sys/pyqrcode-0.2.1$ python
Python 2.7.3 (default, Apr 20 2012, 22:44:07)
[GCC 4.6.3] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> import qrcode
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "qrcode/__init__.py", line 6, in <module>
from qrcode import _qrcode
ImportError: cannot import name _qrcode
>>>
~/sys/pyqrcode-0.2.1$ cd ~
~$ python
Python 2.7.3 (default, Apr 20 2012, 22:44:07)
[GCC 4.6.3] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> import qrcode
>>> qrcode
<module 'qrcode' from '/usr/local/lib/python2.7/dist-packages/qrcode/__init__.pyc'>
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,870
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Haematopota teixeirai är en tvåvingeart som beskrevs av Travassos Dias 1974. Haematopota teixeirai ingår i släktet Haematopota och familjen bromsar.
Artens utbredningsområde är Angola. Inga underarter finns listade i Catalogue of Life.
Källor
Bromsar
teixeirai
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 2,754
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Die Hochschulstadt Mittweida ist eine Stadt im Landkreis Mittelsachsen im Bundesland Sachsen. Sie ist Sitz der Verwaltungsgemeinschaft Mittweida.
Geographie
Geographie und Geologie
Die Stadt Mittweida liegt größtenteils westlich des Zschopautals im Mittelsächsischen Bergland. Die Altstadt entstand am Unterlauf des Altmittweidaer Baches (Gottesaubach) unweit der Mündung in die Zschopau. Die meisten Ortsteile liegen beiderseits des Flusses im oder nahe dem Zschopautal. Prägend ist insbesondere die Lage an der Talsperre Kriebstein im Norden der Stadt. Einzig die Ortsteile Frankenau und Thalheim liegen an Frankenauer Bach und Erlbach, die zur Zwickauer Mulde hin entwässern.
In Hinsicht auf die geologischen Verhältnisse Sachsens befindet sich Mittweida im Zentrum des sächsischen Granulitgebirges. Die Umgebung der Stadt ist von dem im Granulit eingelagerten und hier weitgehend texturlosen rötlichen Granit des Typs Mittweida geprägt. Aufschlüsse befinden sich beispielsweise im Zschopautal. Im Bereich des Hochschulcampus an der Leisniger Straße finden sich als geologisches Naturdenkmal die "Teufelssteine", übermannsgroße Cordieritgneisblöcke.
Nachbargemeinden
Angrenzende Gemeinden sind Kriebstein, Rossau, Lichtenau, Altmittweida, Königshain-Wiederau, Seelitz und Erlau, alle im Landkreis Mittelsachsen gelegen.
Stadtgliederung
Geschichte
Der Ursprung von Mittweida liegt in dem langgestreckten, nach 1160 gegründeten Waldhufendorf am Altmittweidaer Bach, welches damals die Fluren des späteren Altmittweida und Mittweida umfasste. Der Name bezeichnet eine Siedlung mitten in einer (Wald-)Weide. Mittweida wurde erstmals 1209 erwähnt und 1286 als oppidum (Stadt) bezeichnet. Im Jahr 1350 wird das nun selbstständige Dorf Altmittweida südlich von Mittweida als antiqua Miteweide erwähnt. Im Mittelalter war die Stadt von einer Stadtmauer mit vier Stadttoren umgeben. Neben der Kirche befand sich ein Adelssitz, der sich am Standort des heutigen Museums "Alte Pfarrhäuser" befand. Dieser war im 14. Jahrhundert im Besitz derer von Haugwitz. Nach 1360 bildete sich eine Ratsverfassung heraus. Das bedeutet, dass die Stadt von einem Ratskollegium mit einem Bürgermeister an der Spitze regiert wurde. Im Jahr 1398 erwarb Mittweida die niedere Gerichtsbarkeit (Erbgerichte). Der Erwerb der oberen Gerichtsbarkeit erfolgte im Jahr 1423.
Um 1550 zählte Mittweida im Amt Rochlitz zu den mittelgroßen Städten Sachsens. Bereits im Mittelalter waren Tuchmacherei und Leinenweberei die wichtigsten Erwerbsquellen. Durch die Gründung einer Spinnerei im Jahre 1816 begann der Aufstieg Mittweidas zu einer der bedeutendsten Textilindustriestädte in Sachsen. Mit der Eröffnung des Bahnhofs Mittweida an der Bahnstrecke Riesa–Chemnitz erfolgte am 1. September 1852 die Anbindung ans Schienennetz. Zwischen 1906 und 1997 zweigte von diesem die Industriebahn Mittweida–Dreiwerden/Ringethal ab.
Bezüglich der politischen Verwaltung gehörte Mittweida bis 1835 zum kursächsischen bzw. königlich-sächsischen Amt Rochlitz im Leipziger Kreis. Ab 1836 unterstand Mittweida mit den umliegenden Orten dem Amt Frankenberg-Sachsenburg der Kreisdirektion Zwickau. Im Jahr 1856 unterstand Mittweida wieder der Amtshauptmannschaft Rochlitz innerhalb der Kreisdirektion Leipzig und wurde Sitz des Gerichtsamts Mittweida, dessen Bezirk im Jahr 1875 der Amtshauptmannschaft Rochlitz zugeteilt wurde. Im Jahr 1825 erfolgte die Einweihung des Schützenhauses und 1837 die Einweihung der ersten Bürgerschule (heutige Pestalozzischule). 1851 wurde im Rathaus eine städtische Sparkasse eingerichtet. 1858 wurde das Theaterhaus eröffnet, welches 1912 in ein Lichtspielhaus, die heutige Filmbühne, umgebaut wurde. 1863 gründete sich die Freiwillige Feuerwehr und das Krankenhaus Mittweida wurde 1865 eröffnet. Am 7. Mai 1867 erfolgte die Gründung der privaten Bildungseinrichtung als Technikum Mittweida, aus der die heutige Hochschule Mittweida hervorging. Die Schwanenteichanlagen wurden 1876–77 angelegt. 1896–97 wurde die Wasserversorgung in Mittweida mit dem Wasserwerk an der Lehmgrube und dem heute noch genutzten Wasserturm errichtet. 1906 erfolgte die Inbetriebnahme des neuen Wasserwerkes am Dreiwerdener Weg. Die 1895 gegründete und 1902 in Mittweidaer Metallwarenfabrik umbenannte Firma entwickelte sich bis zum Ende des Zweiten Weltkrieges in Deutschland zum führenden Hersteller von Medaillen, Orden und Ehrenzeichen. Nach dem Krieg ging die Firma in dem volkseigenen Betrieb VEB Wälzlagerkäfigwerk Mittweida auf. 1900 wurde die neue Bürgerschule (heutige Fichte-Oberschule) eröffnet. Mit der Eröffnung der Linie Mittweida-Burgstädt-Limbach entstand 1906 die erste Buslinie in Sachsen. Am Schwanenteich wurde 1908 die neue Realschule (heutiges Gymnasium) eingeweiht. 1909 nimmt das städtische Elektrizitätswerk an der Zschopau mit einer Dampfmaschine seinen Betrieb auf, welches 1922/23 um die Wasserkraftnutzung und 1928 um ein Pumpspeicherbecken erweitert wird. Nach Inkrafttreten einer neuen Gemeindeordnung für den Freistaat Sachsen von 1923 tritt Mittweida aus dem Bezirksverband Rochlitz aus und wird ab 1. April 1924 kreisfreie Stadt, eine der kleinsten in Deutschland. 1927 wird das neue Handelsschulgebäude und 1928 das Finanzamt fertiggestellt. Aufgrund der wachsenden Erwerbslosigkeit wird 1927 ein Arbeitsamt eingerichtet. In den Jahren 1929/1930 erfolgte der Bau der Talsperre Kriebstein nördlich der Stadt. Bereits in der zweiten Hälfte des 19. Jahrhunderts setzte ein Tourismus im Tal der Zschopau mit der Erschließung der "Mittweidaer Schweiz" ein. Das Stadtbad an der Zschopau wird 1932 eröffnet. 1934 entsteht der Flugplatz Mittweida an der Diebstraße.
Nach der Machtübernahme der NSDAP 1933 und der Reichstagsbrandverordnung beginnt auch in Mittweida die Verfolgung Andersdenkender. Am 3. März 1933 werden elf Bürger in Schutzhaft genommen und zum Teil anschließend in das KZ Sachsenburg und KZ Colditz verbracht. Alle 24 1932/33 in Mittweida lebenden Juden werden aus der Stadt vertrieben oder deportiert. Nach dem 17. Mai 1933 gehören dem Stadtrat Mittweida nur noch Nationalsozialisten an. Der Neubau der Auenblicksiedlung begann im Jahr 1938. Während des Zweiten Weltkrieges wurden in mehreren Betrieben der Stadt ausländische Arbeiter beschäftigt und in verschiedenen Lagern untergebracht. Weiterhin verrichteten etwa 500 weibliche KZ-Häftlinge eines Außenlagers des KZ Flossenbürg vom 9. Oktober 1944 bis 13. April 1945 Zwangsarbeit in einem Betrieb der Berliner C. Lorenz AG und wurden unter den Häftlingsnummern 55240 bis 55739 registriert. Mindestens zwei von ihnen, Maria Lanella und Wlaska Fedasiuk, starben unter den unmenschlichen Lagerbedingungen. Am 15. April 1945 besetzten US-amerikanische Truppen die Stadt Mittweida zogen sich aber am 25. April 1945 wieder nach Rochlitz zurück. Am 7. Mai 1945 trafen sich in Mittweida die alliierten Streitkräfte der US-Army und der Roten Armee, woran eine Tafel am nördlichen Widerlager der einstigen Eisenbahnüberführung Hainichener Straße erinnert. Die eigentliche Besetzung Mittweidas durch die Rote Armee erfolgte am 14. Mai 1945. Mittweida blieb im Zweiten Weltkrieg von größeren Schäden verschont. Am 5. März 1945 fielen einige Bomben im Bereich Chemnitzer Straße/Dreiwerdener Weg. Dabei wurden vier Menschen getötet.
Mittweida gehörte nach der Besetzung 1945 bis zur Gründung der DDR 1949 zum Land Sachsen in der Sowjetischen Besatzungszone (SBZ). 1947 erfolgte die Eingliederung der Stadt Mittweida in den Landkreis Rochlitz und die Stadt verlor damit ihre Kreisfreiheit. Durch die zweite Kreisreform in der DDR im Jahr 1952 wurde Mittweida dem Kreis Hainichen im Bezirk Chemnitz (1953 in Bezirk Karl-Marx-Stadt umbenannt) zugeteilt, der 1990 als sächsischer Landkreis Hainichen fortgeführt wurde. 1952 erfolgte die Übergabe der ersten Neubauwohnungen auf der Goethestraße. Das ehemalige Gewerkschaftshaus "Rosengarten" wurde im Juni 1953 als Pionierhaus übergeben. 1953 kauft die Sozialistischen Einheitspartei Deutschlands (SED) das ehemalige Gelände des 1913 eröffneten Erziehungsheimes an der Chemnitzer Straße und nutzt die Gebäude als Bezirksparteischule für den Bezirk Karl-Marx-Stadt. Heute werden Teile der Anlagen durch das Landratsamt Mittelsachsen genutzt. Das Krankenhaus Mittweida wird 1957 Kreiskrankenhaus, heute die Landkreis Mittweida Krankenhaus gGmbH. 1959 wurde der Abbau von Braunkohle an der Torfgrube, welcher mit größeren Unterbrechungen ab 1840 erfolgte, endgültig eingestellt. Das Neubaugebiet im Bereich Lauenhainer Straße/Lutherstraße wurde ab 1963 erschlossen und mit großen Wohnblöcken bebaut. Die endgültige Fertigstellung des neuen Stadtgebietes erfolgte 1982. 1977 erfolgte die Einweihung der neuen Polytechnischen Oberschule, heute die Bernhard-Schmidt-Schule. 1978 wurde das neue Freibad an der Leipziger Straße eröffnet. 1982 ging der neue Busbahnhof an der Zimmerstraße in Betrieb. Die ersten freien Kommunalwahlen nach dem politischen Umbruch in der DDR fanden am 6. Mai 1990 statt.
Mit der Wiedervereinigung Deutschlands und der Wiedergründung der Länder im Gebiet der ehemaligen DDR zum 3. Oktober 1990 gehört Mittweida zum Freistaat Sachsen. Durch die Vereinigung der Landkreise Hainichen und Rochlitz entstand im Jahr 1994 der Landkreis Mittweida, wodurch Mittweida bis zu dessen Eingliederung in den Landkreis Mittelsachsen im Jahr 2008 Kreisstadt war. Mit dem Verlust des Kreissitzes wurde Mittweida im Jahr 2008 der Titel Große Kreisstadt verliehen. Das Verbot der in Mittweida tätigen rechtsextremen freien Kameradschaft Sturm 34 und der Prozess gegen einige ihrer Mitglieder sorgten 2007 und 2008 für ein überregionales Medienecho. Die Gruppe war 2006 in Mittweida gegründet worden und hatte in der Region mehrere brutale Überfälle verübt. Im Jahr 2009 richtete Mittweida Sachsens größtes Volksfest, den 18. Tag der Sachsen, aus. Den Titel Hochschulstadt erhielt Mittweida im September 2015 verliehen. Mittweida ist Teil der Kulturregion zur Kulturhauptstadt Europa 2025.
Gedenkstätten
Friedensbrunnen auf dem Marktplatz zu Erinnerung an den Ersten Weltkrieg
Mahnmal in den Parkanlagen "Schwanenteich" für die Opfer von Krieg und Gewaltherrschaft
Gedenkstein an der Feldstraße zum Gedenken an das Außenlager des KZ Flossenbürg
Im Stadtgebiet sind insgesamt 20 Stolpersteine zur Erinnerung an die Opfer des Nationalsozialismus verlegt.
Eingemeindungen und Verwaltungsgeschichte
Die heutigen Ortsteile der Stadt Mittweida gehörten über lange Zeit verschiedenen Herrschaften an. In der folgenden Tabelle wird diese Ämterzugehörigkeit dargestellt.
Nach der Auflösung der Ämter kamen die Orte unter die Verwaltung des Gerichtsamts Mittweida. 1875 wurden die Orte der Verwaltung der Amtshauptmannschaft Rochlitz unterstellt. Ab 1952 gehörten alle heutigen Mittweidaer Ortsteile zum Kreis Hainichen, mit Ausnahme von Thalheim (1926 aus Ober- und Niederthalheim gebildet) und Frankenau, welche zum Kreis Rochlitz gehörten. 1994 wurde aus dem Kreis Hainichen und dem Kreis Rochlitz der neue Landkreis Mittweida mit der Kreisstadt Mittweida gebildet. Seit 2008 gehört die Stadt Mittweida mit ihren Ortsteilen zum neu gebildeten Landkreis Mittelsachsen.
Einwohnerentwicklung
Entwicklung der Einwohnerzahl (ab 1960 31. Dezember , in Klammern Kernstadt ohne Eingemeindungen):
Des Weiteren sind mehr als 6.600 Studenten an der Fachhochschule eingeschrieben, die jedoch nur zum Teil als Einwohner gemeldet sind. Mittweida gilt als die Stadt mit den meisten Studierenden pro Einwohner in Deutschland. Für 2020 werden 459 Studierende pro 1000 Einwohner ermittelt.
Politik
Stadtrat
Der Stadtrat von Mittweida als Hauptorgan der Stadt nach der Süddeutschen Ratsverfassung setzt sich aus 22 Stadträten, die in der letzten Kommunalwahl am 26. Mai 2019 neu gewählt wurden, und dem Bürgermeister als Vorsitzendem zusammen. Folgende Tabelle zeigt das Wahlergebnis 2019 und die Sitzverteilung nach vergangenen Wahlen.
Für die Bildung einer Fraktion im Stadtrat sind mindestens zwei Mitglieder notwendig.
Übersicht über die Fraktionen im Stadtrat von 2019 bis 2024:
CDU: 10 Mitglieder, Fraktionsvorsitzende Katrin Schütte
AfD: 5 Mitglieder, Fraktionsvorsitzende Anke Seidel
Die Linke: 4 Mitglieder, Fraktionsvorsitzender Torsten Bachmann
Bürgermeister
Der direkt gewählte Bürgermeister ist Vorsitzender des Stadtrates, Leiter der Verwaltung und vertritt die Stadt nach außen. Der Bürgermeister ist hauptamtlicher Beamter auf Zeit. Seine Amtszeit beträgt sieben Jahre. Seit 2008 trägt er die Bezeichnung Oberbürgermeister. Die letzte Wahl des Oberbürgermeisters fand am 12. Juni 2022 statt. Dabei wurde Ralf Schreiber mit 96,7 % für eine zweite Amtszeit wiedergewählt.
Übersicht über die Bürgermeister seit 1833:
Beigeordnete
Der hauptamtliche Beigeordnete ist erster Stellvertreter des Bürgermeisters und vertritt den Bürgermeister in seinem Geschäftsbereich. Der Geschäftsbereich umfasst Schul-/Kultur-/Sport- und Sozialangelegenheiten, Angelegenheiten des Eigenbetriebs sowie allgemeine Verwaltungsangelegenheiten. Der Beigeordnete wird vom Stadtrat gewählt. Übersicht über die Beigeordneten seit 2002:
2002–2015 Ralf Schreiber
seit 2015 Holger Müller
Stellvertretender Bürgermeister
Neben dem Beigeordneten bestellt der Stadtrat einen Stellvertreter des Bürgermeisters. Der ehrenamtliche Stellvertreter wird nur in Fällen der Verhinderung des Bürgermeisters und der Verhinderung des Beigeordneten tätig. Übersicht über die Stellvertretenden Bürgermeister seit 1994:
1994–2001 Matthias Damm (CDU)
2001–2019 Jürgen Kitzing (CDU)
seit 2019 Siegfried Schnee (CDU)
Kreistag Mittelsachsen
Mittweida ist im Kreistag des Landkreises Mittelsachsen seit 2019 mit drei Mitgliedern aus dem Wahlkreis 6 (Mittweida, Altmittweida, Rossau) vertreten. Die Vertreter sind der Oberbürgermeister Ralf Schreiber (CDU), Christian Schwerin (Bündnis 90/Die Grünen) und Torsten Bachmann (DIE LINKE.).
Landtag Sachsen
Mittweida ist seit 2014 ein Teil des Wahlkreises Mittelsachsen 3. Die Wahlkreisabgeordnete ist Iris Firmenich (CDU).
Wappen
Blasonierung: "In Gold ein schwarzer Löwe mit roter Zunge und Bewehrung." Dieser Meißner Löwe, erstmals im Jahre 1423 nachweisbar, geht auf die Markgrafen von Meißen zurück.
Städtepartnerschaften
Mittweida pflegt Partnerschaften mit Bornheim (Nordrhein-Westfalen), Viersen (Nordrhein-Westfalen), Česká Lípa (Tschechien) und Gabrowo (Bulgarien).
Daneben bestehen freundschaftliche Kontakte zu folgenden Orten:
Thalheim-Gemeinden (T(h)alheimer Treffen), Slawutytsch (Ukraine), Weiz (Österreich), Peterborough (England), Lambersart (Frankreich), Bornem (Belgien), Bardejov (Slowakei), Molde (Norwegen), Calau (Deutschland).
Sehenswürdigkeiten
Museen
Auf dem Kirchberg befindet sich das Heimatmuseum "Alte Pfarrhäuser". Teil des Museums ist das "Johannes-Schilling-Haus", welches Plastiken, Skizzen und Erfindungen des Bildhauers und Schöpfer des Niederwalddenkmals, Johannes Schilling zeigt. Im Heimatmuseum befindet sich weiterhin die Loest-Ausstellung, welche persönliche Gegenstände des in Mittweida geborenen Schriftstellers Erich Loest zeigt. Am 23. November 2022 wurde in der Kirchstraße 16 das Haus "Altes Erbgericht" als neuer Ort für Sonderausstellungen und Museumspädagogik eröffnet.
Seit 1992 gibt es das Raumfahrt-Museum Mittweida von Tasillo Römisch.
Bauwerke
Auf dem Marktplatz steht eine rekonstruierte kursächsische Postmeilensäule mit einem vierfachen Doppelwappen, wie es nur noch in Leisnig und Zwickau vorkommt, und der Marktbrunnen mit Jugendstil-Friedensengel.
Die evangelisch-lutherische Stadtkirche Unser lieben Frauen auf dem Kirchberg stammt aus dem 15. Jahrhundert. Ihr Turm ist 60,25 m hoch. Die Alte Schule dient jetzt als Kirchgemeindehaus. Die Pestalozzi-Schule ist ein weiterer Nachbar der Stadtkirche, auf einem Stein ist das Jahr 1876 zu lesen.
In der ca. 800 Jahre alten Dorfkirche von Ringethal befindet sich die kleinste Silbermann-Orgel Sachsens. Das Pfarrhaus wird als Freizeitheim genutzt. Das Schloss wurde 1743/44 errichtet und wurde zuletzt bis 1996 als Schule genutzt. Das Raubschloss Ringethal ist eine künstliche Burgruine aus dem Jahr 1804, die auf einem Felsensporn über der Zschopau, an Stelle einer ehemaligen mittelalterlichen Burg errichtet wurde. Die Zschopaubrücke bei Ringethal ist eine 1999 errichtete Spannbetonbrücke. Auf ihr steht die Porphyrskulptur des Rittergutsbesitzers, der 1863 an dieser Stelle eine Steinbogenbrücke erbauen ließ. Neben der Mühle Ringethal steht eine Wasserkraftanlage (zwei Turbinen mit einer Leistung von zusammen 370 kW).
Vom Pumpspeicherwerk Mittweida bei Neudörfchen führt ein Rundwanderweg durch den Bürgerwald zum Staubecken, dem ehemaligen Oberbecken des Kraftwerkes.Die ehemalige Baumwollspinnerei auf der anderen Seite der Zschopau erinnert an die industrielle Vergangenheit der Stadt. Flussabwärts kommt man zur Hängebrücke, die den Ortsteil Kockisch mit der ehem. Liebenhainer Mühle verbindet.
Im Nachbardorf Zschöppichen befindet sich Schloss Neusorge aus dem 18. Jahrhundert. Elsa Brändström, der Engel von Sibirien, betrieb in dem Schloss von 1924 bis 1931 ein Kinderheim für Kinder ehemaliger deutscher Kriegsgefangener.
Parkanlagen / Waldgebiete
Schwanenteichanlage, Technikumanlage, Goethehain und Stadtpark in Mittweida
Baum- und Gesteinspark in Ringethal
Bürgerwald bei Neudörfchen, Schweizerwald
Galerie
Wirtschaft und Infrastruktur
Verkehr
Durch Mittweida verläuft die Hauptbahn Riesa–Chemnitz. Die abzweigende Nebenbahn nach Dreiwerden/Ringethal ist stillgelegt. Im Bahnhof Mittweida halten stündlich die Regionalbahnen Elsterwerda–Chemnitz der Mitteldeutschen Regiobahn, die ohne Halt nach Chemnitz Hauptbahnhof durchfahren. Zusätzlich verkehrt stündlich die Linie C14 der City-Bahn Chemnitz, welche bis Chemnitz Hauptbahnhof alle Unterwegshalte bedient. Dort geht sie auf das Straßenbahnnetz über (siehe Chemnitzer Modell) und fährt durch das Zentrum und den Campus der Technischen Universität bis Thalheim/Erzgeb.
Der städtische Busverkehr mit vier Linien wird von der REGIOBUS Mittelsachsen GmbH durchgeführt.
Mittweida liegt neun bis elf Kilometer von der Bundesautobahn 4 entfernt. Anschlussstellen sind Hainichen, Chemnitz Ost oder Frankenberg.
Ansässige Unternehmen
Cotesa GmbH – Hersteller von Faserverbundbauteilen für die Luftfahrt und Automobilbau
Jeld-Wen – Türen- und Fensterproduktion
Kreissparkasse Mittelsachsen
REGIOBUS Mittelsachsen GmbH
Tenowo, eine Tochter der Hoftex Group
Volksbank Mittweida eG
Medien
Freie Presse, Lokalausgabe Mittweida
99drei Radio Mittweida (produziert von der HS Mittweida)
medienMITTWEIDA (produziert von der HS Mittweida)
Mittelsachsen TV (ehemals Stadtfernsehen Mittweida)
Mittweidaer Blick
Regelmäßige Veranstaltungen
Altstadtfest Mittweida
KlangLichtZauber Mittweida
Inselteichfest in Ringethal
Medienforum Mittweida
Campusfestival Mittweida
beta Mittweida
Gesundheitswesen
Seit 1996 gehört das Krankenhaus Mittweida zur Landkreis Mittweida Krankenhaus gGmbH, einem Krankenhaus der Regelversorgung mit 195 Betten. Alleiniger Eigentümer der Gesellschaft ist der Landkreis Mittelsachsen. Seit 2010 ist die Landkreis Mittweida Krankenhaus gGmbH Lehrkrankenhaus der Technischen Universität Dresden. Das Krankenhaus in Mittweida bildet zusammen mit dem Klinikum Chemnitz das zertifizierte Brustzentrum Chemnitz.
In Mittweida gibt es zwei Medizinische Versorgungszentren, ein Neurologisch-Psychiatrisches Versorgungszentrum mit niedergelassenen Ärzten als Trägern sowie das Medizinische Versorgungszentrum der Landkreis Mittweida Krankenhaus gGmbH mit 20 Ärzten in Mittweida, Flöha, Rochlitz und weiteren Außenstellen.
Bildung
Hochschule Mittweida – University of Applied Sciences
Berufliches Schulzentrum Döbeln-Mittweida, Schulteil Mittweida mit Fachoberschule
Städtisches Gymnasium Mittweida
Johann-Gottlieb-Fichte-Schule (Oberschule)
Pestalozzi-Schule (Grundschule)
Bernhard-Schmidt-Schule (Grundschule)
Verein zur Förderung der Beruflichen Bildung an den beruflichen Schulen Mittweida e. V.
Berufsschule und berufsbildende Förderschule (staatlich anerkannte Ersatzschule)
Musikschule Mittelsachsen, Standort Mittweida
Volkshochschule Mittelsachsen, Standort Mittweida
Stadtbibliothek Mittweida
Öffentliche Einrichtungen
Landratsamt Mittelsachsen – Außenstelle Mittweida
Filmbühne Mittweida (Kino)
Finanzamt Mittweida
Polizeirevier Mittweida
Freizeitzentrum Mittweida
drop in – Jugendtreff
Freibad Mittweida mit Beachsocceranlage, Beachvolleyballplatz, Streetballanlage und Skateranlage
Stadion "Am Schwanenteich"
Stadtarchiv Mittweida
Jugendherberge Falkenhain an der Talsperre Kriebstein
Jobcenter Mittelsachsen
Tafel Mittweida des Vereins Netz-Werk e.V.
Persönlichkeiten
Literatur
ohne Autor: Stadt Mittweida – Informationsbroschüre mit mehrfarbigem Stadtplan. NovoPrint-Verlag, Fellbach 1996.
ohne Autor: Mittweida – Kreis- und Hochschulstadt. Verlag Geiger, Horb am Neckar 2003, ISBN 3-89570-874-7.
Benny Dressel, Heiko Weber: Mittweida. Reihe Zeitsprünge, Verlag Sutton, Erfurt 2005, ISBN 3-89702-846-8.
C. A. Funk: Zur Geschichte der Stadt Mittweida und ihrer Umgebung. Mittweida 1898.
Christian Hermann: Mittweidisches Denckmahl Das ist/ Beschreibung der Stadt Mittweida In Meissen nach dero Rahmen und Ursprung. Chemnitz 1698 (Digitalisat).
Frank Schleußing (Hrsg.): Mittweida – Ein Blick zurück: 1890–1930. Verlag Geiger, Horb am Neckar 1991, ISBN 3-89264-552-3.
Stadtverwaltung Mittweida (Hrsg.): Zur Geschichte der Stadt Mittweida. Mittweida 2009, ISBN 978-3-937386-21-8.
Eine Überlieferung des Stadtgerichts Mittweida für den Zeitraum 1515–1853 zu Gerichts- und Lokalverwaltung, Straf-, Zivil- und Freiwilliger Gerichtsbarkeit, Kirchen-, Schul- und Lehnsangelegenheiten sowie Gerichtsprotokollen befindet sich im Sächsischen Staatsarchiv, Staatsarchiv Leipzig, Bestand 20613 Stadt Mittweida (Stadtgericht).
Weblinks
Atlas Mittelsachsen
Einzelnachweise
Große Kreisstadt in Sachsen
Ehemalige kreisfreie Stadt in Sachsen
Ort im Landkreis Mittelsachsen
Ehemalige Kreisstadt in Sachsen
Ersterwähnung 1209
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The professors at TX State are not only extraordinary teachers, they are extraordinary people with a passion for creating meaningful music and fostering a supportive community of hard-working students. The collegiality and mutual respect in the department - faculty and students alike - make it one of the most open and inspiring I have ever experienced.
I am deeply and sincerely impressed by the commitment, creative vision, and extraordinary ethic of rehearsal and performance maintained by the Texas State University Music Department.
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DEATH ON EARTH
Also available in the Bloomsbury Sigma series:
Sex on Earth by Jules Howard
p53 – The Gene that Cracked the Cancer Code by Sue Armstrong
Atoms Under the Floorboards by Chris Woodford
Spirals in Time by Helen Scales
Chilled by Tom Jackson
A is for Arsenic by Kathryn Harkup
Breaking the Chains of Gravity by Amy Shira Teitel
Suspicious Minds by Rob Brotherton
Herding Hemingway's Cats by Kat Arney
Electronic Dreams by Tom Lean
Sorting the Beef from the Bull by Richard Evershed and Nicola Temple
For Lettie and Esme
DEATH ON EARTH
ADVENTURES IN EVOLUTION AND MORTALITY
Jules Howard
Contents
Introduction
PART 1: THIS IS A DEAD FROG
1Life and Death in the Universe
2Senescence and What Waits for the Lucky Few
3Fear and Loathing in Birchwood
4Free Radicals and the Secrets Within
5This is a Dead Frog
PART 2: THE EXPERIMENTAL PIG PHASE
6The Circus under the Tent
7Sex and Death: The Contract Killer
8Coffee with the Widow-maker
9Suicide, Snowy Owls and the Executioner Inside
10 This is Not a Sheep
11 The Grotto Salamander and the Guano
12 The Horrid Ground-weaver
13 Dark Matters
PART 3: JOURNEY TO THE END OF THE SHITATITE
14 Bring out your Dead Ants
15 Mourning has Broken
16 Who Wants to Live Forever?
17 No, This is a Dead Frog
Epilogue: The Meaning of the Loa Loa
Acknowledgements
Index
INTRODUCTION
Neck ligaments. A cross-section of a trachea. An eyeball. In front of me is a white shelf filled with cylinders of varying sizes that contain a host of pickled parts. Swollen human hands, bleached spines and knee joints, some sort of sawn-off skull cap, brains in jars. This is not my usual day out. Some body parts are in cylinders, some in Perspex rectangular cubes; all are resting within some unknown embalming fluid that seems to bleach things in just the right nightmarish sort of way.
I walk to the next set of shelves. I stop. I sip my coffee and calmly put it back on its saucer. I realise I am shaking – the teaspoon on my plate starts knocking rhythmically against the coffee cup like I am a tiny alarm clock. I am ringing, and people start to look my way. I try to gather myself. The irony is that I am genuinely a bit alarmed by all of this. The room is about the size of two tennis courts – there is a good space in the middle, overlooked by two tiers of metal balconies that loom above us. The glass ceiling covers the hundred or so attendees to the event in a sepia glaze, as though we're in a bizarre lucid dream from which we can't escape. For a century or more this enormous room was an operating theatre; thousands of medical procedures and post-mortems have been undertaken here. And it really was a theatre: the light from above, the balconies in tiers that would once have been home to hundreds of students, eager to perfect their science and their future trade. This is a strange place to be.
I am attending something called Death Salon, an American movement holding its first event in the UK. It's taking place here, at Barts Pathology Museum, just around the corner from the financial sector of the City of London. According to the blurb on the welcome pack in my hand, Death Salon is an event 'that brings together intellectuals and independent thinkers engaged in the exploration of our shared mortality by sharing knowledge and art'. It had sounded really interesting, partly because I have always wanted to be an 'independent thinker'. I am pleased to report that I have achieved this aim admirably. Here I am independently thinking about things like tracheae, intestines and tiny testicles bobbing up and down in a preservative solution. I am here for three whole days, I realise. Three whole days.
I look around at the other attendees – there certainly is quite a mix of punters here, old and young. It is the first conference that I have attended for years where the gender bias is very female-heavy. This is a welcome change. I'm struck by how many young people there are, too – not just studious sorts, either. The style here isn't exactly preppie. It's something... it's something I've never seen before. Many of the attendees have a kind of... mortician chic. The men have so much style – geek glasses are in, as are leather satchels and skinny jeans. Some wear pinstripe suits and trainers. I notice one man wearing bowling shoes and managing, inexplicably, to pull it off. And the women, too. There's an air of burlesque about some: flowing curls, long clinging black dresses and black nail varnish. Many of them have fringes. Not for the first time in my life, I stick out like a sore thumb. I continue drinking my coffee, my little coffee spoon trilling like my beating heart.
My literary agent Jane was one of the people who had told me about Death Salon, and she's actually attending. I see her in the front row talking to another of her clients, a kind-looking lady who is here to give a presentation about her experiences of grief after the death of her mother. Just as the presentations are beginning I stumble down a row of chairs, heading to one of only a handful of empty ones at the far end. I catch Jane's eye from the back of the room. She gives me a thumbs-up and looks at me gleefully. She mouths the words 'ISN'T THIS WONDERFUL?' from across the room. I give her a slightly saggy thumbs-up back. I find a seat and gather myself. I'm here to write a book, Goddammit. I'm here to begin my journey.
Everyone says not to start work on a book until it's been commissioned. Only now do I realise why. Like Alice, I'm falling into a rabbit hole from which I'm struggling to escape – if the book isn't commissioned, this is a journey I will end up making unpaid and my family will, for a few years, hate me for it. Jane and I are still waiting for the green light but, what the hell, I'm starting anyway. Death, life and evolution seems like too interesting a topic to ignore any longer, and hopefully the book will be commissioned so everything is going to be ok, I think. Jim, my editor at Bloomsbury, has recently been giving me little supportive messages, but he's deeply worried that the whole death idea won't pan out. His normal friendly manner has become edgy of late; I can tell that he's worried that his colleagues won't go for it. One of Jim's concerns is that he doesn't think a book will sell if it has 'Death' in the title. But he has other worries... One of which is that he doesn't think a book will sell if it has the word 'death' on most pages. Jim has warned me that people don't like to think about death. And that people don't like to buy books about people that think about death. Jim doesn't like it when people don't buy books, which is why he's advised throughout NOT TO START THIS BOOK until it's green-lit. He's anxious. That's ok, I tell him – this book will be different. I won't be writing a clichéd book about how DEATH IS NATURAL and that THERE'S NOTHING WE CAN DO ABOUT IT because people always say stuff like this and it's all got a little patronising.
In human terms – well, for me – I hate thinking about death. I hate it. I haven't written a will. I haven't got a retirement plan. I have no health insurance. Plus, I have just discovered that I also have a surprise suppressed squeamishness about human body parts in flasks of alcohol. But I love nature. I love evolution and the myriad ways in which natural selection makes and creates things more incredible even than humans can imagine. I love the diversity. The variety. The varieties. I love the colour, the roles, the niches, the behaviours, the true stories, the magic, the wonder. Surely death plugs into these wonders? I had said to Jim. Surely death is the universal thing that awaits all of these things? I had pitched the idea a few weeks ago to him. 'Jim,' I said. 'Jim, there is a story to tell about the impact that death has had on evolution, and on the niche-filled planet on which we find ourselves in the twenty-first century. I think there are miraculous acts that death imbibes into nature; acts that power it; acts that power its diversity. I want to chart this. I want to chart death's impact on nature and evolution and look at it in the context of our own mortality.'
I have unfinished business with death, after all. In my previous book Sex on Earth I had brought together a collection of ideas about sex in the animal kingdom. In the book I felt the world (and particularly some parts of the media) needed to appreciate a wider view of sex in nature, unburdened by human interests about whose penis is larger and which animal can orgasm for the longest. I stood up for pandas as creatures as fully evolved for sex as anything else. I took on penis-obsessed news editors, extolling the virtues of studying female reproductive anatomy alongside studies of male reproduction. I shouted up for mites and slugs and spiders and, I hope, allowed readers to re-evaluate their opinions about creatures many would rather step on than sexually appraise. I stood up for diversity. I stood up for sex. But with every story there was a nagging problem that never left me. It was simple: animals evolve to become masters of sex but... why don't they evolve to avoid death, or to live longer lives? This question was in my mind the whole time. Think about this for a second, if you will. Why must everything die? Why can't multicellular life evolve ways to replenish cells for longer, thereby allowing them greater opportunities for sex? Surely genes for such modifications would flourish, so why is it not something we see more of? Why is death so pervasive in nature? Why aren't there more immortals, whose genes could theoretically flood gene pools with sexual survivors? Questions, questions, questions. We live on a planet where life shares one primary drive: to make more of itself. After four billion years of evolution the world has filled up with animals that survive and reproduce ably. But death? Why would that persist? Why hasn't natural selection fixed death and filled the world up with immortals? It's not like death happens in one or two genera, or families on the periphery. Everything dies, I had thought. Somehow, it powers life and everything we see around us. Why? Why is the world like this? Questions, questions, questions.
I'm not totally new to the science of death, by any means. As I mentioned, I have had a deep interest in animal sex for many years, and there are a host of examples where the life principles of sex and death rub comfortably up against one another in such stories. Famous examples include those salmon species that migrate as juveniles from rivers into the ocean, and then return to rivers to spawn, where they then die. The female spiders (and possibly mantids) that devour their male partners during sex. The female mites that have evolved not to lay eggs externally, but instead allow their offspring to hatch from eggs within their body and then eat the female from the inside out. The female toads that often drown after being grabbed and wrestled by seven or eight eager males during breeding bouts. The mayfly species that live as larvae in freshwaters for a year or two yet live for only a matter of days as paid-up flying sexual adults. You'll know all of these stories, I'm sure. But these are just for starters. We all are the product of liaisons between creatures that got sex and death in the correct order. Untold trillions didn't, and untold trillions don't.
But there are other phenomena related to death that appear throughout the zoological literature which are simply a bit odd and make no immediate sense: tortoises that can survive for centuries; caterpillars that, according to some definitions of life and death, die – that become cellular goo within a chrysalis then manage, inexplicably, to reorganise into an animal we call a butterfly. And then there is the bigger picture: why is it that 99 per cent of species are already extinct? How does death contribute to life? What does it give us? And what causes cells to age? Can ageing be stopped? Can we live forever? And, would we really want to? This is where the scientific rubs up uncomfortably with the mortal mind and the modern experience of being an animal in a modern human world. I wondered if I could cross that line and try to understand why, on the whole, we humans are a little bit strange about death.
Researching the sex lives of animals for my previous book, I felt enormously appreciative of the scientists whom I interviewed. Each was making great strides in our understanding of the evolution of sex, and many were trying to explain exactly why it is so prevalent across the tree of life. They wanted to talk about it. They loved it. But death is equally prevalent across nature and I haven't ever heard anyone, really openly and clearly, explain much about it in zoological terms. It seemed to me to be a part of the biological sciences still kept in the dark – frowned upon, maybe. Ignored. Spooky, perhaps. I am drawn to topics like these, it seems... So it seemed like an interesting one for a zoological writer to explore. We all know death, but less about the science. Nearly all of us will know the shock of death, the awfulness, the suffering and the deep life-changing impact that the death of close family and friends (and pets, of course) has on us. But do we talk about the zoological side of death? No, we don't. So let's give it a go, I said to Jim. Let's do it. And so my journey had started. I was beginning, even if I was still waiting on the book being commissioned.
Over the three days of Death Salon, something that started out as a slightly ghoulish and macabre experience developed into something totally different – it actually became a place of life. I listened to what living people are legally allowed to do with the dead bodies of their relatives. I heard about the history of CPR. I learned exactly how organ donation works, and how bodies can be donated to science. I saw graffiti-decorated coffins. I saw my first CT scan of an autopsy. I sat there, agog, as someone took off all of her clothes and we were asked to draw her holding a golden skull, her memento mori. I saw a virtual human autopsy. At one point a man stood up to tell us about a miniature railway he'd built with a toy-town cemetery, and how each tiny plastic ghost had been carefully teased off a job lot of novelty Halloween earrings he'd bought at Claire's Accessories. I saw people smiling and laughing and laughing – yes laughing, having fun – in the face of death. But over those three days at the conference I was always an observer; a bit of a loner who was sat quietly in the corner. Death Salon opened up my eyes to human death, yet no one, in the three days of the conference, mentioned biology. My world – of science, of life, of evolution – was barely mentioned. I found this rather strange. Death, as we know it, is a biological condition; it's that other whirring cog in natural selection's clock.
What follows in this book is my attempt at unravelling the many complicated threads surrounding biological death. The word 'journey' in popular science is pretty much the most overused descriptive going, and so I can only apologise about this. But this book really did become a journey – a journey, I hope, as life-affirming as it gets. It's a journey without taboos or (I hope) clichés. A journey guided by science at (almost) all times. A journey through the minds of the scientists that study it. And a study of the great merry(ish) journey that all life must take, from birth, to sex, to death and back in some other earthly form that is probably, at some point, going to be worm-like. And, predictably, it was a journey that almost killed me... Thank goodness (and Jim) it got commissioned. Thank goodness (and Jim) I got back from where it took me. Whether anyone chooses to read it is, of course, another story. But thanks, at least, for getting this far.
PART ONE
THIS IS A DEAD FROG
CHAPTER ONE
Life and Death in the Universe
What is life? thought Erwin Schrödinger. The answer was simple: it was something to fill his time. A subject to write a book about. So he did. Though many know him best for cats in boxes (or not), it's with life that his ideas first united and then fragmented domains of science. He published What is Life? in 1944. Based on a series of public lectures at Trinity College in Dublin the year before, Schrödinger's book really was a rare gem: a fairly readable account of the how and why and what of life on Earth. Four hundred people attended Schrödinger's original lectures on the subject, even though they came with a warning that 'the subject-matter was a difficult one... even though the physicist's most dreaded weapon, mathematical deduction, would hardly be utilized.' What is Life? really was breathtaking, though. Not only did it attempt to reconcile the world of biology with the realms of chemistry and physics, it was also an early contender for first speculating on the existence of an 'aperiodic crystal' that could carry genetic information through the generations in complex configurations of molecules (read: DNA). Among the many things covered in the book, Schrödinger identified life as perhaps the biggest paradox in the universe. Life just shouldn't occur, he realised. Yet it does. He attempted to explain how and why.
Think about the universe. It's chaotic. Mightily chaotic. Suns burn brightly – their energy radiating off into more loosely organised forms of energy (you and I call this, mostly, heat). Mountains erode. Continents split. Complex chemistry, produced under pressure or from lightning that befell planets like ours, falls apart with time. Radioactive particles smash and split. Chaos reigns. It really does. In the language of physicists, states drift naturally toward entropy – disorder, chaos, mixed-upness. Allow me to offer an analogy to explain this. The classic analogy of states drifting toward disorder involves libraries. Picture yours now... now imagine there were no librarians there. Imagine people coming and going from the library, taking books and bringing them back, every week or so. Some of the books will be put back in the wrong place or will be left haphazardly on tables or on top of the shelves. Give it a few weeks and you'd barely notice a big change, of course. Go back in a year, however, and you will probably start to have trouble finding what you want. There will be gaps in the shelves; some of the books will be stacked horizontally or left on the floor; the astrology books will be muddled up with the astronomy books; the spines of the romantic fiction will be worn; the Malcolm Gladwell books will have all their pages folded. You get the idea. Come back in two years and things will be even worse. Things will be messy. Five years, worse still. Ten years later? Total chaos. Come back in 200 years and the library will barely be standing. Come back in 500 and there will be nothing of the books but dust. Come back in a million years and the strata will contain nothing but the mud upon which the building stands. And that's if you're lucky. And that's chaos, ladies and gentlemen. Without someone (or something) being paid to maintain order, things drift into mixed-upness – that's how nearly all things work (it's also a good argument for why we should pay librarians much more than we currently do).
This understanding of states moving endlessly toward disorder (in a closed system) was first offered up by Newton: it was, famously, his Second Law of Thermodynamics. It explains everything we see out there. Except for in jellyfish. Or hamsters, for that matter. Or worms. Or walruses. Or wallflowers. Or winkles or white-tailed sea-eagles or, well, you get the idea. For in life, something strange happens. Cells don't leak and slop into one another after 10 minutes or 10 hours. Bodies don't just erode and fall apart and become functionless everywhere one looks. They are complex. And they remain so throughout life. Their patterns and make-up are the antithesis of disorder. Bodies are honed machines, and they work. They remain, throughout life, ordered. Unrotten. And this is rather strange when you think about it, because so few other things in the universe manage this.
'How does the living organism avoid decay?' This is the question Schrödinger attempted to tackle in What is Life? And the answer, he realised, is that it pays. To temporarily avoid death throughout their life, animals must pay. They must invest energy. In this respect, their cells and cell processes are like career librarians, holding back the chaos. Pushing against inevitability. Eventually the cost will become too high and they cease to be, of course – they die. Disorder whirls out from their organised bodies, much of which is recycled back into order within the life of others on Earth. But there is more even to life than this, Schrödinger realised. Far from it being a freakish unexpected one-off in the universe and flying in the face of Newton's Second Law, physicists like Schrödinger realised that there was a certain inevitability to life. For there is a universal quirk of animals which many of us take for granted: we take energy from the sun (albeit by eating plants that have taken energy from the sun or animals that have eaten plants) and we produce heat. We make a highly disordered form of energy (heat) from an ordered one (light). We are part of the chaos, in other words – as well as paying the universe for the thrill of living, we also help maintain its universal tendency toward chaos. We fit right in. As absurd as it sounds, you and I are nothing more than heat pumps (though some pump more heat than others).
So, life plays by the rules. Life emerges because... well, because it can. It fits into the universe's way of behaving; it emerges because it fulfils a natural universal tendency toward an overall increase in entropy, essentially. Schrödinger's explanation was a good one. And like all good explanations, it has stuck around precisely because it has proved so hard an argument to better. One assumes that all life across the universe will obey this fundamental law; that life can be defined by its energetics. So that's it. All finished. We've defined life. That's that done then, right? Well, no. For there are other definitions of life, and there are other definitions of death. And it is with these definitions that my journey begins.
A grandfather stands with his five-year-old grandson in the busy canteen of one of the world's finest natural history museums. He faces a dilemma. The queue for the cafe is very long and it'll take him ages to get served. He can't stand around with a grumpy five-year-old for 15 minutes, he thinks. But he needs a coffee, desperately. What should he do? He thinks. He considers his options. And then he makes a decision. He does something no one else does in modern times: he looks around the tables in the busy canteen for people who look friendly and caring and who definitely won't take his young grandchild off in a van if he asks to leave him with them. He scans the room. Who looks trustworthy? There are older people scattered in little groups talking to one another. Not them, he thinks. There is a small group of students. Not them either. A lady on her own reading a book? No, not her. And then he sees them. There are two people animatedly discussing something, talking very deeply and looking very intensely at one another while one of them scribbles things in a notebook. One – a woman – is friendly and talking passionately. The other – a man – is furrowing his brow and keeps looking up at the ceiling while scratching his chin pretentiously. Those people are us.
Perfect, the older gentleman thinks, for reasons I now struggle to comprehend. He walks over to us with his young grandchild in tow. 'Excuse me,' he says with slight reticence. 'Excuse me, but would you take my grandchild while I go and queue?' He rethinks the wording of his sentence. 'Will you... look after my grandchild while I get a coffee?' 'Oh...' we say. 'I'll be right over there,' he says. He points at the coffee bar. We have been chosen. We are trustworthy. It's quite a nice feeling. We smile a little nervously. 'Erm, yes... sure, ok...' says Louisa, smiling politely. 'I'm only round the corner,' says the gentleman. 'Just in the queue for a coffee... you know, it'll be fine.' He makes it sound like the most normal thing in the world to leave his grandchild with strangers. In some ways it is. Or it was. It's an honour, really; an honour to be chosen for looking like the people least likely to steal this child. 'Erm, yes, of course, yes,' I say. 'Yes, that's fine. Sure.' The boy sits down, looking a bit uncomfortable at having to sit with two complete strangers. 'Sit straight Harry,' says the grandfather. 'Come on, sit right.' He jiggles Harry about in his chair. The boy shuffles and sits up straight facing us both, still with his eyes locked firmly down at the floor. He looks up at us sheepishly and places his little hands on the table. The grandfather trundles off to join the back of a very long queue. We both look at the young lad. 'Hi,' I say. He says nothing. 'Hi,' says Louisa. He says nothing again. He doesn't know it yet, but he has just stumbled into one of the weirdest conversations he may ever know. It is about life and death in the universe, and whether this little child might be part of the first generation to discover it on a planet other than Earth.
I was sitting with Dr Louisa Preston, a freelance astrobiologist, TED Talk supremo and, well, expert in lots of impressive things to do with space. I had been introduced to her at a book launch a few months before and she'd been one of those interesting people I thought I'd quite like to keep in touch with for zoological purposes such as this. 'What do you do?' I had asked her at the party. 'Well, I search for life on other planets,' she had replied. Conversations like this do not happen to me very often – I felt like I had won some sort of competition. 'What planets?' I'd said meekly. 'Mainly Mars,' she had said, casually. She told me that she was most famous for using infrared light to excite leftover organic molecules in rocks, unveiling the tell-tale signs of once-living organisms. She hoped one day to use this technique on the rocks of Mars, to see whether such biomarkers really are or are not present on planets other than ours. She'd be a perfect place to start the book, I'd thought when we met. Perfect in a number of ways. Louisa had spent her career considering all forms of life so she'd be good to talk to about definitions of life and death. Might we expect death on other planets that harbour life? I wondered. Her perspective on life and death would be so universal (in the truest sense); a world away from all the Victorian body parts in jars that I had been forced to politely inspect whilst drinking my coffee at Death Salon a few weeks earlier. I emailed her and asked if we might meet in the Natural History Museum, London. This was, surely, the perfect place for a journey like this to begin. In its collection are 80 million specimens, and all of them are dead.
We had sat laughing and talking animatedly before Harry, the little boy, had arrived. Louisa had been very keen that before tackling the big question of 'WHAT IS DEATH IN THE UNIVERSE?' we first discussed what, exactly, the definition of life in the universe should be. To Louisa, this was (and is) the vital bit. The vital question. It was like a palate cleanser before the main course. In fact, just before we were interrupted by the little boy and his grandfather, Louisa had been trying to question me on whether I believed that a mule was alive or not. 'Of course a mule is alive,' I had said bluntly. 'Of course,' she had agreed, smiling wryly. 'But a mule is missing one of the central definitions of life because it is unable to replicate.' 'Oh,' I murmured. 'People say a definition of life is reproduction,' she continued. 'Well, a mule is sterile. It's not alive.' I gave her a withering and disgruntled 'OH DON'T GIVE ME ALL THAT PHILOSOPHICAL CRAP' face, which she read masterfully. 'C'mon,' she laughed. 'It's true. One of the classic criteria of life is that it can reproduce, regulate itself, metabolise, grow, move, excrete. Mules can do all of the things on this list, but they can't reproduce. So does that make them not alive?'
I gathered myself in the moments Harry, the little boy, was thrust momentarily into our care. He really was going to find this conversation more than a little strange, I realised. Only a minute after his arrival, Louisa had me justifying a long-held belief of mine that my refrigerator is definitely not alive. 'Why not?' she said, clearly enjoying herself at this point. 'Fridges can regulate their temperature. Thermostats respond to changes in the environment in much the same way that a living thing would. By some definitions there are those that would say that your fridge is alive.' I managed to pull a face that this time said to Louisa 'My fridge is definitely not alive.' Louisa looked puzzled at me, unable to read my face. She continued in this vein for a while, naming other examples of things that some would justify as alive, but that, like fridges, are definitely not alive. 'And fire!' she laughed. 'Fire's a great one!' Louisa particularly liked talking about fire, it seemed. I caught the little boy giving us another fleeting glance. Louisa didn't notice. His grandfather had barely moved in the long queue. 'In every sense fire should be a living organism,' she said. 'It grows, it eats, it reproduces, it spreads, it regulates itself – lots of its products are maintained within the flame, almost like how cells work. So what makes it not alive?' I waited a few moments, silent, waiting for her to continue. I realised then that she was not being rhetorical. 'Why is fire not alive?' I heard myself say. There was some silence at this point as Louisa waited for an answer. I drew breath, thinking about it a little more... 'A FIRE IS... A FIRE IS JUST NOT ALIVE!' I offered up grandly. 'The problem is,' she said. 'when you start down the line of asking about what life is, it's easy to get drawn into the very dangerous realm of talking about a life force, or a consciousness, or a vital spirit.' She shook her head. 'That's a mistake we don't want to make.'
Though it was admirably tackled by Schrödinger, he certainly wasn't the first to ask the (im)mortal question 'WHAT IS LIFE?' In fact it is arguably one of the oldest and most philosophically well-trodden questions in science. Among the first to discuss it were materialists such as Empedocles (c. 490–430 bc). They argued that life was caused by an exact and appropriate mixture of 'elements' called earth, water, air and fire (the 'roots of all'). Not long after the materialists came Democritus (c. 460–370 bc), who was among the first to promote the idea of a soul – a kind of manifestation of fiery atoms that interact in a certain way to produce what our minds define as 'you' and 'I' – our 'spirit'. Such ideas were chewed upon further by the French philosopher René Descartes (1596–1650), who held that animals (including humans) worked more like machines, assemblages of parts that together produced an emergent property: something you or I might describe as a life and a soul. Descartes's ideas and his more rational approach to the definition of life challenged the fuzzy notion of a soul, or, at least, encouraged discussion of what the notion of 'soul' is and how it might interact with the physical body.
In the centuries that followed other definitions were put forward, including the more recent (and even more rational) scientific definitions to which Louisa had alluded and that many of us (including me) remember from biology school: 'MRS GREN'. Many textbooks say that life is defined by Movement, Respiration, Sensitivity, Growth, Reproduction, Excretion and Nutrition (MRS GREN). And under the rules of MRS GREN Louisa is right: mules might not be considered truly alive and fridges and fire might be (and please, please, no one ask about viruses – things, it seems, get very messy indeed when people start asking whether viruses are alive). Overall, when one considers life, one thing is clear. MRS GREN definitions of life are clearly a bit lousy.
'What definition do you work to, then?' I had asked Louisa. Her response was simple. It's the same as NASA's. 'Life is something that undergoes Darwinian evolution,' she said. So that's what she is searching for: evidence of evolution on planets and moons other than our own. 'How exactly does one search for evolution?' I asked, slightly confused. 'I know. I know,' she laughed. 'For my kind of work, it's a pretty ridiculous definition. I mean, we're hardly going to sit there staring at something that might be alive, waiting for it to evolve. How can we test that? We can't really. But it's the best and perhaps most all-encompassing definition we have. So that's what we work with.' And so it stuck. In a weird sort of way, though, this definition of life being Darwinian in nature pairs nicely with Schrödinger's when it comes to life and death. Both life and death are inherently linked to one another, after all. Life is a flamboyant and whacky conveyor belt that ultimately moves things endlessly from a state of borrowed order toward a state of chaos. And life breeds more life through Darwinian evolution. 'So if that's your definition of life,' I said to Louisa, 'then what is your definition of death? How do you define death in the universe?' The question hung in the air. There was a brief pause. Harry squirmed. Louisa thought about it some more. 'I don't know,' she admitted. 'I guess I don't really think about it that often.' This surprised me, a little.
So how can we consider death, exactly? What is death? How might we define it? By ploughing into this question we find ourselves, frustratingly, back in that same rats' nest of definitions. Most agree that death describes the state that exists when life... runs out. But I find this too woolly a definition. For instance, for the Victorians a stopped heart meant you were dead. It was as simple as that. But now it doesn't. Because of defibrillators, a stopped heart is only a symptom that can be potentially fixed, provided too much time hasn't elapsed. Death hasn't occurred. Another example is with drowning: there was a time when a drowned man or woman was considered definitely and most certainly dead, but then, once CPR was hit upon, they weren't. In both of these cases death was a term used when describing something lacking any remaining potential for life. But this isn't fixed or written in stone.
Nowadays we consider death as being a fixed, easy-to-label state, but actually our clinical definitions aren't that much further on from those of the Victorians. Even today occasional medical cases show that our definitions of death may be wrong and need changing. In the late twentieth century those in a vegetative state were still considered by many to be 'brain dead' – yet those in such a condition can continue to grow and develop, and even give birth. So the term 'brain dead' is clearly not accurate any more, and not appropriate either. Things we consider 'dead' now may not always be so, which is a fascinating thought. But allow me to consider this thought experiment with non-human animals. Consider those creatures that undergo cryptobiosis, able to survive for long periods as lifeless shells or hardy eggs. Consider, for instance, the tiny sexless metazoans that live in birdbaths (among other places), the bdelloid rotifers, which expel all water from their bodies and form a hard stone-like ball when their puddles dry up. Think about them. They can last for seven years in this dehydrated state. They undergo no growth or metabolism, nothing like that, in all that time. They are surely not alive in this state... but they are surely not dead either. They might revive. And then there are the sea monkeys (brine shrimps), which can undergo cryptobiosis like bdelloid rotifers but for far longer, perhaps for centuries in some cases. Not all of these dehydrated life forms will find water. Many of them may blow away or be buried in places without water, and many will break down over years or decades, eroded by the elements. Entering chaos. But at what point do we say that these creatures have died? At what exact moment could we call the time of death for a dehydrated seed such as this, as a doctor might? This is surely impossible. It's hard to escape woolly definitions, it seems.
'HARRY? HARRY!' A loud voice broadcast itself over the busy museum cafe and sliced through our conversation. 'OVER HERE!' The grandfather returned carrying a tray with a cafetière, a soft drink and some biscuits. He'd been ages. I realised at this point that we had both totally forgotten about Harry. I looked immediately to the seat next to us and was thankful to see him still sitting there. He was swinging his legs underneath the chair, looking a bit solemn and pretending not to listen to us again. 'Harry, this table,' said his grandfather, gesturing him to leave us and come over to his table nearby. I gave the grandfather a nod and a polite wave. He smiled and gave us a little thumbs-up. The little boy slid himself off the chair and went to join his grandfather. I wondered what in God's name this child was going to tell his grandfather we had been talking about.
Louisa told me more about her work investigating Mars, describing it as a new and exciting frontier in the search for extraterrestrial life. 'Mars is accessible. It's where we can search easily, but also it's had a history like Earth's. It had an atmosphere. It had water. It had an environment probably much like the early Earth.' 'But should we really expect to find life there?' I asked. She shrugged. 'Life arose here on Earth,' she said, 'so there's really no reason why it couldn't have evolved on Mars as well.' Louisa clearly loved Mars. Her voice was full of awe and passion and she started to talk much more quickly whenever it was mentioned, which may have been the coffee, but I really didn't think it was. 'The geological processes during Mars's history are so different to ours,' she said. 'It doesn't have plate tectonics, for a start. It hasn't destroyed its history as happened so often on Earth. We can look at the rocks from the beginning of Mars's history and they could still preserve fossils or evidence of early life on the planet.'
She told me about the ExoMars rover, which goes to Mars in 2018 with the sole mission of finding life. 'It could be that in the next few years we drill into the surface of Mars and find that protein,' she said. 'That crucial evidence: evidence of life outside of Earth.' 'And what do you think everyone will say if you find it?' I asked. I have often fantasised about that moment, as we all have, I think. When we realise, as a species, that we aren't alone in the universe. 'Well...' she said. 'I think the public will probably be incredibly disappointed.' She sighed. This wasn't what I had expected. I had expected Louisa to have entertained ideas of global celebration, peace and unity spreading across humankind; an acceptance and early understanding that we weren't alone and that we should look after each other a little better. 'Why will everyone be disappointed?' I asked. She shook her head sadly. 'They'll be disappointed because everyone wants to find life on Mars, and then we'll stand up in front of a global audience and say "So everyone, we found a fatty acid!"... and they'll be like... A FATTY ACID? No bugs? No aliens?... A FATTY ACID?' We both laughed.
It struck me at this point that the popular view of astrobiologists is that they are searchers for distant life, but in reality most of Louisa's job is about looking for death. Evidence of former life, through fossils and fossil biomarkers, rather than life. I mentioned this observation to her. 'That's actually quite interesting,' she agreed. 'Yes... death is essentially what we're looking for...' She looked into her empty coffee cup. 'I've never thought of it like that. But you're right, death is almost certainly what we'll find on Mars.' She continued to stare at her coffee cup. 'I guess, yes, all I study is death, really. Fossils... remnants of dead organisms. All of the building blocks of life I look at are what's left after something has lived, died and degraded – been destroyed, basically.' The disorder again.
We sat in silence for a few moments. I looked over at the little boy. He was talking animatedly to his grandfather, who was listening intently to what he was telling him. Grandfather looked interested but there was a tiny bit of concern and seriousness in his eyes, as though he was deeply worried about what Harry had been describing to him at that moment. It dawned on me that Harry could be telling his grandfather that his fridge was quite probably alive and that the thermostat is unable to produce sterile offspring. But then another thought crossed my mind. I wondered if it was the first time that anyone had discussed death in front of that little child. Hardly anyone speaks about death in front of children. Had that moment with us been Harry's first time? And I wondered if what we'd talked about had damaged him or whether, perhaps, it had done him good. It was a thought I knew I would come back to. And I did a few months later.
Louisa and I said our goodbyes to one another and promised to keep in touch. She wished me well with the book. I wished her well with finding new life on other planets. It had been a useful place to start, on the whole. Hearing about Louisa's work had been fantastic, but finding a clear definition with which I could begin my journey had proven quite hard. As Supreme Court Justice Potter Stewart famously said of pornography, 'I know it when I see it.'... Well, I guess I was left to think this way about death. We know death when we see it, in much the same way we know life when we see it. On the train home, I thought about where to go next. And then I realised something. Louisa had been a little surprised when I had mentioned that, really, she studied death in the solar system and not life. Well, in a funny sort of way, I was the opposite. I had assumed I would be studying inert things whilst researching this book, dead things like the fossils in the museum, but really I would be studying life. The potential for life. To understand why frogs, on the whole, live for a few years, I would need to look at living frogs. To understand why spiders occasionally kill one another I would have to look at living spiders. To understand why some jellyfish apparently manage near-immortal feats I would have to understand the life of a living jellyfish. I would have to see living things and speak to living scientists. And suddenly I got it. This wouldn't be a book about death at all, I realised. It would be a book about life. I would be studying life. I would be reporting on life. This would be a life story. A proper life story. And in the bits in which it wasn't a life story, when death was inevitable or had actually happened, the spectre of potential life would still lurk, even if it was in the form of other creatures like worms, blowflies or scavenging foxes.
CHAPTER TWO
Senescence and What Waits for the Lucky Few
'He's going to be a little bit floppy here, just be careful.' The vet deftly hauls the bulky fish from a water-filled tub on the floor and gently places it upon a foam bedding on top of the operating table. It wriggles slightly but seems quite calm. It is about the size of a salmon. According to the aquarium it's a copper rockfish. There is activity all around: technicians gather around the table on which it flaps in its foam bedding. There is some to-ing and fro-ing in the background of the shot. Someone places a hose into the fish's open mouth to keep the gills oxygenated, while someone else has the simple task of keeping the fish's skin nice and moist. This looks an easier job. Yes, the fish seems surprisingly relaxed about all of this attention. Someone clamps it in place on the bedding. It looks less relaxed now; it flips and waggles a bit. Ready to operate, one of the two lead vets pulls the overhanging lamp up close to the fish's cold head and gets ready to perform.
Where its eye should be, the fish has a gaping pink eye-socket, which recedes deep into its skull. It is missing its eyeball. The vets look anxious. Suddenly a host of bystanders appear at one end of the room – this is what they've been waiting a while to see. A vet is going to do something to the fish with one eyeball, but the viewers (including me) aren't yet sure what that might be. They quietly watch the two lead vets do their thing. I am sitting and watching this miles away on my laptop. 'So...' says the male vet, holding what looks like a needle and thread. 'So where do we...?' He gets up close to the eye socket and looks very closely at it. 'Do we do him there?' He points to the top of the arch of the socket above the missing eyeball. 'Or there and there?' He points to another part of the socket. The female vet leans in. 'I normally put it up against the fish first...' She takes an object from her hand and places it into the fish's empty eye-socket. It is a cheap-looking plastic googly eye. She arranges the cheap-looking plastic googly eye neatly into the socket. 'Nice job,' someone says quietly in the background. The operating room seems increasingly tense and there is definitely a hint of excitement in some of the bystanders. The male vet continues: 'So I just use a needle to make a hole through the bone...' He carefully moves the needle, pulling through the thread. 'And then I try to run the suture through the same hole.' Someone in the background looks slightly nauseous at this point. Water continues to pump via a tube through the fish's gills. The fish shudders ever so slightly. Minutes pass. The video cuts forward. We are near the end of the operation now. And then, 'So... we're cutting the suture.' The male vet remains calm under the pressure, narrating each movement. Almost there... 'Getting rid of the little tags...' Almost there. 'And... nice,' he says.
Everyone admires his handiwork. He looks pleased. And he should be. He has just successfully sewn what looks like a plastic eyeball onto the side of a fish's head with the skill and dexterity of a young Jim Henson. And this really did happen. The unusual operation was undertaken by experts at the Vancouver Aquarium, and the video of the operation is freely available online for all to see. It's interesting. Interesting because it tells us a little something about animals and the rarity of their reaching old age. Why did this copper rockfish need a googly eye? The answer is that it had developed cataracts. It was old. The cataract had occurred in only one of its eyes, resulting in that eyeball being surgically removed, but this hadn't worked out well for the rockfish. Other fish in the aquarium had been observed to 'bully' the one-eyed rockfish (which they are rather prone to do), so Vancouver Aquarium decided to do the right thing and reached for the needle and thread, and the Hobbycraft Multipack of Googly Eyes. Cataracts are one of many diseases of old age. And, kept away from predators, aquarium fish age in many of the same ways that we do. Cataracts can be quite common. Ageing is natural.
So why do we all age? Why don't we just carry on living in perpetuity? Why can't we be immortal? It is one of the questions that has plagued humanity for centuries. From ancient Greece's Tithonus – requested to be made immortal by Zeus without anyone throwing in the bit about eternal youth – to almost every Hollywood star you care to name, our obsession with ageing is absolute and (ironically) timeless. So why do we age? Why can't cells just continue to replace themselves in a predictable and healthy manner forever? Why do animals fall apart in old age? And why do cataracts often feature as a symptom of old age in animals as seemingly unrelated as fish and humans? Dig about in the science of senescence (as ageing is called) and you'll quickly come to realise that the answer is, almost spectacularly, that no one is entirely sure. Not that this really matters; as with all of zoology's known unknowns, scientists over the last century have gathered into camps supporting a host of different hypotheses that may explain what might be going on, particularly at a cellular and molecular level, to produce the phenomenon we call ageing. There are many hypotheses out there, and I will outline the three most common nice and early in this chapter before returning to them in the course of this book.
The first hypothesis to explain ageing is that cell damage simply builds up over time. As generation after generation of new cells is created within the body, accumulated DNA damage occurs that somehow affects cell renewal. These errors build up. Bit by bit, organs fail to repair properly. Bit by bit, cells become dysfunctional and the diseases of old age result. The second of the main hypotheses for ageing relates to 'free radicals' – the highly reactive atomic particles generated particularly when mitochondria (the biological battery-packs present in each of our cells) manipulate oxygen to fuel the energetic reactions required for life. Free radicals have the potential to stress a cell's function, that much is certain. It may be that they lead to an accumulating cellular burden with age, much like the first suggested cause. And then there's the third hypothesis: that of a telomere. As you will know, all of the cells in your body contain chromosomes in which are housed your genetic blueprints. The structure of these chromosomes is interesting: each of them, when pulled apart, is capped at each end by a 'telomere'. Telomeres are special lines of genetic code which act a little like the plastic protective tips at the end of a shoelace. Experiments suggest that, for each successive division of a cell, the telomeres shorten. This puts a finite limit on cell division. The hypothesis is that, somehow, this shortening puts a kind of cap on the number of replications a cell can undergo, potentially limiting the activities of bone marrow and arterial lining, where repeated division is conducive to sustaining life. The result, as with the other hypotheses, is cellular breakdown: what you and I call ageing. There are certainly other possible explanations for ageing, but these three (accumulating DNA damage, free radicals and telomeres) hog much of the limelight, partly because they have been studied the most intensively.
Research into senescence is anything but an unappreciated zoological backwater. Understanding ageing is becoming a key battleground for those from a host of scientific disciplines, many eager to tackle diseases of old age that include cancer, cardiovascular disease, arthritis, osteoporosis, type 2 diabetes, hypertension, Alzheimer's disease and cataracts. These are natural diseases in many ways. But how could natural selection have produced them? Could there really be a point to these diseases, or are they simply by-products of some other process? This question has rattled scientists for a generation.
Among the first to offer a Darwinian perspective on animal ageing was the British biologist Peter Medawar. Medawar became the so-called 'father of transplantation' through his pioneering work on immune tolerance and organ transplants. He understood that every animal alive at any given time has a particular chance of dying. In fact, this probability of death was integral to his theorising about ageing (senescence) and why animals age like they do. Medawar's 1951 inaugural lecture at University College London, An Unsolved Problem in Biology, went on to underpin all three of the modern theories for senescence by flipping the problem of death on its head. Rather than focus too heavily on any given species, he asked why it was that natural selection didn't 'cure' all animals from ageing and dying. Natural selection is adept at solving problems, right? Yet death is the biggest problem of all, surely. So why is death so prevalent in the animal kingdom? he wondered. Why hasn't it been whittled into shape by natural selection, as one might expect?
Medawar was the first to appreciate that the answer lay in probability. He realised that, even without considering ageing, there is a statistical likelihood of death for any creature at any given moment. All animals will die eventually; that's 100 per cent likely. Some animals might die when still relatively small and young, when they become easy prey for something else. Some species might be more likely to die once mature and in competition for mating resources (like nests) or searching for mates. We all have a chance of death, and this probability changes during our lifetime. In humans, statistically, once we reach 30 years of age our chance of dying doubles approximately once every eight years. It's as simple as that. It may seem obvious to us now, but in 1951 this idea of probability was an important insight. Medawar understood that for every second that a bacterium swims in a pool of water, for instance, there is a probability of death that glows like a neon sign above its head. The given bacterium may die through predation, cosmic radiation or misadventure, and plenty else. It could be besieged by virus particles. Squashed or dehydrated into oblivion. Every day that a bacterium lives it is rolling the dice, unaware that one day its numbers will come in. And they will come in eventually, no matter how expertly that bacterium piddles about in that particular puddle of water. Natural selection, Medawar realised, simply favours the animals that get on with the business of reproduction before their chances of dying increase. An organism in that puddle that breeds every two days, for instance, will far outcompete an organism that breeds every two weeks or two years. Simply, gene pools become flush with those best primed for reproducing before the statistical chances of death increase.
At its most simple, Medawar's idea was that natural selection didn't sort out senescence because it was drawn to the battleground of life; it was drawn to sex. The only language of transmission it knows is through reproduction. And those sexy genes, high on life and sex, think nothing about solving the problems of old age. They think only of carrying on. As ageing individuals we, according to Medawar, have been left high and dry by our genes' insatiable desire to spread at all costs before death gets us. In nature, when death doesn't get animals early, the lucky few that remain will see senescence expose itself to pick them off anyway. And that googly-eyed rockfish, kept safe in its tank, is just that. Like us, it lives a different kind of life. One, on the whole, without predators. Medawar's idea was a catchy one. It influenced a generation of scientists with it, but doubts still remain about whether, and to what degree, his idea works in the real world. Could senescence really be as simple as Medawar described? Could the signs of ageing really just be the result of sloppy maintenance that can't be fixed by an unthinking selection machine obsessed with sex and cutting-edge replication? We still can't be totally sure.
In 1966, the evolutionary biologist George C. Williams offered up another way in which senescence may appear naturally in a way that is similarly unfixable by natural selection. He proposed something called 'pleiotropy' – a situation where the flipping of genes on and off can cause multiple, seemingly unrelated traits to expose themselves, either instantly or later in life. To Williams, the problems of old age come about as side-effects of things that help animals have better sex earlier in life. Williams's example was to imagine a hypothetical gene that alters calcium metabolism in a way that both strengthens bones in youth and occludes arteries in old age. In this situation, natural selection would be drawn to maintaining the healthy strong bones of fertile youth – those genes would spread, regardless of the consequences later in life. In many ways Williams's view works in the same way as Medawar's. Sexy genes spread better than genes for healthier arteries in old age, which barely spread at all because of the fertility drop that occurs with ageing. Natural selection can barely touch the diseases of old age, let alone try to fix them, and so these diseases remain. 'Reproduction is the beginning of death,' wrote James Joyce. And so it is. Sex and death really are two sides of the same coin.
And so the googly-eyed rockfish lives out its life. Its wonky eye is an expression of a fleet of genes obsessed with sex, which barely gave a nod to trying to fix a common disease of old age. Stare closely enough and you will see yourself reflected in that googly eye. The universe has given you a statistical chance of death, and natural selection has acted accordingly on your growth rate, your brain development and your puberty. Each is programmed with sex in mind, not cosy senescence.
Does this make you feel small and helpless and a bit insignificant? I confess that exploring all of this does make me feel a little helpless about ageing. But don't feel too glum, because there is a silver lining and it comes down to a simple observation in nature. It may not always be this way for us. Many populations of a given species appear to evolve longer lifespans quite quickly in evolutionary terms, particularly in habitats that lack predators. Give an opossum an island habitat with fewer predators, and a couple of thousand years later the opossums will live twice as long, ageing at half the rate of their mainland competitors. Their lifespans change. Brook trout offer an even more spectacular example: their introduction into cold, nutrient-poor waters in California's Sierra Nevada has seen their populations quadruple in lifespan. Where once they lived six years, now they can expect to live for 24, with the only apparent catch being a delay in sexual maturation. Fiddle with the statistical chances of death and animals evolve, not within millions of generations, but hundreds. The writing is on the wall. Senescence isn't a phenomenon etched in stone. Senescence is fluid. Natural selection, if needed, can pull the strings of ageing, which means that there may be a genetic component to ageing. The brook trout and the opossums offer us a startling revelation: diseases of old age – all of them – might be something we can delay. And by fiddling with genes, we may discover that they can be delayed greatly. Perhaps immeasurably.
The study of ageing really is far from a scientific backwater; it is recruiting geneticists, zoologists, biochemists, molecular scientists and physicists. They are queueing up, eager to weigh in with their own given insights. And why? Because they are drawn, like so many humans before them, to the prospect of immortality. But this time it's real.
CHAPTER THREE
Fear and Loathing in Birchwood
'Anyone want a dead magpie?' her message on Twitter had read. My eyes lit up. Me, I thought. I want a dead magpie. That's exactly what I want. I really did. Genuinely, I really did want a dead bird. I had quite wanted a dead magpie or crow as part of some initial research I was undertaking on how corvids (the family which includes crows, jackdaws, magpies and jays) respond when finding dead members of their own species. My plan was simple: I would get my hands on a dead magpie or crow or jackdaw and rest this corpse gently in the middle of my local corvid haunt, a spinney in a nearby field in which a jackdaw colony rubs up against small flocks of crows and magpies. What would they do when I placed the magpie on the floor? How would they behave? Would they inspect it? Become anxious? I was interested. Sure, it wasn't exactly a randomised controlled trial at this point but it was a start, I thought. I had to have this dead magpie. I had to have it. I'd travel for this dead magpie. So that is exactly what I did. I travelled to Birchwood to meet Alison Atkin, bone expert, archaeologist and self-anointed 'deathsplainer'.
Birchwood is near Warrington, which is midway between Liverpool and Manchester. I had never travelled to Birchwood before. I like going to new places – it was quite exciting. As the train pulled in it looked a clean, ordered place. Birchwood is what we in Britain call a 'new town' – a place without historical infrastructure, where county planners in the 1970s could work unimpeded by irregular angles laid down by the Victorians. So Birchwood is a place where everything sits at 90 degrees, and into which paving slabs are perfectly flush up against each other, which makes the place look very neat and tidy and organised. There are cycleways and pedestrian zones in Birchwood. Lots of seventies-style flats and other rectangle-shaped objects. And tree-lined avenues, which is something you don't often get in Britain, given that trees take up space and space is at a premium in many parts of this relatively tiny island.
I walked along the station not knowing quite what to expect from Alison. Would she be like the people at Death Salon? Would there be the same air of mortician chic in her? Would she approve of what I planned to do with her dead magpie? I really didn't know because our correspondence hadn't been particularly detailed up to this point. In fact it wasn't detailed at all. It was: 'Who wants a dead bird?' [PAUSE] 'Me.' And that had been pretty much it. We'd arranged it all, in fact, via Twitter. I had wondered whether Alison did this often, clandestinely meeting strangers at train stations and handing them dead things. My palms were sweaty. I looked up. There was only one person waiting in the arrivals section behind the turnstiles and it was, I guessed, Alison. Thankfully, she was smiling and she looked friendly and normal. She had a bag in her hand – it was an enormous plastic carrier bag in which I imagined the dead bird lay. On the side of the bag were capital letters encouraging supermarket shoppers that the bag be reused. The letters read 'TESCO: BAG FOR LIFE'. I wondered if Alison – a Canadian – was demonstrating to me that she possessed a true sense of British irony. She had a wry smile on her face. I think she did.
It had proved quite hard to predict how long it might take to hand over a dead magpie. What's the etiquette? I'd wondered. In my ticketing plans I'd allowed myself two hours between getting the train to Birchwood, taking the magpie off Alison and leaving Birchwood again, but actually, as it turned out, the hand-over had taken a little over 60 seconds. Having about 119 minutes to kill, we decided to walk the streets of Birchwood and talk more about her work and the world of zoological death that I was now entering. I felt that Alison was going to prove useful to me – I was after all a relative beginner in the field of dying – but I wasn't yet sure how. I wanted to know about Alison's experiences having an academic career that involved, in every sense, death. I wanted to have what I knew she had: a rational approach to discussing death that is underpinned by science, but that isn't graphic, crude or cruel in its delivery.
On our way to the coffee shop I told Alison about my publisher's understandable anxiety about me writing a book about death, and how there was concern that people might not like to read about death and dying, or buy books about it. She chewed on this for a few moments in silence before looking at me: 'Death happens,' she said bluntly. 'That's pretty much what I spend most of my time reminding people. Death happens.' 'Right,' I said, jotting this down. Death happens. Alison is an osteoarchaeological researcher, which means she is interested mostly in digging up human remains (bones) and studying them. She tells me that her main research interests include mass fatality incidents such as the plague, and how she was specialising in looking at methods to identify the hundreds or thousands of unidentified or misidentified bodies buried after such catastrophic events. The burial sites after mass fatalities are often chaotic in their structure, she told me (something that is still the case today in cases of genocides or sudden disease outbreaks), so Alison is trying to work on methodologies to unpick the chaos, as it were.
We sat down for a coffee in a busy coffee shop not far from the station. 'You ever work with kids?' she asked me as we sat down. I nodded and considered mentioning Harry, the little boy from the museum. 'A bit,' I replied. 'Kids love death,' she said thoughtfully. 'They love it. You bring skeletons into schools or museums and kids surround you. They have so many questions. They want to know "Where do you get bones?" or "Who was this person?" and you can see their parents wincing a bit in the background.' That's what I felt the grandfather had been doing. Sort of... wincing... when I saw Harry detailing to his grandfather the conversation he had overheard from us about death. 'And do you tell the kids who the bones were from?' I asked. 'Yeah,' she said. 'I don't dress it up. I don't use terms like "passed on" or "passed away" – nothing like that.' Her open face had turned suddenly more focused and serious talking about this. 'When I work with children I use "death" and "died" and "dead" and "dying",' she said. Each word was clearly spoken. 'Label it properly,' she said, offering me advice. 'Frame it properly, otherwise you risk miscommunicating death. And that can be a big problem.'
To Alison, there is a big problem with society, and that is that we fail to talk openly about death. This, she told me, was where the whole deathsplainer thing came in. Alison was trying to alter the zeitgeist a little by encouraging frank conversations about the bit that happens after we live. 'It's important we talk more as a society about death,' she explained. 'When a kid loses a pet do the parents allow their kids to hold it? Or even see the dead body?' I thought about this. 'No, I'm not sure they do,' I answered. 'When a kid sees a squashed frog,' she continued, 'they want to ask about it and we don't always want to talk about it but... I dunno...' She paused. She held out her hand as if she had an imaginary dead frog in her palm. 'LOOK!' she said. I looked at the imaginary dead frog in her palm. 'THE FROG IS DEAD!' she said assertively. I nodded my head. 'That's what we should be saying to young people: THE FROG IS DEAD,' she repeated. I thought again about Harry. And I thought about my own kids, and how we had avoided talking about death to them, sometimes choosing instead the awful 'It's only sleeping!' line when coming across a dead creature, something I realise I am deeply embarrassed of when I come clean to Alison about it. But it had made me wonder, as rather a bastion of science and rational thinking, why on earth I'd said this. Why hadn't I been clearer from the start with my young kids? It wasn't sleeping. It was dead. Alison was quite forgiving about all of this. 'So many people say that to young kids,' she said. Perhaps people like me avoided talking about death with their young children because we ourselves were scared shitless of it. Maybe it really was as simple as that. We're scared and we don't want them to be scared.
The conversation moved on, and the subject changed to dead birds. 'What sort of person gives dead birds away through Twitter?' I asked her. The nonchalant way in which she had offered up the magpie online had made Twitter seem like some sort of zoological version of eBay or Loot – as though she offers up dead animals all the time. 'Do you?' I asked. 'Do you offer up dead things all the time?' 'You wouldn't believe the appetite for dead specimens out there in academia, and the importance of dead things to reference collections,' she told me. 'We have freezers in the basement of our department full of dead fish, full of small mammals, dead birds...' She paused and looked up at the ceiling. 'I think there was a dead badger in there at some point.' She mumbled this last bit very quietly. I tried to picture her freezer. I'm sure each specimen is well labelled and it's delightfully clean and well ordered, but in my mind's eye all I can picture is a gruesome chest freezer from some gory eighties movie. I later ask my scientist friends about the weird dead creatures they, like Alison, have temporarily stored in their own freezers. Their responses include wrens, hedgehogs, shrews, mice, squirrels, field voles, bullfinches, rats, snakes, ants, polychaete worms, leeches, gerbils, an echidna and a muskrat, as well as larger items that would horrify even the most academically weathered spouse of a zoologist. I can only imagine the face my wife would pull if she opened our freezer and saw the head of a coyote, a porpoise torso or a neat row of brains from several species of monkey, for instance (for those interested, the best I've managed in my freezer is a long-eared bat).
We finished our coffees. 'Wanna see something weird?' she said. 'Always,' I responded, without skipping a beat. What the hell, I still had an hour to kill. But what Alison showed me a few minutes later was no time-filler. Alison swerved me into a new zoological realm, one I would otherwise never have thought to investigate. And through it I saw a different side to death. It was an experience that carried me somewhere else. Somewhere I'd never been. Something I'd never seen. And it spun me off, now really and truly, on the beginning of my journey...
'Wanna see something weird?' Alison had asked. Five minutes later we were around the corner from the coffee shop looking at a silken tunnel that had opened up before us like some sort of nightmarish cave. We were indeed looking at something weird. This used to be a tree-lined avenue, Alison had informed me. Now it was something else entirely. The whole avenue had been totally and utterly wrapped in silk. It had become a white tunnel; it was like a winter wonderland a few months too late. I was gobsmacked. 'This all just turned up a couple of weeks ago,' Alison said, enjoying my comic-book response to this absurd spectacle. 'Isn't it just the most wonderful thing?' she laughed. I muttered an expletive at this point – that was the best I could manage.
We wandered into the tunnel. I was speechless. You could almost park a bus under the silken cloak suspended from the tops of branches overhanging the pavement. Great white curtains of the stuff; sheets of silk. But this was no PR stunt or artificial outdoor art installation – this was a stunt created by nature. It was a stunning thing to see up close. What was this natural spectacle doing in Birchwood, of all places? We were walled in by it. It was everywhere. And caterpillars, not spiders, had apparently produced this spectacle. Carefully pulling the silken web apart I could see them – there were hundreds of thousands of black and green caterpillars, each tiny, maybe a centimetre or two long. There were so many that, in parts, their combined weight made them sink through the silk in great netted blobs that dangled from the ceiling like stalactites. Hanging like this they looked unnervingly like socks full of maggots.
We walked among them, these larval dollops, my mouth hanging open in disbelief. It was mesmerising. Certainly it was one of the strangest things I think I had ever seen in my life. And it was in Birchwood, England. It really was like a novelty winter wonderland. I pulled and poked at the silk again. The threads had become so intermeshed that they had formed a solid latex-like sheet made up of hundreds of thousands of individual drag lines left by the solo explorations of thousands of individual caterpillars. So many journeys had been made by so many caterpillars they'd created this sheet, a mesh – now it was a kind of fabric; a solid sheet so condensed that it felt and looked a little like white rubber. This backstreet in the middle of urban Birchwood had been made organic by these caterpillars. Even many of the paving slabs below had been covered in the stuff. Alison and I wandered around, taking photos, awestruck. 'Isn't it just the most amazing thing?' she said again. 'It's amazing that it could just pop up here like this, in the middle of such an urban place. Amazing.' 'Amazing,' I uttered. I still wasn't capable of much speech at this point. Underneath the great sheets one could see that the caterpillars were going happily about their business, stripping foliage from the trees like columns of Roman troops on patrol. Actually, there weren't many leaves left.
Local residents, upon seeing us show an interest in the caterpillars, had come from their houses to join us, asking us if we knew what was behind the curtain of silk, discussing and speculating about this strange army. They were bewitched, mostly. And also disgusted. They were disgusted and bewitched. Their suspicion was that these caterpillars didn't belong here. Too exotic, they thought. This is Britain, for goodness' sake. This is Birchwood. Weird stuff doesn't happen in Birchwood, I could tell that they thought. In some of these people's eyes the caterpillars couldn't be trusted. What would happen when they ran out of food? Would they come for the gardens? they wondered. Tongues were set wagging... For many minutes we poked and probed the strange structure, taking notes and photos. But then, sadly, it was time for me to go. Alison and I didn't say much on the walk back to the station. I think we were both a bit dazed from it all. She handed me the bag of bird. We said our goodbyes and promised that we'd keep in touch. And we did.
Upon leaving Birchwood I did some research into what we'd observed. What we had seen were bird cherry ermine caterpillars, apparently. Ermines are neat little moths, a wintry white colour with little rows of black dots upon the wings. They are renowned (though I confess I'd never seen it before) for wielding silk like some sort of protective curtain, though protection from what exactly is as yet unclear. Silk, evolution's most brilliant thread, was here being wielded in a suspiciously altruistic 'panic-room' form. Safe under the 'tent' from intruders in avenues like these the ermines go about their work, specialists in absorbing the tree's atoms and reassimilating them into caterpillar form and then into adult moth forms that emerge in midsummer. According to entomological accounts, each year various parts of northern Europe become festooned in this silk should the caterpillars' foodstuff (bird cherry trees) have a good year. In an archived Dutch newspaper I found reports showing rows of cars and bikes parked under cherry trees, that had become consumed in the mysterious stuff during late spring. I read elsewhere that one of these vast latex-like sheets appeared and spread itself all over the hawthorn bushes at the entrance to Belmarsh Prison in London, to the confusion of inmates and everyone visiting. Such infestations only occur perhaps once every three or four years and culminate, as they run out of leaves on which to feed before pupating, in the caterpillars spreading far and wide in search of other forms of nutrition.
Sometimes, it seems, the ermines do go on the rampage. 'In Finland I have seen a trail of thousands of larvae marching along a railway line,' says Professor Simon Leather, an entomologist at Harper Adams University on his popular blog Don't Forget the Roundabouts ('They didn't survive the passing of the 08:50 from Helsinki,' he reports dryly beneath). Leather also recounts hiding from the rain under silken sheets produced by bird cherry ermine moth caterpillars. What we had seen had been like that. The silk could have sheltered us from the heaviest of storms in that Birchwood street. Hours of rain and I think we would still have been bone dry underneath it.
Apparently the bird cherry trees themselves rarely die from these infestations. It's likely that they can weather heavy infestations like those that we saw, provided they are sporadic, which they often seem to be. On the whole, leaves come back the following year and life continues for the bird cherries. This was good news, and it filled me with a bit of hope. One of the passers-by Alison and I had spoken with had displayed something approaching anger about the whole thing – that the caterpillars had stripped the trees of their vigour, and ruined the look of the avenue in spring. I had heard another passer-by later on calling them 'pests'. Both of these comments had rankled me a little. I'm not the sort to really show it, but 'pest' isn't a word I like to hear used about animals. Plus I understand enough about parasites* to know that the true killers among them rarely last long; the most evolutionarily long-lived parasites are those that take a little, but not too much. So, to me, the ermines weren't pests. No way. The ermines were farmers, really, and the leaves were their crop. I felt almost sorry for them. Yes, you know what? I did. I felt sorry for those little caterpillars. When I remembered standing underneath that enormous snow-white canopy, I could see only life. Yet many of the passers-by didn't see that at all. They saw only the associations with death and pestilence.
And so it happened – two weeks later my fears were realised. I should have expected it, to be honest. I received word from Alison that they were gone – the whole avenue of cherry trees had been cut down. Local residents had complained about the ermine caterpillars – the caterpillars had been deemed a health risk, apparently. The whole avenue of trees along with all of the caterpillars had been chipped. Lost. Gone. Dead. The local housing association gave a statement to the Warrington Guardian, and here is what they said: 'The infestation was reported to Your Housing Group by a number of residents, and given the trees' proximity to surrounding residential properties, and the extent of the infestation, the decision was made that it would be better to remove the trees completely.' I had come to Birchwood to pick up a dead bird, but I had wound up embroiled in something else that was to become a deeper part of my story of death. I had rubbed up against my foil for the first time: humans. Humans and our strange and sometimes perversely arrogant attitude to other life forms on Earth. Humans and our total terror about anything that reminds us of our own mortality. It proved not to be my last run-in with this peculiar species.
As Carl Zimmer observes in Parasite Rex, there was a time when society viewed parasites as nothing more than troublesome hangers-on. Annoyances. Disgusting evolutionary by-products. But then our attitude changed. With the advent of the Cold War, the Alien franchise (among a host of sci-fi parasite films) and (most importantly) a new evolutionary understanding of how parasites function, our societal view began to change. In more recent years, it seems to me, there has developed a grudging respect for the wily perniciousness of parasites, as there should be. But it is respect nonetheless, and I am thankful for it. For there is a new and vibrant ecological understanding of the breathtaking constellations that form when parasites are added into our standard model of food chains and food webs. We overlook their role in life and death at our peril. Quite literally.
Though we consider parasites as agents of death, they are far from it; they are much more valuable than that. They can be harbingers of new life, and that's just for starters. In terms of speciation, particularly, they are likely to blossom upon every new form of complex life that natural selection produces. If an individual species of fish should find itself in a newly separated lake, for instance, each of its many parasites may become wedded to the form into which that fish will evolve. Parasites get swept up in the speciation melee. In events like these, one new fish might result in something like 10 or 20 new parasites, or so it's imagined. Indeed, this speciation parallel between parasites and hosts explains some of the patterns we see in taxonomy. Take this example: add up all of the known mammal, reptile and bird species and you'll come to a figure of almost 25,000 species. Not bad, you might say. But then look at parasitic wasps. There are 100,000 species of parasitic wasp that taxonomists have so far named. One hundred thousand. Ermine caterpillars fall somewhere near this pack, capable of occasional ransacking of specific species of trees to which they have adapted, once every few years. Some individuals undoubtedly try it more but their hosts die, so... well, they die too. The world has filled up, in a strange sort of way, with 'nice' parasites, on the whole. Parasites that seem almost to value life over death. The ermines, then, are no different. Yet we offer creatures like this barely a nod of appreciation or any form of inter-species kindness at all.
You might hate them for what they did to the trees, but don't. The trees probably weren't sitting and taking it. The war between caterpillars and trees is at least 50 million years old, and that particular housing association had only recently blundered into it. Trees have had plenty of time to evolve weaponry to combat caterpillars, plenty of time to fight an embittered cold war. So, please, don't feel sorry for the trees. Many can handle themselves – most have evolved some level of toxicity, for starters. Many plants, including trees, extract minerals from the soil and turn them into allelochemicals, some of which will target independent caterpillars' tastes, killing them or (at least) discouraging them from feeding. Of course, in most cases, a genuine arms war is what has resulted. The caterpillars have fought back or, at the very least, many have wised up. Some caterpillars, for instance, bite leaf veins and allow the toxins to bleed out before beginning to feed. In fact, toxins are why so many caterpillars feed on the edges of leaves: here, away from the larger veins, toxicity is at its mildest.
Of course, trees employ other tricks to push back the invading caterpillar army, some of which are staggering in their unthinking ingenuity. How they do so is largely unknown, but many trees almost sense that they are being bitten and they muster up a different kind of chemical cocktail in retaliation to caterpillars – a molecule aimed not at the caterpillar, but at the caterpillar's own parasites; a chemical message that diffuses out of the tree and floats around in the air, acting like a biological flag that waves to passing parasitic wasps, which promptly fly down and lay eggs upon and within the specific species of caterpillars to which their tastes have evolved. What's most incredible is that many trees appear to know the exact species of caterpillar feeding upon their leaves, and which exact parasitic wasp they need to draw over to dispatch it. Perhaps this is why ermine moth caterpillars employ such webbing? Not as protection from birds, as some think, but as protection from invading wasps. Perhaps. It doesn't seem like anyone's too sure about this yet, but it really could be that simple (if natural selection works the way we think it does, then predict a family of parasitic wasps to evolve with web-scissoring jaws at least by the end of this particular geological period).
There is more in the tree's arsenal than this, though. Some trees can influence other naturally occurring parasites to take care of their caterpillars for them, and what they do with these parasites is even more impressive than the whole parasitic wasp 'come-get-them' thing. It really is fantastic. Some trees waft out secondary compounds that influence the infection rates of caterpillars with baculovirus – a curious package of viral DNA trapped within a double membrane, which acts a little like a smart bomb in its caterpillar-killing efficiency. It starts with one accidental ingestion by a hungry caterpillar. The baculovirus enters the caterpillar's gut and multiplies within its local cells before spreading via the caterpillar's tracheal and circulatory systems around the body. Wherever the virus goes, more cells are infected. Before long the caterpillar becomes a chugging and industrious virus factory, and eventually it becomes swollen with billions of these virus particles, ready to burst. But it doesn't burst. What the baculovirus does next is chilling – it manipulates the caterpillar's physiology in two ways. First, it stops the development of the caterpillar, inhibiting moulting (one assumes this keeps the skin tight and fit to burst). But the second thing it does is mess with the caterpillar's mind. By fiddling about with proteins in its brain, the baculovirus makes the caterpillar seek out light. Zombie-like, the caterpillar struggles up the tree. Obese with multiplying virus particles, it heads toward the sun. Nearer and nearer the light it heads – upwards, upwards, upwards. Then the pressure within the caterpillar builds... Eventually it's too much... The caterpillar pauses... And then it happens. Its tightened skin ruptures and an enormous pressure is released; a fountain of billions of virus progeny rains down all over the leaves below, covering the leaves and petals upon which other hungry caterpillars feast. The infection starts over, 100-fold this time. The message is simple: don't mess with trees. Trees are like NATO – they don't start wars, but they know how to play the game, and they are probably a bit shady (pun intended) and untrustworthy at times. They are anything but victims, in other words. Yet humans are so quick to consider trees as such.
Parasites, it seems, have a truly unfair reputation as agents of death. Those ermines didn't have to die. And neither did those trees. Together the caterpillars and the trees had created something wonderful. In all of the neighbourhoods in all of Europe, the bird cherry ermines had erupted, including there in that street in Birchwood, and I was trapped momentarily within their silken spell. I was not to know at the time that this chance event would wind me deeper into death's spell, but it did. And I'm still not sure whether it was for better or worse.
It was only when I was sat on the train on the way home from Birchwood that I suddenly remembered the Bag for Life, which had been perched precariously on my lap. I clutched it close to my chest, anxiously aware that I was responsible for getting a dead magpie back across to the other side of England without accidentally spilling it across the floor, onto someone's lap or into an open pram. In every train station we passed I felt the hot eyes of security guards across my person. I breathed deeply and slowly. I hoped I wouldn't have to explain what was in the bag. I hoped I wouldn't have to have it confiscated. I had big plans for this dead bird. It had to get home intact. And thankfully it did.
Note
*Am I really arguing that caterpillars aren't herbivorous grazers, but are actually parasites instead? The idea sounds, to a zoological pedant perhaps, like heresy. But, loosely-termed, feeding relationships between animals do occasionally cross over like this. Parasites are organisms defined by having a non-mutual symbiotic relationship where one organism gains at the expense of another organism. Isn't that the relationship between trees and their caterpillars? Caterpillars share many features with classic parasites like many lice and mites. They possess specialised adaptations for feeding and holding onto organisms many times their size. They reproduce more quickly than their hosts. Often they depend on them for survival. In fact many caterpillars have evolved to depend solely on one given food plant for the progression of their life-cycle. Caterpillars tick many of the boxes to be considered parasites. And so I think it's acceptable, in these pages at least, to think of the relationship as parasitic. So there.
CHAPTER FOUR
Free Radicals and the Secrets Within
Could the rate at which we age really lie in our genes? I was still thinking about the opossums and the brook trout. Might we one day really be able to tamper with ageing artificially? The thought had occupied my mind for months. And then, suddenly, I came across a truly bizarre story – a throwaway anecdote, really, involving humans. The anecdote came from Nick Lane's Life Ascending, and it refers to the second of the theories outlined earlier in this book for why we age: the free radical theory of ageing, where highly reactive and short-lived atoms wreak cumulative havoc within cells.
The story is as follows. In Japan there exists a small subset of the population with a common variant in their mitochondrial DNA that alters a single DNA letter, resulting in a tiny reduction in free radical leakage. The result of this variant in mitochondrial DNA is nothing short of spectacular. By the age of 80, recipients of this 'faulty' gene were found to be half as likely to visit hospital for any reason at all, and they were twice as likely to live to 100 years. One faulty gene and they were half as likely to visit hospital. One faulty gene and they were twice as likely to reach 100. I found this statistic mesmerising. Utterly staggering. Could taming free radicals really be the key to solving the world's numerous healthcare crises? Maybe. There are certainly many animals that do just this. And they do quite well from it in terms of lifespan. In fact, one species does very well indeed...
Like a shrine, it stood in front of us. Preserved in its Perspex display case, it sat atop a shiny black pillar on the laboratory workshop, just like a priceless Ming vase. And this is almost exactly what it is – without price. An artefact from the past. Aged: as old as a Ming vase, in fact. The students and postdocs working the various microscopes had paused when Ming had come out of its cupboard. I got the feeling that Ming isn't allowed out very often. They had paused, almost as if to pay their respects. 'Can I take a picture?' I asked Dr Paul Butler, my guide for the morning. 'Of course,' said Paul. 'Let me put it over here where the light is better.' Paul picked Ming up and took it to the edge of the laboratory next to a sunlit window. He stood back to let me get a good shot. Ming looked resplendent, like an antique polished soapdish, and we both stood in silence taking it in. The uniform striations along its shell looked almost like they had been put there by a comb dipped in paint. Though the millimetre-wide grooves ran in parallel lines across its shell, there were some slightly wider, bleached grooves that looked a little like breaks between tracks on a vinyl record. And to trained scientists, they were being read as such.
Ming was the oldest known non-colonial animal in the world, explained Paul. It had become a global celebrity because of this fact. Ming seemed remarkably indifferent to its relatively newfound status, for: a) Ming is dead; and b) Ming is a clam, Arctica islandica (an ocean quahog), lacking in advanced cognitive capacity. Ming was certainly old, though. By reanalysing the growth rings on Ming's shell in 2013, Paul's team determined that Ming had been a staggering 507 years old when it died (previous analysis had estimated an age of 405, which was still record-breaking, but still... 507!).
Ming is now kept in a special cupboard in Paul's lab at Bangor University's School of Ocean Sciences. Most academic institutions become quiet places in the July weeks. Not so in Paul's lab. Throughout my visit, each corridor was filled with the piercing sound of postgrads using lathes to grind mollusc shells into workable fragments for further analysis. Whole banks of microscopes were being manned by students and technicians, each counting and measuring the striations upon their molluscan study specimens. I was there for only a few hours but I could have stayed for days. I really could have. I liked Paul. Having been a software consultant for more than 25 years, he moved from London to north Wales 10 years ago to start a new life as a scientist. He achieved that goal with gusto. Now he leads a team that is using mollusc shells to create a 1,000-year record of seawater temperatures, contributing to our understanding of climate change and how it is acting (and has acted) in marine environments in recent times.
We stopped and chatted to his students, many of whom had their eyes glued to screens midway through their striation measurements. The microscope images of shells were nothing short of beautiful. In some ways, they looked a little like the surface of Jupiter, with a smidgen more order; parallel stripes of cloudy greys, oranges and browns stood out like rainbows on the screen. As in trees, each stripe of colour on these shells represented a single year's worth of growth: they were growth rings, and the size of each is directly influenced by available food, which is itself influenced by sea temperature (Paul's team analyse the shell's chemistry to measure this). By analysing huge numbers of shells, Paul and his students have managed to create a kind of shell-growth archive that provides a way to measure polar sea-temperature change over the last 1,000 years. The ocean quahog shells have become a bit like a climate-change monitoring station; they provide further evidence that the world's climate is indeed changing.
When Ming's record-breaking age was announced to the world in October 2013, newspapers took great pains to put its mighty age into historical perspective. The Daily Mail wrote that Ming 'lay on the ocean floor throughout historical milestones such as the English Civil War, the Enlightenment, the Industrial Revolution and two world wars'. Some went with the fact that Ming was born seven years after Columbus discovered America. Others wondered whether its name, Ming, was something to do with the Lib Dem politician Sir Menzies 'Ming' Campbell, who often finds himself chastised for being a shining pillar of longevity, to put it nicely.
For me, well... I felt none of these things when I spent time with Ming. For me, it seemed unfair to put human history up against it. For there are better ways to add perspective on Ming's life – more animalistic, zoological, interpretations. I found myself expressing awe that, since its 'birth', 16 or 17 generations of my direct ancestry had reproduced and died. Since Ming seeded itself onto that hunk of rock on the seafloor, 169 generations of frogs had spawned and metamorphosed and died, and 507 generations of mayflies had made their maiden flights and then perished. Viewed like this, as a continuum of animal life, Ming is an outlier. But we're all on that spectrum, with our genetic lifespans plotted alongside others of our own species – all of us whittled by natural selection toward a given life history, based in large part on the unseen probability of us living or dying on a given day. Clams fit rather nicely into Medawar's hypothesis that beyond a specific age the evolutionary benefit of longer life becomes negligible. After all, having a thick shell and doing very little in the way of pootling around on the seafloor means that the chances of a clam dying in a single day is rather small (at least until the advent of dredging). Without much death, there's less hurry; lifespan has expanded. But how does a clam take it to such extremes as this? How does a clam get around the problems thought to be associated with ageing? Why don't they expire, smashed and ravaged by decades of free radical abuse, for instance? The answer in their case is that somehow they have managed to tame them. Somehow they have become masters of their free radicals. And they aren't the only ones: many long-lived animals, often on distant branches of life's tree, have evolved the same trick. A trick that one day we may uncover too. A trick that might help us live a great deal longer.
Research into the damage caused in cells by free radical build-up began with an American named Denham Harman. Few people can boast a patent to their name. Fewer still can boast 35 patents to their name. But then Denham Harman came into Shell Oil as a research chemist at exactly the time that the industry in petroleum products began booming. In the early part of his career Harman spent months and years looking for uses for petroleum by-products – essentially he was looking for ways to make money from the waste (interestingly, one of his patents was for the compound used in those yellow plastic strips designed to kill flies). Of particular interest to Harman was what happened to the free radicals produced in and after reactions with petroleum products, and it was this interest that pulled him away from industry and into the arms of academia. Harman was drawn toward the idea that the free radicals that leak from energetic reactions within mitochondria somehow build up, unleashing chaos much further down the line. He had little to go on at this point; it was a hunch, really. These free radicals – essentially rogue atoms missing an electron – roamed cells, in his view, pairing up awkwardly with other atoms. Sometimes these free radicals pulled electrons clean off other atoms, turning new atoms into free radicals, passing on the problem and beginning a chain of 'hunt the electron' within cells. Eventually, Harman imagined, such a rogue free radical might interact with an atom that sits in a particularly vital molecule – a molecule with an important cellular function, say. He imagined that if this were to happen too often, cells would hit problems. Ruin enough of these vital molecules with free radicals and your cell ages, Harman hypothesised. He set to work looking for evidence to support his hypothesis.
Harman experimentally observed the impact of free radicals on short-lived mice dosed up with radiation. He found that after loading radiated lab mice up with antioxidants, they fared better – they lived, on average, longer. It wasn't as simple as he imagined, though. In Harman's tests, he was unable to alter their maximum lifespan, but he could experimentally increase the average life expectancy by up to 45 per cent, mainly through the use of the antioxidant butylated hydroxytoluene (BHT), a molecule widely used in the oil industry to prevent free radicals from oxidising fuel. Science operates most efficiently when someone comes out of nowhere with big ideas, and Harman was that scientist. Like white blood cells surrounding a cocky invading bacterium, academics soon surrounded him, probing and pushing around his ideas, trying their best to squash them where they lay. But what they found was that Harman's hypothesis was interesting enough to be considered: free radicals did somehow appear to be involved in cellular ageing. Though researchers exercise extreme caution when it comes to making general statements about the relationship between cell death and free radicals, many have come to be swayed by the evidence found to support the relationship. If you slow the free radical damage you can slow the ageing. That's Harman's legacy.
So let us return to Ming and animals like Ming. Do ocean quahogs somehow tame their free radicals? The answer is yes, somehow they do. By comparing polar bivalves* with temperate ones (whose lives are often shorter), Eva Philipp, a molecular cell biologist at the University of Kiel, reported in 2007 that polar bivalves 'not only show lower metabolism but also show lower free radical generation, higher antioxidant capacities and in line with this a slower decline in mitochondrial function and accumulation of oxidative damage products with age'. They've mastered the art of free radical wrangling, in other words. And they aren't the only ones, it seems. There are many other wranglers of free radicals out there, which we are only now coming to understand. The birds, particularly, are striking examples.
Rather than root themselves to the seafloor and do very little, like clams, birds manage to live a life of extreme metabolism, and they manage it for years longer than many mammals could ever dream. There is a chance that I have watched puffins the same age as me (34), which is impressive enough, since puffins are actually quite small, but there is a wild Laysan albatross that is still pumping out chicks on Midway Atoll at the tender age of 63. The oldest bird in captivity, Cookie (a Major Mitchell's cockatoo at Brookfield Zoo, Illinois), is still going at 83 years old. This is incredible, by Planet Earth's standards. A lucky pigeon may live 10 or 15 years whereas a similar-sized mammal – say, a rat – would be lucky to live three. Birds really are an anomaly.
Hummingbirds are a particularly striking example. A tiny hummingbird's heart pumps up to 1,000 times a minute as the bird zooms from flower to flower to flower. They are one of most intense metabolisers in nature. You'd think they could only last weeks at such a pace but, incredibly, they can survive for 10 years, consuming an estimated 500,000 litres of oxygen (per kilogram) during this time. On paper, with so much metabolising going on they should be riddled with rogue free radicals, but... they're not. Or they don't seem to be. Nick Lane's book Oxygen: The molecule that made the world does the mathematics far better than I could: based on a hummingbird's oxygen consumption and its longevity, the average bird's exposure to free radicals should be 10 times that of a similar-sized mammal like a rat (and maybe twice that of a human). Surely, they should be accumulating toxic levels of free radicals?
Gustavo Barja, a biologist at the Complutense University in Madrid, Spain, and his team have built upon Harman's early work on free radicals using birds as their model. By investigating pigeons, Barja confirmed that the mitochondria from pigeon tissue ate up three times as much oxygen as rat mitochondria. Yet the amount of free radicals produced in these reactions was far less. In fact he found that pigeons produced only 10 per cent of the free radicals that rats produced. Just 10 per cent. How they do this is still anyone's guess. And they aren't the only ones, like clams, to have somehow made free radicals impotent, robbing them of their destructive powers. Somehow, mechanisms to deal with free radicals have evolved in many animals that natural selection has thrown into positions of power, or at least niches like flight, where predators are almost non-existent or are stopped, on the whole, in their tracks. Bivalves, opossums, some turtles and some tortoises – all of them may, to varying degrees, have pulled from out of the evolutionary toolbox a probable wielding of antioxidants to allow for a longer lifespan. Why? And how?
Scientists (now thousands of them) are making great strides to answer this question. Flight appears to be particularly associated with the taming of free radicals because bats also manage, somehow, to control their release. Another link that highlights the relationships between flight and free-radical taming is that some non-flying birds, like ostriches, no longer appear to control their free radicals in the same way. They become more like ground-dwelling mammals of similar size (though they still fare better than most non-birds: a healthy ostrich might live 40 years).
There are yet other creatures that appear to tinker with how they deal with free radicals, and one of them may offer us a striking method through which we might modify our own longevity in future. The larva of the pearl mussel, Margaritifera margaritifera, is a particularly interesting example. It's a parasite that lives for part of its early life within the gills of Atlantic salmon, where it requires an extra year of the salmon's life to continue its own full development. There are early indications to suggest that the pearl mussel larva might somehow introduce a peptide into the fish's cells that mops up free radicals to ensure the fish achieves longer life, thereby allowing the tiny pearl mussel larva to complete its own life cycle and survive to adulthood. The parasite wants the fish to live longer. Fish infected with Margaritifera margaritifera are more resistant to tumours, and their wounds heal more quickly too. Though the exact mechanisms through which this tiny mollusc achieves longer life in the salmon aren't totally understood, there will no doubt be some scientists who wonder whether this little larva could be engineered so that it could attach to a human, an idea I rather like. It'd be like the Babel fish in The Hitchhiker's Guide to the Galaxy: just inhale some pearl mussel larvae up into your lungs every now and then and – rejoice – enjoy 40 more years of healthy life! The idea sounds ridiculous, of course. But then, why not? Not for the first time in this book, I find myself wondering about how much I would pay for such a treatment. Indeed, I think I would probably pay at least £50 a month to rent a pearl mussel larva...
At this point, I sound like I'm saying free radicals explain ageing and that this theory of why and how we age explains everything. But it doesn't. Not totally. For there is evidence to the contrary. For instance, in 2009 experiments with roundworms indicated that hobbling the production of naturally occurring antioxidants (which mop up free radicals) actually increased lifespan rather than decreased it. And then there are naked mole rats. They really are strange in all sorts of ways, and it's with them we should finish this chapter because... well, they shoot the free-radical hypothesis to pieces.
When German naturalist and explorer Eduard Rüppell first discovered the naked mole rat he assumed it was somehow diseased, so strange do they look. Hairless, aged, twitchy. Raging. They hang upon life's tree as if held by a novelty fridge magnet that no one can remember being given. They look totally out of place on Earth. But of course, they're not. Natural selection makes places, after all, and there are niches for those that can fill them underground, providing animals don't mind that they will probably end up being chiselled by natural selection into strange and (to some) rather ugly shapes (some scientists call naked mole rats 'penises with teeth') and sexual arrangements. Like ants and termites, naked mole rats have evolved a complex social arrangement, where underground colonies are populated by workers that support a single breeding queen who (literally) bullies them into subservience. If you care to look at a naked mole rat individual you will notice that it looks haggard and aged, and this is partly because many of them are, yes, haggard and aged. They live a long time. Where a similar-sized mammal may be lucky to live three or four or five years, it was discovered (through captive collections) that naked mole rats manage six times that. Many naked mole rats end up approaching 30 years, which is almost Ming-like, comparatively. Because of this, like pigeons and hummingbirds, they have become a model animal for those interested in age research, aided by the fact that they are relatively easy to keep in lab conditions, and relatively easy to monitor.
In environments with fewer predators (such as in flying vertebrates, or for shelled invertebrates like quahogs) natural selection appears drawn toward producing bodies that invest more heavily in parts and maintenance. Naked mole rats have become almost like high-mileage concept cars in their levels of maintenance. They are, like Ming, outliers. But the more we learn about naked mole rats the weirder it gets. Firstly, their cells appear to be ravaged by oxidative damage from free radicals, yet the strange thing is that it doesn't seem to bother them in any real way. Research suggests that their lipids, proteins and DNA are up to eight times more damaged by free radicals than in mice. Yet they appear totally fine with this. They continue as normal. The second thing that's weird about naked mole rats is that their cells appear to contain a host of strange proteins, which somehow assist other proteins to keep active and in good condition. And the third thing is this: naked mole rats don't appear to suffer from cancer. They just don't get it. This one is particularly weird because nearly all animal life can suffer cancerous growths, and nearly all animals have weapons to keep cancers in check; weapons that are, most of the time, very effective. Somehow, naked mole rats have gone further. They've nailed cancer. Naked mole rats are foolproof. Survivors. Battle-axes. And no one knows yet how they do it. Maybe it's from them that we might better combat the illness that riddles the lives of so many that we know and love.
From Medawar to Harman; from bats to birds to mole rats and Ming – animal life is showing us the way. The way to live, if not forever, then for longer. The way to live healthier lives in which we might only visit hospitals a handful of times during our lives. But free radicals, interesting as they are, offer us only hints at what is going on. The real action happens in those parts of our cells where free radicals are made: the mitochondria. For it is in our mitochondria that the story of ageing begins and ends and where the action really hots up. It is no wonder that many scientists are now focusing on mitochondria when looking for answers. By incorporating them into our cells, we got the keys to the castle... if only we could understand the bloody locks.
Note
*Bivalves can be loosely described as molluscs that live their lives within two hinged shells. They include oysters, scallops, clams, cockles and mussels. Many species burrow but some, like clams and mussels, are adapted for life (as adults) on rocks near the shore or on the ocean bottom.
CHAPTER FIVE
This is a Dead Frog
'THIS IS A DEAD FROG.' Alison was my deathsplainer and these were her words when we met. They were words which rang in my head as I arrived home from the north-west with the dead bird under my arm. I thought hard about her opinion that we need to talk more about dead things with children. My skin crawled that I had ever said to my own children that some dead things we came across 'were only sleeping'. Alison's voice echoed in and out of my inner monologue. 'We need to give them access to it,' she'd argued. 'We need to get them used to the idea of life and death.' I pulled the bag to my chest. Perhaps this dead bird would give me my opportunity, I thought. Perhaps this would be my time. My eldest daughter, Lettie, was then three and a half years old. She was approaching what I'd class as full human cognition, her neurons connecting in such a way that she was starting to understand that other people have ideas and emotions that were different to her own. Now was the perfect time, surely, to talk to her about death. This would be the moment.
I went into the backyard and placed Alison's bag on the patio floor, and beckoned her over. 'What's that?' she asked, playing in the garden. I opened the bag and began to explain. 'This is an animal that I have collected from a friend,' I said, speaking clearly and calmly. I pulled out the ice cream tub which had been wrapped up tightly in cellophane, with a further layer of kitchen towel over the top. I was crouched down on the floor, with her standing a few feet away looking slightly suspicious. I began to unwrap it. 'Erm...' she said. 'What... what is it?' I peeled off the layers of cellophane and gently reached into the tub to grasp the peaceful-looking body of the magpie in both hands. It felt surprisingly floppy when I first grasped it around the mid-body. Its head rolled back when I began to lift it out, giving its expression a kind of exasperated quality. It felt surprisingly warm, like there was still some life left in there, which I suppose there was (just not magpie life). It was beautiful, though. Really beautiful. The warm sunshine caught the reflective green character of its wings and neck perfectly. It looked composed in death. Arranged, somehow. The wonderful remains of this creature rested in the centre of my hands, its eyes closed, beak tight shut. There was no blood. It was a peaceful thing. This was it, I thought. Here we go. I looked my three-and-a-half-year-old in the eye. 'This is a dead bird,' I said brightly. She said nothing. I tried again: 'This is a dead bird.' I said it slightly louder this time. Nothing. She looked at it without saying a word. She pondered though, which was a start. She looked quietly confused for a few seconds, as if expecting the bird to do something, and then smiled at working it all out. 'Ahh,' she said proudly. 'It's sleeping.' She put her finger to her mouth as if to tell me to be quiet lest we wake it up. 'No... no.' I looked her deep in the eyes once more. 'It'll never wake up,' I said. Lettie was silent. 'It lived for two or three years,' I said. 'But now it's stopped. It stopped living. It's dead.'
Oh shit. I immediately realised the mistake I'd made. Three-year-olds are obsessed with their age. Totally obsessed with it. Would she take this as my perverse way of telling her that she wouldn't live to see her fourth birthday? That she might die like the magpie after her three years of life? She said very little. She chose not to move away though, which was something. There's loads of things for three-year-olds to do: spill things on the sofa, run around, make a mess, not help clean up. She chose to do none of these things. She chose to stay with me and the dead bird. I took that as a good sign. I stroked it gently, running my forefinger down the back of its head and down its spine toward its long tail feathers. Still Lettie said very little. I must give this another go, I thought. I mustn't mess this up. We must talk more about death without me somehow scaring her. I encouraged her to come a bit closer. I stroked the magpie a bit more and beckoned her to do the same. It looked so clean. It was surprisingly calming. Lettie didn't want to stroke the dead magpie. She did look closely at the magpie's face, though. 'It's eyes are closed,' she said. 'It's sleeping,' she said again. I smiled patiently. 'No.' I calmly recited once again the rules: all animals live for a bit and eventually they die. 'It's not sleeping,' I said. 'It's dead. It has stopped living.' She slowly started to get it, I thought. 'Yes, it's dead,' she agreed a minute later. 'It got died,' she said. 'Dead,' I corrected quietly. Marvellous, I thought. We looked more closely at it. I pulled its wing gently out so we could marvel at this spectacle, a flying theropod dinosaur. I told her about the fate of the dinosaurs, how this magpie's ancestors survived whatever it was that killed the rest of the dinosaur family and how amazing that was. At this point I started, as happens a lot when I talk to my children about theropods, to lose her interest. She glazed over. It was time to stop. I carefully packed up the magpie back in its ice cream tub.
'Will the magpie still grow?' she asked later that day. I was glad she was still thinking about it. 'No, it won't,' I said clearly. 'Dead things do not grow.' She paused. 'It won't grow,' she said, imitating my solemnity. 'It won't grow because it's dead.' Brilliant, I thought, she's got it. 'And I won't grow either until I'm dead,' she added quietly. I paused. 'Wait... What?' I ran over to her. 'Lettie, no, you'll still grow. Lettie, you're not dead!' I said this to her with a deep seriousness. In fact, I didn't let her get into bed until I was sure that she grasped that she was alive and definitely not dead. Forty-five minutes later I turned off the light. This was going to be harder than I had anticipated.
I turned my attention now to the dead magpie and my original plan. The reason I had fetched it from Alison was to learn about how, and to what degree, other corvids (the family that includes crows, magpies, rooks, jays and ravens) might examine this dead bird. Would they view it as an interloper? Would they feed off it? Would they express stress or anxiety at the sight of it? Would they mourn or have a 'funeral' as some scientists believe that they do? Or would they completely ignore it? I knew that, probably, it would be the last, but still, I thought I'd give it a try, just for interest, really. I bought a camera-trap to record what would happen to the magpie after I left it out there in the field, exposed. But where to put it? Our small cottage sits within an enormous colony of jackdaws, and occasional gangs of magpies also make themselves known to us, cawing and clacking a passage through the trees under which we park our car. There is a small clump of trees with a bare mound beneath that forms a stage for their interactions, and that seemed the perfect place to leave the dead bird and prime up the camera.
I left the magpie there that night, set the camera-trap up and returned each day to collect the memory card and see what had happened over the course of each 24-hour period. I had never done anything like this before. It was actually very exciting. Each day I sprang out of bed eager to see what kind of soap opera might have been recorded on the previous day as these social birds hustled and bustled around the dead magpie, possibly mourning it (I allowed myself to imagine) in all sorts of strange and unique ways. At least, this is what I had hoped. In reality it didn't work out quite like that. It didn't work out that way at all. Each file on the memory card was a 10-second bit of video footage, and on the first day of recording I had nine files to watch. I had been very excited at this. Might I see a world-first? I wondered. Something amazing that could find its way into this book? I clicked on the video files. No. The answer was no. The first video clip showed a woodpigeon shuffling through the leaves, totally oblivious to the dead magpie. The second video clip showed a woodpigeon, the same one, I suppose, shuffling through the leaves pecking here and there at scraps. The third showed two woodpigeons. They ambled in opposing directions from the centre of the frame. Not once did they stumble across the magpie. In the fourth video literally nothing happened. I'm not sure what set the camera off here – probably a butterfly. The fifth was the same. Oh well, I thought, there's always tomorrow. In each video file, the magpie lay there like Juliet on a plinth awaiting Romeo, its feathers ruffling slightly in the breeze like a black shawl. It made a beautiful image in many ways: a sleeping woman in a black cloak, being slowly consumed by summer leaves gathering upon her.
In the following 24 hours the camera trap picked up more videos of woodpigeons. And there was a squirrel too, piddling around in search of nuts. Day 3 was better. On day 3 I caught the movement of a larger animal. It was a cat. In the early light of dawn, the eyes shone like fire in the infrared footage. First it looked at the camera suspiciously, then stealthily approached the magpie. It gave it a few sniffs before looking warily around. I wondered if it might play with it, or pull it about a bit, but it didn't. It took a few moments and then it surprised me: it curled its legs underneath its body and, quite surprisingly, lay down next to the bird. It blinked its eyes slowly. The cat looked very content. The footage ended. It might have had a little sleep. Hmmm, ok, I thought. The next video clip was in daylight, a few hours later. The magpie was still there and the same, very annoying, woodpigeon was wandering around in its usual annoying way, stumbling around like a dull-eyed teenager looking for a wallet among sofa cushions.
And then, on the fifth day, just as the magpie was starting to really smell and I was becoming worried what the neighbours might say, something happened. I visited the camera-trap as I had done every morning, and I found that the magpie was gone. Gone! I was delighted. Eagerly I pulled the memory card from out of the camera and headed back to the kitchen, hoping beyond hope that whatever happened to the dead magpie had been caught on camera. Lettie was having breakfast as I did this. I dumped my laptop onto the table beside her as she ate her cereal, and I inserted the memory card. There was only one video. Would it be the one?
Lettie finished her breakfast and came over to sit on my lap as the video loaded. Nothing much showed up at first. Silence. Just the magpie in its usual position. A few moments passed. And then, from deep out of shot, a fox cantered in, its nose pressed firmly to the floor like a bloodhound in an airport lounge. Then the fox stood stock-still, it's long body framed perfectly in the shot. It came upon the magpie. It looked haunting and spectacular in this well-framed shot; its tail bushy like a paintbrush, its eyes, as it looked at the camera, like lit torches. It approached the magpie, sniffed it a bit, and then, like a lion gently picking up a cub, it put its jaws around the magpie's midriff and lifted it gently up. I thought it would leave at this point, but it didn't; instead, it swivelled its body away from the camera and pressed its rump up to the lens. Its tail lifted up, it squatted slightly, and from its anus it issued forth an enormous dollop of faeces, right up close to the lens; it felt like it was coming through the fourth wall. Then, its load lightened and with bird in mouth, the fox trotted merrily out of view. The video clip stopped. Wow. I chuckled, finding the whole thing totally brilliant and just, well, wonderful. I noticed, though, that Lettie, on my lap, did not find it funny. She sat there, still. She had a face of icy concern. 'Was that... was that in our...' she quietly murmured. Tears pooled in her eyes. 'Was that wolf in our garden?' I gave her a warm cuddle. 'It's not a wolf! It's a fox,' I said breezily. 'Foxes are ok. They're lovely. They hoover dead stuff up. They help nature.' This didn't really help much. 'That was our bird!' she said, suddenly indignant.
I didn't really know what to say to that. It wasn't ever our bird. It didn't belong to anyone. There was a pause. Her sense of injustice seemed to pass and she went back to being scared again. Foxes have as bad a reputation as wolves in Britain. Every single cultural reference her little brain has received so far in her little life has painted foxes and wolves as monstrous. Foxes are bad guys in many of her books and TV shows: Peter Rabbit, The Little Red Hen, Dora the Explorer and Br'er Fox. And now here I was, showing her videos of the foxes that live just outside the back door, right outside her bedroom window, stealing things, like dead birds, that she held dear. She gave me a look that indicated that her whole worldview had changed for ever, and we should all give her a few days to catch up so don't rush her, ok. I chose not to tell my wife that it was all my fault. First there was the dead magpie. Now the death-eating fox. This was my second opportunity to talk about death with Lettie, but... I felt it didn't go well. I could have done better. I kept messing it up. If this had been a test and Alison were judging, I felt like I would have failed. I chose not to tell Alison any of this, of course.
Six months later I would have another opportunity to make things right. My third. And this really was the big one. We had unfortunately heard of the death of an elderly relative, Lettie's great-grandmother, and we were all very sad. Lettie had visited Great Grandma with us frequently, first in her flat in the East Midlands and then, as she deteriorated, in a nursing home. We broke the news to Lettie after dinner. 'It's sad,' I said as we prepared for bedtime. 'We're all very sad.' 'Yes,' she said. We'd warned her it was coming, so in many ways she was ready. She was certainly suitably morose when we told her but it was hard to know what she really felt about it. A small part of me wondered if she was acting out how we were behaving like it was some sort of game. When she spoke there was almost a theatrical lilt to it. 'Great Grandma has dead,' she said, quite seriously. She looked at the floor, a mournful look on her face. I coughed. 'Umm, died,' I corrected her. 'Great Grandma has died.' 'Yes, dead,' agreed Lettie. 'Yes, she is now dead,' I said sadly. As I put on her pyjamas she shook her head sorrowfully whilst looking at the floor. 'Yes, dead,' she said. 'She has dead.' I had to correct her about this. It seemed important that she get it right. I paused and drew breath. 'Great Grandma has died,' I responded. She looked at me with sad eyes. 'Yes, she is died,' she said, her eyes full of mourning. I paused and took a few deep breaths. 'Yes, she is DEAD,' I said. 'She did DEAD,' Lettie confirmed. We were speaking quite loudly now, her raising her voice to counter mine. I rubbed my eyebrows and composed myself. Another deep breath. 'Yes,' I said calmly. 'Yes,' I repeated. We can tackle all this later, I thought. I stopped talking for a while.
As I tucked her up for the night, I nudged Lettie one more time into death-chat, just in case there was anything else she wanted to say before bed, partly out of concern for her mental well-being but also because this had all become very interesting to me. 'I miss Great Grandma,' she said, arranging her teddies next to her pillow. 'We miss her too,' I said quietly. 'She died,' she said again sadly. I stroked her arm. 'I know, but she lives on...' I said. 'Great Grandma lives on in our heads.' I tapped the side of my head, smiling. I gave her a kiss and walked out of the room. Glancing back as I turned off the lights I saw her face. Lettie was sitting bolt upright in her bed clasping her head in her hands, with a look of confused terror on her face. I had just told her that Great Grandma had died and was now living in her head. No wonder she was freaking the hell out. I quickly turned on the lights and rushed back in laughing insanely. 'She lives on in our hearts!' I said, my voice shrieking wildly. 'In our HEARTS!' I said. 'Sorry, darling! My mistake! I meant we remember her in our hearts!' I was almost screaming. 'OUR HEARTs!' I said again. Lettie gave me a look. She knew something weird had just happened. I feared at this moment that I might have just shattered the emotional development of my eldest child.
A few days passed, and we all talked more about death and the upcoming funeral quite a bit, so that helped. This funeral was to be a big hurdle in helping Lettie to understand death, I'd realised, but to be honest by now Lettie was becoming something of a death-pro. She had come on leaps and bounds each and every day since we'd taken to discussing it. Alison, my deathsplainer, would have been proud of me. Honestly. Things were going much better. Lettie knew the correct phraseology, the grammar; she could express sadness and say really surprisingly comforting things. We'd succeeded, I thought. At the funeral itself she was an exemplary mourner. She sat with head down throughout the whole thing. She sang 'All things bright and beautiful' with the appropriate amount of sadness mixed with happiness at all the jolly bits. She put her hands together and looked like she was praying really hard too, again at all the right moments. She commented on the flowers and cuddled family members outside when it was over. An exemplary mourner. She really was. We all said so. We drove to the wake, which took place in a lounge outside Great Grandma's old flat in the sheltered accommodation where she had lived before the full-time care. Lettie played with the other kids at the wake while the adults all made small talk and caught up with one another and talked about Great Grandma's long and quite happy life.
Things took a turn later that afternoon. After about an hour Lettie came up to me requesting a visit to the toilet and it was then that she betrayed her true understanding of death. We had walked down the corridor to the visitor toilets and we had found that they were engaged. 'Hey Lettie,' I said. 'While we're waiting for the toilet to become free shall we go and walk down the corridor to see the front door of Great Grandma's old flat?' 'Yes!' she said firmly. 'I want to do that!' Then she stopped and thought it over again. Yes, she thought. She gave me a look that suggested to me that yes, definitely, this would be an appropriate thing to do. And so off we went. We walked down the long snaking corridors toward the door to Great Grandma's flat, which was now empty. And then, as we approached the door to her old place, I noticed I was now walking alone. Where was Lettie? I looked behind me and I couldn't see her. What had happened? Then she came around the corner. And she was creeping. She was tiptoeing down the corridor toward me. 'Lettie?' I asked, slightly nervously. 'Lettie, what on earth are you doing? What... what are you doing?' She looked at me with incredulity, surprised I'd even have the gall to ask. She put her index finger to her lips. 'Sshhhh, Daddy,' she said as she approached the front door. 'You'll wake Great Grandma!' she hissed.
Oh dear, I thought. So I had failed. No, actually, she had failed. Failed to grapple with what death is. But I had failed too. I had failed because I'd assumed too much. I had totally misinterpreted her understanding of death. I had projected my own experience of what it is to mourn onto her. Thank God Alison wasn't there, I thought. Alison would have her head in her hands at this.
It was deeply interesting how Lettie had us convinced, though. Convinced that she had understood death. She had convinced us that she knew Great Grandma was in the coffin. But she hadn't grasped even the most basic bit: that Great Grandma had gone and she was no longer asleep in her bed. That she had been burned in a coffin and now she didn't exist, apart from in a nebulous atomic form floating around in the sky, and in ashes. That she had gone. That she had died. That she was dead. I wondered about whether, even if I had seen corvids apparently show an interest in my dead magpie, I could ever be sure what they knew about death. I realised again how hard animals are to read. I couldn't even work out my own child, for goodness' sake. Our perceptions of death are complicated. I had a long way to go.
PART TWO
THE EXPERIMENTAL PIG PHASE
CHAPTER SIX
The Circus under the Tent
In life, it's the occasions where you have to wear waterproof trousers that are generally among the most interesting. Dashing through streams, pond-dipping, surveying rock-pools – warm memories are made of such experiences. But there are other reasons for wearing waterproof trousers. For instance, there are those rare occasions when you are told you may have to crouch down inside the collapsed carcass of a putrefying pig corpse. This, as it happens, is one of those days. 'If you're writing about death you have to go and see Peter Cross at TRACES,' was Alison Atkin's final piece of advice after handing me the dead bird. 'What's TRACES?' I had asked. 'Well, it's a bit like a body farm,' she said. I had heard of body farms on CSI. They have body farms in America. I had to go. Alison set it up.
I am in a 'secret location' near Preston in the north-west of England, and Peter Cross is my guide. As well as being an accredited forensic anthropologist, Peter is also a lecturer in forensic anthropology at the School of Forensic and Applied Sciences and he runs TRACES (Taphonomic Research in Anthropology: Centre for Experimental Studies), which was established by the University of Central Lancashire. Peter doesn't immediately strike me as someone at home in the lecture theatre. In our early emails he seemed more of a practitioner than a lecturer, somehow (though he later tells me he won 'Lecturer of the Year' in 2013 so... well, what do I know?). A previous meeting I had arranged with him had to be postponed after he was almost called to assist with forensic identification after a fatal plane crash in eastern Ukraine, close to the border with Russia. TRACES is largely the result of Peter's hard work. At its most simple, TRACES is essentially a large tract of land within which pigs are left to decompose under a range of conditions. The rates of decomposition for each variable are measured, creating a kind of death-measuring station – a 'rot-clock' – with potential application in human forensic cases. Say, for instance, a man's body turns up after months and months left in a waterlogged field; TRACES research on dead pigs left in wet fields can support forensics teams in their attempts to ascertain a potential time of death for the human remains.
I can safely say that I have never been to a research station like TRACES. I feel slightly out of my depth during my visit, and slightly insecure about the whole thing. So why am I going, you might wonder? I decided that it'd be useful to learn more about the ecosystems that emerge on the bodies of dead creatures, and Peter has kindly volunteered to be my guide, provided that I wear my own wellies, refrain from taking photos on my phone, and bring my own washable waterproof trousers. As we drive onto the site, Peter sets the scene: 'One of the key questions that's asked when a body is found is often "When did this person die?"' he says. 'What we focus on here is understanding the variables that influence the decomposition process and therefore may have implications for the accurate estimation of post-mortem interval.' He brakes suddenly and gets out of the Land Rover to open the gate to the site. Getting back in he adds quietly, 'That time period between life and death is much more tricky than CSI will lead you to believe.' There is a slight glint in his eye as he says this, so I sense that Peter doesn't like the hit TV show CSI – I make a mental note to avoid mentioning it or anything like it throughout our time together.
Today would be mostly about pigs, then, I think happily. In parts of North America, as many readers will be aware, forensic scientists use real human (donated) bodies for this kind of forensic research, placing them in institutions loosely called 'body farms'. At present this isn't the done thing in the UK, so we use pigs instead. 'Though it might be possible in the UK with a change in legislation...' says Peter. 'Well... it's not been done before here, and there are still mixed feelings about it within the anthropological community,' he explains. 'After all, is it ethical for us to study the decomposition of a human body?' I shrug my shoulders. There are benefits to using pigs, though. Peter prefers using pigs as human-models mainly for the strength of empirical data this opens up. 'Firstly, with pigs,' he says, 'you have more bodies to work with. In terms of replicate numbers, our experiments are... well, let's just say that they're more robust. We can have replicate groups of 20, 30, 40 – whatever we want. With pigs, we can test hypotheses very robustly, and this has real value.' I suspect this isn't the first time that he's talked to visitors about the relative merits of pigs. 'In this kind of research,' he says quite happily, 'there will always be a place for pigs.'
We park up. The TRACES lab itself is housed in a little courtyard at the entrance to the site. Next to the parking spaces there are some empty bathtubs dotted around, and some empty aquaria. There is a hose to hose everything off, and, I assume, to hose us off when we finish here. Peter walks toward the large metal outbuilding in which the lab is found. He beckons me in. Inside is a collection of tables, a kitchen, a couple of lab benches and an enormous tractor for carting the pigs around on site. The lab is well ordered. Everything has a place. There are hygiene posters on the walls, labelled drawers and hangers for lab coats and waterproofs and a footwell for the wellies. As Peter changes his shoes, I head over to a lab bench upon which sit a host of assorted pig bones. I scan the bones. The only ones I can immediately recognise are the vertebrae and, unsurprisingly, the ribs (which I have seen countless times on people's dinner plates). Then I notice a few more. There's a jawbone. A stocky femur. Scapula. There are many teeth. I try haplessly to plug them into a piece of lower jaw while Peter dons his waterproof trousers. The small talk continues between us: postgraduates, dissertations, academia, collections. Peter takes a bit of warming up, and I sense that, underneath, he might be a tiny bit worried I'm devising a trite 'UNDERCOVER CSI!' piece – a vainglorious article that sexes up the steely-eyed scientists who solve murders in their spare time by slotting together pig skeletons and lining up dental records and gunshot residues and the like. He doesn't know that at that exact moment I'm quietly pondering whether pigs lose their baby teeth like humans do (which, it turns out, they do).
'Ready?' says Peter suddenly. Already he is walking off into the site itself. I hurry behind him out of the lab and we make our way up a long farm path, lined on each side by thick scrub. It's a steep path and we climb upwards sharply, enough to make me a little out of breath. There is plenty of activity in the bushes as we stroll past. A pair of magpies monitor our passing. A mixed flock of great tits and blue tits moves above us, and some long-tailed tits flitter from one side of the path to the other, moving with purpose through the trees and bushes like a troop of investigative chimps. Peter opens a large gate in front of us and announces our arrival onto the site proper. An enormous flat expanse on the hillside stands in front of us, which is almost bowl-shaped in parts. There is a real nature-reserve look to it: managed mosaics of grassland and scrub (some succeeding into beech saplings and hawthorn) give way to an unmanaged area that is peppered with meadow flowers, and newly planted woodland borders about half of the site's 13 acres. A slight wind moves before us, grooming the grassland. It's a secluded spot, with only one entry point: perfect for studying what happens to dead pigs without worrying about what Peter calls 'human interference' (I don't ask what this means but I assume it is deeply frowned upon).
Looking across the flattest part of the site from the entrance, it's possible to see a series of wire-mesh wooden frames dotted around. These are placed in long rows and under each one are the remains of a dead pig, some of which have been here for more than three or four months, Peter tells me. The nearest wooden frame is about 20 metres away. We start walking toward it. 'At this point people often vomit,' says Peter deadly seriously as we trudge through the long grass toward the long-dead pig. As we get nearer and nearer I expect to be overcome by stench. But, no. It's actually fine. I manage ok. As we approach closer I expect to see some sort of body lying there. But, no. There's not even a proper body with mass or anything, just a collection of some kind of detritus lying on the floor. A messy collection of bits. And that's when it hits me. Only when we stand directly above the remains of the pig do I suddenly smell it; the stink wafts up in an invisible foggy cloud, entering my mouth, my nose and my pores. Staining my clothes. It's not disgusting, exactly – it's just... powerful. I don't feel nauseous or anything like that. In fact, if I were to describe it, I'd say that a dead pig, after three months in the sun, smells exactly like pork scratchings, the treats made from cooked pig skin and fat offered up in British pubs. The pork-scratching smell probably shouldn't have come as a big surprise to me; looking down upon the dead pig's body, long sheets of skin and fat are pretty much all that remains, baking in the sunshine. Lying there now, its body resembles a badly cut piece of grey carpet about the size of an ironing board. It looks nothing much like a pig. Long, thick hairs protrude from the carpet, I suppose, but I can't see any bones. No teeth.
I'm a little surprised at this, what turns out to be the first of many dead pigs that day. Coming upon it by accident, one might almost assume this was an oily puddle of thick wet rags, and little more. I put on my most professional voice. 'So... where's the head?' I ask, crouching down next to it. Now that he can see I haven't vomited, I like to think Peter warms to me a little from this point onwards. I like to think I have passed some sort of test. 'Well, there's a reason for that,' he says, crouching down next to me. 'The head is often one of the first places to go in pigs – and humans – because flies are initially attracted to natural orifices. They particularly like laying eggs in the eyes, the ears, the nose – as a result the head is often the first thing to skeletonise.' Orifices. Skeletonise. The conversation has escalated more quickly than I had expected it to. There is a hint of disgust that I do my best to mask. Peter pretends he doesn't see. He sees.
We look more closely at the pig. Its hide looks like plastic in the warm sun; there's a Vaseline-like sheen all over it, with yellow blobs that look a little as though Dijon mustard has been sprinkled in. This waxy substance, according to Peter, is called adipocere. It forms on bodies in wet environments, a leftover product of anaerobic bacteria that flourish upon fatty acids. For forensic scientists adipocere can cause problems, since it forms a boundary between the external environment and the internal environment – a boundary that decomposing agents struggle to cross, and which makes estimating decomposition rates slightly more difficult. Adipocere is a mummifying agent, essentially; some death professionals apparently call it 'mortuary wax'.
We sit there for a few moments, looking at the scene. A few bluebottles come and go, but there doesn't seem to be much going on. Until we look a little more closely. And then they start to appear: hundreds of tiny flies hover and perch upon the skin. They are tiny, like midges really. Some, if they land, run quickly up and down and across the surface of the pig, slaloming the thick hairs that protrude through the grey jelly of the adipocere. These are cheese flies: a worldwide family of flies, mostly about 3–4mm long. Up close they are almost metallic, and quite beautiful. A pair of prominent eyes take up most of the head; two wings are held politely over the back of the body. They have a kind of urgent, desperate grace to them. And the cheese flies are scavenging the corpse, as is their way. Two or three land and wander around to the underside of the mummified sheet out of our view, no doubt looking for darker places to lay eggs. Their grub-like larvae are often called cheese-skippers, for their apparent ability to fling their bodies forward through the air by holding onto the corpse with their grappling mouth-hooks and flipping their back end over their head. Cheese-skippers typically take three weeks to pupate, and are one of many species used by anatomists to determine how long a dead body has been lying there. They are one of hundreds of body clocks that apparently make deceased megafauna (I use the term loosely) their home.
I look a bit more closely still. There are other small flies, too; they dance in and out of the corpse. And tiny beetles. On closer inspection I see a host of green beetles flutter busily in and out, going into a hole that leads into the darkness under the skin. They look like tiny bees going in and out of a hive. I try to get a few photos of these electric-green beetles as they land, to no avail (Peter has let me take some photos on the proviso that I don't upload them onto Facebook; I imagine how many of my friends and family would reach for the 'Report Abuse' button if I ever posted pictures like these). Peter offers to lift the sheet of mummified pig flank so that we can see underneath and I stand back to give him some space. I ready myself for what lies beneath. Peter firmly grabs the pig skin at two ends and pulls it back with purpose, like he's pulling a tablecloth out from a perfectly laid table. There is a sudden gush of activity underneath, as if Peter has pulled the lid off some sort of tiny flea circus, rudely interrupted midway through a performance; a kind of instant chaos in miniature. An invertebrate melee. A host of small beetles retreat desperately under remaining flaps of skin, many appearing midway through copulation. Five or six larger beetles retreat into the surrounding long grass beneath our feet. A couple of micro-moths flitter past us, and cheese flies lazily buzz off to find other corpses to feast upon. There is much more to see with the skin pulled back, I realise. And it looks more like a pig now. The pig's teeth and jawbone are dotted around one end of the mass, while vertebrae are pulled out of place – ransacked, almost – and show remnants of once having been a chain (I would say they are now a loose arrangement). Rib bones on the floor separate the activity of the remaining tiny beetles into paddock-like enclosures.
This is all incredibly gross, but also wonderful in equal measure. In my years of turning over bits of wood looking at invertebrate life beneath I have never seen such... occupancy. In the centre of the chaos sits a football-sized mass of thick viscous yellow foam that looks like some sort of swirling primordial-ooze-cum-circus-tent. I try and make out whether the foaming ooze is the remains of the pig or an emergent property of the life that has since stirred within it. After a bit of scrutiny I am still none the wiser about this foamy blob. I get up close with my camera. It moves slightly. Peter reads my face. 'Ahhhhh, that...' he says with a certain amount of ceremony, '... that is a maggot mass.' Ok, I think. Of course. Peter crouches down once more beside me. He looks closely at the foam. 'So... hmmmm... these look like first instars... yep, so this is the second wave of maggots,' he says with sudden certainty, standing up. He looks at me. 'The second generation of maggots feed upon the tissues that remain in the chest cavity.' He stops. He reads my face. I hide a tiny little gag reflex. I try to pretend it wasn't a gag, but it was, and I have to wait for the feeling to pass. 'Wow... thousands of them,' I say, trying to sound like a pro. But I'm a fraud. He knows I just retched. He knows I'm a fraud. Still, I tried. It was involuntary really. It was, after all, a reflex. I'm a little bit weird about maggots for reasons I have never been sure about. Embarrassed, I hear myself lay out my credentials to Peter: that I'm a zoology nut and this is my life and it's only maggots that do this to me. Maggots and spiders. Maggots and large spiders and engorged ticks. Peter looks momentarily unimpressed. He says nothing. The sight of those maggots really does disgust me, though.
I take a moment, a few seconds to myself, before getting up close to watch the mass more closely. I gather myself fully and crouch down. This time I feel better. It is fascinating. It really is. Each individual maggot is about the size of a nail-clipping, yet together they have formed an orgy of decomposition; a great swirling snarly mass of purpose. These, according to Peter, are bluebottle maggots. Laid in their thousands and protected in the carcass, there is so much to eat that they have no need to move far; each maggot becomes surrounded and supported from all sides by other maggots. They feed together, and this foamy mass is what results. I watch closely again. Imperceptibly, like a minute-hand moving, the ball of them almost seems to have a life of its own. Revolving. It sort of swivels like a gas giant. I don't expect you to be quite as enamoured as I suddenly turned out to be but... you know, there was real beauty to it. Truly, it was beautiful for a few moments. The whole thing was. And then – woosh – I suddenly dry-retch again. Peter clears his throat and pretends he was looking the other way.
I'm amazed that the pig's skeleton hadn't looked at all as I had expected. I'd imagined it remaining articulated or looking somehow like a perfectly preserved museum skeleton. But it had looked... vandalised. 'You'd be surprised what a large mass of maggots can move,' says Peter, smiling. 'And why is it so foamy?' I ask. 'Well,' says Peter, 'when maggots are actively feeding they stir up the decomposition fluids with air and this forms a thick bubbly foam.' He sticks his fingers into the foam, pulling it apart like curtains, to reveal a fresh maze of cleaner-looking maggots writhing beneath. Peter tells me that, by working their way between sinews and joints, the maggots loosen the skeletal structure. Gravity then does the rest; the skeleton falls apart. I comment to Peter about how it looked like the maggot mass was swivelling. Though I'm sure it was a trick of perspective (or my head spinning), apparently, yes, maggot masses may in fact slowly rotate, though much more slowly than I could really have noticed. The phenomenon, Peter tells me, may ensure that heat is moved out of the centre of the mass, where unlucky 'inner maggots' may face conditions 20° c warmer than at the mass's edge. On the level of selfish genes, it may be that hot maggots head to the cooler edges, dragging cooler maggots into the fiery recesses below. Only further tests (involving the tracking of individually marked maggots, which is apparently very difficult) will reveal the inner physics of maggot masses.
I stare at the maggot mass in silence while Peter attends to something else. It hits me looking at the maggots that in a matter of weeks many of the thousands upon which we gaze will be fully fledged bluebottles, some of which will probably hang around and lay further eggs on this dead pig, and others nearby. Other bluebottles will migrate further, making their way into nearby people's houses or the McDonald's down the road; eaten by birds or hit by cars or fly swats. So many of this pig's atoms will migrate away within the adult bodies of the flies that leave. It seems obvious but... there it was.
We stroll off to see more of what Peter has started to call his 'experimental pigs'. There is a familiar chaos to each corpse that we look upon: the smell, the initial disarray of fleeing creatures, the vandalised bones, the maggot mass. But, like seeing a mass of crowded shoppers from above, order comes from it once you sit and wait and watch for long enough. The cheese flies. The tiny green beetles. The moths. As predictable as wildebeest, giraffes and elephants in their own way. There are the same water holes. Similar scaffolding. Hiding places. Places to bask. Places to bury. I later learn that the green beetles are one of many species of rove beetle. Looking a little like earwigs, 'rovers' have short forewings (or elytra) and long thin bodies that lack pincers. Though it doesn't look like it, they can apparently fly. They move from feeding station (in this case: dead thing) to feeding station (ditto) to live, breed and lay eggs. It turns out there are quite a few rove beetle species out there. In fact, there's rather a great deal of them. Apparently there are more rove beetle species than there are fish, mammals, amphibians and reptiles combined: more than 60,000 species at last count. In the US, one out of every five beetles is a rove beetle. You may know rove beetles – they can move their abdomens from side to side or up and down – a feature for secreting chemicals that aid defence, or perhaps for chemical mimicry. Some are beautiful, with elytra that are deep greens or metallic blues. The largest in Britain is the Devil's coach-horse (adults are about an inch long), which looks and acts very angry indeed when disturbed, but actually is mostly harmless. The rove beetles on the experimental pigs were far shinier and far more charismatic. I came to think of them as Day-Glo fruits of death. According to the books, rove beetles are among the second wave of invertebrates to arrive at a fresh corpse. They had been there quite some time.
It's probably time for a brief description of the specialist waves of invertebrate immigrants that move onto a creature like a pig once it dies. And it really is quite a cast. First to arrive are blowflies, such as bluebottles. As is well known, these are perhaps the most active and fastest colonisers of dead bodies on land. Hundreds may appear within hours. Thousands sometimes. They know death. They know its smell. And they smell it well (but more on this in a second). After this come the cheese flies, the flesh flies (or onion-flies) and the house flies, all of which sow their genetic oats on the fertile soil of death. Some beetle species also turn up early to the feast. The carrion beetles (often called sextons – the Nicrophorinae) are one such. These beetles actively feed on the corpse both as adults and larvae (which, apparently, consume regurgitated food from their parents). As a result, many of these carrion beetles actively compete with blowfly maggots for food; they undergo a race against time to reach a fresh corpse first. Natural selection – which finds a new gear when intense competition erupts between individuals or species – has thus provided many carrion beetles with an incredible ability for chemoreception. They are in an evolutionary arms race against the blowflies; a kind of mad sprint to the death exists between the two groups. Flying through the air, these beetles use their sense of smell to locate hydrogen sulphide, a common chemical released by bacteria in great clouds during decomposition. The same is true of the blowflies with which they compete. Incredibly, some carrion beetles have pulled in hired help: they carry around with them a tiny mite species that devours blowfly eggs – a handy tool for carrion beetles seeking to eliminate any competition that may exist at a new corpse.
After the blowflies, the cheese flies and the sextons arrive, then predictably the things that eat the blowflies, the cheese flies and the sextons put in an appearance. This is where many of the rove beetles fit into the picture. At TRACES I saw them amongst the bloated remains of the pigs picking off blowfly eggs and larvae, carrying them off victoriously in their jaws to hidden depths beneath the flaps of skin. It was like watching from a helicopter as a tiny leopard pulls a tiny antelope into a tiny tree to eat it. But it's not just rove beetles that hunt within the corpse. As decomposition continues and the body dries out a little, other predators turn up. Small chequered beetles (with their long, armoured bodies) may make an appearance. They too are drawn to the broiling maggot mass, coming for the good times and staying for the hospitality that a dead pig provides to their offspring. Rotund clown beetles (great name) may also turn up, again drawn to the feast. Sepsids (often called black scavenger flies) make occasional forays into and around dead mammalian bodies, though we saw none on the day at TRACES. Sepsids apparently sit on grass perches next to the corpse, waving their wings to one another suggestively, enticing others closer, looking for opportunities to mate. Some parasitic wasps will visit the site, undertaking aerial raids on the maggots, immobilising them one by one and laying their eggs within their paralysed bodies (the going rate for some wasp species is 12 offspring per maggot, which seems like a healthy return). Dung beetles too may visit – drawn to the rotting intestines of herbivorous mammals particularly. They work on the raw ingredients of the faeces because, well, why not?
Soon the entire corpse is in the 'advanced decay stage'. Life is everywhere at this point – hundreds of individuals of hundreds of species, and that's not even including the bacteria and fungi that thrive in newly flourishing niches. The role of bacteria is particularly vital in decomposition, for they break down the complex molecules of life into individual elements, like carbon, nitrogen and sulphur, which can then be absorbed by plants and fungi. It really is a wonderful and life-rich place. A food web has emerged from the chaos that looks as rich and full-bodied and enigmatic as any other place on Earth (it is just that those interested in studying it may need to possess a nose and stomach like Peter's).
But, even on a dead pig, there are still other creatures yet to join such a circus. Skin beetles, with oval-shaped bodies covered in tiny scales, are among the most numerous. Their larvae make short work of the dry scraps left on bones and sinews, and are particularly useful in cleaning skeletal museum specimens before public airing. After the skin beetles come the clothes moths (your suits, dresses and jackets are a pale imitation of what their larvae have evolved to devour). But there is more still to come. As the season changes, the corpse is no longer simply a source of food: the remaining bones and sheets of adipocere become a place on which new creatures can climb, and in which shelter and dry egg-laying sites abound. By now the circus has largely come and gone, but the circus scaffolding remains and it has its uses. In come the marauders: the harvestman arachnids, the centipedes and the larger ground beetles, as well as different species of rove beetles, searching for spoils and other late-comers to the party.
These pigs, their dead bodies; it really was a weird experience. A wonderful gathering of the unusual, the monstrous and the bizarre – all of which have made their living for millions of generations from recycling the atoms of the once-living back into the living again. In front of my eyes, watching those pigs, I was watching nature denature itself and spontaneously renature itself into something else. And this is what has happened to almost every animal that has ever lived (until recently, when humans opted out by choosing cremation, selfishly starving many thousands of beautiful rove beetles in the process).
Surprisingly few animals have had their post-life fauna and flora identified, and the theatrical cast that colonises a given dead thing probably differs a little bit (or quite a lot in some cases) for each class of animal that dies. There is diversity among corpses. Among the best documented accounts of animal decomposition are those of marine megafauna, mainly whales, whose bodies drift deep down onto the seafloor post-death. What happens to the enormous bodies of whales is not so different from that which occurs upon the bodies of dead experimental pigs, though there are no insects and there is the added possibility of sharks, which livens most zoological accounts up immensely. No wonder it is a well-told story. Still, I think it deserves its place in this book because it is... well, it is, like the pigs, extraordinary.
There, at the bottom of the sea, away from the influence of weathering and where shallow scavengers rarely penetrate, whale remains can provide the energetic needs for other creatures not for years, but whole decades. Some of the best-studied 'whale falls' (as they're called) are from North America's Santa Cruz Basin. Blurry camera footage shows dead whales on the seafloor 2km below the surface. In the videos (all available online for those interested) their enormous bodies lie there, lit by submersibles that look like space probes. The whales' enormous eyes are glazed over, their great mouths gape. Without life, the whale communicates in a new language: a song to scavengers. As decomposing bacteria flourish within its body, smells are released. These chemical signatures drift through the deep ocean currents, sideways and upwards. They contain messages. Messages that other life will soon intercept and interpret.
Over the coming days and weeks the hagfish are among the first to pick up these messages. Thousands of them undulate and ripple across the surface of the whale like ribbons, making its whole surface appear to writhe. Lacking a true backbone, hagfish represent a distant and rather primitive fish – they have no jaws, only simple eyespots and no true fins. However, to call them basic would be to do hagfish a disservice. Being an early representative of life after the split between vertebrates and invertebrates has its perks, after all, for hagfish possess the best bits of both taxonomic groups. Being worm-like, they are adept at wriggling into the occasional orifice. They can also, if the need takes them, absorb dissolved organic matter across the skin and gills. Like leeches they can go months and months without feeding, drawn toward food via sets of special chemoreceptors that work in ways we can only imagine. Like slugs and snails they can slime up for defence and, like insects, they possess antennae (barbels), tactile organs that come out from the mouth. Yet this is, by all accounts, a fish. A jawless fish. We think of worms and fish being distant; in the hagfish, their shared history is exposed. They are without doubt one of the most under-celebrated forms of life on Earth and they're down there as you read this, wreaking seven shades of hell upon the dead bodies of every whale lucky enough to have escaped the whaler's harpoon in the night.
But it isn't just hagfish. There are other creatures heading the dead whale's way. Along with the rippling hordes comes another fish with its flippers firmly in the past: the sleeper shark. A shark in all but the eyes, which have a zombie-like tone to them – sunken almost into the toothy jaw. Sleeper sharks look very stoned almost all of the time. They slowly plunge their jaws into the bleached whale flesh and twist their heads in sluggish jerks that tear it from the body in plugs, which they then swallow whole. Rattail fish (more properly called grenadiers) – ghoul-faced deep-sea fish – also make an appearance. As do the shrimp-like amphipods and crabs. Predictably, it isn't long until the zombie-worms (great name #2) join the party.
During this early stage of decomposition, 60kg of meat may be consumed each day by the denizens that have made the dead whale their new home. Many will have sex in and around the whale, too. Many, many, many creatures make use of this time of local bounty. Time passes, though. The whale begins to change. After months of activity its boat-sized body begins to fall apart and scatter itself; its bones become exposed, and organs protrude and rupture, spilling more organic matter onto the seafloor. New real estate is born during this period. New exploitative organisms appear – they are the enrichment opportunists, and among them are snails, worms and bacteria. Amongst the worms are the snotworms (great name #3) and bone-eating bristly marine worms (#4), which are part of the polychaete family. They squeeze into the whale's bones and, with the help of bacteria, break down and digest the fats and proteins present (how they find a dead whale in the first place is still anyone's guess, but it's likely they arrive as swimming larvae). Over decades these worms, working in tandem with bacteria, devour the enormous bones almost totally, whilst other bacteria swarm in great mats over their surface. And it is upon these bacterial mats that other animals then gather. Mussels, clams, limpets and sea snails; they feast for decades, possibly a hundred years or more, on these bacterial mats. One animal has made a reef. It all started with one whale.
These strange ecosystems at the bottom of the deep seas have probably been present for hundreds of millions of years. Where now such animals flourish upon the bones of whales they once would have fed on extinct marine reptiles like plesiosaurs, mosasaurs and ichthyosaurs. If whales understand death, one presumes they'd be flattered by the life they can sustain for so many, for so long, after their passing. But alas, it is only sperm whales and beaked whales (which make regular trips down to such depths) that may ever know what awaits them. Perhaps they are filled with horror when they come upon such a scene on the ocean floor? Perhaps they gather together and mourn? Or dance? Or tell stories? Unlikely, but still, we may never know.
After two hours of walking the site with Peter I became no more hardened to the sight of entrails and drying pig flesh than I was at first. I certainly didn't gag again, mind. But I definitely found myself close to gagging a lot of the time. By the end of my visit to TRACES the smell of pork scratchings was ingrained so deeply within my lungs that I was worried I might be a health risk to family members later that night. My clothes stank of it. Totally stank. 'Have you got used to the smell?' I had asked Peter at one point. 'Doesn't really bother me,' he said. 'I still smell it, I register when it's strong but...' He shrugged a little. 'I lived on a farm when I was younger and every job I've ever had to do was in some way related to death. I've smelt it all of my life.' Graduating from farm work, Peter worked for 15 years in the abattoir industry, enforcing regulations that ensure meat is prepared safely and to certain standards. After veterinary public health he moved into forensic anthropology, working over a number of years investigating mass graves in Guatemala and, later, in New York doing some death-scene investigation work and undertaking more forensic anthropology during time with the New York Office of Chief Medical Examiner. After New York, Peter came back to Britain where his research interest in death further blossomed, and his dream of a research school like TRACES were made real.
What I particularly liked about Peter was the respect he had shown whenever the conversation had turned to human death and human suffering. As we had stood in front of a decomposing pig hanging from a tree (to mimic a human hanging victim) he had talked with sadness about the human hangings that he had tended to. He talked almost with his head down, suddenly becoming quite shy and almost mournful. He was sombre whenever real human death was mentioned. At no point did he play up the harsh brutality of his work. At no point did he shoot for the ghoulish or say anything macabre. He wasn't trying to impress me in any way. This was his work: death was his science. I realised now why he probably didn't like the whole CSI thing, and I'm glad that I had never really thought to bring it up. I had noticed the same serious tone in Alison's voice when she had talked about the victims of plague that have become her study area. Even though hundreds of years had passed, and these people were now just bones and not much else, her science was never cold or uncaring. Human remains were still human, like her. Human remains; the bit that remained. Her job was about people. It was about lives. Peter's and Alison's areas of work are not easy. Occasionally they must come across scenes that must be intensely emotional; scenes of past murder, suffering, even genocide and disease. I think the world is made a better place through jobs like theirs. I respect them both a great deal.
On my return to the real world many people asked how the trip to see the pigs went. 'What was it LIKE?' they asked. 'What did it smell like? What did they look like?' For a couple of weeks I was like a soldier coming home from leave being surrounded by civvies with a perverse interest in war stories. I held back the gory bits. I tried to be like Alison and Peter: rational and just, well, just... cool. But still I thought about it. I was particularly ashamed that I had gagged upon seeing the maggot foam. I was ashamed that Peter had seen. Ashamed of myself. The truth was I really had been momentarily disgusted by what I had seen. It felt involuntary. It had been out of my hands, really; I had no choice over it. It just kept happening. The maggots, I don't know... they unnerved me. It was the first time I've ever felt disgust in such a visceral way. I was momentarily intrigued about this feeling – in fact I thought about it a lot.
Mostly though, my memories of those pigs were about the amount of new life I saw. It was the beetles that I remember most fondly and which captivated me so. So much variety. So much diversity. I could wash off the smell of pork scratchings, sure, but the beetles remained burned into my memories and my experience of the day. The circus under the tent. The comings and goings. That each and every one had descended from generations of individuals that had made another creature's death their own precious precursor to life. God may have an inordinate fondness for beetles (so the old quote goes), but the enormous diversity of rove beetles betrays the mind of any potential Creator as having an inordinate fondness for death. I had loved it. But, still... I had gagged. The experimental pigs had produced within me a strange mix of feelings.
CHAPTER SEVEN
Sex and Death: The Contract Killer
It was my first real paid job in wildlife conservation. It had been offered to me so that I could contribute a small amount of my time to scientific research into frogs and their diseases, on one proviso: that I manage the Frog Helpline. This was the very early 2000s and most of the British population had no access to the internet in any way, shape or form. These people needed help with their frogs. These people needed help with their frogs urgently. These people needed a Frog Helpline. I was to become one of a handful of people in the history of the world to be able to offer free amphibian counselling over the phone. It was simultaneously the most brilliant and the most awful job in the world.
That's unfair. On the whole, I liked speaking to people about the relationships they had garnered with their backyard frogs, newts and toads – albeit I probably did this in an accidentally mawkish, patronising way. But I learned a key thing from this job, for it was the first time I appreciated the scale of death in nature. And this death was primarily frog-related. Each year we had hundreds of calls about dead frogs to the helpline, and they often came in spring. There were moments when some callers had cried with sadness at the annual loss of life in 'their' frogs during breeding time. 'There are at least 20 dead frogs!' they'd shout down the line. 'They're littering the pond! What is happening? What do I do?' they would shriek. What are you supposed to say in situations like that? I had received little or no help or advice about what to say about this from my supervisors. No one had thought to give me training for this sort of thing, so I'd tell them... I don't know... to net the dead frogs out of the pond safely and put them in the compost, I guess.
Most, after some counselling, accepted these strange incidences of frog death as another mystical quirk of amphibian-kind: hopping, breathing through their skins, singing, sometimes changing colour, sometimes poisonous and... sometimes, you know, dying all at once. It just seemed to add up... Frogs really are weird; this was really just another way in which frogs were weird. Many of the callers who expressed deep sadness to me were worried that the sudden mass death of frogs was their doing somehow. That they were to blame. They had been racked with guilt that if they'd changed the water or not cleaned out the pond the previous year it would all have been ok and the mass frog deaths would never have happened. I told them it wasn't their fault. Sometimes this helped; sometimes the caller was not convinced. Some people refused to take on board my assertion that this was totally normal and that many animals died en masse after reproduction. 'NO!' they would argue. 'It had to be disease,' they'd say. 'There had to be a reason!' Sometimes this would result in soggy packages being sent through the post with my name on them, the contents betrayed by being frog-shaped and stinking to high heaven. The words on the front of these envelopes were always scrawled excitedly with something like 'JULES HOWARD: A SAMPLE!!!' as if it would somehow make my day to receive something like a dead frog in the post and perform an autopsy on the mail-room table (even a book about life and death is no place to describe to you the horrors that lay within such packages). The truth about frogs really is simple, though. There is no mystery. Well, there is almost no mystery, I should say. Allow me to explain.
In very simple terms, it goes like this. Frogs have a contract with death, the same as anything else. This contract stipulates that they are going to die. Whatever happens, it's simple: they will die. So the frogs have a choice in what they do next. They can 'choose' to invest everything in one massive bout of sex right now (what I will call for the purposes of this chapter TYPE 1 FROGS), which will result in them almost certainly dying from exhaustion. Or they can 'choose' to have quite a bit of sex now and try to maintain their body for another year for more sex the following spring (the TYPE 2 FROGS). For frogs, this is a tricky choice to weigh up. The fact that there are a great many things out there that cause frogs to die – dry weather, disease, predators – means, inevitably, that natural selection is often drawn toward the TYPE 1 FROGS; hey presto, the world fills up with frogs who aren't too fussy about dying midway through (or hopefully just after) sex. That's economics. That's asset management. That's frogs. Of course, there isn't really 'choice' (at least in frogs), there's simply variation upon which natural selection has acted, is acting, and will always act. Frogs really do have it tough, but they make the best of it through their sex lives. And there really are many, many ways for frogs to die. I heard some very strange stories when I manned the helpline. Cases of exploding amphibians were one such weird one. It was a phenomenon I would come to hear about fairly routinely from 2005 onwards, thanks to one unusual news story.
'Toads in an area of northern Germany are being killed off by a mysterious disease – they are exploding,' reported BBC News rather breathlessly that year. 'Thousands of the amphibians have died in recent days in a pond in Hamburg's Altona district, with their bodies swelling to bursting point.' According to locals, at least 1,000 toads had died in this manner in a matter of days. All of them apparently swelled up to three and a half times their normal size and then simply exploded where they stood. What could cause such a thing? No one knew. Specimens were taken. Lab tests were inconclusive. There was no viral infection. No signs of a fungal infection either. Rumours flew around (bizarrely) that the phenomenon was linked somehow to some local racehorses kept in a field nearby, though no one seemed exactly sure how. Inexplicably, others talked of toad suicide, thankfully falling short of suggesting it had been some sort of ritual or pact. After a few days of this speculation German authorities chose to close the site, and the pond was inevitably dubbed 'The Pond of Death' in the popular press.
It took a few weeks for people to realise what was going on. In fact, it all came down to one man's relentless enthusiasm for solving amphibian mysteries. After examining living and dead specimens local expert Frank Mutschmann had noticed something strange about the dead amphibians. The toads' livers had been removed, he observed; apparently pulled through a circular puncture wound on the belly. 'There were no bite or scratch marks, so we knew the toads weren't being attacked by a raccoon or rat, which would have also eaten the entire toad,' Mutschmann told The Independent in May 2005. 'It was clearly the work of crows, which are clever enough to know the toad's skin is toxic and realise the liver is the only part worth eating.' Case closed. Except... for what reason did the toads appear to explode? The answer to this part of the mystery comes down to the common toad's impressive threat display. When exposed to predators common toads quickly open their nostrils and fill their bodies with air, blowing themselves up rather like a balloon. The strategy works well (particularly against grass snakes) but it is less effective if you have a hole in your belly through which other organs, like intestines, may inevitably become extruded with force. Presumably the local crows had stumbled across this delicacy and, being wily and inquisitive, the organ-harvesting practice had spread. To all intents and purposes, the following morning the toads did, in fact, look to human observers like they had exploded. But they hadn't. They had simply been operated on by the crows.
What's most surprising is that it ever became international news at all – exploding toads were by no means a new thing. In fact the 'exploding toads' phenomenon had been recorded in Germany in 1968, as well as in Belgium, Denmark and America in the years since. And I came across a few incidents of exploding toads on my days working the helpline, and never thought too much about them. It was nature. Normal. Normal-ish. Throughout much of the temperate world, spring is the only time of year when frogs and toads congregate, so naturally there will often be predators queueing up for a go. Herons getting rich on the stuff. Owls making ponds part of their night-time raids. Cats driven out of their minds with the profligacy of all those amphibians. Out-of-control Jack Russells in country parks; crows, magpies, jackdaws – the lot. Otters provide us with further interesting behaviour when it comes to eating toads. Sometimes I would receive reports of otters deftly collecting breeding toads in their hundreds, carefully biting the (non-toxic) legs off each, and depositing the bodies into a little pile next to the stream or river. Some otters were apparently known to peel the toxic skin off the toads before feasting on the skeleton and internal organs; they too were said to leave the skins in a little pile.
Passers-by coming across sights like these the following morning were often horrified. But a zoologist stumbling upon such a scene might have a different perspective – the message reads loud and clear to them. They might think: 'The chances of death here are quite high: these animals are probably going to be quite sexed up.' As I learned from my enquirers to the frog helpline, amphibian life really is hard. In environments of death, like those that occur during monstrous amphibian breeding congregations, animals have evolved to get their sex in relatively quickly. In Darwinian terms, it's better to have loved and lost than never to have loved at all. Common toads and frogs aren't truly semelparous though – they don't breed once and then die like Pacific salmon and mayflies – but many species like frogs are close to it. They sometimes dabble in it, let's say. In niches where death is likely, or an almost clear certainty, natural selection is drawn to the last throw of the dice. But it isn't always as simple as that. Death sometimes plays its card in hidden and secretive ways. Semelparity isn't always what it seems.
Take the example of Pacific salmon, for instance. Sure, swimming upstream through a gauntlet of predators like wolves and bears certainly would increase one's chances of death a great deal, but actually it may be that semelparity evolved in these salmon for another reason. It seems that salmon invest heavily in egg size, since larger eggs produce stronger fish fry which have a higher chance of survival when migrating back to the ocean to mature into adults. With a finite amount of energy in the pot, female salmon must fuel this egg investment with something. It may be that female Pacific salmon pay for this investment in eggs with their lives. Or it might be a mixture of the two things. Either way, the unshakable contract with death stands... even if the contractual wording is in a rather hard-to-read font.
A classic case of semelparity occurs in a small family of mouse-like marsupials, the antechinus. And again, the contract has come to take a strange and unusual form. What natural selection has done to male antechinus is almost grotesque. In nearly all species, male antechinus invest everything at the end of each year in one massive testosterone-filled sexual bender. Males attempt to have sex with every female toward which their legs can carry them. During this time the male's body gives up totally on maintenance. Males become riddled with gangrene as they quest for females. Their hair falls out in great tufts. But this doesn't stop them. Still the males go for it. Their immune system almost completely ceases to be, but still they rampage. Even with their insides bleeding and many of their vital organs totally corrupted, the males still show an interest in sex. After days and weeks of this, many males actually become a disease risk to females. They become (almost) the walking dead. Still they go on with the sex, though. Still they go. And then finally they succumb, all of them, to the degeneration of everything else in their body. It's over for them, but hopefully not for their offspring: the genes for semelparity persist. But from where did antechinus get their semelparous ways? What does their contract with death look like?
There are three hypotheses to explain male semelparity in antechinus. The popular view is that the mass death of males somehow means that the following generation is blessed with extra food resources (the contract being that males commit to death but succeed in securing a good inheritance package for the kids). Then there is the second view: that female survival is unpredictable, so males evolve to get it where and when they can (males commit to death but hopefully manage to have sex with a female that survives). And then there is the third view, which offers neither the selflessness nor the machismo of either of the first two hypotheses. The third hypothesis is that antechinus evolved semelparity not because of predators but because the females made them do it. And it is from Ed Yong's superb blog Not Exactly Rocket Science that I discovered more about this intriguing hypothesis.
In 2013, scientists (led by Diana Fisher at the University of Queensland) looked at the lifestyles of the 12 antechinus species and investigated other insect-eating marsupials, 52 species in total. What they noticed was that the further away from the equator they searched, and the more seasonally abundant the habitats became, the more likely it was that males would die after breeding. On the whole, species with 'suicidal males' were more common in seasonal climates where insect populations flourish in summer and then die back in winter, and suicidal males were less likely in climates where insects persist in good numbers all year round. Fisher and her colleagues think that as the ancestral antechinus species moved south from the equator, their breeding windows evolved and changed – rather than breeding all year, their breeding season became primed to coincide with the seasonal glut of insects. In other words, their breeding windows shrank enormously. This observation gave rise to Fisher's own hypothesis: the third hypothesis. The third hypothesis to explain semelparity in antechinus males is that they have been squeezed by the females' much shorter reproductive windows. All of their reproductive potential must be met in a matter of days and weeks, rather than months. The competition for sex is therefore rather intense. So intense, in fact, that it has become better for males to die trying than not to try at all. This is sperm competition at its most extreme. For these males, sexing-to-death is the only option left. The only game in town. Semelparity probably occurs in antechinus and not, say, in rodents due to the fact that antechinus are constrained somewhat by their marsupial ancestry. Where mice and rats can have multiple litters during the glut times, marsupials are stuck with a life-history plan that sees them give birth to tiny larvae-like young that require plenty of nurturing. In fact, four months' worth of nurturing. Males really do only have a limited window in which to act. Their contract with death offers little by way of wriggle room.
This small clutch of marsupials are the only mammals that actively have sex until they die. The only ones. And that makes them inherently interesting in all sorts of other ways. For instance, why is this behaviour so rare in mammals? And why is it so rare in any vertebrates, for that matter? Scientists continue to debate the many evolutionary drivers chugging away behind the scenes of semelparity, and the truth appears often quite hard to unpick, at least currently. The second question is particularly interesting, though. Why is semelparity so rare in vertebrates? The only land-dwelling vertebrates that exhibit total semelparity (apart from antechinus) are some of the Hyla frogs (including, fittingly, the gladiator frog) plus a handful of lizard species. And that's it. So why is it so rare? Perhaps vertebrate bodies, like German automobiles, cost a lot to make. Perhaps it's easier to keep them ticking over than to scrap them and buy another? We don't know. It's still a mystery. Invertebrates, it seems, are the opposite to us in this respect. It seems that invertebrates may be very cheap to make, so semelparity appears in many insects (particularly butterflies, cicadas and mayflies) and spiders and molluscs as well (including some squid and octopus species). Plants too, on the whole, appear to be quite cheap to replace. In fact, many species of plant favour semelparity. Some bamboo species, after decades of waiting it out, are known to suddenly flower and then die en masse, all at once (this has been known to cause local hell for panda populations as their required food source suddenly begins to wither and die in front of their eyes). Most grain crops and domestic vegetables are also semelparous. Their sex lives are influenced in direct response to the likelihood of dying that exists out there in the real world.
Death really is a contract, and animals have evolved to exploit its loopholes in the way that best suits them and the spreading of their genes. On the whole, though, you either throw down your hand and bet big, or bet small and hope to visit some other tables. Either way the house will always win in the end. That's the contract. Nearly all of the animals I had come to meet and would come to observe on this journey into the murky netherworld of life adhere to this contractual agreement with death. Nearly all of them share this basic principle. They will all die, sure, but in many cases their bodies have evolved to make the best of it; often to get rich or die trying. One assumes it will be the same on all planets that may or may not harbour life.
It has been more than 10 years since I worked on the frog helpline, but I still think about it often. It was my first regular experience of discussing animal death in such zoological terms. I felt really sad for the people who had come across such scenes in their gardens. Often they really were very upset by all the death, and I am not sure if I convinced many of them that it was all natural and totally fine, and that it wasn't their fault. I guess I will never know. I can't help but feel like I was communicating it all wrong, though. I wondered if I could have sounded more rational and scientific when discussing death, without sounding cruel or blasé or insensitive to their disgust and apparent dismay and sadness. The truth was I didn't have a clue. I was as muddled and confused about death as the public who were ringing in. I still am. Death seems like the most rational thing in the world. Yet we find it so hard to grasp sometimes. But that, in itself, is very interesting, I think.
CHAPTER EIGHT
Coffee with the Widow-maker
The images of the foamy maggot mass stayed with me for ages. It wasn't the maggots themselves. It wasn't the maggots individually. It wasn't the bones or the skin. It was... I don't know. It was the mass. The foamy mass of them. It brought on disgust. Total disgust. Are all humans genetically primed for disgust? I wondered. Is disgust an evolved avoidance technique to keep us away from the things that might kill us, as is often said, like maggots and snakes and things (perhaps like caterpillars) that look a bit like maggots? My mind slowed. Questions coagulated over the weeks that followed. Did the ermine caterpillars have it coming? I thought. Were they killed off because they reminded us of death? Were they killed off because of our disgust? I couldn't shake these thoughts. And then I had another encounter with disgust. A few months later I was pulled into the world of spiders for an unrelated project, and I got to thinking about spiders. Was it the same with them? I wondered. Could our disgust with spiders be equally evolved? A lucky break came my way and through this lucky break I got to see spiders and maggots from a totally new, and slightly unnerving, perspective. This is the story of that encounter.
In northern temperate countries, it's often September when the vast bulk of spider species are at their largest and most obvious. Hence, each year, in the UK at least, there is always a run of ridiculous scare stories – reports of spiders as big as dinner plates, spiders finding their way into people's mouths or ear-holes or nostrils. In recent years, though, these stories have taken a new twist. A single new spider species has come to steal the column inches normally devoted to such stories, and it has even stolen the front page on occasion. It's the noble false widow spider, a venomous spider (ok, someone needs to say it: all spiders are venomous) apparently capable of killing and maiming, even though the reality is that it's about as dangerous as a needle and thread left on a kitchen sideboard with no one in the room. But that doesn't stop it being a story, of course. In recent years, the press have absolutely gone to town on this poor spider. They've absolutely milked it for all it's worth. In the UK we have very little in the way of venomous creatures so this might be a perspective thing, I don't know. Either way, the noble false widow has become THE THING TO FEAR in modern times. The thing to hate. I don't like this kind of misplaced hate. I never have. It feels dirty and mean-spirited and ill-informed. Because of this, in the last two years I have been fairly vocal about them, patiently informing the public that the threat posed by the false widow spider really is minimal and trying to instil a love (or at least an acceptance) of spiders in the hearts and minds of the British public.
To be honest, I don't particularly like spiders (in fact, I'm actually a little phobic of them), but... I don't know... it's a principle thing, I guess. I don't like to see humans express such vocal hate, even if it is only toward spiders. This year, after a false widow piece I wrote for The Guardian, something incredible happened. I was contacted. Contacted out of the blue. I was contacted by a man. The man through whom it had begun; the journalist who had launched a thousand headlines by first running with the stories about false widow spiders. The man responsible for all of the public's recent fear and terror. 'I'm the one that started it all,' he had messaged me. Really? Wow! I'd written back to him quickly: 'It'd be great to meet!' 'Sure,' he wrote back. And so it happened. I was going to get a face-to-face meeting with a man I'm going to here refer to as John. John: the journalist who had dented the zeitgeist in such a way that many people woke up each morning thinking only of the threat that everyday spiders could pose to them, making everyone incredibly jittery and nervous. John said he'd prefer to remain anonymous if that was ok, in case his former employers heard he'd been spilling trade secrets. No problem, I'd responded. We set up the rendezvous – a coffee shop in east London. I looked forward to it.
Everyone in Britain right now is jittery and nervous about false widow spiders. Everyone in Britain now knows about them. Everyone knows someone who's seen one. Everyone is jittery and nervous and it's almost totally all John's fault. I was a tiny bit confused about why John was happy to want to meet me in person. In fact, why had he felt the need to contact me in the first place? What had urged him to say hello? I was his enemy, wasn't I? I wanted good things for spiders, didn't I? Perhaps he wanted to right an old wrong, I thought. Perhaps this would be his redemption. Was he racked with guilt at the fear and panic he had caused in the general public? Was this his confession? Truth be told, I had been worried that he might somehow want to trick me into exposing something new about spiders. A factual titbit that might get him another million hits. But I had got it wrong. When we met, John was actually lovely. A really nice guy. I had half expected him to be toothy, rat-like and fiercely mouthy but, sat next to me in the coffee shop, he was nothing but open, friendly and warm. There was nothing particularly shady about him at all. He wore baseball shoes like mine and a denim hoody, and in a nice little Sainsbury's bag he put on the table he had some flowers for his mum. Looking at him, he actually came across as almost a bit shy; really not as I had imagined at all. In fact, as we made small talk I realised we shared some things in common, both working in industries where the work is sparse, both juggling work with having young children. This wasn't how this meeting was supposed to go. I had imagined it'd be like the coffee scene in Heat between Al Pacino and Robert De Niro – him the gangster cooking up lies as part of a racket, me a loyal defender of the arachnids he aimed to discredit – but no, it was more... it was more Central Perk than that.
The public obsession that John had started surrounded the noble false widow spider – also known as the rabbit hutch spider – a non-native species that has been living in Britain for more than a century. This fairly innocuous-looking spider – smaller than the garden spiders that frequent our window sills and doorways – has certainly spread in geographical terms in recent decades (our houses are the most wonderful caves, after all). And yes, the noble false widow can just about bite if mishandled: their fangs are capable of penetrating skin, opening up one's body to secondary infections, some of which, if you are desperately unlucky, can kill. So yes, there is that. The spider is capable of causing death in much the same way as an abcess can become excruciating painful and, if left unclean, can lead to serious infection. A threat, sure... but statistically, a highly improbable one (readers of this book from other countries will no doubt delight in the fact that this spider really is about as dangerous as an unwashed sewing needle and that us Brits are the most pathetic wimps when it comes to venomous creatures). The blind terror that this humble little spider can elicit in British people has reached epidemic status. And John, looking at me and smiling sweetly, must surely shoulder some, if not all, of the blame.
'The way it started was interesting,' John said, drumming his fingers on his coffee cup. 'I was at work a couple of years ago and I was interested in reading about spiders that are found in east London.' He sipped his coffee and paused for effect, almost like it really was a confession. 'I was just flicking through stuff online really,' he said. 'And then I came across a tiny story – a really tiny, tiny little story – about the false widow spider and the fact it had made its way to Essex. They were on the increase a little bit. And that was it...' He looked up at me. 'That was my story,' he said. 'I wrote the story. And that was it, really.' He shrugged slightly. 'Really?' I asked. 'It was that simple?' He nodded. 'I wrote a little piece for the paper's website – nothing much, just a few paragraphs,' John said. 'I showed it to my editor and he read it. He liked it. My editor looked at me: "Seriously, go to town on this. Go to town," he said. So I did.' John smiled. The memory warmed him. 'Straight away, the story topped all other news on the website – and that was only referring to east London. We started wondering... how well would it go if we went national?' He sipped his coffee again. 'I spoke to my editor again. "Well, let's broaden it," my editor said. "Let's say these spiders are on the rampage across the entire country!" So I did.' 'Rampage?' I heard myself say quietly. 'I talked to the graphics guy,' continued John. 'I got him to do a map showing the spiders to be all over the place across the entire country. And that was it.' That was it. The story flew. 'False widow spider on rampage in Britain' said the headline. The subhead read: 'A DEADLY spider that can kill humans with a single bite is on the rampage in Britain.' We were off. The story flew across news channels, online, Facebook, Twitter, broadsheets, red-tops... all of them bought into it.
'But... wait,' I said, trying not to sound confrontational (which is easy because I'm not at all confrontational). 'Killer spiders?' I tilted my head. 'They don't kill people!' 'I know they don't kill anyone,' said John. 'We all knew they don't kill anyone, but the way we saw it was, well, if you were allergic or something, you could die. They could... kill you... technically.' There was a pause. John looked at me for reassurance. I pulled a face that was somewhere between a smile and a wince, which seemed to resolve the situation. 'So anyway,' he went on, 'from that point onwards, they became KILLER SPIDERS! MILLIONS OF THEM! ALL OVER THE PLACE!' He flashed his palms beside his face in mock terror. The thing is, he wasn't kidding. The story really did get everywhere from that point. It blew up totally. It was the Daily Star's number one story for many weeks. So what happened next was actually very predictable. 'So...' said John, '... obviously, my editor wanted to replicate that story. It was inevitable, I guess.' And so they did replicate it. And then some.
'FALSE WIDOW ALERT: MILLIONS OF KILLER SPIDERS ON LOOSE IN UK' (8th October 2013).
'FALSE WIDOW ATE MY LEG!' (10th October 2013).
'MUM'S TERROR AS FIFTY FALSE WIDOW SPIDERS RACE TOWARDS HER!' (13th October 2013).
'KILLER FALSE WIDOW SPIDERS ATTACKED MY LITTLE GIRL!' (17th October 2013).
'FALSE WIDOW SPIDER BITE LEAVES GRANDFATHER FIGHTING FOR LIFE' (23rd October 2013).
'We started doing more of them,' said John. 'And then others started picking up on the false widow story: the Mirror, the Daily Mail... even Sky News joined in.' I asked John whether, as a journalist, it was annoying when others leap aboard a journalistic gravy train like this. 'It was annoying,' he agreed. 'But it was also quite flattering to know that I started it, you know?' Again, I pulled my strange nod-smile-wince. There was another brief pause. 'The more we did it,' John continued, 'the more I started noticing that the spiders were making the front page of the paper quite a lot. It was...' John paused again, momentarily debating whether or not to tell me something I might find particularly insightful. 'Go on,' I smiled. 'Well,' said John, 'I got told that by putting spiders on the cover of the paper we would achieve an eleven per cent spike in sales.' 'Eleven per cent?' I said. I could barely contain myself. 'Wow! Eleven per cent!' We both said 'eleven per cent' a few more times. My jaw had dropped. 'Eleven per cent,' he replied. At seeing my reaction he seemed unable to gauge what face he should now pull. He was half very proud and half very ashamed. Perhaps mostly proud, I think. 'You look at the newspaper's web stats for the year and, of the top 10 highest-grossing stories, I think three of them were about spiders.' I was staggered that there was such an appetite for scare stories out there. Totally amazed. We stared out of the window in silence watching the busy street outside. If stories like this can raise sales by 11 per cent, I'm surprised there aren't more spider stories, I thought. Perhaps the noble false widow spiders had been lucky to have remained relatively hidden on these shores for so long...
I had expected John to take it all as a bit of fun; to pooh-pooh the punch of his stories as trivial and meaningless. But I could tell that he understood that his stories really had impacted on society. Something really did happen as a result of these pieces. It took place on 22nd October 2013, after a busy week of false widow spider stories, when it was announced that a school in the Forest of Dean, on the borderland between Wales and England, was to shut down temporarily because the geographically widespread false widow spiders had been discovered (apparently) on site. A letter to parents was immediately sent out. No doubt about it: with identification of at least one false widow on the site, there was a chance of spider bite. The school had to shut for two days. The spiders had to go. Thousands (probably hundreds of thousands) of invertebrates living on the site were fumigated, all because of a potential spider that posed about as much threat as a cactus (hell, the fumes left from the fumigation were probably more threatening to pupils). And it was all John's fault. Sure, no one had died because of John's stories. But hundreds of pupils had lost out on their education. Hundreds of parents had to face the unbelievable annoyance of spontaneously having to arrange childcare (which is unbelievably annoying). And it was all John's fault. Many say that such scare stories are harmless, that they don't have a noticeable impact and that there's no conservation significance if only a few more spiders get stamped on. But there was a real human impact from this story. Two days' learning lost. Panic. Ill-informed hysteria about a threat so tiny that it makes wasps and bees look like genocidal maniacs.
I brought the story of the school up with John. I asked him if he felt guilty about it. 'Yeah, a little bit,' he said. 'It was kind of weird, yeah – I felt guilty...' He paused. 'But then... I said to you just now that I started the false widow story, but perhaps it would have started anyway? Someone would have come across it,' he said. 'Surely with time, someone would have come across these spiders and written something similar.' He looked at his coffee cup. I could tell that there was another confession coming up. He paused again. 'When the paper started going overboard with it, I sort of decided I didn't want to run it any more. We did too many,' he said. 'We milked it.' He put on a mock voice and flapped his arms a bit: 'FALSE WIDOW SPIDER ATE MY LEG!' he said. 'SPIDER ATE MY FOOT! MY HAND FELL OFF!' We laughed. 'In the end the same stories were everywhere. Too many other papers were using it. It all got a bit... samey... in the end.' He sighed. 'I did feel guilty about it, though. I did.' He looked up at me earnestly. He considered his words a little before continuing. 'In the end,' he said, 'in a weird sort of way, my integrity was at stake. I'm not going to win a Pulitzer any time soon, but this isn't exactly the kind of story that I set out to write. I wanted to write the truth but... I guess I'm a bit of a web-traffic whore too...' He smiled. 'We all are,' I said. He nodded. 'I stopped doing them in the end,' he said quietly. 'It was time to stop.' John has no doubt that others will continue his legacy, and I fully believe him. In the coming years I suspect that we will hear more about the noble false widow. Others will carry on the legacy that John started, for the simple reason that fear and spiders and people improve sales by 11 per cent.
As we packed up our things I asked John why the stories had done so well. Why did it fly? John was instantaneous in his response. 'People like a villain,' he said almost matter-of-factly. 'If you can take a story and make it about a villain, especially if it's potentially life-threatening, then people listen.' To John, the spiders were destined to end up on the front page in the same way that if Peter Benchley hadn't written Jaws, someone else would have. Stories like these are inevitable, I guess.
I drove home, my head swirling with thoughts. At times we have a strange mutualistic relationship, journalists like John and I. He needs loud-mouthed science-literate people like me to get his quotes and give his stories more authority, but I need people like him to write scary stories so that I can write comment pieces about why spiders aren't scary and we should all love spiders a bit more. No media outlet would let me write about spiders without a hook like the one he provides. It's strange. What can I say? It's deeply messed up but, well, this is the strange loop in which many naturalists and zoologists nowadays find themselves. A web, really. A trap. Spin. The spider's trade and our own have become one. We need one another. But the school closure had resonated deep within me. I didn't like it. A thousand young people's education had been affected, a thousand families. I didn't like it one bit. 'Though it sounds remarkably improbable, we may have to accept that nature occasionally has the audacity to encroach fleetingly into our lives,' I'd written in The Guardian a few weeks previously. 'We may have to accept that, no matter how hard we try, we can't sterilise every single aspect of our lives from spiders.' But the evidence was there, plain to see, in how that school had reacted. We had already started trying to sterilise everything. We wanted them dead, just like we had wanted the ermine caterpillars dead. Was it because they were a genuine threat to life, or was it something deeper?
The meeting with John had come at an opportune time. I was still frustrated at Birchwood council's response to the ermine caterpillars. Do spiders and maggot-like caterpillars deserve such treatment? Is it really in our genes, as we are so often told, to hate such creatures? Is it natural for us to be scared of animals that we associate with death? I think possibly, but probably not.
Darwin was among the first to notice the universal human response to disgust. In The Expression of the Emotions in Man and Animals (1872) he wrote:
With respect to the face, moderate disgust is exhibited in various ways; by the mouth being widely opened, as if to let an offensive morsel drop out; by spitting; by blowing out of the protruded lips; or by a sound as of clearing the throat. Such guttural sounds are written ach or ugh; and their utterance is sometimes accompanied by a shudder, the arms being pressed close to the sides and the shoulders raised in the same manner as when horror is experienced.
Darwin was basically right. Type 'disgusted face' into Google and you'll see for yourself: row upon row of faces of all ethnicities with the heads pulled back into the shoulders, their upper lips pulled up to their nostrils, a kind of snarl almost, with their eyelids half closed. Often the face is pulled to one side. It's the classic URGH face (I'm doing it right now, for effect). It's easy to label this as a clear evolved reaction: a simple instinctual response to limit our contact with potential pathogens, pulling away our various orifices and brain extensions (eyes) from the objects likely to kill us. But this could also be a 'just-so' story – things look fit for a purpose, so they probably are.
The truth is that it may be more complicated than this. Much more complicated. Smell appears to be a key conduit to instigating a human disgust face. Particularly the smells of death, it seems. The two smells that waft most freely from the dead (in plants or animals) are cadaverine and putrescine. These two simple molecules are released in great clouds that waft upwards as key proteins in decaying bodies are split apart and break down. Put simply, the more protein an animal has, the more putrescine and cadaverine molecules are produced and the more potent we find the smell. Cadaverine and putrescine have proven rather a handy scent for animals to become sensitive to, as I learned by spending time with the dead pigs. Scavengers are attracted to them, for instance, while many things positively avoid them. What is particularly interesting is that fish may have broadly similar systems for cadaverine and putrescine detection to what we have, suggesting a deep history of death-aversion inherited (possibly) from shared ancestors. Key olfactory receptors are often called TAARs (trace amine-associated receptors). In zebrafish, for instance, some TAARs latch onto cadaverine molecules and send electrical signals to the brain, which the fish register as odour. They work very much like our own receptors, which are also TAARs. Indeed, similar TAARs-like systems probably occur in invertebrates too, not least blowflies, who use their own sensory equipment to locate (rather than flee from) dead bodies. Such insights as this really do hint at the ancient origins of such a signalling system. All of us have probably found death unappetising for millions of years, though we may never have consciously understood why until this point in time.
That we have sensory equipment that detects the smells of death is pretty much what one would predict from natural selection: that the key equipment to notice things associated with death, and respond accordingly, has survival value. What appears less clear is what exactly it is about death that drives this evolved response. Is it because dead bodies are a pathogen risk to animals? Or is it because avoiding dead bodies means that living animals avoid getting into similar scrapes, whether it be contact with a predator or any other unknown threat such as disease? For some animals it could be either or it could be both. We will probably never know. The fact that many animals respond similarly to the smell of faeces (another pathogen breeding ground) may provide a clue, though. Spoiled food, faeces, death, disease – they're all sides of the same square: in other words, evolved recognition software that says AVOID WHERE POSSIBLE. Faeces-avoiding behaviour has been observed in sheep, cows and horses and probably also serves to reduce the chances of such animals accidentally gobbling up parasitic worm larvae, which often live in faeces. It's said that many primates (and wild reindeer) also display such faeces-avoidance behaviours, led largely by smell. Death – or rather parasites – is possibly why.
Could human disgust really be an evolved human universal? Professor Paul Rozin of the University of Pennsylvania is today's leading proponent of the idea, arguing that the response keeps us from ingesting items that may be riddled with pathogens, such as blood, decaying meat, faeces or vomit. If Rozin's hypothesis is right, it gets me off the hook for retching upon seeing my first maggot mass. If he's wrong, I guess I must hang my head in shame: I am simply a massive wuss. If Rozin does prove to be right, then perhaps the public's response to the ermines was ok – the ermines really did have it coming for behaving like writhing maggots dripping in great silken stalactites on the passers-by below. And it really was very maggot-like. So was their destruction simply a case of mistaken identity? It will forever remain a mystery, probably.
And what about the spiders? I thought. Were we born to hate spiders? According to the press, yes. This popular notion has developed in recent decades that humans have indeed evolved to fear them. Journalists are so quick to believe this that they no longer check if it's really true. But have we? Is it in our genes? Have we really evolved to hate spiders? In reality, no one can be sure, so perhaps I can offer up my two cents on the subject.
There is a weakness in the central pillar of this idea about us having evolved to hate spiders, and that is simply that human cultures around the world – unlike with disgust – appear to vary in their responses to spiders. Not all cultures immediately display a disgust face. Not all of them shiver and are terrified. And not all humans are scared of spiders. In fact, strangely, it appears to me that what we see with spiders appears to be the opposite of what we might expect through natural selection. One would predict that adverse behavioural responses to spiders would be most prevalent in the ecological zones in which biting venomous spiders are most common. Yet this isn't what we see. Britain has no venomous spiders directly capable of killing, yet we stand on chairs and many of us do seven shades of hell's worth of screaming upon seeing one. Folk from other countries (particularly Australia – a nation that has, on the whole, learned to live alongside venomous creatures) must laugh at us. And there are other observations that don't seem to fit the facts. You'd expect, for instance, children, being smaller and more susceptible to death by envenomation, to be especially wary of spiders. But no. That's not what I see. In my experience of working with thousands of young people, often watching and sometimes handling spiders, they start off loving them until about age four or five or six, when suddenly their attitudes change. They begin to run a mile at the sight of a spider, sometimes only at the mention.
And there are even more problems with this received wisdom about spiders being a thing that we have evolved to detest. For instance, other animals are far more threatening than spiders and we certainly don't display the same disgust or fear about them. Mosquitoes (through malaria) are a killer of more than one million people each year and evidence suggests that we have been troubled by the malaria parasite for at least 80,000 years (probably longer). If we have evolved to fear spiders, you'd think we'd evolve to fear mosquitoes too, right? But no. The sound of a mosquito buzzing past one's ear remains little more than an annoyance at best. Few of us wet the bed with terror upon hearing one. Few of us get on a chair and become paralysed with fear. (I sound like I'm belittling the torture and agony of those who are phobic. This is not my intention. I am actually a bit phobic of spiders myself, remember? But I think that I got my phobias from awful childhood experiences with spiders, not from my genes. And as an aside: I find clowns and collections of holes* scary too. No one would ever argue that this is genetic.) So if I'm right and it's not genetic, then what is it with spiders? Why did John hit the mother lode when writing about his false widows? What part of the cultural funny-bone was he tweaking?
North America has its own version of the false widow spider, called the brown recluse spider. The popular notion is that this little spider is rampaging state by state across the continent, lurking in dark corners waiting to bite. As with the false widow, the popular press seems to get itself into a whirl whenever (rare) brown recluse bites result in (even rarer) disgusting secondary infections that require surgery or, worse, prosthetics. Like the noble false widow, the brown recluse has captured the American public's imagination. Many Americans are, it seems to me, quite terrified of them. People report bites and skin lesions from all over North America, even though the species only lives in a thin line of states between the Rocky Mountains and the Appalachians. There are the same scare stories too. The same images of necrotic infection, blamed on the spiders, that we see in the UK. People know what they saw: what they saw was a brown recluse. Similarly here, people know what they saw; what they saw was a noble false widow. But the reality is that spiders – all over the world – are incredibly hard to identify and tell apart, many even by experts. Species are often misidentified, and these misidentifications often unnecessarily cause fear and panic and terror.
Consider this case study: in 2005, the arachnologist Rick Vetter (from the University of California, Riverside) asked the American public to send in specimens that they suspected to be brown recluse spiders. Of 1,773 specimens sent to Vetter from 49 states, less than 20 per cent were actually brown recluses. In subsequent similar research, discussed in Wired, Vetter showed that similar misidentifications had occurred by those who called themselves entomologists, physicians and (worryingly) pest control operators (the cynic in me calls foul play). Like the false widow, the brown recluse spider has hardly crawled from the depths of hell. The biggest specimens only reach 20mm for starters. In fact, the brown recluse can barely bite at all, its fangs being hardly able to penetrate human skin. They certainly don't hunt or stalk humans. Far from it. In the spider's home range, humans and brown recluses probably live in something close to harmony, where neither much bothers the other. In one extreme example, a 2002 survey by Vetter of a 19th-century-built occupied home in Lenexa, Kansas, found 2,055 brown recluses living with a family, 400 of which were likely to have been big enough to cause envenomation. No one had been bitten in that house, ever.
In fact, there are many interesting similarities between the brown recluse and the false widow spider, but most interesting is how they have captured the media interest. Our ears prick up when hearing negative stories about them. We love it. 'The press has, by and large, painted spiders in a negative light,' says entomologist Chris Buddle of McGill University in Wired. 'People jump at the chance to hate spiders. It's easier to vilify them than to adore their biology and natural history.' We think nothing of the days and days and days and days when nothing bites us or bites those that we love. Yet as soon as we hear a story about spiders it is as if our worst fears have been realised and confirmed: spiders are out there, ready to bite, and we've been lucky to make it this far alive. We tell as many people as we can. We chatter. We talk. We share. We are eager to spread the word about encounters with spiders, even if the word is hokum. Are we the only animals to do this? For a few weeks after meeting John, I wondered if there were any parallels with other social animals in the animal kingdom when coming across potential agents of death. And then I came across one. A study involving, once again, those most intelligent birds, the corvids.
Do any non-humans get a kind of hysteria about novel threats to life? Yes, it seems that some might. This is a study about fear from a zoological perspective. A study that displays perfectly, I believe, why we all get so het up about spiders. And it really is a simple and very cleverly designed experiment. It was a 2011 study undertaken by scientists at the University of Washington, led by John Marzluff (who co-wrote Gifts of the Crow, mentioned again in Chapter 15), which looked at how American crows responded when faced with novel and unusual threats. They did this, simply, by becoming the threat. Researchers trapped, banded and released 15 or so crows before releasing them unharmed, and they wore a mask whilst doing this. A rubber caveman mask. The crows, naturally, didn't like to be banded. They made a mental note: the human with the caveman mask is a total bastard. Avoid the human with the caveman mask.
But what the researchers saw in the wild crows that lived locally from this point onwards was incredibly interesting and totally surprising. At first, the crows responded in a predictable way to this unpleasant bit of manhandling. Crows that had previously been captured demonstrated typical scolding responses to the male or female researchers wearing the caveman mask, something the researchers referred to simply as 'individual learning'. The crows remembered the encounter, in other words. It had logged in their brains. But then things started to change... The researchers started to notice that other crows began to scold them when they donned the mask. Even if they hadn't themselves been manhandled, they still protested. And then more protested. They too would caw and scold and gather and mob. And then more and more crows would join in. The implications were clear: the crows were passing the information about threats on to one another. The birds were displaying horizontal learning, something previously thought to be mostly a primate thing.
But there was more – individuals also passed the information on to offspring (called 'vertical learning'). News was spreading throughout the local corvid population and it was about a threat: watch out for the bastard with the mask. There was a kind of culture, in other words. But still the information about the caveman kept on spreading. Within five years, the 'learning enabled scolding' expressed in those first mishandled crows had spread at least 1.2km from the place of the original mishandling. The crows had watched one another's responses to novel threats. They had learned from one another, just like us. Crows use a simple low-risk mechanism for transmitting information about threats. They don't need knowledge about the severity of the threat; they just learn from one another. They just take it in. To them talk is cheap, in other words. It was a truly fascinating finding, and further evidence of just how wily and impressive corvid cognition really is. In fact, for me it is one of the most intriguing (and almost chilling) discoveries in animal behaviour in recent years: that crows pass on information about threats. They pass on information about the life-threateners; they help one another live by gossiping about the things that might kill them.
Naturally, upon hearing about this research with crows I wondered whether we're the same with spiders. I have no evidence for this, it's just a hunch really. But seriously? I mean, look at our behaviours... We humans have an inherent interest in life-threatening situations. We like telling stories about it. We like passing it on. And it's not just spiders I'm talking about here. Pick up a newspaper: you'll read about disease, war, plane crashes, earthquakes, drownings, murders, suicides, injuries, car crashes and plenty else to do with death. People who say death is taboo are mostly wrong. We love talking about death. Or rather, we love talking to one another about novel threats to life. We like sharing it. It brings us together. We learn from it. The study on the American crows really did capture my imagination on the subject. And when it comes to spiders I can't help feeling we are the angry mob of crows soaring around the field, sensitive to the threats expressed by our peers and our parents, but unable to perceive properly the real and present threat to ourselves. Every Facebook share about deadly spiders is a kind of 'CAW'. Every headline in a red-top newspaper a 'whoop' or a 'scold'; a cheap information exchange that is so easy to share it doesn't really matter how true it really is. We are the crows whooping and scolding and circling and John the journalist was my man in the mask, the person who discovered how easy it was to acquire readers and brew up a storm. A cultural explosion. A man who stumbled, for a few months and years, upon a gold mine. A journalistic trope that preys, unlike the spiders, on us and on our instinctual habit for gossip about death. A trope infused with death. A trope that we probably haven't seen the last of – and won't any time soon. Watch out for it. And try if you can not to join in.
Note
*This is a genuine phobia called trypophobia. Before you ask, I have no idea what childhood experience gave me a fear of lots of holes.
CHAPTER NINE
Suicide, Snowy Owls and the Executioner Inside
It was the morning of 8th November 1946. It took place in the middle of the Atlantic on a routine journey from New York to Gibraltar. The crew of the USS General LeRoy Eltinge were out on deck, staring perplexed at the pair of objects that had landed on the radar aerial overnight. Big, white, fluffy – they looked like they belonged there; that they do this all the time, locate ships in the ocean to have a bit of a break from all the flying. The captain was thankful that they had chosen a particularly large radar aerial to land on; though these rotund ghostly owls were heavy and imposing, this particular radar aerial was pretty strong – they were causing little disturbance to his delicate instruments. In fact, they may have been there for a while without anyone knowing. Still, they couldn't carry on the whole trip with two snowy owls sitting on the aerial. What if they flew to another aerial and damaged something? thought the captain. What if they broke his ship? No, that wouldn't do. They had to go. The captain ordered the ship's horns to sound. Ahh, brilliant. That worked, he thought. The owls quickly took to the air. They flew around for an hour or so, just long enough for the crew to wonder if they might leave forever. But then they returned. The captain tried again with the whistle. The owls flew around a bit but then returned. And again. And then again. The USS General LeRoy was the only object worth landing on for hundreds of miles – the owls weren't going anywhere. The records don't say what happened next. They probably carried on with their voyage, their mysterious cargo – the snowy owls – lost, alone and hungry.
But this wasn't the only boat to have had snowy owls perch upon it that year. Other ships reported similar encounters. Three hundred miles south-east of Newfoundland, for instance, the transport ship James Parker was boarded by a lone snowy owl. The owl sat on its foremast contentedly, to the bemusement of the crew. Then there was Acorn Knot, heading from Nova Scotia to Reykjavik, 500 miles out to sea. Again, it was the same story: a snowy owl emerged from the mist and perched itself on the boat's mast before later flying off. Overall that year, ornithologists received 24 reports of snowy owls on ships. What in God's name could have caused such a phenomenon? The answer was lemmings.
Lemmings are nature's most famous cyclists: some years they live in peace and harmony with nature in the Arctic, mowing up moss and reproducing contentedly, but then... more and more and more they reproduce... suddenly, months later, it becomes utter chaos. There is no longer enough moss under the snow to go around, so starvation ensues. A frantic search for more moss begins and a mass invasion of new territory occurs – a very famous mass invasion. Many, or most, lemmings leave the area and die in their search, leaving their predators to go hungry. On the whole the foxes become wily, turning to other food sources locally. But the snowy owls depend on the lemmings. The snowy owls fly – some head south through Canada towards the US, even turning up in towns and cities, while many others, it seems, take to the sea. Some of these find boats to rest upon. Many, many more will die, falling namelessly into the waves, starved and alone and forgotten. We may not see another year quite like 1946, when USS General LeRoy Eltinge and others noticed the mysterious appearance of snowy owls sitting on the masts, but there have been other invasions since. The moss regrew, after all, and the lemmings repopulated so the owls lived well for a bit. And then they didn't again, so off they fled. But one thing is clear in all of this: though 1946 was a particularly terrible year for lemmings and for snowy owls, neither species was displaying suicidal tendencies.
Where and when lemmings got their mass-suicide tag is largely unknown. Stories of their great plagues appear throughout medieval literature, with many people appearing to believe that somehow these creatures, in the good years, spontaneously generated in the heavens before falling from the sky during storms, and later dying in their thousands. 'The Gods they work in mysterious ways,' these medievals may have argued, but I hope that at least one or two of them may have questioned why an almighty being would display such apparent delight in throwing millions of rodents down at them like they were some sort of multi-ball bonus in a great cosmic pinball machine. The seventeenth-century Danish physician Ole Worm first put right the notion that these creatures were created in the sky from nothing. 'Lemmings are real,' he realised, taking his first step into a brave new world where things could actually be real. 'They must be brought here by the wind!' he declared, though I paraphrase. It took the great Carl Linnaeus (the self-appointed 'prince of botany') to see lemmings put correctly in their place as particularly wondrous and exquisite rodents, and nothing much more than that; natural in their origins and natural in their behaviours, except for the whole suicide thing, which was definitely still a bit otherworldly. This popular notion of them being mysterious suicide artists has largely persisted into recent times.
At this point I have a mental exercise for you. I want you to conjure up in your mind's eye a picture of lemmings hurling themselves off cliffs in their thousands. You might find it particularly easy to imagine, because you've probably seen the footage somewhere. The footage of them leaping – hundreds upon hundreds of them – off a cliff is one that has become etched into the cultural zeitgeist. A generation, including mine, that said: 'Lemmings commit suicide: I saw it on TV.' Of course, you'll probably know now that lemmings don't actually commit suicide. Instead you'll probably appreciate that these mass deaths are the result of the mass exoduses (during boom years) toward unpopulated areas after local food exhaustion. During this period, individuals of many lemming species may inevitably find themselves crossing rivers, streams and, occasionally, leaping off boulders and rocks in search of less densely occupied locations. Many die in the struggle. But there in your head, you might still be able to conjure up that image: hundreds upon hundreds of lemmings flinging themselves off a cliff and into the water and dying. I can see it as I write this: close-up shots taken from below of them pouring out and over the cliffs. Falling like grains of sand down the cliff's banks. Overhead shots of them tumbling and spinning through the air, splashing into the waters beneath. Mid-shots of lemmings splashing into the water, consumed in slow motion, down into the icy depths of the Arctic Sea. Still they come. Still they tumble. I can see it so clearly and I suspect you can too.
There's a reason you and I might remember it like this. It's because we're imagining the footage used in Disney's ground-breaking 1958 nature documentary film White Wilderness, which I suspect came to be stock footage for a host of subsequent nature films. I rewatched it recently. In its original incarnation, the American narrator talks with a dramatic and tight-lipped intonation like something out of a World War Two propaganda film: 'They've become victims of an obsession – a one-track thought: "Move on! Move on!"' he narrates urgently. 'This is the last chance to turn back, yet over they go, casting themselves out bodily into space... and so is acted out the legend of mass suicide...'
What's perhaps most incredible (and which I had never appreciated until now) is that those lemmings were probably pushed over that cliff. Yes, PUSHED. In an exposé that shook the world of natural history programming, a 1982 Canadian TV magazine accused Disney of using a rotating platform to force lemmings over the cliff for them to film. Lemmings, the Canadian TV magazine show argued, were piled onto the rotating platform and forced over and over onto one another. Eventually, too overcrowded on their little platform, they plunged over the edge and into the waters below (which, incidentally, were said to be in Calgary, not in the Arctic). It remains unclear how much Disney knew about the whole thing, but what's interesting to me is how clearly the image remains in our heads. And in the cultural zeitgeist. In reality, nature is rarely as brutal as we sometimes like to imagine. Evolved acts of suicide are present, sure, but not in the way popularly imagined.
Most famous, in the zoological suicide stakes, are the spiders. Small males of many species may approach larger females, plug in a sperm-filled palp (a penis-like organ), and then they'll literally throw themselves at her jaws whilst still plugged in. Sure, he'll die (yes, there is that) but the behaviour (if scientists are reading it right) might well be evolved. It pays out in genes, in other words. After all, they say, on paper a female eating a male will be far too busy eating to allow any other male a chance to approach for a sexual encounter. Genes for this behaviour therefore spread, they say. But is it really that clear? I always feel, told like this, that the female sounds like she's being duped. This is unfair on female spiders, because it's quite likely that the behaviour, if evolved, has in fact co-evolved – it has benefits for both sexes. Her offspring will undoubtedly benefit from all the nutrients that the male has within him; he's a provider of nutrients and she, a provider of eggs. And then there is also the possibility that, at least in some species, this is all just some awful mistake – that the scientists are reading it all wrong. It could be that, for instance, midway through sex the male accidently moves his body in such a way that the female's killing instinct is activated and he is instantly impaled on her fangs and eaten. It really could be that simple, sometimes.
What's really going on with all this killing and eating of mates has been a matter of some debate for spider experts, and it continues to be. But now, thankfully, they have a new group of scientists with whom they can exchange notes: the malacologists. For some molluscs may wield this same trick during sexual encounters. In 2014, for the first time ever, this kind of behaviour was observed in the common reef octopus. In fact, it's now been spotted three times in common reef octopuses. Females have been observed to throttle males with a single tentacle during sex and carry their dead prize off to a cave, one presumes to eat them. It may be that, as with spiders, the motivations of females and males to commit such acts will be difficult to unpick. But the idea of a whole new, relatively distinct class of creature, with impressive cognition (which, in some ways, mirrors our own), undertaking such behaviours is intriguing. Incidentally, this observation may explain why some male octopuses have evolved such a long penis-tentacle. It may possibly be a way to keep females at arm's length – literally. The fact that these female octopuses are reported to constrict their mates in such a slow and sensuous manner is an additional bonus for those warmed by the lurid.
Sex and suicide may sometimes be intimately linked (as we learned in Chapter 7), but not always in the ways popularly imagined. It's certainly fair to say, though, that there aren't many examples of animal suicide where sex isn't somehow part of the plan. Sure, I suppose there are the infertile drones of ants, wasps and bees that occasionally stick up for one another in their attempts to protect the nest. But even this is ultimately about sex: about infertile drones protecting the sexual queen, for instance. Other eusocial insects, including some termite soldiers, go for a similar tactic – a suicide approach called 'tar-babying' (named after the fictional character in the nineteenth-century Uncle Remus stories). These soldiers intentionally rupture special glands in their body to produce a sticky secretion that immobilises enemies like ants – they basically blow themselves up. Even they, though, like the ants and wasps and bees, have their eyes on the prize: genes. It seems that if dying helps your chances of sex and replicating your genes, intentional dying – suicide – may evolve.
But it's not as simple as that. Watch some creatures and you will see that sex apparently ceases to occupy their minds. They forego food and walk like zombies up blades of grass, eager to be eaten. Eager to die. They swim round and round in apparent ecstasy near the surface of the water, eager to be consumed. They have a death wish. They are desperate for death. These animals have suicidal tendencies, not to further their own genes but to further the genes of the parasites that have taken up residence in their bodies. They are now being mind-controlled. This is nature at its most awesome.
Toxoplasma is a classic mind-controlling parasite, with an interest in causing suicide. If you're reading this on a crowded bus or a train, then it's likely that the person on your right or your left has Toxoplasma. Or you, of course. Toxoplasmosis is a disease which you will probably have heard of if you have cats. Under a microscope, Toxoplasma looks a little like a tiny sausage. And it is tiny. This tiny protozoan has a thing for members of the cat family because cats are the only vehicle in which Toxoplasma can fully become sexual and have sex. It spends its life moving from host to host, up and down the food chain, awaiting an opportunity to FINALLY end up in a cat's digestive system. In their wildest dreams (if they could dream), all of them hope to one day end up in a cat's intestines. That's where the action happens. It's all they aspire to be: a protozoan that has sex in a cat's intestines. Most don't make it, of course – they lie (as oocysts) in the soil and dirt and water, hoping to contaminate a rat, a mouse or (worse) livestock or (worse still) us. But getting into one of these animals is ok since the Toxoplasma can manipulate its odds of getting into a cat by helping its hosts get eaten by cats. What Toxoplasma does to mice and rats is the stuff of legend. Rodents suffering with toxoplasmosis start to become very unlike rodents. For a start, they begin to show less fear of cats. And they actually start to seek out the smell of cat's urine, drawn to it like the song of the sirens. There are other changes, too, that Toxoplasma inflicts on its hosts. Infected rats cover greater distances when they travel. They explore more; their anxiety responses are hacked into by the parasite and they race into uncertain situations like an insecure drunk freshman eager to make new friends.
As I mentioned, it's highly likely that someone you know has toxoplasmosis, or perhaps you yourself – once they're in, they're in. In most healthy people, the protozoan quickly enters a latent phase; it forms tiny cysts in nervous and muscle tissue and sits it out, hoping upon hope that you may be eaten by a lion or a tiger or maybe a clouded leopard or a serval or something, which is possible but distinctly unlikely. For the vast bulk of Toxoplasma in human hosts, they've bet on the wrong horse. Realistically, we are dead ends in the great travelling life of this absurd and ridiculous protozoan. Worldwide, perhaps 30 per cent of us carry them. Thankfully, in this latent state, they do little to impact on our lives (though some people report flu-like symptoms at first). If you are an infant or suffering from weakened immunity or pregnant it can be serious, however.
Strangely, there's evidence that Toxoplasma can mess with human minds in a similar way to how it acts on rodents. There's evidence that infected people may be less bothered about the smell of cat urine, for instance, and, believe it or not, there's also some evidence that infected human individuals are more outgoing and dress differently from uninfected individuals. No matter how you look at it, Toxoplasma is an evolutionary dynamo. No doubt about it. A dynamo. Where other parasites, like fleas and pubic lice, have been persecuted into oblivion by humankind, Toxoplasma has ridden the pet industry bubble – and it is a bubble that doesn't look like bursting any time soon. Toxoplasma got in on the ground floor, before domestic cats hit big on Earth, and like a Trojan Horse it has spilled its soldiers into our warm and cosy lives. Incredibly – and no one has any idea how this has happened – it is even found in New Zealand's Hector's dolphins. This is a story much more engrossing and real and terrifying than a bunch of lemmings jumping off a cliff in Calgary, at least in my view.
So, back to lemmings. The lemmings really do jump from the cliffs in times of chaos. It really is chaotic behaviour and this is mainly because lemming populations don't behave normally. Unlike in many rodents of Arctic regions, lemming population crashes look jagged on a graph. In lemmings one doesn't see the smooth peaks and troughs seen in most rodents, caused by rising and falling populations of predators. In lemmings it's much more spiky: UP, DOWN, CRASH, BOOM. Jagged, in other words. The reason for this is because lemmings aren't thought to be limited by predators. They are limited, on the whole, by food. Too many lemmings under the snow nibbling the moss, hidden from predators, means suddenly that numbers can boom. A time of plenty then becomes a time of sudden sparseness. So what else is there to do but run? They run and that's when the chaos ensues. But it isn't suicide; not like it might sound, anyway. Animals don't, on the whole, commit suicide for reasons other than sex. Animals, on the whole, don't kill themselves unless their parasites want them to.
But there is another way to think about suicide. In many ways suicide is, actually, very common in nature. In fact, suicide is incredibly common in nature... it's just that it happens within us. Within our bodies. It happens within us every day. Every hour of every day. Every minute. Every second. Cell suicide. We have had to become masters of cell suicide to live in such complex bodies. Without mastering cell suicide we would see the same chaos that is evident in lemmings: the same overpopulation, the same riotous spreading, and the same illusion of a broken society. We would be multicellular beings out of control.
Caspase enzymes are the key mechanism through which cell suicide occurs. It's easy to imagine these enzymes acting rather like cellular kill-switches. Nick Lane (in the brilliant Life Ascending) describes caspases as acting in cascades 'in which one death enzyme activates the next in the cascade, until a whole army of executioners is let loose upon the cell'. Caspases are essentially the mechanism that delivers programmed cell death, a process called apoptosis. Apoptosis is incredibly valuable to life in multicellular bodies. Famously, the cells between our fingers and toes, when in embryonic form, are killed off through apoptosis. Our bodies are cut to shape by it, essentially, and caspases are the mechanism through which this all happens. Apoptosis accounts for the loss of a tadpole's tail, too. In fact apoptosis is observable a great many times during development. Apoptosis removes the teeth buds from baleen whales, for instance; it also gets rid of the pelvic rudiments of snakes and it almost totally eliminates evidence of the existence of eyes in embryonic moles. But to consider apoptosis as simply a developmental sleight of hand would be to downplay its significance dramatically. For apoptosis is something you are performing right now without knowing it – whilst reading the last three sentences alone you've destroyed about 10 million cells through it. Oh, and there go another two million. Well done. Every second your various cells are being snipped up into fragments that are digestible to phagocytic cells with minimal fuss and damage to neighbouring cells. That's apoptosis.
Apoptosis is a must-have tool for multicellular life. Without it there would be no us, no fish, no bats, no frogs, no lemmings. And why? The answer is simple: apoptosis stops cells going rogue, dividing rapidly and causing, in the worse cases, cancer. It finds and murders the single-celled transgressors trying to break free from our multicellular approach to life. It kills them. And caspases are its weapons of choice in this battle. They really are the executioners. Cell death is an everyday thing, something that we are all masters of. You owe your life to it. Almost every cell you had in childhood has gone, mostly through apoptosis; nearly all of your body's cells have been killed off and replaced. Even when old, we live our lives in bodies made, mostly, of new cells. Our totality is within generation upon generation of cellular blooms that form in the wake of cells that have died. Blooms controlled fastidiously by death. By caspases.
Where and when multicellular life evolved the ability to wield caspases to enable cell suicide is anyone's guess, but it must have happened very early in evolutionary history because of one curious observation: caspase enzymes are found in us and they are also found in cyanobacteria. Actually, this makes total sense. Caspases aren't used by our cells at all, but actually by our mitochondria – the ancient symbionts that live within our cells, with a deep history as once free-living single-celled organisms (prokaryotes) tamed and given pasture within our eukaryotic, multicellular selves. The writing is on the wall: our success as multicellular life forms isn't because of us, but because of our mitochondrial hitch-hikers, possessing the tools to cut back the cells that behave and replicate too wildly. In other words, we have mitochondria to thank for each and every day that we are alive. But there is more to the story than this. For instance, how and why did mitochondria (or their ancient free-living relatives) evolve the ability to commit suicide through caspases? Why would natural selection select for such an ability? It makes little sense in Darwinian terms, for single-celled organisms to go around killing themselves, after all. Thankfully there is one organism that may offer us clues. It is called Trichodesmium, and in many ways it might offer us an insight into why such ancient organisms required the tools for suicide.
Great blooms of Trichodesmium, a cyanobacterium, are occasionally known to cover hundreds of square miles of open ocean, making the sea blood red in places (in fact the name 'Red Sea' probably comes from Trichodesmium). These blooms (each made up of floating single photosynthetic cells) can last for weeks and perhaps months, thriving on minerals carried from rivers or via upwellings from the deep sea. But then they die. The caspases are activated within their cells. All of the Trichodesmium, almost overnight, cease to be. So why? Why do they commit suicide? It's still largely a mystery, but the answer is probably something to do with viruses. Today and perhaps for billions of years, these enormous algal blooms are preyed upon by an army of viral parasites, each eager to break into cyanobacterial cells and reprogram them into their own unique brands of virus factory. There are rather a lot of these viruses out there, as it happens. In fact, a litre of surface seawater contains about 10 billion virus particles. So why do the cyanobacteria kill themselves? One guess is that when the nutrients start to dwindle even slightly, it may pay more in surviving genes for individual cyanobacteria to pull back from the advancing army of viral parasites, hobbling the virus's frantic evolution into ever-new forms of perniciousness. The viruses fall back whilst some of the cyanobacteria sit it out on the floor as hard cysts and revivify themselves later, possibly when the viruses have washed away or become denatured somehow. In theory, these new individual Trichodesmium get a head start before the viruses re-evolve once more to cause havoc. And they will gather again in huge numbers, of course, as they have probably done for billions of year.
To Trichodesmium, a healthy sprinkling of death puts the viruses back in their place, allowing the cyanobacteria a head start when the good times return. As with the lemmings there will be peaks and troughs, sure, but a bit of die-back can sort out the predators and allow the nutrients to build up once more. It can be healthy to kill yourself, in other words – provided some of your relatives manage to encyst on the seafloor and live and blossom again. And so it could be that the ancient free-living ancestors of mitochondria that gave rise to those that inhabit our cells went through a similar viral assault before nudging their way – quite literally – into our lives. It's going to be difficult to prove this, of course – but it's a tempting hypothesis. I for one love the idea that we multicellular animals can persist in multicellular form because of an ancient war fought in the sea between our mitochondria and viruses.
We owe the mitochondria for our weaponry, and the mitochondria might owe the viruses for theirs. Of course, we may never know. What's clear is that the evolution of cell suicide had a dramatic impact on life on Earth. We couldn't live without it. It allowed us to build order in otherwise selfish aggregations of single cells through wave after wave of execution. Through such cell suicide, powered by mitochondria, multicellular life suddenly gained a hand in survival. Those early twigs of life in which mitochondria featured grew fast and gained strength and would come to form three great bows of multicellular life that exist today: the plant kingdom, the fungi and, of course, animals – each prolific wielders of caspases, courtesy of their mitochondria. Each prolific wielders of death. Organelles that work together to pull back from chaos; that pull back from the spiralling madness of disordered cells that appear like a hundred thousand lemmings fleeing outwards, leaving behind them emptiness, starvation, bodily death; no order, no aggregation. A true and utter chaos. Mitochondria deserve more of our time. They deserve more of our thanks. Mitochondria provide our energy, they provide the weapons through which we can keep our multicellular bodies from becoming unicellular, and, possibly, they possess properties to keep free radical damage at bay. Through this, possibly, they may contain the mother lode: immortality... or something a little like it. Screw lemmings – if anything deserves the Disney treatment, it's them.
CHAPTER TEN
This is Not a Sheep
From over the hills to the left they had loomed. At least a hundred at first. Then two hundred. Looking up higher into the atmosphere I had seen more. Five hundred. Still just dots, really. Five hundred dots. They formed an enormous spinning column, these dots, like distant wreckage swirling within a tornado. Debris with menace. There was a faint mewing from the sky, so light as if to be almost imagined. My family, part of the audience, were within a crowd of perhaps three hundred people that had gathered specifically to see this, arguably one of the western world's most impressive gatherings of scavengers. There was a small lake in the middle of the bowl in which we sat; our conversations and nervous laughter, as the dots came nearer, echoed over the water, our noises held in by rows of dense pine trees that overlooked us on all sides. An echo-chamber. After a few minutes they came nearer still. We sat underneath them, as if in stands, like an expectant crowd. It really was like a stadium, and we were the expectant hordes, baying for blood. We looked up. A few minutes later it looked like there were thousands of them. They were getting closer. They were red kites.
In recent years seeing the red kites has become THE THING TO DO in Wales. The 'feeding station' (as such sites are called) in which we were sat at Bwlch Nant yr Arian was designed to give small numbers of the threatened red kites 'a helping hand' in the late 1990s. Now there seem to be thousands. Red kites had faced incredibly serious declines across Britain, and this was deemed a nice way to help their resurgence at one of their strongholds. And it has helped them locally. Each day (including on Christmas Day) hundreds of kites from miles around visit this site to congregate and feast upon offcuts presented by a local butcher. It works like this: a nature reserve manager carts the butcher's meat (in a wheelbarrow) across the site to a little well-maintained mound in the middle so the audience can clearly watch the birds coming in. The scraps are thrown across the mound, and the birds take it in turns to get their fill. My youngest had not yet been born at the time we visited, but Lettie (then a baby) and my wife Emma were there. We had perched ourselves on soft mounds of moss on the hillside as the soaring birds of prey made their approach. There was a buzz about the place, like a music festival about to start; people sat on picnic blankets and nibbled homemade sandwiches, and many had their cameras ready and pointing at the mound on which the offal was to be presented. It dawned on me that many of the nice shots I've seen of red kites in magazines were probably taken here, where it's incredibly easy to take exceptional photos of red kites since there would be about 1,000 opportunities to see them up close looking charismatic and enigmatic and swoopy. Here, as I would come to see, taking good shots of birds of prey would be like shooting fish in a barrel.
Through my binoculars I could see, up the hill by the car park, the offal being prepared near the visitor centre. Great bags of it were being tipped into the wheelbarrow as the red kites circled ever closer. I looked toward the sky again. Their charismatic forked tails were now clearly visible, and they lazily flapped on lanky wings, biding their time. My appetite was thoroughly whetted, not least from the buzz on TripAdvisor. 'I was not disappointed! It was a truly mesmerising experience!' said one of almost 200 five-star reviews we'd looked at the night before our visit. Words like 'Breathtaking!' and 'Awesome!' and 'Clean toilets!' littered the comments pages. 'Even our dog was transfixed...' said one reviewer. (Imagine being a small dog surrounded by 1,000 birds of prey. Would you be transfixed? Yes you would.)
Then there was activity. When the wheelbarrow of offal was being wheeled down, there had been a sudden change in atmosphere; these enormous birds came suddenly lower, right above our heads, weaving within trees and ghosting over the edge of the grassy arena like great pterosaurs from the Mesozoic. Their shadows flashed over the crowd like angry spirits. It was wonderful. A real spectacle was beginning. But then things took a personal turn for the worse. Emma gave me a little nudge. She nodded at the baby, who had chosen this exact moment to soil herself in a particularly violent way. The smell was not very good. This was a problem for us: the toilets were about a half a mile away and whoever went would miss the whole damn thing. But there was another option: the baby could be changed high up on the hillside behind one of the pine trees, away from the crowd and where no one could see. I looked at Emma pleadingly. Could she go? She had pointed at her ridiculous sandals, completely inappropriate for climbing up the wooded hillside behind us. 'That's fine. I'll go then,' I'd mouthed so that the people around us couldn't hear, doing a terrible job at hiding how annoying this all was. 'That's fine,' I hissed. I gathered up the nappies, the wipes and the soiled baby and started walking up the hillside into the dark forest at the exact moment that the roadie with the wheelbarrow of offal came down the long path toward the sacrificial mound. Pandora's box was about to be opened and I would miss the whole thing... unless I hurried.
I scurried up the hill with her in my arms, as the devil birds made their approach. As I looked for footholds on the steep banks beneath the trees I could hear them now. Calling. Hundreds of them. Mewing from all around with a penetrating excitement. I guess it was hunger, but it sounded almost like song. Out of breath and sweating I found a suitable moss-lined cleft behind a tree, high up and far away from the crowd. I began changing the baby. I could hear excitement from the crowd below; I guessed that offal was now being unloaded, thrown in great chunks onto the mound that was just out of view behind trees. The red kites had started making their dive-bombs. It was definitely beginning. I tried to focus on the job in hand...
There is a reason I am telling you a story that involves my daughter's faeces. It's integral to the story. The faeces is what made me come up here, away from everyone else, remember? And from up here the scene was magical because, at the top of the steep bank looking down, I was at the same altitude as the birds. I could see what they saw. My daughter and I were in the middle of the pack; red kites above us, red kites below us. We were among them. The kites came screeching between the trees, sometimes almost at arm's length from us. They weaved between the branches, their wide lanky wings locked open, arched and rigid like those of a starfighter. It was like being in the middle of a beautiful war. And I could see the crowd from up here so clearly. The picnickers, the photographers, the nervous dogs. They were a proper crowd. An audience. We stood watching them. The crowd began whooping with joy, laughing, smiling. Drinking fizzy drinks. Opening bags of crisps. This was entertainment to them; by paying a small car-park fee they had become paying customers, and this was their reward. No wonder this place had got such brilliant reviews, I thought. The visitors here could see and admire something from the distant past. Hundreds of scavengers, scavenging. Doing what they used to do in Britain hundreds of years ago. Scavenging – a behaviour we rarely get to see in Britain any more.
And it started to hit me. The whole thing... the crowd, the birds, the wheelbarrow... it was a scene that didn't quite belong in the modern world. It dawned on me that this was a kind of theme park. A novelty experience. A day out. And had I been down there, amongst them all, I would have failed to notice any of the cultural significance of it. I would have been caught up in observing these wonderful birds for their grace and their power and their beauty, oblivious to the human perspective. I would have missed seeing the humans and the kites juxtaposed against one another. I realised at that moment that what I was watching spoke volumes about a world we once had and a world we've mostly lost. For aerial scavengers are amongst the fastest disappearing creatures on Earth, and theirs is a story that deserves a chapter of their own in this book. And so here is my best attempt at that story.
Red kites are one of those literary birds from previous centuries that we almost forgot about and that we almost lost forever. Long, sword-like wings and a deep V-shaped tail; they fly as if in a perpetual state of indifference. They are graceful birds. Although not total scavengers (they occasionally take small mammals and reptiles and even earthworms), they are an animal that was once closely associated with death across much of western Europe, particularly in medieval times when they became creatures equally at home on sewage tips or on battlefields. In Shakespeare's Coriolanus London is referred to as 'the city of crows and kites', a reference to the commonness of such a large and prominent bird. In The Winter's Tale Autolycus says: 'When the kite builds, look to your lesser linen' – a reference to the apparent phenomenon of kites stealing clothes from washing lines to furnish their nests (indeed, so common were these creatures centuries ago that they were known also to 'snatch bread from children, fish from women and handkerchiefs from hedges', according to the English naturalist William Turner, writing in 1544). It's probably not fair to say that the birds were revered, exactly, but red kites served a useful purpose in those times as hook-billed street-cleaners (unwanted scraps? Let the theropod dinosaur with a six-foot wingspan come to your door and take them away!).
Things changed in a big way for the kites, though. In the mid-fifteenth century, as the agricultural industry blossomed in Britain, the lazy flight of the red kite took on a more sinister note. In the eyes of the elite these birds ceased to be collaborators in nature's great story. Suddenly they were competitors. It was deemed that they wanted what the rich had: livestock. Their hooked beak and strong claws were all the evidence needed – they were killers. No doubt remained. Though they were previously given a degree of legal protection (for, God bless, services to public hygiene), the knives were sharpening. In 1566 the law changed and the tide turned for red kites in Britain. Rather than celebrate such creatures, almost overnight the kites became legal vermin. As with jays, ravens and (strangely) woodpeckers, the killing of kites by rural folk was now to be positively encouraged. It was to become a kind of sport, a bit of fun. No surprise, then, that at the end of the nineteenth century there were barely any red kites left at all in Britain. Many of the kites was killed brutally. And for those that remained, things got even worse. In the twentieth century legislation to improve biosecurity was introduced: many farmers began to remove dead livestock from fields to reduce the spread of livestock diseases, and so one of the kites' main sources of food, carrion, was being taken away.
It's a wonder that any red kites survived at all, but some kites got lucky – a relatively untouched UK stronghold remained and with it so did hope. This small population was in central Wales. It had miraculously clung on, helped by volunteers who stubbornly guarded nests from egg-collectors who, for a short while, threatened their very existence. This is where their story picks up. Over the decades that followed this population stabilised; in fact, it stabilised so much that conservationists realised that this central Wales population could be used as a breeding ground from which other sites around Britain could be repopulated. So, in 1989, conservationists began on an ambitious project to do just this. By translocating birds from Wales (as well as Sweden and Spain), new populations have now been established in England in the Chilterns, Northamptonshire, Yorkshire and Cumbria. Northern Ireland is another place where reintroductions have had encouraging results. As of this moment there are 16,000 pairs of red kites in Britain and, for the first time in centuries, red kites are now occasionally spotted over the City of London, just like in olden times. They're coming back, in other words. Reclaiming their niche: death. Though some are still shot or poisoned (illegally) by landowners and gamekeepers, the red kite has become a global success story for people, like you and me, who like the thought of big creatures living wild. It's a story with which all conservationists enjoy regaling their children, whenever red kites are spotted circling high above on long car journeys: 'When I was a kid there were almost none left...' we say with great pride. We don't have many conservation success stories in Britain; this is one we like to celebrate. This is one of Britain's biggest remaining aerial scavengers. And every continent has its own. For now, anyway...
Among these continental cliques, of course, the vultures are the ones we recognise best. Books and TV programmes tell us that these, truly, are creatures that have evolved an almost perfect design to feast upon the bodies of the recently deceased. If red kites are refuse-collectors, then true vultures are more like mobile industrial chippers; homing in on freshly decaying matter and turning it into mush in minutes. Broadly speaking, vultures aren't a single family; rather, they are two, spread across every continent except Australia and Antarctica. One, which biologists divide into two closely related subfamilies, lives in the Old World. The other, the New World vultures, have sprouted from a different part of the avian family tree entirely, but have evolved convergently many of the same features as the Old World vultures.
Among the most celebrated of the vultures' adaptations for life on the corpse are their bald heads. Famously we're told that the vulture's head is largely devoid of feathers because, well, sticking your head into a blood-spattered ribcage is not conducive to maintaining good head-feather condition. This is one of many untruths about vultures. The reason for their baldness may actually be far more prosaic. Some scientists suggest that it may be thermoregulatory – having a semi-bald head may be a simple mechanism through which to reduce the likelihood of your face (or brain) cooking in the hot sun. And, fair enough, it's true: many vultures do live in warm climates.
Vultures have other adaptations for life on the bones. Their stomach acid is exceptionally corrosive, for example. Helpful for digesting smaller bones, certainly, but probably also useful for destroying micro-organisms that associate with putrid carcasses, like Clostridium botulinum (which causes botulism), hog cholera and anthrax bacteria. In 2014, an analysis of black and turkey vulture digestive systems revealed that their gut micro-organisms differ markedly from our own. Where ours house a veritable mishmash of micro-organisms, vulture guts are dominated by just two types: Clostridium (which produces botulism toxins) and the dreaded Fusobacterium (implicated in a number of serious blood infections). These produce poisons. Poisons that the vultures appear totally fine with. What are these poisons doing there, you might ask? No one is particularly sure. It could be that the vultures have evolved an immunity to them, or that possessing stomach acids 10 to 100 times more corrosive than our own means that these poisonous micro-organisms can't get up to much. Scientists are still looking into it.
There are tales of New World vultures possessing another neat trick to do with death: the ability to projectile vomit their stomach acid when threatened by ground predators, which sounds rather impressive if only in a frenzied Aliens sort of way. As with the bald head, the truth is probably a little less exotic, but it may have evolutionary significance nonetheless. After all, heavy vultures take longer to take off, so it might be that vomiting is a bit like throwing out the ballast before take-off. Scientists aren't too sure about this one either. And there are other evolutionary quirks that vultures possess. One is that they frequently urinate all over their legs; a behaviour thought to be adaptive since nothing removes potentially fatal corpse residue quite like uric acid (murderers take note). Oh, and urine is cooling (apparently) too (murderers: your call). But it is their adaptations for locating dead megafauna that have caused most stir and argument among zoologists. After all, how exactly do vultures get to a dead body so quickly? And from how far might such vultures travel? And what senses do they use to locate these dead bodies? These were once big questions for Victorian naturalists. So heated did the discussion become that it was almost inevitable that two opposing groups would form: one arguing that vultures used smell (this group became the 'Nosarians') and another group arguing that they used sight to locate dead and dying prey (the 'Anti-nosarians'). How they resolved this argument is worth explaining, not least because it outlines the wonderful manner in which great scientific battles can be won and lost through simple experiments (I retell it here recounted from Benjamin Joel Wilkinson's excellent – and freely downloadable – book Carrion Dreams 2.0: A chronicle of the human–vulture relationship).
Leading the charge for the Nosarians was the British naturalist and explorer Mr Charles Waterton. Waterton believed that vultures 'snuff the smell / of mortal change on Earth... / Sagacious of the quarry from afar...' But the New World had its own talismanic truth-seeker when it came to vultures. The chief Anti-nosarian was no less than the noted ornithologist John James Audubon himself. The reason for his conviction about this was simple. Audubon had previously observed that a vulture had once approached when he had covered a bale of hay in deer skin. The vulture had approached the strange-looking hay bale and pulled at the 'flesh' ('much fodder and hay was pulled out'), apparently confused that the corpse had turned out to be a ruse. There were no smells of death yet still a vulture had appeared. Audubon had thought about this. Audubon built his hypothesis: he was to become a powerful Anti-nosarian. Vultures located corpses by sight, he proposed.
Audubon and Waterton met at a formal talk in London in December 1826, and it was from this meeting that the energetic intercontinental debate about vultures raged. From this point forth, the Nosarians and Anti-nosarians each searched for supporting evidence for their own hypothesis whilst searching for evidence to refute the claims of the other. It wasn't pretty. At one point Waterton said that Audubon's ideas were so half-cocked that 'he ought to be whipped'. Insults aside, in the end it was the superior methodological approach of the Anti-nosarians that set the stage for the winner. Buoyed by Audubon's initial observation of vultures investigating bales of hay wrapped in deerskin, Charleston's Reverend John Bachman took Audubon's methodological baton and ran with it, employing the academic services of members of Charleston's prestigious Philosophical Society to help him out.
Together Bachman and his team of philosophers thought about how they could uncover experimentally the truth behind whether vultures (locally, black vultures and turkey vultures) found prey using their eyes or their noses. They had a great idea. First they got their hands on a dead vulture, covered it in rice chaff, and watched what happened. As Audubon predicted, no vultures visited, even though the corpse stank (almost literally) to high heaven. Then they tried something else. They placed some rotting meat under a platform, so it was invisible from above, yet through which air could pass. The smell 'went far and wide' but still, after 25 days, not a single vulture visited. Only dogs. Lots of dogs came. It couldn't be smell that the vultures were attracted to, they thought. They were getting closer.
And then came Bachman's truest moment of creative genius. He commissioned a local artist to paint a picture – a vision he deemed would be sure to attract vultures from the sky: an enormous painting of a plump sheep with its body alluringly eviscerated. Bachman and his groupies took the painting to the meadow, placed it on the ground and watched what happened. And something did happen. For perhaps the first time in the history of the universe a bird came down from the sky to try to eat a painting. Then more vultures turned up to try to eat the painting. Then others. Then more. The vultures 'commenced tugging' at the great work of art. Then they 'seemed much disappointed and surprised' to find that they couldn't eat a painting, and the little rabble of philosophers watching in the nearby undergrowth all agreed that it had 'proved very amusing'. The test was repeated more than 50 times. They tricked the vultures again and again. Even when offal was placed near the painting the vultures failed to locate it, heading straight to the artwork still. It was a momentous bit of methodological mastery (who says art and science don't mix?).
In 1834, Bachman and his team wrote up their findings and sent them east toward Europe. The Americans, led by Bachman and Audubon, had won the debate. The Anti-nosarians had nosed it. The British, led by Waterton, had lost. They had lost... mostly. I say 'mostly' because, of course, things aren't always that straightforward. Further research (without artwork) showed that black vultures do appear to depend almost solely on sight, but that turkey vultures, on the whole, don't. They have a capacity for smell, too, which they do appear to use while seeking items to scavenge. Much to the disgust of the British Victorians, other raptors in the Accipitridae (the taxonomic family in which both Old World vultures and red kites sit), like most vultures, also have a poor sense of smell; they use sight to home in on dead animals.
This is where the similarities end between vultures and Europe's kites. Currently the plight of Old World vultures and red kites couldn't be further apart, in fact. While red kite populations continue to do well (in the UK at least), Old World vultures are declining at a rate faster even than the dodo once faced. Almost overnight (in geological timescales) numbers of these vultures have plummeted. Literally and figuratively plummeted. Currently 75 per cent of Old World vultures are globally threatened with extinction or are officially Near Threatened, according to the IUCN Red List of Threatened Species. The vulture species worst hit has been Asia's white-rumped vulture: 99.9 per cent of them have gone, according to BirdLife International (who monitor populations and have campaigned fiercely to see an end to such declines). The cause of these vulture declines? It's called diclofenac, a veterinary anti-inflammatory commercially given to livestock. When vultures feed on dead livestock they then die from kidney failure because of an accumulation of the drug in their body. The drug has wiped out 99 per cent of vultures in Pakistan, India and Nepal, yet despite this horrific (and well-documented) decline in Asia, in 2014 diclofenac became available in Spain and Italy. Both European countries are vulture strongholds. Who knows how their vultures will fare.
Diclofenac is the most concerning of a number of threats to modern-day vultures that include persecution (to supply the trade for traditional medicine), habitat loss, the threat of power lines and deliberate poisoning. And it's getting worse. In June 2015, new studies suggested that Africa's vultures are going the same way as Asia's, having declined at rates of between 70 per cent and 97 per cent in just three generations. This makes me incredibly sad. It makes me sad because vultures are fundamental parts of Old World food chains. They are like alchemists, making nutrient-rich fertilising paste from the bodies of dead animals, removing corpses and eliminating their capacity to spread disease. And they are beautiful. They are big and beautiful and I am in love with them, just like I am with the kites. How will they fare? How many vultures will die in the Old World? It's hard to say. We will wait and see, but there is hope that one day they may, like the red kites, have a stuttering resurgence. Vultures have place and purpose. They have poise and value. They are every bit as special as red kites or their New World cousins, which are faring (in most parts of the Americas) better.
Even though it was nothing much to do with me, I am immensely proud of the resurgence seen in red kites. Proud that I sometimes see them over our house. Proud that they exist still. They are evidence that we can change and influence nature in a nice way. A good way. Evidence that we can influence the lives of creatures many (or most) had written off. Evidence that life, given a chance, heals itself pretty well. But the Victorian elements remain. The distrust, for many, of scavengers is still there. In Britain, as I write these words, it seems to me that this uneasy relationship between some landowners and kites is re-emerging. I fear the gentry may view them as threats to the game-shooting industry. Far right-wing parties refuse to believe that they can be truly trusted, having been reintroduced partly because of a legal bill dished out from a bureaucratic EU they no longer want Britain to be a part of ('These birds, they come here from Europe to steal our lambs, blah blah blah...'). I can offer few insights here, but I feel sorry for them nonetheless. They are treated unfairly in much the same way that magpies and crows and ravens are. They, like many of the corvids, are tarnished because their niche involves the dead. It's really not their fault, surely? After all, we cleared the wild animals with which they coexisted for thousands of years, swapped them for livestock and then actively removed death from the system; pulling the rug out from under them. We starved scavengers out, mostly. The kites and magpies and crows that remain are like the unemployed; we are too quick to call them scroungers. We mistrust and label them in the same way.
And that's what I realised most when I saw those red kites at Bwlch Nant yr Arian. As I watched from the hillside after changing that nappy, looking down upon the whole scene, I could see it all. Those kites, hundreds of them. Spiralling down. Forming an orderly queue as we watched and laughed and mocked and ate our prawn cocktail sandwiches below. It was a food bank for scavengers. They were spoiled birds; spoiled versions of the important life their species had once held on Earth. They were once birds with real purpose and poise; a purpose we took away from them. Britain may never support as many red kites as in previous centuries – there's just not enough death out there. So what is there for us to do? For me, I now celebrate each and every one I get the chance to see. And I pray for a tiny bit more death, not life, so that my children will see them too.
Looking out across the bowl, standing amongst the kites with my nappy bag in one hand and baby in the other... it was the first time that I suddenly had misgivings about humans and our perceptions of death in nature; our role as self-appointed enforcers of life and death. I felt it again with the ermine caterpillars. Then I felt it again with the false widow spiders. A deep uncertainty was beginning to run through me about humans and our perceptions of death. Do we fear such creatures because they remind us of ourselves and our own mortality? Are we scared of them because we're scared of death? Or do we hate them because, try as we might, we can't accept the fact that we are painted from the same watercolours; that life and death are equal parts of who we are and how the world works? Is there a part of society that feels differently? I wondered. Were there people out there who love and accept the bits of nature that remind us of death? And there were. There really were.
CHAPTER ELEVEN
The Grotto Salamander and the Guano
The penguin that washed up in the river on the way to Azerbaijan didn't have a name. No one knew much about it really. It was just bobbing around in the water and then fished out by officials. It was an African penguin, native to the southern coast of the African continent. A travelling penguin, essentially. Genuinely. It had been born in Torquay, England, and then, apparently, it had been given to Tbilisi Zoo in Georgia. It had been washed out of the zoo during a heavy flood and had swum 200 miles downstream and been found in the river on its way to Asia via Azerbaijan. What was an African penguin doing in Europe, you might ask? And for what reason was it so very far from home? It is a story, like so many, millions of years in the making. And it involves faeces.
The romantic retelling of this particular story starts in a previous century in a place not far from Torquay: Lyme Regis, a celebrated part of Britain's Jurassic Coast made famous by Mary Anning, the nineteenth-century palaeontologist. The cliffs above Lyme Regis are famous not only for the ichthyosaurs and plesiosaurs that she discovered, but also for the 'bezoar stones' that fell from them. Spiralled and grooved and often stained with black splodges, these unusual stones inevitably became part of the seaside trade. Jewellers made brooches, necklaces and earrings from them and, again inevitably, medicine men bestowed upon them special powers which could be passed on to the wearer.
Unbeknownst to almost everyone at the time, the women were actually being encouraged to wear little fossilised reptile shits. It was true: a market in reptile shit had, unwittingly, begun. Anning was one of the first to suspect that everyone was walking around wearing fossils of reptile shit because, among other things, she found these mysterious bezoar stones in the lower cavities of ichthyosaur fossil skeletons, being readied (once upon a time) for a bowel movement that was never to be. She knew. Others didn't. William Buckland (the Dean of Westminster who went on to be the first to describe the first fossil dinosaur, Megalosaurus) agreed with Anning about this. He undertook experiments on a range of bezoars and discovered within them fossils of fish scales and what he considered (rightly, it turned out) to be ink stains from the sepia-bags of cephalopods (belemnites and cuttlefish, mainly).
Needless to say, soon after the news about bezoars spread through Lyme Regis the bottom (sorry) quickly fell out of the bezoar-jewellery trade. But a trade in something else was to bloom. A trade much larger and more profitable, which went on to feed the world for a while. Buckland, still intrigued about the bezoars, introduced his friend, the noted chemist Lyon Playfair, to the wonder of bezoars, or coprolites as they had been renamed. Together they collected samples, which Playfair pulverised in his lab. As Buckland had predicted, Playfair found the bezoars incredibly rich in phosphates of lime, a key ingredient required to refertilise lost soils. Together these men dreamed big, imagining an industry that could restore the face of the Earth for crops using the fossil faeces of creatures that lived millions of years previously and that no longer had a need for their faeces at all because they were all well and truly dead.
They invited to Lyme Regis a distinguished visitor named Baron von Liebig, a renowned German chemist. They pitched their idea to him; von Liebig liked their idea. In fact he soon published a treatise on the subject (with their support) and went on to build a global industry shipping super-phosphates, not from dinosaurs or marine reptiles, but from the animals that survived them: birds. Their guano became highly prized from this point forth and, in the decades that followed, many millions of square miles of the developed world were made green through the trade. And it all began with innocent earrings and brooches of fossil reptile faeces.
This is the romantic version of events, of course. In truth many early geologists and explorers (including Alexander von Humboldt, whose writings inspired the young Darwin) had noticed the fertilising potential of droppings. Others had reached similar conclusions to von Liebig, far earlier; that guano was highly effective as a fertiliser given that it contained nitrogen, phosphates and potassium, which are all pivotal to plant growth. Still, regardless of how it started, in the nineteenth century the remote islands where seabirds gather in their tens of thousands suddenly had a new value. A global race for their excrement began. It made the Gold Rush look tame. Harvesting took place from islands off Namibia, Oman, Patagonia and California – mirroring the industry that blossomed off Peru soon after von Liebig's treatise. In 1856, the US passed the Guano Islands Act which gave US citizens who discovered guano on unclaimed islands the exclusive rights to deposits (interestingly, nine of these islands are still officially US territories). China also got in on the act of guano-chasing. What started in 1849 as 80 or so Chinese guano-harvesters turned into an industry involving 100,000 of their countrymen two decades later. Predictably, wars were fought over who had control over the most important islands, namely the Chincha Islands War (1864–1866), where Spanish soldiers fought a Peruvian–Chilean alliance, and then the subsequent War of the Pacific (1879–1883), in which Chile seized many of Peru's guano riches. Apparently, so rich were sales of the faecal treasure that taxes coming from these newly acquired lands saw Chile's national treasury increase by 900 per cent by 1902.
Other countries wanted in, not least South Africa, which began to independently harvest its own guano-filled islands, to the detriment of the creature with which this chapter began: the African penguin. African penguins make their nests from guano. They make burrows in the stuff into which their eggs are laid. With less guano going spare because of human extraction, penguins began making nests in the open, exposed to the elements. It surprised no one when their numbers plummeted. In stepped the conservationists and a captive-breeding programme began, sending penguins to far-flung places like Torquay to breed in the hope that one day they might be reintroduced back into an ocean environment now overfished to within an inch of its life and missing all of its guano to boot. So, in a nutshell, this is why there was an African penguin in that river on the edge of Azerbaijan. Our lust for guano started it all.
I had debated whether or not this book needed an exploration of faeces. I'm still unsure, to be honest, but I think it is justified because faeces is, essentially, death. It is a product of life. It is where dead things go through living things; it is arguably the single biggest currency of death that we see in day-to-day life. And, like dead bodies, it is life-giving (which is why the global trade in the stuff emerged in the first place). So allow me a few more moments to talk about guano, if I may. And then we'll be done with it.
The best and most nutrient-rich guano comes from islands that don't receive much rain, where the sparse rainwater leaches the nitrogen-containing ammonia out of the guano but fails to wash it away. The truly best guano often comes from islands next to oceanic upwellings where nutrients surge up from the depths and are feasted upon by fish, which are then feasted upon by seabirds, who then squirt the nutrients from the upwelling onto the rocks in shiny wet new faecal form where they remain until harvested. Many landscapes and seascapes are revitalised by this material that we might be tempted to call 'waste' – in reality it is anything but. It really is life-giving.
Perhaps the best-known example of how valuable to life faeces can be is that of the 'whale pump' – an idea put forward by the marine biologists Joe Roman and James McCarthy in 2010. The whale pump is a system of nutrient transfer from the ocean depths (where whales may feed) into the surface waters where they surface to breathe (and where whales defecate). You or I might picture something heavy, big and brown coming from a whale that sinks quickly into the depths, but that's not the case with whales. Their faeces are known as 'flocculent faecal plumes' – they squirt forth from the whale's anus and then dissipate into a cloudy layer that sits in the surface waters. This layer becomes like newly fertilised soil to the planktonic organisms that dwell there. Life moves in and flourishes using the nitrogen that exists there in huge concentrations. 'Whales and seals may be responsible for replenishing 2.3 × 104 metric tons of N [nitrogen] per year in the Gulf of Maine's euphotic zone, more than the input of all rivers combined,' write the authors in their 2010 paper in PLOS ONE. And that's after centuries of brutal treatment at the hands of humanity. It's giddying to imagine what an ancestral ocean of whales and seals could have achieved in terms of fertilising the ocean surface. More nutrient movement than the guano industry in its prime, certainly. Whaling nations sometimes argue that whales compete indirectly for fish. Well, if Roman and McCarthy are right, it's probably the opposite way round. Whales seed the surface waters with nitrogen. They bring up nitrogen from the depths and create a habitat in which young fish flourish and adult fish feed. And we have the gall to blame them for our reduced fish stocks? No wonder sperm whales have been known to fire massive shit-clouds at passing divers.
Bats are another famous producer of highly sought-after guano. In many caves there are great mounds of the stuff, accumulated over thousands of years. In these unusual habitats, an ecosystem has blossomed that is home to hundreds of guano-adapted invertebrates that include nematode worms, millipedes, mites, springtails, micro-moths and flies of numerous species (there is even a guano-eating amphibian, the aptly named grotto salamander). Mites are especially common. In one New South Wales cave there were found to be something like 12.6 million mites per square metre of guano. As I had learned through the pig corpse, great swathes of predators join the guano-induced party. Rove beetles, ground beetles, pseudoscorpions, centipedes, harvestmen, spiders, moths and parasitic wasps are only some – they feed on the mites, the springtails and the nematodes, particularly. What's perhaps most impressive is how the sex lives of all of these creatures are largely governed by the abundance of bats and droppings in any given month. Even in a cave, without light, there are seasons brought to them by the frequency with which the bats above them produce their faeces (frequent droppings = summer; more infrequent droppings = winter). Life is made of wonderful phenomena like this.
Sadly, as with seabird islands, bat guano is often too good for humans to let sit. Far better, says humankind, to mine it. To sell it. To ship it. And so they have done just this. Bats don't particularly like it when people with machinery enter their caves. They do that thing that bats do in movies where it looks like they're attacking en masse but the reality is that they're all panicking wildly and flailing around not really knowing what to do. What you don't see in films is that some of these bats simply expire and fall to the floor dead during these human intrusions. Many young pups will also die, accidentally dropped by their mothers into the great swarming mass of life waiting beneath. Its likely that many bat populations have been damaged by guano-mining. And with the bats goes the guano. And with the guano go 12.6 million mites per square metre. What a sad loss of life. What a sad loss of lives...
Thankfully, though (depending on how much of a fan of mites you are), guano doesn't have quite the market price it once had and so the industry of guano collection isn't quite as relentlessly barbaric as it once was. In 1909 Fritz Haber came up with the Haber–Bosch process of industrial nitrogen fixation, which now generates enough ammonia-based fertiliser to sustain an estimated one-third of all humans on Earth. Trillions of faecal mites owe their continued existence to this man. Millions of centipedes, too. Still, it hasn't been a happy ending for all guano-loving creatures. Many African penguins remain holed up in captivity; many African penguins aren't where they should be. Yet. Hopefully one day they can return to their island havens, stinking and covered, as they should be, in a thick layer of faeces provided like mother's milk by previous generations.
This has only been a short chapter. I wondered whether to make it longer. I thought about focusing more heavily on faeces, but others have gone there and done a much better... job.* At one point I even considered visiting a sewage treatment works – I made contact with my local sewage treatment centre to find out more about what, exactly, happens to my faeces and the faeces of my toilet-trained children when we flushed the chain. I was surprised to discover that, actually, they weren't enormously interested in me 'popping in', which was a shame because I pay them something like £500 a year for this service. You'd think they'd be pulling people off the street to see what they do with all that money. But no. They weren't really kitted out for visitors, I was told.
And so thankfully (for you) I chose not to chase up this particular thread. I still think this is a bit of a shame. I think we might have a better appreciation of what life is all about if we could see what happens to our faeces. It is the one thing that bonds us, after all: tube-shaped animals with a mouth at one end and an anus at the other. A mouth into which death passes; an anus from which death spews and onto which life returns, if and when we allow it; if we cherish it enough and leave it where it lies as best possible. For it is from shit that some good things come. It is from its faecal plumes that some life blossoms, even if it's just a collection of centipedes and mites. It's still life. And life is, on the whole, quite wonderful.
Note
*I recommend The Origin of Feces by David Waltner-Toews.
CHAPTER TWELVE
The Horrid Ground-weaver
A security guard strides over to us from across the car park looking notably disgruntled, as if his time is already being wasted just by approaching us. I can understand why he's come over, mind you. He is wondering why three people are standing in a car park outside his hardware store looking up and staring at the cliff-face that overhangs it. As he approaches he possibly wonders why one of us is wearing a lime-green t-shirt with a big picture of a house fly on the front. He's thinking: 'Who stands around in a car park and wears a t-shirt with a big picture of a house fly on the front?' He is no doubt wondering also why one of us is playing with an incredibly complicated handheld GPS device, and what this could mean. He may also be confused about my role – a man nodding his head too much, waving his arms a lot and recording the whole thing with a dictaphone.
'Can I help you?' he asks when he reaches us. Andrew Whitehouse, in the house-fly t-shirt, spins around from the cliff-face and faces the security guard confidently. He speaks as if it's the most natural thing in the world to stare excitedly at a cliff, like this is all totally normal, but I think that there's a hint of self-doubt in there too. There's no getting around this. Andrew is, after all, about to ask permission from this man to look for a tiny money spider that may or may not live on his business's property.
'Do you know who manages and looks after this site?' Andrew asks the security guard. 'Erm,' says the guard, suddenly caught off-guard. 'I haven't got the details to hand, but...' The security guard regains his composure. He almost shakes himself back into reality. 'Wait,' he says. 'Who are you? What are you doing here?' Ah. Ah, right. We all look slightly embarrassed at the security guard's sudden grasping of authority. I shuffle around slightly. 'Are you birdwatchers?' the man says, suddenly quite serious. 'Well,' begins Andrew. '... no, we're not birdwatchers... It's worse even than that.' He takes a deep breath, gathering his thoughts before continuing. The security guard crosses his arms. 'Ok,' Andrew says. 'So, here's what's going on: a really rare spider was discovered in this quarry before this retail park was built and before your business moved in here. It's called the horrid ground-weaver.' Andrew pauses. 'Right,' says the security official, deadpan. He nods his head imperceptibly slowly. 'Go on...' Andrew takes his cue. 'It's called the horrid ground-weaver,' he says again. 'It's only known from three sites in Plymouth. Plymouth is the only place on the planet that the horrid ground-weaver exists. And it used to live here, on these cliffs, when this place was a quarry.' Andrew looks up at the limestone cliffs and the assembled boulders that jut out from the sandy soil beneath. The security guard's eyes remain firmly on Andrew. He looks really quite serious. Andrew catches his look and stands firm, determined not to lose his composure. 'We need to know if it's still here,' Andrew says confidently to the guard. There is a pause. 'Ok...' says the security guard, slightly more suspiciously than before. 'Ok...' he says again. Being honest, this isn't going quite as well as we'd hoped.
There are a few moments of silence again. Andrew tries a new approach: a child-like grin. 'This sounds crazy. I know it sounds crazy, but...' He draws breath. 'What we'd actually quite like to do is get up on that cliff, with all the right safety gear, and look for the spider... actually get up there and look, you know?' he says, before adding hurriedly, 'But first, of course, we need to talk to you.' He says this last bit with a big open smile again. The security guard looks at us all. A pause. 'Where are you from again?' he asks. 'We're from Buglife,' says Andrew, as if Buglife is some sort of well-known law-enforcement agency (I half expect him to pull out a badge). There is one final silence. 'Ok,' says the security guard with a slight smile. 'You'd better come with me to speak to the boss.' Andrew walks off with the security guard to the main building, leaving his colleague Jo Gilvear and I standing alone in the car park. Before he goes in Andrew looks back at us, offering us a little thumbs up. He enters the building.
The horrid ground-weaver: a money spider so nondescript they had to give it a funny name so everyone would remember it. So nondescript that, to correctly identify it, we'd have to kill it and examine its genitals under a microscope. So nondescript it eluded invertebrate experts for centuries, until finally being identified as its own species (within its own genus, no less) in 1995. I was in Plymouth hoping to come face-to-face with perhaps one of the rarest animals on the planet.
I got here through John, the journalist responsible for the false widow hysteria. Hearing his voice in that coffee shop, knowing the hatred that he had unthinkingly stirred up against the nation's spiders, I had suddenly felt it my duty to stand up for spiders even more in recent months, being that they are largely quite lovely, at least on the whole. Even though I'm a tiny bit phobic, spiders really are amazing. I can see that quite clearly now. Spiders are an invertebrate class that hit upon a design so perfect for predation that they have cemented themselves into food webs the world over for hundreds of millions of years.
The plight of the threatened horrid ground-weaver in recent months has had me thoroughly ensnared, being that it has largely played out in the public arena, something that doesn't often happen with inconsequentially small and quite boring money spiders. The reason for this public media attention is that the horrid ground-weaver is a spider species that humans are debating killing totally, knowingly forcing it to extinction, in the name of 50 new houses. Sure, there's a small chance it might still exist on the cliff next to the car park where we had just gathered, but it probably doesn't. Its stronghold is thought to be two miles away at a place called Radford Quarry, a former industrial site that has since become a haven for wildlife, and which is now threatened by becoming a housing estate. I use the term 'stronghold' loosely. Really I mean: 'place where it has been seen five times'. Either way, that place, the former quarry, is now threatened and Buglife are calling for it to be saved. A spider, the only one of its genus in the world, which has only been spotted a handful of times ever, is about to have its fate decided by us. By humans. What can I say. The story really appealed to me. It had drawn me in.
Whilst writing this book, I have tried to define life and death, and looked at the death niche and the invertebrates and vertebrates associated with it. But I'd also seen something I hadn't expected: humans killing trees in the mistaken view that caterpillars were monstrous, humans generating advertising revenue from spider scare stories, humans needlessly killing and demonising scavengers. And now, here I was in the middle of another strange human behaviour surrounding death. Here I was in the middle of a pack of humans debating and warring over whether, and to what degree, the total extinction of a money spider really matters to anyone. And the debate was actually becoming incredibly interesting. I mean, consider it for a moment: the history of Earth is littered with extinctions, so why the bloody hell should it matter if a tiny spider lives or dies? But then there was the opposition, the conservationists questioning how we might live with ourselves knowing that we had chosen to cause a total extinction of a species. What's going on with them? How did they get so moral about it? It has been entrancing to watch the story of the horrid ground-weaver play out through the press. Gripping. Really gripping.
So should it matter if we let species go extinct? Contrary to what you might think, I haven't really cemented my thoughts on the issue. I'm willing to have my opinions challenged, I guess. The potential extinction of a tiny spider with slightly hairy legs that lives underneath limestone boulders and that only a handful of arachnologists has ever seen seems a good testing ground for the moral argument for or against extinction, I suppose. Like I said, I was drawn to it. In many ways, our reaction was confusing, partly because extinction – the total death of a species – is so very common in Earth's history. Who cares if we cause it?
Famously, it's said that 99 per cent of all species that have ever lived are now extinct. The death of species really is, like the blossoming of new species, de rigueur in the history of life on Earth. Most notably these die-offs occur during times of mass extinctions, such as that which occurred 252 million years ago (when 95 per cent of marine invertebrates were made extinct) and 65 million years ago when most dinosaurs died out, paving the way for the slow advance of aye-ayes and aardvarks and other nippled creatures. It's becoming increasingly clear that we live in a time of similar such extinction now, possibly at the dawn of another mass extinction – a mass extinction potentially like no other given that, this time, a single creature is the cause. Us. Of the 44,838 species categorised by the IUCN under their Red List criteria, 16,928 (38 per cent) are currently threatened with extinction. Our oceans are dying, we're told. Our rainforests are pillaged. Our grasslands are becoming deserts. According to WWF, the Earth lost half of its wild animal populations in the last 40 years. Half. In the UK, 60 per cent of native species are declining and recent research says that 1 in 10 are on their way to national extinction. These are terrible times to be anything other than a human, a chicken, a cow, a sheep or a crop monoculture.
Yes, extinction really is commonplace. The tree of life on Earth is littered with branches and twigs upon which leaves no longer grow. Though the great boughs stand strong, whole branches have withered and died, or left twigs upon which only a few leaves grow today. In our own primate lineage, fossils show us that our ancestors were once part of a well-twigged and well-leafed branch that has withered greatly. Apes particularly were at one time quite a diverse and funky lot. Now their numbers are sliding precariously downwards; in many ways those that remain on Earth are a shadow of their former diversity. It's a similar story with the horrid ground-weaver – it is a spider that sits within a genus that was probably once thriving and full of life, but that now numbers only a single species. A single leaf on a long-forgotten twig in the tree of life. Possibly, or quite likely, on its way out anyway. Extinct. So why does it really matter?
Jo and I kick our heels in the car park while we wait for Andrew inside, speaking to the manager about whether he's happy with a team of strangers in weird house-fly t-shirts ascending a cliff on his property, potentially risking life and death for a spider many of us wouldn't think twice about squashing with our thumb. Neither I nor Jo are quite sure whether Andrew will come out of the building victorious or with his head down and his shoulders slumped. We make small talk. Jo is a freshwater biologist who is starting a new(ish) life as an arachnologist. It will be her job to manage Buglife's (largely crowd-funded) Horrid Ground-Weaver Project, which it's hoped will find the spider still alive on the nearby disused quarry or here, where it was once spotted two decades before on the cliffs. Should that happen the next step ideally would be to get the spider protected by law and, even more ideally, protected from encroaching housing developments, like those that currently loom.
Jo is excited but slightly daunted at the prospect of raising awareness about what is genuinely a fairly nondescript money spider. 'So tell me,' I say. 'Why is it worth saving?' I deliver the question quite nonchalantly, pretending it's not the only reason I'm there. 'Why does it matter, exactly?' I'm not very good at this style of direct questioning but it seems like an important place to start; a way to figure out why the spider has captivated local people so much. Jo is like lightning with her response. She says it kindly and with feeling and genuine heart, but she does seem to bristle slightly. 'Why would anything going extinct matter?' she says quite abruptly. She gathers herself. 'For me... it's a moral issue. I mean, we've found it. We've found this spider. We know it's almost gone. As soon as we realised that it existed it's become our responsibility. We had to act. Someone has to act. That's why we've got to save it. That's why we're here.' Her voice trails off a little, almost like she's embarrassed that she allowed herself to become so animated. 'I guess we don't know much about this spider,' she continues, more slowly this time. We stand for a few moments in total silence. She looks back to see if Andrew has popped out of the door yet. She looks back at me and then at the floor. 'How sad would it be if this thing could come and go without us ever knowing much about it, or adequately documenting it? How sad would it be for this spider to be this... this... this fleeting thing?' she says.
A fleeting thing, like all things. But a fleeting thing that is facing extinction on our watch. Because of us. I agree with Jo that this makes it different, somehow. I stand there thinking it over. If the arachnologist who first stumbled upon this creature had never thought to identify the tiny spider he'd found, we would never have known it existed. We would never have been forced to act. And it is probably one of only a handful of spiders to ever have received conservation funds to save it. It is certainly the first spider ever that experts are attempting to save through crowd-funding, we can be sure about that. But the question remains: why save it? Why does it matter?
Much of my experience with conservation, as I mentioned earlier in this book, is with amphibians. Amphibians are animals that will always be close to my heart because they are the taxonomic class with which I began my career. And this is a vertebrate class that really is in trouble. In 2008, one study calculated that the current rate of amphibian extinction could be more than 200 times greater than the background extinction rate. This is not good. A key part of my role in that first job (part of which involved manning the infamous frog helpline) was to let people know why amphibians are worth saving. I had to convince people (mainly potential funders and donors) that we shouldn't just let them die, and that we'd need their cash to help save them. But how do you convince people to want to save frogs? Simple, I was told. I'd had the answers to this question drilled into me when I first started the job. The reasons amphibians were worth saving, I was told, were threefold:
1. They eat pests.
2. The freshwater habitats in which they breed are crucial for human life and livelihoods.
3. They might be a source of new medicines and painkillers.
And that was it. Three reasons. That was all it would take, my bosses hoped, for me to convince the public that frogs were worth saving. Three reasons would be all it would take for punters to put their hands into their pockets and pull out wads of cash. I did as they said. I brought up these three reasons why amphibians were worth saving, just as instructed. But the more I spouted out these three reasons for why frogs mattered, the more I hated how they sounded. For a start, I couldn't help this feeling that they were such awful and tawdry reasons. So arrogant and human-centric, somehow. I wished I was confident enough to have screamed something else. Something like: 'WHY SAVE AMPHIBIANS? REALLY? WHY??? WELL THEY'RE SO WEIRD FOR A BLOODY START. THEY ARE VESTIGES OF FISH-LIKE CREATURES THAT NEVER NEEDED TO EVOLVE SHELLED EGGS! LONG-LEGGED! LONG-LIVED! AN INSPIRATION TO JIM HENSON! AN INSPIRATION TO NATIONS! NIGHT CALLERS! NIGHT STALKERS! MASTER NAVIGATORS! EXPLOSIVE SEXUAL DYNAMOS! BODY HUGGERS! MAGGOT CHUGGERS! FEEL-GOOD DAY-GLO PO-FACED PRIMITIVES THAT DESERVE NO SUCH TITLE BECAUSE THEY'RE STILL HERE AND SO ARE WE SO, YES, WE SHOULD BLOODY SAVE THEM BECAUSE IF WE DON'T WE ARE A DISGRACE AND HOW WILL WE LOOK INTO THE EYES OF OUR CHILDREN?' etc. etc.
I really wish I could have said that. Frogs and toads and newts are fantastic in all sort of ways. They are clearly weird. They are clearly quirky. And they're about much more than what we can take from them. But, that's frogs for you... so what about spiders? Why would anyone want to save them? A tiny nothing-much of an invertebrate; who'd want to save that? They're not particularly quirky or enigmatic or charismatic. They're just... tiny spiders. But people really did seem motivated to act; people really were motivated to try to save this tiny spider from total destruction.
When news of the horrid ground-weaver's fate had spread, Buglife launched a petition to influence the planning inspector responsible for considering whether or not the housing estate proposed for Radford Quarry could or could not be permitted. It encouraged the planning inspector to halt the proposal in its tracks; to ditch the housing plans for the sake of the spiders. Of the 9,732 signatures the petition received within a week, many signatories took a few moments to add their own reasons why they felt this little spider was worth saving. There was a little comment box on the petition web page especially for these people. I read through these comments with deep interest. Could they shed light on why people thought that the tiny spiders were worth saving? Maybe. The first read: 'Because it shouldn't matter if it's a panda, a clouded leopard or a tiny obscure spider, vulnerable endemic species are all equally important to the world.' I thought about this. Maybe that's true? I wondered. 'I grew up round here,' says the next comment. 'The spiders are my friends.' 'Can't believe this is in my home town!' says another. 'No doubt these property developers are going to appeal again and again. Let's hope they don't get their way.'
These were interesting reasons to save the horrid ground-weaver and not necessarily what I had expected to read. Not one of the hundreds of comments talked about what we humans might gain from their survival. Not one of the comments talked about cures for insomnia or erectile dysfunction (which is genuinely something some spider venom might cure, for those interested). The arguments that they gave were all moral ones. Almost every one was about love and feelings and emotions. The spiders needed saving 'because every species deserves protection not just the cute and large mammals'. They needed saving because 'we have few endemic species in the UK we should all be fighting to save it not standing by and letting another extinction go unnoticed'. How strange then that as a young conservationist in my first job on that frog helpline I overlooked this moral argument so readily. I never thought that people could be asked to do something or donate to something to be moral. To be better people. How had I so easily missed this?
Andrew comes out of the trade shop. He is smiling. He almost, but not quite, struts toward us. 'Sorry about that guys,' he says smoothly as he gets closer to us. 'I've been trying to crack speaking to them for quite a while. That was great. All done now. Got the contact details of the landlord. Hopefully we'll be good to go.' Jo and I make approving congratulatory noises. Soon Andrew and Jo will return with hard hats and climbing gear. In time they will hopefully be able to better gauge whether or not the horrid ground-weaver still remains here at this site.
We walk back to my tiny red car, scouring the cliff edge with our eyes as we walk, wondering how many horrid ground-weavers there might be scuttling among the rocks. I unlock the car doors and we get in. The plan is to head over to Radford Quarry, which is what most consider to probably be the spider's major stronghold. Andrew directs us out of the retail estate, then up a hill and into a dense new-build maze of streets and houses with new cars parked in front of the drives and on the pavements and on the pavements over the road. (Many new housing estates in Britain seem to have this problem – they seem to dramatically misjudge how many cars most families have. It's two. Two.) Going left and right, packed into the little car like sardines, we bump and bustle into each other as we weave down more busy streets and over what feels like hundreds of pedestrian crossings. Cars squeeze past us. Vans. Lorries. We climb higher across Plymouth, until we're almost looking out over the bay. More streets. More winding. And then we're there. We park up next to a small gravel trackway at the edge of a different new housing estate, and I open the doors and breathe in the industrial fug coming in off the docklands.
Andrew leads the way to Radford Quarry. We start walking down the thin gravel track. We are not the only ones to have trodden this path – there are bike tracks. The path is well trodden. For reasons I have often struggled to fathom, someone has left a dog poo in a blue plastic bag hanging off an overhanging branch. Andrew and Jo don't even seem to notice. Andrew tells me that what this place represents is a remnant kind of limestone and grassland habitat that would have once extended across this whole area and all the way across Plymouth's industrial centres. Radford Quarry is one of the largest patches of exposed limestone that remains locally from this former age. He explains how the Planning Inspectorate are still deciding, and have been for months, whether to permit 50 houses to be built on the site. He talks about how upset the local people have got; how interest has grown in the little spider. If the houses get built, the spiders here will surely die, he explains bleakly.
We walk down a concrete path through thick vegetation and come to a large muddy path, the entrance into the disused quarry. Again, the pathway looks well trodden by pushbikes, motorbikes and dog-walkers. We stop at the entrance. I wonder why we are stopping. Why aren't we going in? At this point Andrew politely points out that there is no way we can go in there (even though lots of people clearly have done just this) because it's not legally public access. Oh, I think. He and his colleagues aren't really allowed on the site and nor am I. No one is, legally. We'd be trespassing, he says. Ah, I think. A small part of me wonders whether if Buglife was allowed regular access to the site they would find all manner of other unusual invertebrates, which would probably make future proposals for new housing estates here that bit more difficult. I choose not to raise this with Andrew and Jo. I am a tiny bit downcast at not being able to enter, though. 'It's private property, so that's that,' Andrew says, resigned. 'But we are hoping we will be allowed further access to the site to survey at some point.' I look longingly up the path and into Radford Quarry, imagining all the spiders that only a few people in history have ever seen alive.
Radford Quarry (if only by looking at the entrance) didn't quite look like the natural place that I had imagined. From where we stood there were about 2,000 houses just out of view on the hillside. Busy streets. Delivery drivers rushing here and there. Traffic lights. Road markings like graffiti. School runs. The former quarry looked to be a pocket of life within all of this activity. There was so much green in there, plenty of saplings and grass. It seemed to be the only place around here that had gone from an industrial slate-grey to a warm green, rather than the other way around. In Britain we call former industrial places like this quarry 'brownfields' as if that's all they are: brown fields. I hate this label. I deeply hate it. It's so shockingly small-minded to describe them so blandly, like hearing someone describing coral as 'pointy sea-rocks' or plants as 'those green things'. Ill-judged. Patronising. Yes, small-minded. Brown? I sigh.
I peel my eyes off the entrance to Radford Quarry and look down at the stones and the green grassy verges to the path we had just taken from the parked car. 'Do you think we might find any spiders outside the entrance, around here?' I ask Andrew and Jo. 'Almost definitely not, but we could have a look for some other invertebrates...' says Andrew, smiling.
In modern conservation, journalists covering stories like the horrid ground-weaver might go for a simple narrative, classically encapsulated as extinction being a tale of 'us versus them'. Of David and Goliath. I guess it's the most grabby way of telling the story, but in many ways this is too simple a view. Extinction is very rarely a two-dimensional war between individual species. It's an oversimplification to talk of it as a battle of occupancy between one species (normally us) and another species (like horrid ground-weavers); it's much more complex than that. Breathtakingly so, in fact. In reality, extinction is complex and multifarious, and it demands of us a different mental picture to grasp it properly, one originally constructed by, of all people, Charles Darwin.
Long before publishing On the Origin of Species Darwin wrestled with his (then vague) notion of natural selection, and how it operated in nature. His idea was simple, sure – a series of successful copying mistakes is not hard to apply in one's mind – but Darwin knew that the concept, in this form, was too linear. It wouldn't work for Darwin. He needed more. Darwin knew that the world is anything but linear. It's complicated. It's messy. Darwin needed a metaphor to graphically communicate his big idea to his audiences, but more importantly he needed a metaphor to toy with, so he could pull apart what his idea looked like, exactly, when applied to the natural world. On 28th September 1838 he realised it. After reading Thomas Malthus's Essay on the Principles of Population he scribbled the following into his notepad: 'One may say there is a force like a hundred thousand wedges trying [to] force every kind of adapted structure into the gaps in the economy of nature, or rather forming gaps by thrusting out weaker ones.'
It sounds simple, but this was a rather enormous insight to have. Indeed, many Darwin scholars (including Stephen Jay Gould in his wonderful essay The Wheel of Fortune and the Wedge of Progress) think it was his biggest. Gould, in particular, argued that it was this metaphor that drove his theory of evolution by natural selection forward to publication 20 years later. For in that metaphor is everything one needs to know about the death of life's lineages and what extinction actually looks and feels like. Darwin later honed the metaphor further. In his manuscript for the longer unpublished version of On the Origin of Species his metaphor became more elaborate and even more delicious. He wrote:
Nature may be compared to a surface covered with ten thousand sharp wedges, many of the same shape and many of different shapes representing different species, all packed closely together and all driven in by incessant blows: the blows being far severer at one time than at another; sometimes a wedge of one form and sometimes another being struck; the one driven deeply in forcing out others; with the jar and shock often transmitted very far to other wedges in many lines of direction.
And that was what I thought of when I was on my hands and knees looking for that bloody spider, aware of all the houses and the hustle and bustle of city life that surrounded us. The horrid ground-weaver is the tiniest of wedges in a writhing nebulous wobbly mass of a million wedges. It is one of the tiniest of nearly all wedges in nature; occupying a simple, simple, simple niche: that of cracks between limestone rocks in a limestone quarry in Plymouth. The human wedge (which is being struck particularly hard around here) is upsetting this tiny wedge, threatening to squirt it out of the pack and into oblivion. But in an ecological sense, the spider probably doesn't really matter much at all. Sure, there might be a period of rejigging, but the wedges of other species won't collapse upon one another. The other wedges will probably not even shift should the spider indeed slip toward extinction. And so, to nature, the horrid ground-weaver is instantly forgettable. Darwin understood that extinction, as well as being a very real part of the fate of many creatures, is also a measure of the squeeze in nature. A squeeze ultimately limited by how much there is to go around. And this is probably why, in some perverse way, I'm quite sad at the thought of not getting to see this spider. I had wanted to see it very much. I had wanted to hold one. To give it new value – a human value – by holding it in my hands and by looking at it face-to-face: wedge-to-wedge.
Sadly, though, we fail to find a horrid ground-weaver. We see plenty of pillbugs (a kind of woodlouse that can roll into a ball). Thousands upon thousands of them. They are the shiniest and most pristine pillbugs I have ever seen in my life; it looks like someone has been here just before us to polish them. Each looks resplendent. There are bristletails, too, prehistoric-looking creatures that look a little like miniature horseshoe crabs with long tail feathers. Then there are the jumping spiders, which hop and scurry out of view with every step we take, and the velvet mites, the wolf spiders, the pseudoscorpions. Occasional peacock butterflies, taking a few moments to sun themselves upon the grassy banks of the path. There are also millipedes, ground beetles, flower beetles, rove beetles and midges; rich ecosystems written in fonts almost too small to read. But, alas, no horrid ground-weaver.
As we walk up and down the path outside of the quarry, Jo informs me that her plan over the next few weeks, if all goes well, is to build bridges with the landowners to gain access to Radford Quarry to survey for the horrid ground-weaver. Her aim is to get out here with bug-vacs (read: hoovers) and to set up pitfall traps to look for the spider. There's even a possibility, she tells me, that later in the year local students will be encouraged to gather and do a full hand-sweep of the area like police officers scouring a crime scene. 'We'll find it,' says Andrew confidently from up the path, hearing Jo speak. I have visions of him as an old man, still traipsing around this place with his bug-vac saying rosily 'we'll find it again...' after 50 years of searching.
And so I have to accept that the horrid ground-weaver has eluded us. I won't get my moment, I realise. As we stroll back to the car I find myself confessing to Andrew and Jo about how troubled I have become with the idea of why, in a world of death and extinction, we should become so bothered about conserving all species, including tiny spiders, into perpetuity. Andrew is pleased that I brought it up, I think. 'Yes, the horrid ground-weaver isn't going to blow people away like seeing a blue whale from a boat,' he said, half smiling. 'But every species has an equal right to live on this planet, no matter which way you look at it.' Jo reiterated what she had said earlier: 'We can't knowingly let it slip away now that we know it was here. To do so would be wrong, somehow...' I realised that Andrew and Jo were actually very moral people, but not at all in a preachy way.
Andrew got a little quiet from this point onwards. 'Extinction is wrong,' he said as we neared the car. He was suddenly very serious. I asked again why this little spider mattered so much to him. 'It's not going to change anyone's life if this thing goes extinct, I agree with that statement,' he said, thinking it over. And then he stopped and turned to us both. 'Except for mine,' he said sadly. 'My life would change if we let it become extinct, because I'll feel sad that we let it go. That I'd been part of its extinction. I'd be gutted. I'd be gutted and frustrated. I would just be so sad.' We headed home.
If conservation is about the moral imperative, surely Andrew and Jo are taking part in one of the most moral acts ever witnessed by humankind. They are saving something not for our children to see; saving something not for medicinal gain; saving something not for the value it has as a controller of pests or pestilence; saving something not for its quirkiness or the special skills it possesses. Nope, none of these things. They are saving an animal which has no cognition or knowledge of its own existence in any way. It literally has no purpose other to make more horrid ground-weavers, and even its ability to do that is questionable. Yet still they want to save it. And incredibly, Andrew and Jo have never even seen a live one. They've never seen or held or watched up close a living horrid ground-weaver in the flesh. Yet they care. Somehow, against all odds, a small (and growing) group of entomologists and amateur enthusiasts really do care about it.
There is no meaning in nature. Unless you give it meaning, that is. And extinction doesn't always matter, unless you think it matters. Unless you give it meaning, I mean. We are the first animals on Earth to have done this. To have given extinction meaning. We can't be all that bad, then... can we?
CHAPTER THIRTEEN
Dark Matters
Was I getting a bit weird about death? Was all this talk of maggots and disgust and extinction and money spiders warping my mind? I was starting to worry. I was well over a year into my journey. I decided I needed to seek professional help. Help from professional zoologists. I wanted to know how they dealt with the relentlessness of it all, the endless thinking about death. Of the handful of zoologists I approached about this, one replied almost immediately. She was Anne Hilborn, a cheetah ecologist based at Virginia Tech.
I had followed Anne for many months on Twitter, partly because the habitat in which she bases her studies seems so tough and so brutally different to the professional world which I inhabit. She spends much of her time in the Serengeti, and one of her study animals is the cheetah. The photos that she posts on Twitter are particularly and fantastically real: starving cheetah adults, lions with ticks under their eyes, hyenas covered top-to-tail in swarms of biting flies. That sort of thing. The world in which she bases her studies seems so stark that, in some ways, it's a breath of fresh air to me. I sensed Anne would be worth approaching. I sensed that, given her line of work, Anne thinks a great deal about death given that, in cheetahs, that's pretty much most of what she seems to see. Dead baby cheetahs. And there's a reason for this. In cheetahs, juvenile mortality rates are staggering. They appear to die far more than anyone had ever predicted before they thought to look. From a three-year cheetah tracking study in the nineties (undertaken and led by the ecologist Karen Laurenson) it was found that for every cheetah born, only 5 per cent – only 1 out of 20 young cheetahs – survived to adulthood. This had been a real surprise. The other 95 per cent of young cheetahs were found to die in lots of ways. Many were victims of starvation or abandoned by their mothers during forest fires or incremental weather events. Most were killed by lions or spotted hyenas (though strangely, they were often left uneaten).
The loss amazed me when I first heard about it. I'm used to such statistics in frogs (where each blob of frogspawn might have 1,000 or more eggs with only three or four hatchlings making it to adulthood). But these were cheetahs. Big bloody cats. What the hell was nature up to? If animals mourn, then cheetah mothers must spend their lives in constant distress and turmoil. How do the female cheetahs deal with all the loss? This was the first question I put to Anne and her response was suitably rigorous. 'Very few of our cheetahs are seen regularly so we almost never see cub death or its immediate aftermath,' she said. 'I think I have seen pictures of a mother cheetah carrying her small cubs that had been killed by lions, but I can't remember the details... I assume it was for only a very short amount of time. I am not sure if that qualifies as mourning or not. It's interesting to think about how or when cheetahs might accept or recognise that a member of their social group who has been missing is actually dead. I don't have any definite observation or data on it.' Cheetahs appear so often on TV documentaries, I had kind of assumed we knew everything about them. But, according to Anne, many parts of their lives still seem very secretive. They are hard animals to get to know, it seemed.
What I liked about Anne was that she felt free and easy talking about death on the savanna; it had almost become second nature to her. And she talked personally about how it had affected her own attitude to death as a result. 'As a child I loved animals in a very sentimental way,' she wrote to me. 'Over years of fieldwork on various animals my feelings have changed. Doing fieldwork in Alaska on sockeye salmon you see a lot of carnage. We work on really small streams that for a week or so are crammed with salmon trying to spawn. These streams are so small, sometimes the water does not cover the backs of the fish and they are ridiculously easy prey, not only for bears but also for gulls,' she wrote. 'Gulls go for the eyes, and will pick them out of live salmon. And salmon can survive for quite a while without eyes. I find something particularly horrifying about having your eyes pecked out, so I always tried to kill live fish who'd lost their eyes (with a swift knife slice through the brain). We'd also see live salmon that had been mauled by bears still swimming around with bites out of their backs, or slash marks on their sides. Seeing this sort of thing daily does "toughen" you up, and I've gotten pretty good at not feeling much emotion at seeing things die.'
What Anne said next really interested me, because it is almost exactly how I have come to feel about death whilst researching this book. 'Sometimes I wonder if being toughened to death is a good thing. I think it makes me a better biologist and it allows me to do the fieldwork and research I love. But occasionally I think that maybe I've gone too far, and my lack of feeling at the sight of death means I have become callous, and that people who are distressed at the sight of gruesome pictures might be right.' This was me in a nutshell. Recently I seemed to be spending a great deal of my time worrying about whether I'm starting to come across as an Ultra Naturalist; a life- and death-obsessed person with whom normal people can no longer connect. Death is so inherent to life, it's becoming quite natural to me to introduce it into everyday conversations. I try to hold it back, but sometimes it slips out. Over coffee with a friend, I might mention that I recently stood in a field of dead pigs or held a 500-year-old shellfish or something like that. It's almost out of my control now. I worry that I'm being judged for it.
'Not all biologists are the same,' Anne wrote. 'I've worked with people who laughed and joked about killing salmon to take blood samples, and with people who thought my fascination with bones and dead things was morbid and distasteful. But in general I would say that watching a lot of death in the natural world does tend to harden people and strips away sentimentality about death and any 'Disneyfied' ideas about animals living in 'harmony' or 'peace'. As far as I can tell most animals die in a manner humans consider gruesome. Either they are eaten by predators (often alive), killed by conspecifics, starve to death, or die of some nasty disease. I know of very few 'easy' or 'happy' deaths in the natural world. A quick death by a predator is probably the death that would be considered 'best' by human standards.'
Is life really that brutal? Is it really as simple as living and dying, often in ways that we might consider totally horrible? Often with oodles of suffering involved? Often with great pain and great waste of potential? Must this rational zoological outlook on life and death be quite so bleak? It certainly sounded very bleak when I thought about it. But maybe I was looking at it wrongly?
A few weeks after corresponding with Anne it was toad season. The spring toad migration is one of my favourite times of the year. I generally like any animal you can pick up, intensely eyeball and probe, and put down without it being in the least bit bothered and, for me, this totally encapsulates what toads are like. With its dry, almost scaly skin, orange eyes and a slow waddling crawl, it has almost been designed via natural selection to fit perfectly into the coat pocket of an 11-year-old boy or girl. Toads are such resilient little things. Tough-skinned, rugged-stanced. No wonder they are rooted so deeply within the fossil record.
But toads are not so resilient that they can withstand getting hit by a modern human invention like, say, a car. If they get hit by a car they are not resilient at all. They simply die. Or they twitch their limbs in assumed agony for a little while and then die. Many of Britain's roads are littered with their corpses each spring. The TV quiz show QI (and I have no idea where they got this fact) says that 20 tonnes of toads are killed on Britain's roads each year, which is nothing if not incredible. But it's no surprise to me. There are a lot of European common toads out there and you could say that evolutionarily speaking the toads bet on the wrong horse: they went for poisonous skin and stamina over the speed and wariness that frogs, generally, possess. In a world of human vehicles they chose... well... 20 tonnes? That says it all.
Rescuing toads from roads is one of those activities that you'll normally find a friend of a friend does. Normally that friend of a friend is: a) eccentric; b) kind and loving, perhaps overly so; or c) having marital difficulties and needs an excuse to leave the house. Most toad patrollers are any combination of these three things. I am definitely one of these things (you can decide which, but I'm pleased to report that it isn't c). In temperate climates, on the whole, amphibian migrations take place during runs of consecutive warm, wet nights (particularly after or during rain), often in early spring. To see them yourself at this time of year, look at a Google map and pick out local reservoirs, lakes and big ponds. After dark, travel slowly and safely on roads near these freshwater spots and you will probably see them trundling along, particularly on more humid nights.
Toads are more picky about their breeding ponds than frogs. Whereas in northern Europe frogs prefer shallower ponds, toads appear to prefer bigger, deeper bodies of water. But such breeding spots are rarer than small ponds and this is a further source of bad news to toads: they must travel further to get where they need to go than frogs, navigating more and more obstacles, like roads and housing estates, in the process. Some populations of toads have been doing fine, it seems. Others – where roads are busier, for instance – are less fine. In Britain, with more and more roads, our toad populations are facing death by a thousand cuts; they're declining so slightly in so many places for so many reasons that barely anyone has noticed or is able to do much about it.
Each year during toad season there are five ponds that I normally visit, keeping tabs on how local populations are doing. Why do I do this? I'm not sure. It's partly out of duty, but also because I like to see and pick up toads and this is the only time of year I can really do it. It's exhilarating in some ways, driving down small roads, looking for tell-tale shapes like dead leaves that move slowly in front of my beams. It's like a really, really, really, really tame version of a night-time safari, which is to say it's still very exciting. Anne Hilborn would approve, I think.
I pull up to my first site. It's a small B-road near Great Brington on the western edge of Northampton. The toads here like to breed in the moat-like pond that surrounds Princess Diana's burial site, which is quite a nice thought (I think it's what she would have wanted). In many ways the site is typical: on one side of the road is a hill upon which a woodland sits in the distance, and down there, on the other side of the road and over a large brick wall, is where the large pond lies. Toads wake up from their winter slumber in the woodland and, en masse, make a move down to the water, crossing fields, hedgerows, a small ditch, and now this road. I think they must find little holes in the wall to squeeze through, but I have never actually seen them do this.
There are plenty of toads about tonight. Fifteen are already dead on the road. A large female has had her head squashed by a car and her unfertilised spawn has fired out of her rear end. This is particularly sad because female toads take more than three years to mature – as a result, to a meta-population, the life of each female really does count because it is capable of restocking tadpole numbers with such vigour. But not her. And not here. Most years I don't think much about all the death – they are casualties, and I'm here to try and help the living toads – but this year things feel slightly different. This year, the dead ones are as interesting to me as the live ones. I shine my torch on each one, assessing their size, their sex and their missed potential. My interest in death is changing me.
Toad crossings are always much sparser than you might imagine them to be. The toads move so slowly, they look more like an army of the undead crossing a graveyard than a sweaty tangled sexed-up throng like they appear on TV documentaries. But it is the number of them that keep coming that makes it all so impressive. For hours and hours, night after night, they keep coming from that woodland, heading over the road to the pond. By helping so many cross, by counting up the living and the dead, one gets a real feel for the statistical likelihood of survival, and, almost, the whole energetics of toad populations and what they bring to an ecosystem. You get a really good feeling that each life and each death matters for something. And also one gets a feeling for what death brings, in particular. I think again of Anne and her super-rational view; the inevitability of suffering and death and how perniciously it appears throughout nature. Is this just the way nature has to be? Are animals doomed to suffer within never-ending food chains? Partly. But not totally.
Charles Elton is perhaps the scientist who has been most instrumental in our understanding of the ecological principles surrounding food chains, ecological niches and the concept of pyramids of numbers within ecosystems. Yet how he got such insight is interesting. It didn't just come to him. In 1921, early in his academic career, Elton decided to undertake fieldwork in Spitsbergen, an Arctic island with vegetation so low that Elton could tootle about watching predator and prey interact with little fear of humans. Elton spent a great deal of time watching the Arctic foxes go about their business, being the most easy animals to pursue and observe from a distance. And it was their movements that were to give Elton the insight he needed; insights that would later bed in whole generations of ecologists.
He watched and took notes. The Arctic foxes spent much of their time feeding on the birds – ptarmigan, sandpipers and buntings among them. So Elton observed them. He noticed that the birds fed upon smaller things: insects, grubs and seeds. In our busy world, it is easy to become drowned in the complexity of ecosystems and food webs, but there, on the tundra of that island in the Arctic, it was plain to Elton because there was so little else going on. It slapped him in the face. It was really, really simple: there were hundreds of thousands of insects, feeding thousands of birds, feeding hundreds of foxes. The observation that food chains organise themselves into layers like this was probably known to other scientists, and that something like a tenfold multiplier is often apparent between each layer, but until Elton came along no one had thought to ask... why? Why is life like this? Why does it form, on the whole, such predictable layers and food chains? No one had thought to properly ask why and seek to answer the question methodologically until that point; until Elton pondered that exact question in the middle of the Arctic watching foxes chasing birds and birds chasing insects.
There are other questions that come up when considering things such as food chains and food webs. For instance, why are large wild animals on the whole rare, but creatures lower down on food chains more common? Why could I see thousands of toads on a spring night yet Anne will only see a handful of cheetahs in a week or so, for instance? Famously, Elton saw in his mind's eye a pyramid of numbers to describe this. And indeed, for each 'trophic' level, there was often 10 times the number of the next step up: tens of thousands of insects, thousands of birds, hundreds of foxes. Elton was tempted to view this arrangement of trophic levels simply in terms of biomass so that, for instance, if you put hundreds of thousands of insects into a blender you'd have the same amount (biomass) of protein-shake as you would putting thousands of birds into a blender (please don't), or hundreds of foxes (stop).
But Elton realised something, something that modern biology textbooks remind us of frequently: this isn't what we see in nature. The volume of flesh in each trophic level isn't the same. The volume of flesh available decreases as one moves up the food chain. In essence, top predators take up less flesh than you'd think, by looking at the amount of flesh fleshing around in the trophic level before. It was the same with the mid-trophic levels. And the levels further down. In food chains, flesh seems to go missing... but where? Where does the missing flesh go? It was a mystery. Elton just couldn't work it out so instead he put the question out there in 1927 for other academics to solve. It took two decades before an answer was proposed.
The answer to the problem of the missing flesh came from two Yale scientists, Raymond Lindeman and Evelyn Hutchinson, who solved it by thinking of animals not as animals, but simply as calories. A parrot. A mayfly. A gibbon. A killer whale. Lindeman and Hutchinson viewed these creatures simply as spontaneous and temporary bags of calories. They viewed the life actions and behaviours of these creatures as being funded by the calories they have in their respective bodies, and they appreciated that these unusual-looking bags of calories could invest their calories in different things should they wish: finding more calories, investing calories in reproduction, or perhaps saving calories by sleeping. The point they realised is that you can't make calories out of nothing and that all calories come from something. All of us are going about our business frittering spent energy (often in the form of heat) from the burning of calories. Lindeman and Hutchinson understood that every hot breath that radiated heat from every animal that ever lived removed calories from a food web, starving the trophic level above. Starving the predators of more calories, in other words. I like considering this view of life, every now and then. In fact, I rather like the thought that every time I breathe out or walk around I am restricting the amount of energy that can be used by the predators above me in the food chain (fuck you, polar bears!).
Elton's early-twentieth-century ideas about ecology percolated, aided by Lindeman and Hutchinson, across the whole of biology during the fifties and sixties. Just as DNA had sucked biology into the realm of the chemists, Elton's ideas were among the first to pull biology into the world of physics, made more graspable by Schrödinger and his book What is Life? described earlier in this book. Yet, we rarely seem to talk so publicly about Elton and Lindeman and Hutchinson as we do Schrödinger. They deserve more of our celebration, I think. Without them our understanding of life, death, the universe and... everything... would be severely impaired. They were the first to understand that the laws of thermodynamics play out each day, like a grand marble run, in the ecosystems that sustain life. The laws of physics only allow for so many toads and so many cheetahs, it seems. According to this view of life, every suffering juvenile cheetah, left hungry and wanting, is a victim of universal circumstance. But within each, of course, are calories for something else. A lion or a hyena. A crow or a magpie. A vulture or a red kite. Eltonian physics led to a view that life is a convoluted opportunity for something else, constrained in its potential by our universal propensity for giving off heat. Should that make us feel a bit less morose about all the suffering? Maybe. But there is a hidden part of this picture. A missing part of the puzzle that is causing many modern-day ecologists to rethink Elton's big idea. For there is another place that all that flesh goes. It doesn't all flood out into the universe as heat. Some of that missing flesh can be found in the parasites.
For decades, parasites were the dark matter of food web energetics. Overlooked. Forgotten about. Downplayed. Yet now, many scientists argue that parasitism is actually evolution's favoured method of predation; taking from the living to give to the living, in other words. A number of studies support this once outlandish claim. In estuarine systems, for instance, the yearly productivity of flukes (parasitic trematode worms) is actually higher than the biomass of birds, according to evolutionary ecologists Daniel L. Preston and Pieter T. J. Johnson in their Nature paper, 'The evolutionary consequences of parasitism'. Then there is the fact that the biomass of the fungi that attack plants (in experimental grass plants set up in Minnesota) was comparable to the herbivores that graze them. And then there are the seabird islands. Some islands in the Gulf of California are two or three orders of magnitude richer than others in the populations of lizards, scorpions and spiders that inhabit them. The reason? The more seabirds an island supports, the more seabird ectoparasites they bring: mites, ticks, lice, fleas.
Preston and Johnson's verdict about the role of parasites in food webs is powerful: 'the classical Eltonian pyramid... may need to be revised,' they write. It may be that animals in the middle trophic levels are the richest with respect to their parasite diversity, given that they offer places to larger communities of parasites (toads, for instance, have plenty of nooks and crannies for species to evolve into) and are susceptible to a greater number of potential predators (some of which the parasites will consider final hosts). It may turn out that, in nature, unlike in human life, everyone gets a piece of the middleman.
Anne Hilborn's super-rational view of animal death had stuck in my head. At first glance it had felt quite saddening to read her thoughts, but I realised that, this toad season, I was developing another way of looking at the sadness and the suffering. There is very little wasted potential when wild animals die, since life was being created all along. The toads had created and provided calories for generations of parasitic flatworms, mites, nematode worms and countless other creatures, plus many single-celled life forms yet to be described. And many of these organisms had been eaten by something else, powering the food web in a different direction. Their lives weren't 'wasted', in other words. In nature, very little is. And neither will those toads' lives be wasted in death, as the foxes and magpies each morning attest, as they scrape them off the roads before the flies get to them.
According to Froglife, the NGO that coordinates toad crossings (as they are called) in the UK, 76,710 toads were rescued last year (2014) by patrollers like me and 8,729 were observed to have already died that year, squashed on the roads by passing cars. In the nights that followed that first toad patrol this year, I counted 62 dead overall on the roads next to my sites. But by the end of that week it didn't seem so sad and miserable somehow. The toads weren't wasted because they didn't make it to the breeding pond. They had provided life all along. They were bags of calories, burning bright. They had given that light to others. And they would continue to burn within the bodies of countless other things, with a brightness ever so slightly dimmed.
Oh shit. I realised at this point in my journey that I was definitely starting to sound a bit weird and possibly slightly insane. The conversation with Anne hadn't really helped. The professional help wasn't seeming to do the trick. There was no doubt about it. I was turning weird. I was going somewhere with all of this, but where?
PART THREE
JOURNEY TO THE END OF THE SHITATITE
CHAPTER FOURTEEN
Bring out your Dead Ants
It's a laboratory that holds space for 80 or so students. Today, however, there is only a single human present. He sits in the corner alone at a bench on the far side of the room, hunched over something. He is studying it. The spring sunshine floods over him, coming through large, expansive windows. Students have picnics on the lawn outside; they chat and have fun. The birds sing. He notices none of these things. His mind is on other matters. We approach him. In his white lab coat he looks almost angelic – no, he looks like a deity. And to the ants whose lives he manipulates, that's kind of what he is. Adam leads me toward him and, as we cross the room, I attempt to work out what the hell he's doing.
'This is Stace Fairhurst,' Adam says as we get close to him. Stace gives me a big smile. 'Hi,' we both say. I go to shake his hand but at the last minute I realise he is holding a pair of tweezers in which a tiny ant struggles. Stace continues with his work. He carefully leans over his desk and, with his tweezers, places the single ant in a plastic tub on the desk in front of him. Inside the tub is a tube; a single corridor which splits into two, forming a Y-shape that looks a little like female reproductive anatomy. Stace and Adam explain what is going on. The experiment Stace is undertaking is simple: each worker ant is plonked at the bottom section of the Y and can move toward the left tunnel of the Y (which is being pumped with smells of dead ants and fungal waste) or the right-hand tunnel of the Y (in which there is nothing being pumped in but clean filtered air). Stace tells us that he has been placing worker ants in this contraption for days to see what they do and he is nowhere near stopping yet.
'Wait...' says Adam suddenly. We all stare at the ant in the plastic Y. It dillies and dallies at the entrance of both tunnels. It waves its antennae slightly. 'Wait, it's going to go...' Adam commentates. 'She's going to go... go... going... THERE!' The ant crosses a tiny line on the floor of the Perspex box, indicating that it has made its choice. This little ant chooses life: it avoids the corridor that smelt a little like death. Stace makes a note in his notebook and reaches for the tweezers again. The ant is pulled out of the box and is put back into the nest behind him. Another ant is taken out with the tweezers and takes its place in the Y-shaped contraption. This is just one of many experiments overseen by Adam and Stace (of the University of Gloucestershire) as they attempt to answer important questions about life, death and ants.
I should say early on that I already know Adam. I know Adam because he is Professor Adam Hart from the University of Gloucestershire, but also because he's often on the TV. This is the first time we've met in real life, though. In real life it is even more apparent that Adam is the most youthful professor I've ever seen. He is enthusiastic about everything (even car-parking arrangements) and incredibly media-friendly. Throughout our interview he delivers complicated sentences slowly and arranged correctly, making them really easy for transcribing, which is a kind thing for him to do. Whenever I talk he looks at me with his full attention and does noddies like a pro. He's warm and open. Smiley. Funny. Knowledgeable and very lovely. Adam has invited me down to talk about how ants deal with dead colony members. In his lab he keeps many colonies of leaf-cutting ants, which are one of his many research interests. He sees a lot of death.
We stand there, all of us, watching the next ant as it goes into the Y-shaped box. This little worker ant tentatively moves toward the corridor that smells of death. Then it stops. It walks up and down a bit before committing fully and retreats back to the mouth of the Y. We wait a minute or so for it to do something. It does nothing. And then, quite confidently, it turns to the right and heads down the corridor in which clean air is being pumped. Another ant has chosen life. Stace scribbles the result down. I try to look at his sheet. 'Which corridor is winning overall?' I ask. Neither Adam nor Stace bite. Stace gives me a little knowing nod and a smile. 'We should really wait for the results, don't you think?' he says. 'Of course,' I say quickly. 'Of course.'
Adam beckons me over to one of the ants' nests on the table behind Stace. The nest is wonderfully contained inside a long glass tank that is about 150cm by 30cm. The colony itself sits on a wooden platform in the middle of the tank, as if on an oil rig. It is held on four stilts above about two inches of water; an island from which the ants cannot escape. Upon the platform thousands upon thousands of leaf-cutting ants mill about on a pile of privet leaves. They nibble these leaves into small chunks which they carry back to the nest, which is housed within a series of plastic tubs that look like spent Ferrero Rocher boxes. In these tubs the leaves are being composted, their fungal food is growing and the next generation of ant larvae are being raised and fed. There are many, many ants in the tank and most of them look like they have no clue what on earth they are doing.
I peel my eyes away from the throng scurrying around on the pile of leaves and scan beneath the platform, looking at the water below. Adam tells me that there is a tiny bit of detergent in the water so that ants are unable to travel upon the meniscus and make an escape. My gaze returns to the ants on the top of the platform. Some of the ants stand on its edge and appear to look wistfully up at us through the open top of the glass tank, waving their antennae slowly back and forth as if to channel their thoughts of escape into the universe. There look to be tens of thousands of ants in there. 'Have there ever been escapees?' I ask Adam tentatively. He tells me a story about leaf-cutting ants climbing up the filter pumps in someone else's lab, and how the staff came in the next morning to find a line of ants carrying tiny chunks of toilet paper back to the nest from the restroom. I don't know if he's joking or not. I let out a nervous little chuckle and quietly check my shoulders, my hair, my face, my legs, my torso and my upper arms for rogue leaf-cutting ants.
There are many tanks of leaf-cutting ants used as part of Adam's research. Each is a city, a self-contained universe for ants. Each is a sample. 'Each queen in every one of these tanks may live 20 years or so,' says Adam as we look at a different tank. 'Given time they can turn something small into something enormous.' We peer into another tank. 'That's a hundredth of the size of a real nest,' he says, smiling again. 'In real life these nests are just... they're just enormous! They're absolutely massive!' Adam is loving this, and his passion quickly worms its way into me. We both talk in excited tones, like we're still at school. 'They're the size of a house underground!' he says. 'A hundred chambers, each the size of a basketball, each stuffed with their special fungus...'
He talks fast and full of excitement and, for a few moments, I decide to just sit and listen to him, like I'm watching him on BBC2 or something. 'And you've got massive amounts of waste in there,' he says, pointing at another colony. 'Massive amounts of waste coming from out of the nest. Massive amounts! Just consider the amount of dead ants that come out of these nests!' He takes a breath. 'The Queen? Sure, she might live 20 years or so, but the workers? The workers...' He smiles again. 'They might only live a few months. And, listen to this...' He looks at me quite eagerly again. 'In a wild nest there might be eight million workers, and each of those eight million workers might only live for a few months... Imagine that!' I imagine a long train of dead ants being carried out of the back end of the nest. 'So the death rate is just... well, it's huge,' Adam concludes.
All of the ants in Adam's tank are from one species of South American leaf-cutting ant. Adam tells me that in the wild these leaf-cutting ants excavate waste chambers beneath their nests into which their waste is then thrown. Leaf-cutting ants are renowned for this strange behaviour; other ants don't do it this way. According to Stace and Adam, other ants create enormous waste piles outside, usually downhill and often near water so that their chemical signatures can be washed away. This is where the dead ants are carried, and these waste mounds are often worked by the oldest, dying, workers. Apparently, sometimes when ants have finished up burying their own, they quietly dig their own graves and expire into the mass. 'You see this sometimes even in labs,' Adam tells me. 'The oldest workers dig deep pits into the waste as they're working it, and then look back up and think "Oh wow, this is comfortable" and basically die sitting in their own graves.' We laugh at this. I guess it's because we consider ants so unthinking – so resolutely without aim or purpose – that it's hilariously predictable that they would be so laissez-faire about their own death, making a polite space within the rubbish dump in which to die. Ants seem to consider death like a robot might.
Stace reaches for another ant and we gather around once more to see what the next little worker ant will do. 'I think there is one thing that strikes me with all of this talk about death,' Adam says as we watch. 'When we look at death in nature, and even with death in humans, so much of the ceremony around death is fundamentally about the single fact that a dead body is a big stinking problem that needs to be solved immediately.' We all nod our heads. 'A stinking problem,' I hear myself agree. 'And that's what ants do so well...' Adam smiles another of his little grins. 'They solve it. They solve the problem of death,' he says. 'I wouldn't say there's no ceremony with the ants, though – lots of ant species create dead piles that aren't unlike cemeteries in some ways – but basically they're just getting rid of bodies as quickly as possible. And that's it.'
We stare at the ants for a bit longer and a queue of questions forms in my mind. There is one big question I want to ask first but I'm waiting for the right moment. One that's top of the list – a question that betrays my own morbid fear of being buried alive. 'How do ants know that another ant is... dead... before they lift it up and cart it off to the dump?' I ask. I have visions of ants looking at their sleeping siblings toying with the idea of taking them 'downstairs' because they appear to be sleeping particularly deeply. Adam and Stace look at one another. 'That's actually a really interesting question,' says Adam. He takes a few moments to organise his thoughts. 'Hmm... it depends. Whether it's because they identify something about another ant that suggests it is dead, or whether it's because they identify something about it that's not alive... it depends. It could be one or the other. Or both.' The truth is that no one really knows for sure. Adam introduces me to the idea of what he calls jokingly (and some scientists take rather more seriously) the notion of a 'vital smell'. 'There's a lot of different studies looking at that exact question of whether it's the lack of a smell of a living ant – the vital smell – that's key,' he explains. 'But there's necromones too, which are the smells that are distinctive to death. Oleic acid is the classic. If you soak a rice grain in oleic acid they'll treat it like a dead ant. They'll do this every time.'
But there are other signals that ants give to one another to prove that they are alive and well. As we stand and watch the ants running up and down the platform it's obvious to see that they are constantly touching one another with their antennae (Adam calls this 'antennating' – a word I hadn't heard of until then), feeling for behavioural responses and cues and signals that only living ants give off. 'I suppose we could anaesthetise some ants and see what happens to them to stop them antennating, or you could wash the smells off them, and see what the other ants do.' He thinks for a moment. 'It's interesting...' He trails off in thought and I know he is mentally imagining a paper he will one day write.
I have immediately taken to Adam, and the pondering moments like this one are why. Suddenly his train of thought jolts onto a new groove in his stream of scientific consciousness. 'There is a bigger problem with death,' he says, 'perhaps more problematic than how you get rid of the body.' He beckons me over to another tank. 'When an ants dies you've also lost a worker – there appears a sudden gap in the workforce which needs to be filled. How they fill this gap is fascinating.' Adam explains that too many leaves coming into the nest sees the workforce shift toward nest-builders and not enough leaves coming in means the ants shift the workforce toward creating more foragers. 'Death is a big part of their life,' Adam says thoughtfully. 'Death is a big part of how they organise themselves.'
We go back to Stace, who has just watched yet another ant make a tiny choice. He leans over and gently places the ant with his tweezers back onto the wooden platform in the tank behind him. I try and keep my eye on where this particular ants goes now it is back in the nest, but it is impossible. It has become an indeterminate part of the great throng of workers swarming all over the place. Just another ant.
Adam calls me into the next room. This one is a smaller lab. On the far wall are six glass tanks on tables organised into a long row. These tanks look bigger. The colonies are arranged in the same way: densely populated platforms, nests in Perspex boxes – the sea of death below each one, keeping them all from flooding out into the labs and into human lives. In these bigger tanks we can see more easily how the ants dispose of their dead, since each of the tanks is due for a clean. In the waters below each colony are the submerged ghostly corpses of ants that have been tossed into oblivion over recent days from the platform above. 'They're the dead that have been jettisoned off the side; dropped by workers from off the bottom of the colony,' Adam says sombrely. The dead ants lie motionless on the bottom. I get nice and close to one or two, looking through the glass at them. Their legs are curled up around their bodies, their head arched back and their jaws still open. They wear expressions of suffering that I'm well aware that they do not have (being that they are ants and are limited in the number of facial expressions they can have, namely one or possibly two).
I look up at the underside of the platform on which the colonies sit. Hanging off each wooden platform are three or four little brown stalactites. They appear to be made of tiny grains of stony mud. I look at them really closely. A handful of ants crawl up and down these strange stalactites, and I notice that one or two carry little blobs of grit, which they drop into the water before climbing upwards and back to the colony. Adam sees me staring. These mud formations that dangle off the bottom of the platform are what Adam calls 'shitatites' because they are, in fact, made up of congealed faeces and dead fungus dropped from the platform above. Over weeks and months occasional grains of these droppings have coalesced and become solidified – they now form a drooping mass of hard faeces and fungal waste that has become a handy new pier upon which new ants can clamber down to get nearer to the water below if they so wish.
We spend a few minutes in silence, watching the shitatites. I watch the journey of a single worker ant: it walks from the rabble of ants walking around on the top edge of the platform and makes its way over the edge and round and underneath. It walks effortlessly upside down, almost seeming to relish the quiet and open space, away from the din of its workmates above. It makes a comedy path around on the lower edge for a few moments, going left, going right, then retracing its steps. Stopping. Spinning around. Going back. It really doesn't seem to have much of a clue. It finds a shitatite. It climbs down the shitatite until it is only a few centimetres from the murky waters below, and for a few moments it hangs upside down off the tip, held by only three of its legs. In that moment I find myself hoping it will fling itself off into the water, which is a strange thought to have because I'm normally quite kind to animals, but I like the idea of telling a story where a worker ant shows signs of suicide. A second or two passes. It does nothing. Still nothing. And then, something: the ant pulls itself back onto six legs (still upside down) and opens up its jaws. A tiny bit of grit falls into the water below, where it slowly sinks through the water and rests on the bottom, like a heavy stone thrown into a lake.
The ant now attempts to ascend the shitatite back to the colony above. It has trouble doing this; there are a few moments where it desperately struggles to find a foothold on its climb back up. Its first pair of legs fail to find a grip and it hangs there for a few moments on three legs again. The tiny ant looks momentarily like Luke Skywalker hanging off Cloud City at the end of The Empire Strikes Back, but it finally resolves its situation; it finds some sort of inner strength and hauls itself back up the shitatite to join the rest of the colony on the platform above. Within two or three seconds, amongst the myriad ants swarming over the leaves, we are unable to see where it goes. It has become them again.
Adam and I watch the great swirling mass of workers for a few more moments. Then a few more. I realise we haven't spoken for at least a few minutes; we have become drawn into their world. It's me that eventually breaks the silence. Almost dreamily I ask: 'Do you ever get bored of ants, Adam?' Adam speaks equally dreamily in his response. 'No, they just seem so...' He really thinks about his answer to this question of whether ants are boring. He really contemplates it. 'No,' he says. 'No, I would never find them boring. There's a determination to what they do. Just look at them...' He beckons to me to come closer to the tank in front of which he stands. 'Come up close to this one,' he says. I come closer. 'Look at a single ant. Pick out an ant with your eyes and watch it.' I pick out an ant and watch it. 'Most of the time what they appear to be doing is either very little or... they're just irrational. Watch this one with the leaf...' He points to a single worker near the edge of the platform holding a flag-shaped piece of leaf in its jaws. It stumbles this way and that with the weight of it. 'Look at it,' says Adam. 'It's going the wrong way for starters. It's heading away from the colony, coming precariously close to the edge of the platform. It doesn't really know what it's doing,' he chuckles. He's right. It looks totally lost. 'And look at the others nearby. They're just milling around really. They don't know what they're doing either. But then step back.' We pull our heads back and look at the colony as a whole. 'Look at it as a colony,' he says, 'and you can see, clearly, on the whole, that there are patterns: a line of ants carrying leaves into the nest.' Indeed, there is a pattern. Leaves going in. Ants coming out. 'Stepping back, you can see it,' he says.
He's right. I had viewed the ants like clockwork soldiers in an army, regimented and unfaltering, but really they reminded me of shoppers in a mall – all doing various things and visiting various shops but overall spending money and helping the mall pay the bills. It was complex and very messy. But there were patterns. Leaves (on the whole) move toward the colony. Soldier ants (on the whole) stand guard. Worker ants (on the whole) head toward the shitatites and drop little balls of faeces and their dead into the void. On the whole, the colony works. It is mesmerising to see them like this in these tanks, in a world so observable to us humans. They'd make great pets, I think, if you have ample supply of fresh leaves and possess understanding friends and family and pets and landlords and have no children and possess good access to detergent. Great pets.
'A dead body is a big stinking problem that needs to be solved immediately,' Adam had said earlier, referring to the situation that many colonial animals find themselves in when it comes to death. The solutions that natural selection has come up with to solve this problem are surprising in their diversity. In many bee species, for instance, there are 'undertaker bees' who are specialised in the role of removing the dead (and there apparently seems to be a genetic component to this behaviour, too). Social wasps also display such behaviours. And then there are the termites. In recent years one research team has exposed a great deal about the unusual behaviour of termites when it comes to dealing with dead nest-mates. Their study was rather simple, and not totally unlike those that Stace and Adam were undertaking at the University of Gloucestershire. A research team from Universiti Sains Malaysia and Kyoto University investigated the responses of four different species of termite when introduced to termite carcasses in various states of decay. Traditionally, the scientific literature had it that termites avoid their dead (called, predictably, necrophobia), but their research, published in 2012, uncovered the much more dynamic world of complex death-management that occurs in termite mounds.
Upon artificially introducing termite corpses to a nest, the responses were often found to be the same: the first workers to come upon the carcass would immediately pull back and recruit other (unexposed) workers over for a second opinion of the corpse. This was standard behaviour. From this point forth, however, the four termite species showed different responses. Workers from two of the species reapproached the termite corpses and investigated them. If the dead termite was deemed to be recently killed, and decomposition was in its early stages, these corpses were carried off and 'recycled' (they were eaten). But if dead termites had been left for too long, the termites considered them inedible and they were carried off as waste.
The other two termite species behaved totally differently when coming across the dead. There was no consideration; no recycling or waste removal of dead termites. No, none of that. The other two termite species were observed to simply 'wall off' the locations in which the dead termites had been found, creating disused tunnels, sometimes filled with dead colony members, never again to be entered. Why do they do this? It could be that this behaviour reduces the likelihood of disease and parasites spreading through a colony. No one's quite sure yet.*
'A big stinking problem that needs to be solved immediately' – hearing this line made me consider the human response to dealing with our dead. It was inevitable really that I would choose to bring this up. The elephant in the room, I guess. Though we are not social in the same sense as ants or termites, we are social in many of our habits and our housing. The same stinking problem applies equally to us as to them. Here are some figures which I have pulled from Bernd Heinrich's wonderful book, Life Everlasting, about humans and how many of us choose to deal with our dead in the modern Western world. These statistics are as follows. Of the 22,500 active cemeteries in the United States, the combined materials they use to cater for the human dead are: 30 million square feet of timber; 100,000 tons of steel; 1,600 tons of reinforced concrete; and (get this) almost one million gallons of embalming fluid. But that's fine, you're thinking; you were going for a cremation anyway, right? Well, annoyingly, cremations are hardly the eco-alternative one might wish for. According to Heinrich, the combined fuel used to burn all those bodies is enough to power perhaps 80 trips to the moon and back, not to mention the damage that the airborne mercury may cause in pollution (cremations are the second highest cause of airborne mercury in Europe).
It's quite depressing. Be under no illusion: in the developed world, death is big business. It's been monetised. It really has. The funeral industry is worth $20 billion to the annual economic activity of the United States. Twenty billion dollars. They want you. And we want them, because we think our life is worth it. And because we want to get rid of the big stinking problem, I guess.
On the drive home from visiting Gloucestershire I thought long and hard about my own feelings of what I want done with my body after death. I decided that I had half a mind to let the ants have a go with me after I'm done. In fact, if I could distance myself from the disgust for long enough, I came to quite like the thought of giving my body to a colony of scavenging ants. Of my flesh becoming the flesh of eight million ants in my death. Me: part of the action. Part of something big. Part of something organised. For the first time in my life, I realised I could have purpose in death. And I could choose what. I think, if I really considered it, I could make some quite interesting life from my dead body; I just have to opt for what life I want to crawl out of me. It felt strangely life-affirming to think like this; not at all what I had expected when this journey into death had begun. My body: a vessel. Not a metaphor for anything. Not a figurative vessel of memories; not a vessel on its way to a higher place or a spiritual heaven. A proper vessel. A physical vessel. A vessel for something else to make use of after I've finished with it. I just had to make a choice. The question is, which corridor would I choose: the left or the right?
Note
*I wondered about other social animals. How do they deal with their dead? I wondered about the naked mole rats that featured earlier in this book, for instance. Finding nothing in the literature about this I made contact with one of the world's leading experts in naked mole rats, Dr Chris Faulkes (a Reader in Evolutionary Ecology at Queen Mary, University of London). Here is his response: 'Yes, an interesting question, and annoyingly one that we cannot answer! I can find no reference anywhere to what may happen to the dead animals from the limited fieldwork that is published (on naked mole rats). My colleague Nigel Bennett has never dug up a corpse in 30 years of fieldwork on various mole-rat species, and neither have I. It is tempting to speculate that they may drag corpses into a toilet chamber where they become buried and eventually sealed off when a new chamber is excavated. But nobody knows.'
CHAPTER FIFTEEN
Mourning has Broken
This is the story of a chapter that could never be; and it begins at the end. I am sitting at a desk in a Best Western hotel looking at myself in the mirror while the cognitive scientist Dr Alex Thornton speaks to me on the phone. My shoulders are sagging. He's hammering me hard, and it hurts because I know he's right. In the mirror I look tired. Tired about whether, and to what degree, animals know death like we humans do. 'How do you know that my grief is the same as yours?' says Alex. 'How do you know that I feel things like you do?' This is the second time he's asked me this on his crackling line. 'How can you tell, really?' It dawns on me that Alex is enjoying this. Alex is chewing on me like a great big philosophical steak. My head hurts. I pull at my face in the mirror. There are bags under the bags under my eyes. Death is taking its toll on me. The notepad on the hotel table is dry. Alex goads me a little. 'Go on, Jules...' he says. 'How do you know that I feel love and mourn and grieve just like you do?' A pause. I want to choke out a little sentence but nothing much comes out. 'You don't, do you?' says Alex. A few more seconds pass. 'You don't know. You can't know,' he concludes.
Alex is challenging me about the popular notion that many animals grieve and mourn and feel loss and sadness like we do, and his view is that it's not something we may ever know. I had rung him in desperation. This has been by far the toughest part of the book to write. Six months of research into animal mourning has got me nowhere. Absolutely nowhere. I'm drowning in a sea of anecdotes that float like chunks of ice around me; as soon as I clamber onto one, I lose my footing and slide off back into the sea of uncertainty. I was desperate for something firm to hold onto. Good evidence. Any story about animal mourning with a sample size greater than one or two, for instance. 'I guess I can't,' I admitted to Alex. 'I guess I can't say with certainty that you and I feel the same things in the same ways.' 'Exactly,' he says.
I consider telling Alex about the time when I thought my four-year-old daughter totally understood the death of her great-grandmother but then later I'd caught her creeping past great-grandmother's old flat attempting not to wake her, even though we'd seen her being cremated 90 minutes beforehand. On reflection I choose not to mention it. At this late stage in my research I can recount hundreds of tales of animals that show hallmarks of mourning or grief but I honestly cannot say with any certainty whether, and to what degree, they may or may not be real and true understandings of death as you or I know it.
I drum my fingers on the desk, realising that this chapter may be bound for the bin. Alex is right: if I can't fully understand and guarantee his feelings and emotions, and he mine, then how can we know cognitively what animals think when those around them die. Alex has me philosophically pinned, like a metaphorical wrestler in a WWE ring. I look around for a metaphorical folding chair which I can swing at him violently, releasing me from his grip. 'What about chimps?' I say. 'They mourn... I've seen it on telly.' Even as I say it, though, the words sort of limp out of my mouth. I begin to recount to Alex about a haunting nature documentary I had recently watched in which a female chimp carried around her dead offspring for days and days on end, seemingly unable to accept its death. The tiny corpse had dried up and become waxy, almost mummified. It was heart-wrenching to watch. The story had formed a centrepiece of a BBC show crafted to make us feel closer to our primate cousins in terms of our ancestry and shared cognitive skills. Alex's response was instantaneous: 'Sure, it carried around its dead offspring... but a simpler explanation is that she didn't know that her offspring had died,' he says dryly. This leaves me momentarily speechless. What? I think. What Alex is saying seems just so heartless. Alex reads my silence. He carries on: 'Look, there's a massive tendency for us to ascribe these sort of things to creatures that we feel we're related to,' he says. 'But if we saw the exact same thing happening in a mouse most people wouldn't think twice about it.'
He pauses and then continues on the theme of chimps. 'Listen, there's been about six million years of evolution since we split from chimpanzees: plenty of time for novel traits to evolve. And there are all sorts of things that are different in humans and chimpanzees. Do I think that in this case, in mourning the dead, we're similar? I don't know. I don't think there's any way that we can really answer it.' He goes a little quiet for a moment, considering his words. 'One thing I would say is that people have been studying chimpanzees in the wild intensively since around the sixties when Jane Goodall set up her studies, and in that time there have been a handful of these supposed 'grieving' events, but chimpanzee researchers have come across loads of dead chimps. Chimps die,' he says bleakly. 'If apparent grieving events happen it's exceedingly rare. It's not like in human societies where almost every time someone dies there's massive social disruption.'
I agree with him about this. When humans die the behavioural responses that this death elicits do seem incredibly powerful and are easy and clear to observe: there is often wailing, screaming, crying, sobbing, holding, touching, embracing, for instance. Sometimes this can go on for days and weeks and months and years. We seem different to the rest of nature in this respect. But I struggle internally with Alex's super-rational approach to understanding animal grief. Something about it doesn't sit right. I've spent my life communicating to people that humans are animals; that, in nearly all ways, our bodies and brains work to nature's rules and that we have evolved (mostly) through natural processes that apply equally to mushrooms, midges or marmosets. Yet, here I was entertaining the idea that we might be the only creature on the planet to understand truly the finality of death. It feels heartless, I tell him, to suppose that chimps carrying around their dead chimp babies might not be feeling emotional pain like we do. Alex disagrees. 'I don't see it like that,' he says firmly. 'Why is it heartless to admit you can't answer something? For me, the excitement in studying nature is that there's so much we don't know. Sure, some questions are really hard to determine but they're fundamentally answerable. But some are fundamentally unanswerable.' He pauses. 'This is one of those fundamentally unanswerable questions,' he says firmly. 'To me, it's much more satisfying to be honest and say "Look, we don't know what's going on here" rather than saying "OH! IT'S DEFINITELY MOURNING!" because once you start down this line, you're no longer in the realm of science, you're in the realm of faith.'
Pow. And that was the knockout blow. The metaphorical bell rang: ding ding ding. Nothing hurts a scientist like the F-word. Nothing. After we hang up, his words continue to sting like a wet slap across my cheek. Science or faith? I think. I sit on the hotel bed looking at the pile of reference books I've been lugging around for what feels like months, dancing with an uneasy thought...
I had got the idea to visit Simba after talking to the famous bird-handlers Lloyd and Rose Buck. I had explained to them that I had once, in my car, accidently run over a jackdaw and that I'd parked up and watched its mate come from out of the bushes to inspect its dying partner. I'd always wondered what had been going through the surviving jackdaw's mind during this moment (in fact, I based a chapter on this particular bird in Sex on Earth). Was it feeling loss at losing its breeding partner? Did it understand the finality of the event that had just taken place? How much distress was it in? Or could it, perhaps, have simply been inspecting the eyeballs; weighing up the energetic value of the flesh that lay before it, maybe? Lloyd and Rose said they had something to show me. I drove down to Bristol to see them.
Simba was a crow, an 18-year-old carrion crow. As I stood in amazement, he perched on Lloyd's arm and looked at me and Rose purposefully. I had rarely been so close to such a stocky bird. His head was surprisingly furry; his waxy black feathers were neatly arranged down his wings and across his back like a leather cape. His black legs looked like they were covered in PVC, almost like he was wearing motorcycle trousers. He strode up and across Lloyd's arm and shoulders like a miniature Darth Vader marching up and down a starship bridge. It was intimidating being around Simba. It really was. I felt he might suddenly choke me with his mind.
'Rose, go and get the feathers...' Lloyd asked, smiling excitedly. Lloyd looked around at me. 'Watch this,' he said, his eyes widening. 'You'll like this...' He grinned. Rose walked into a nearby shed and pottered around a little behind the scenes. She came out and stood in front of us and then pulled a handful of crow feathers from out of her jacket theatrically. She threw the feathers on the floor in front of Simba. And then it happened. It was so sudden. A behavioural change came over Simba that I had never seen before. The atmosphere became suddenly charged. Simba paused, looked down at the feathers and immediately ruffled his feathers out. Deep from within his body came a series of measured long and deep caws. 'CAW CAW CAW CAW' Simba squawked. There was a rhythm to it. 'CAW CAW CAW.' The warm breath was visible from his throat. 'CAW CAW CAW.' With each exaltation Simba threw his head upwards, keeping one eye right on the mass of wet black feathers. It seemed to terrify him. 'CAW CAW CAW.' There was a rasping quality to it; it became a kind of roar. 'CAW CAW CAW.' Not what I'd expected from a bird at all. 'CAW CAW CAW.' It echoed across the pond in front of us, silencing the hordes of waterfowl that had honked and hollered constantly since we arrived. Upon seeing the feathers, it was as though Simba had momentarily become possessed. It was... a response. A behavioural response.
'He never reacts this way to anything else. Only black feathers,' Lloyd shouted over the din. I barely heard him. 'He never makes that call for any other reason,' Rose said. Rose picked up the feathers from the floor, returning them to a pocket in her jacket. Simba immediately stopped making the noise; there was a moment and then he went back to normal. He carried on walking up and down Lloyd's arm as if the whole thing had never happened. Rose and Lloyd looked at me. I had an idea. I picked up a nearby clump of white downy goose feathers and threw them down in front of Simba. Silence. Simba looked at them briefly, then continued striding around busily upon Lloyd shoulders. Then Rose chucked the black feathers on the floor once more and we all watched as Simba went bananas again. Rose picked up the feathers again. Simba reverted to normal as if nothing had ever happened. It was incredibly interesting to see so clear a response. What it meant was... anyone's guess. Was this reaction typical? I thought. Was this behaviour common to crows and other corvids? What did it say about the corvid state of mind? Was it related to death, somehow? I had questions. More questions.
Throughout my death-journey, the question I have been asked most by friends and family is: 'Are you going to write about when animals mourn?' In recent months people have become really drawn to telling me their anecdotes about when their pets mourned or grieved after the loss of family or their kennel-mates. People have told me about horses they knew and how they buried their dead stable-mates in hay. They have recounted stories to me of dogs that stopped eating at the death of their owners, and stories of cats losing their hair after their kittens were taken away. People have sent me links to videos of swans committing suicide after the death of their partner; police dogs resting their paws on the coffins of their dead police officer owners. Elephants, horses, dolphins, cats, dogs: all behaving strangely around corpses of their own kind or even those of other species with whom they might have bonded. Rabbits that pine when split up. Dogs that apparently become anxious and restless at the same time that the house-cat is being put down. 'How can it not be sadness?' they say. 'How can it not be loss like we feel loss?'
I couldn't answer these questions. It really is a difficult phenomenon to confront scientifically. I realised this early on. I'm sure there was something going on with their anecdotes – in fact, I had agreed with my friends and family that there was probably something afoot. But what? Their stories were anecdotes and I wanted more than that. I wanted some science, I guess. But it was proving hard to find. Their anecdotes told me that some animals can and do show signs of apparent distress caused by, or linked somehow to, the death of conspecifics or offspring or owners. But their anecdotes couldn't tell me why it happens, the mechanisms through which it happens, or how common or easily predictable such behaviours might be. Dogs don't always show distress. Neither do cats or horses or monkeys. The whole issue of animal grief was problematic for scientists, as Alex warned me later on the phone. But Simba had come along. What I had seen in Simba seemed a simple test: a stimulus response that seemed repeatable, predictable; that might tell us something about the corvid understanding of death or its association with it. So Simba kept my interest for a while.
I had assumed that the kind of raised response to feathers I had seen in Simba might be very well known in corvids but... it wasn't. It didn't seem to be, anyway. I spoke to friends and colleagues who knew nothing about it, who had never seen this behaviour for themselves and had never heard about it from others. As I searched I could find only two references to this strange behaviour in the literature. The first is this: in Marzluff and Angell's Gifts of the Crow (a wonderful account of the intelligence displayed by corvids) there is a story about a Native American dancer leading workshops for tourists at an amusement park. When using black dyed turkey feathers to make headdresses, he is said to have heard a wild crow cawing from afar, and then watched as a mob of angry crows arrived. The birds mobbed the public, scolding anyone who wore black feathers in their headdresses. Only when the gentleman leading the workshop apparently decided to call an end to the event did the corvid bombardment cease. Apparently he never used dyed feathers in these displays again.
The other mention of corvids becoming agitated around black feathers comes from the greatest ethologist of his (perhaps all) time, Konrad Lorenz. In King Solomon's Ring he recounts a similar distress response from jackdaws after taking his wet black swimming trunks out of his pocket and giving them a shake after having a dip. He was the subject of furious attack for doing this; a reaction he put down to his floppy wet swimming trunks looking a little like a floppy dead jackdaw. So intense was the aggression in this encounter that the jackdaws drew blood from Lorenz.
And that was it: two cases – a Native American dancer and Konrad Lorenz. These were the only two cases I could find of this strange corvid response. I spoke to other corvid experts and none had seen this behaviour with their own eyes. No one could give me much to go on. Simba was set to become another anecdote of hundreds where animals behave in surprising and strange ways upon being shown things that remind them (or us) of death.
There really are hundreds of anecdotes out there. Log in to YouTube. See for yourself. There are a host of strange and obscure videos of animals responding in unusual ways when exposed to their own mortality or the mortality of those with whom they have bonded. Amongst my own personal gems is footage of a 'hero dog' rescuing an injured dog from a busy Chilean highway. It drags the other dog between busy lanes, beeping cars and screeching traffic, to safety on the verge. There's another amazing video of a macaque rescuing (and seeming to resuscitate) a fallen troop member that has been electrocuted on train tracks. The macaque picks up the steaming, apparently dead, body in its arms, pulls it about a bit, pushes it, pokes its face, squeezes its torso then chucks it in a puddle a few times, and, hey presto, the electrocuted dead monkey comes back to life (though it looks actually very ill, even after being revived).
There are other videos like this. There's one haunting video in which a Hawaiian green sea turtle lumbers out of the sea to 'pay its respects' at a little grave made by locals for another turtle (a female they had named Honey Girl) which had been found dead on the beach in the days previous. The turtle appears to struggle 10 metres or so out of the water and rest its head next to the grave, gazing up at the photo of Honey Girl on the memorial ('It was almost as if he was coming up to say goodbye,' says a local resident in the news report). These videos have thousands of hits, but while watching each one I found myself wondering what the fate is of videos in which animals don't do much, or fail to display the behaviours we class as mourning. Presumably no one wants to watch videos like that.
I continued searching for an answer to explain why Simba had behaved so strangely upon seeing the black feathers. There had to be something in the literature to confirm or deny it. There had to be. And then... I found something. And it was in the scientific literature, too. This research was on another corvid, the western scrub jay – a close cousin of the carrion crow. The western scrub jay is a native of western North America, a perky medium-sized bird with bright blue head and white throat and a 'harsh and scratchy' note to its voice. Like the carrion crow and other European corvids, the scrub jay is a common resident of suburban and wooded areas, in which it hunts in pairs or family groups in spring and summer and within larger non-family groups away from the breeding season. It does appear that scrub jays respond to death, and here's how it happens. The experiment (undertaken by experts at the University of California and described in the journal Animal Behaviour in 2012) placed a number of objects – including real and stuffed dead jays and stuffed specimens of great horned owls, along with some control objects – into different residential backyards. The researchers watched how each wild group of scrub jays reacted to each novel object. First, they carefully put a stuffed owl on the floor at one site (a natural predator). The scrub jays responded predictably, congregating together and occasionally swooping upon it in a mobbing behaviour. This was expected. Their tests showed that scrub jays also behaved this way upon being shown a stuffed scrub jay. This was expected too; scrub jays often treat outsiders with trepidation, ever-suspicious of potential lone guns and resource-stealing intruders.
But when the researchers placed a western scrub jay that was clearly dead in the middle of a colony they noticed something not expected at all. The scrub jays in the study population were observed to congregate around the dead body, forming cacophonous aggregations. Among the calls heard by the researcher were 'zeeps' and 'scolds' and 'zeep-scolds'. Apparently these information exchanges were so intense the animals were observed to cease foraging for food for hours at a time. They were rattled, it seemed, by the sight of a dead scrub jay. It made them react. It made them respond. And they did it again and again in a predictable way.
Evidence. Finally, some sort of evidence. Why do they do it? We don't know. What do they get from it? We don't know. The authors of the study suggest that this behaviour could alert group members, warning them to a potential danger (a kind of 'WHO KILLED THIS BIRD AND WILL THEY KILL AGAIN?' noise), but of course this is a hunch requiring further scientific scrutiny. I like this study, though. It seems so repeatable. Something any backyard owner could action (should they find themselves in possession of a stuffed owl or a dead scrub jay). But even this type of research is steeped in confusing language. For instance, the authors of the study use the popular parlance of 'funeral' to describe such aggregation behaviour in corvids, and this is the only point at which I start feeling a bit uncomfortable. A funeral? A funeral, really? The term, applied to animals, makes me feel... I don't know... uneasy. Who let that get through? We seem so desperate to make them like us that even our scientific language seems somehow to jump the shark.
If there is one thing that the scrub jays taught me, it's that if you want to obtain predictable, strong conclusions about how animals respond to death you need a good sample size and a neat experimental method. In most cases of apparent animal grief, this is sadly lacking. For many animals, that's fair enough – it may prove too difficult to test. In wild elephants (the most famous of animal mourners), only once has anything close to such a study taken place, to my knowledge. This study used bones.
In Elephant Memories, the famous elephant researcher Cynthia Moss recalls her initial surprise at seeing elephants respond to the bones of familiar family members. After bringing back to her camp the jawbone of an elephant matriarch she was amazed to observe (a few days later) the matriarch's family approach the camp and the matriarch's seven-year-old son pay special attention to the jawbone, probing and stroking it and turning it over gently with his feet. Moss was interested to test these observations experimentally so she set about, with colleagues, testing their responses by presenting different skulls of megafauna (including those of elephants), samples of ivory and control blocks of wood to different groups of related elephants. The results were interesting. When presented with skulls of elephants, rhinos and buffaloes, the elephants spent more time investigating the elephant skulls. So far so good, you might say. But when presented with three elephant skulls, one of which was from a former familial matriarch, the elephants showed no greater interest in familial bones than the bones of strangers. I wondered why this evidence wasn't more commonly known or cited. I had never heard about it. I wonder whether this information doesn't make it into most TV nature documentaries because it doesn't fit the narrative that elephants are incredible mourners and that they are just like us, which they may or may not turn out to be. They may mourn in ways we cannot imagine or understand.
Near the end of my tether, I decided to think of other ways to get my sample size up. Where could I find thousands of individuals of a cognitively advanced species, living together, being housed similarly and raised in the same repeatable conditions over and over again? I thought long and hard about this. In fact, I thought about it for many months. And then it hit me. Donkeys. Donkeys are kept in paddock after paddock in Britain, often rehomed in special sanctuaries. Donkeys often form pair bonds, unlike most livestock. They form very strong bonds with one another, I'd always been told. Surely sometimes one must die, leaving a partner on its own. Surely, donkeys would be where I would find some answers. Repeatable experiences. Trends. Something approaching evidence. I emailed The Donkey Sanctuary in Sidmouth, Devon, to see whether they would talk to me based on their experiences of looking after 3,000 donkeys spread across eight farms and caring for another 1,500 donkeys in private foster homes. What was their experience of animal mourning? I asked. They responded. Suzi Cretney, their PR manager, invited me over to meet with their head of research, Dr Faith Burden, to show me around. A week later I was on my way to Devon.
I know very little about donkeys. My beliefs about donkeys are pretty much the ones that have been fed to me through mainstream media: that donkeys are hard-working; that donkeys are stubborn; that donkeys are a bit world-weary – that sort of thing. As we sat in the Donkey Sanctuary cafe surrounded by paddock after paddock after paddock of donkeys, Suzi and Faith gave me a crash course in what donkeys were like in reality. And I realised I had got them all wrong. 'When you think about donkeys...' said Faith, opening her can of soft drink, 'think about where they come from: try and remember that, inside each one, is a wild donkey. That's really important.' I jotted this down. 'I mean, they've only been domesticated for 6,000 years so, you know, you can't really take the desert out of them. It's a part of them,' she said. 'Most of what we see, hear and study about donkeys physiologically and behaviourally all comes back to that earlier life: that wild donkey in the deserts of Ethiopia.' I noted this too. 'They're not glamorous animals,' Suzi told me from across the table, 'but they're animals on the backs of which civilisations have been built. Literally: they built whole civilisations.'
I poured my tea. I quite liked that we had started off with this. In popular culture, there is a feeling that people that care for donkeys are somehow twee and eccentric. I was a tiny bit worried that Suzi and Faith would be actually very twee and eccentric. But they didn't seem to be. They seemed lovely. And scientific. Very rational people. And they were quick to understand the predicament I was in.
I explained about the problems I had in getting to grips with such an amorphous phenomenon as animal grief and mourning. I explained that I had almost ditched it from my research. 'Could donkeys offer me any insights in this?' I wondered. Suzi and Faith looked at one another, deciding politely who should answer. Suzi smiled at Faith, beckoning her to take it. I wondered if they had talked much about this subject before. 'Well,' Faith began. 'Donkeys are a contrary animal to understand, that's for sure. They're not like horses. There's no stallions or harems of mares. They're often either solitary or living in pairs. In some ways that probably makes them strong-bonding,' she said, looking at Suzi for some sort of reassurance. Suzi looked at me. 'They bond closely,' she said, paraphrasing a bit. 'They have to stick together. If there's only two of you, and one of you dies, you have as much invested in companionship as life alone. You'll notice it. It's a big deal.' 'How that translates in domestic situations is what we see here,' said Faith. 'Some donkeys here are so tightly bonded you can't separate them by a fence, let alone a stable.' 'So what happens when one of them dies?' I asked. There was a brief silence. Faith cut through it: 'Some donkeys respond to death with overt symptoms of distress, but not many, and by no means all. That bit's really important. Not every donkey behaves the same around dead donkeys.'
They gave me some examples. They talked of some donkeys going off food for long periods after the loss of a companion, braying and even trying to jump from their enclosures on some occasions. They talked of anxiety. Nervousness. But they also told me of the variations of behaviours and character types that donkeys have. They talked about the donkeys that don't express much at all after the death of a companion. They talked of some donkeys apparently ending up much happier alone.
What I found very interesting was that, with these behaviours post-death being so difficult to predict, the Donkey Sanctuary plays it safe. 'For instance, if a donkey is to be euthanised,' Faith told me, 'then the companion donkey is given an opportunity to be there too. This is standard practice at the Donkey Sanctuary.' I was impressed. It seemed nice that, even though they couldn't guarantee a donkey's response, they were prepared for the worst. 'That's what we do here and we always advise others to do the same with donkeys that have bonded companions,' Faith said. 'I'm guessing you've seen many euthanasias in your time...' I commented. 'Yeah, quite a few,' she said. 'How does it work, with the remaining donkey watching euthanasia take place?' I asked. Faith looked quite sombre all of a sudden. 'We let them stand there for as long as needed, depending on the behaviours they exhibit.' She twiddled the ring-pull on her soft drink. 'Some of the behaviours that you might see are very striking.' 'Oh?' I said. 'The companion donkey might sniff them. They might try and get them up. They might bray. They might run away.' She paused then. 'It's hard not to anthropomorphise,' she said, looking at me, slightly embarrassed at her response. 'I know,' I said. 'I know, it's hard...' she continued. 'I'm a scientist, you know? But then...' She smiled a bit. '... Then, of course, there are those donkeys that just aren't bothered. They take one glance and give a look to the dead companion to almost say "I never liked you anyway".' We laugh a little at the thought.
I asked Suzi and Faith whether, and how often, they used the words 'grief' or 'mourning' to explain the behaviours they occasionally saw – particularly Suzi, who worked in PR, whose job it was to help frame these animals as creatures worth donating money to save. 'Scientifically, I'd label it as distress,' said Faith quite assertively. 'Yep, that's how I'd describe it. It's distress.' I looked at Suzi. Suzi thought about the question for a moment. 'In humans, regardless of religion, regardless of where you look, you'll see a marking of the passing,' she said. 'But... we're talking here about donkeys responding to the death of one another. Not family members, or anything like that. News of a death – the death itself – doesn't ripple throughout the herd. They're not all affected. And they're not all affected, all the time, even if it is their best friend,' she told me. As Suzi talked I could see Faith thinking more about the question. 'So, what's the correct terminology for you?' I asked. 'Distress. I think distress is a good word,' said Faith.
We all paused. There was a silence. It was the only silence in our entire conversation. I felt that distress really was the right word. Perfect, really. Nearly all humans know sadness and loss at losing someone close and many, unfairly, have felt this pain sharply numerous times (many of us feel it when we lose pets, too). Though it's hard for us to know truly the emotional states that people other than ourselves feel, I think it's a reasonable guess to say that you hurt like I do at funerals. That you cry. That you feel an intense weight of sadness. That it really hurts. You may, like me, have literally fallen over at the news of someone close to you dying. Literally, fallen. Make no mistake – for the bulk of us, these are loud and powerful emotions. And they're relatively universal, too, across human cultures. This is mourning. This is grief. The more I had researched this topic in animals, the more I came to feel that the words we choose really matter. There is no animal that responds as predictably to death as humans. In fact, no other animal appears to come close. Freely labelling other animals as grieving or mourning then threatens to belittle what is an incredibly intense period of emotional turmoil in human life. At its worst, it makes a mockery of one of the most interesting things about our species. So 'distress'? Yes, I'm happy with it. I realise that I am happy, like Suzi and Faith, with the word 'distress'.
As we finish off our lunch, Faith tells me that her plan, working with UK universities, is to document in greater detail the events that take place after death, investigating and isolating behavioural patterns that could be the basis of further study. I was really pleased to hear this. That's what this area of science needs – creative ways to find out more about what may or may not being going on. We shook hands warmly, agreeing to keep in touch. Suzi said I was free, if I wished, to wander around and go and look at the various donkeys scattered in the nearby paddocks, which I gladly did. Sometimes they came over to greet me and allowed me to give them a little scratch or a pat on the head. Sometimes they didn't.
A few more weeks passed. I decided to keep this chapter in the book. I mentioned earlier how difficult a chapter this had been to write. I think now that this was partly because I had wrongly sought to bracket animals into two lots – those that understand death and those that don't – and look for the science to justify the categorisation of each. I failed to appreciate one enormous thing: that an animal's cognitive ability to understand death could actually be a continuum. It could be that we're all on a spectrum of understanding death. It's a bit like rats and laughter. They say that rats emit a high-pitched laugh when they are tickled, but would a rat understand a 30-minute satire sketch? No. There's a spectrum there. It may turn out to be a bit like that with death: that animals feel something of what we feel surrounding death, but nowhere near the complete human experience (assuming, that is, we can define such a thing – something Alex Thornton had pinned me on).
But there was one other peculiar thing that I had noticed about animal mourning and animal grief. It was this: it struck me that this had been the only question I was asked about again and again when telling people that I was journeying into death. It was always the same thing: 'Oh, will you talk about animal mourning?' they'd ask, before reeling out the anecdotes about their pets and friends' pets. This question followed me around for months and months. It really did. Why? Why were we all so interested in this particular aspect of animal behaviour? Why is whether animals grieve or mourn of such interest to animal-lovers?
At the end of this chapter I'm left still wondering. Maybe it's nice to imagine that our animals might miss us? Perhaps. But I wonder now if it might be something deeper. I can't help feeling that, deep down, it's simply horrifying for us to consider being the only creatures in the universe that can imagine what's going to happen to us after we die. The only ones aware of our fate. The only ones to sometimes question our fate and seek a more emotionally friendly alternative. I think, deep down, it's lonely being the only ones at the top. The only ones in the know. And that, probably, is what makes us most human. Our own label is defined by our distress.
CHAPTER SIXTEEN
Who Wants to Live Forever?
Deep within the recesses of University College London there are worms. Nematode worms that regularly have a UV light shone upon them. Normal nematode worms show up as blue under these lights; they slither across microscope slides in a perfect S, like heartbeats on an ECG. But occasionally something else happens to the worms – some of them suddenly seem to ignite. There appears a bright blue spark within their intestines. It spreads out across the worm's body, and a blue explosion washes over the worm like a forest fire consuming all in its way, leaving only charcoal – death – behind. This phenomenon is called 'death fluorescence'. Originally thought to be a marker that results from the ageing process, death fluorescence is now thought to be a straight-up marker of dying cells, and it is especially visible in these simple translucent nematode worms. Death fluorescence is true death, in other words.
It is mysterious and slightly eerie to watch videos of these worms being consumed in such a way. But it is also quite pretty – pretty because nematodes are really quite wonderful creatures. There are 25,000 named nematode species, though it's likely that there are a million or more species out there for us to discover, should we wish (sadly not many people wish this). Perhaps half of all nematode species are parasitic (which doesn't help matters). Nematodes are of particular interest to scientists because they are some of the most simple animals on Earth that have a tube-shaped body with a mouth at one end and an anus at the other. They are built like us, in other words, except much, much more simply. And within their genes we find programming instructions for how to build and regulate and care for that simple body plan. Nematode genes work, on the whole, in the same way that they work in our own bodies, thanks to the common ancestor that we shared with them about 600 million years ago. Their genes are our genes, mostly.
The world's most famous nematode – the fruit fly of worms if you will – is Caenorhabditis elegans. It is everything you want in a lab animal. See-through, free-living, easy to keep (it lives in the wild in soil), and scientists know its genome and the normal development of each of its 959 (in hermaphrodite females) and 1,031 (male) cells. Caenorhabditis elegans is tough. C. elegans specimens from the 2003 Columbia shuttle disaster were found to have survived after falling to Earth in a four-kilogram locker. That's how tough they are. Touchingly (if you like that sort of thing, which I do) their descendants were put into space by the shuttle Endeavour.
In earlier chapters I have explored the competing theories that may explain animal longevity, and I have discussed the impact of free radicals on animal cells when it comes to ageing. My research brought me into the realms of a host of animals that live longer than simple body size would predict. I came across cataract-ridden rockfish, wrote about naked mole rats defying all the odds, and I held in my hands Ming in its Perspex box – an animal that lived for more than half a millennium. However impressive this may sound, there is a problem with studying these creatures. In fact there is enormous difficulty in studying gerontology. All of these creatures make pretty poor study animals, because you have to wait 30 or 40 or 400 years just to see how they fare after experimental manipulation. As a result many scientists are rather turned off studying an animal that ages at the same speed as themselves. Smaller creatures are therefore more in vogue for gerontologists; scientists can obtain results much more quickly from something that lives days or weeks rather than years.
And so it is for this reason that C. elegans has become one of the favoured study creatures for this sort of thing. At this very moment, researchers are studying and observing and experimentally manipulating C. elegans in their tens of thousands, all over the world. For within them, say many scientists, are the mechanical workings of life and death. Within them are genetic mechanisms that can be picked apart like cogs and springs in an attempt to understand to a greater degree the causes of ageing and ultimately death... and, crucially, whether it can be fixed. These scientists are interested in a cure: a cure for ageing. A cure for age-related diseases. They're in it for the mother lode, essentially. As close as we might ever get to immortality...
But there is another reason that C. elegans hogs much of the ageing limelight. C. elegans can do something incredible. As it grows, this species can modify its lifespan depending on the environment. Starve C. elegans and they pull back from reproduction and invest in life. Feed C. elegans and they reproduce as normal and promptly die after a matter of weeks. Starved individuals live up to three times longer than well-fed worms, which is a striking result, no matter what your opinion otherwise of nematode worms. What's particularly incredible – and what C. elegans allows us to see clearly – is that key sets of genes appear to broker the whole deal. Life or death – genes 'choose' based on how much food there is. They choose life if there's not much to go around. They choose death if there's plenty to eat and all the sex is done and dusted. These special genes are important: they are the so-called 'gerontogenes' that control ageing. Master them and we master ageing, say the scientists who study them.
That small periods of starvation (or calorie restriction) can serve to prolong life may not be news to you, of course. Diet fads, daytime TV shows and many, many, many lifestyle books (which will all sell a great deal better than this) may have told you about it in recent years, and it's fair to say that the basic principles may turn out to be true across many animal species. For instance, studies where rats have been fed 40 per cent less over their life show that they live 50 per cent longer than their siblings and they suffer less from the diseases of old age, too. The same findings appear to hold strong in some fish species and also in dogs (and yeast, interestingly).
Though good data are lacking in humans (partly for the reasons outlined above: namely, who wants to wait 90 years for results?) it's likely that calorie restriction will have at least some effect on humans, too, though what effect we can't say. Calorie restriction doesn't always seem to pay off. Wild mice, for instance, fail to show any increased longevity when their calories are restricted. Indeed, longevity studies on calorie-restricted non-human primates have had conflicting and quite confusing results. Either way, the gerontogenes – the genetic brokers of life and death – are of key interest to scientists. Gerontogenes have within them the potential for extended life. They could be used to make us live longer... if we want to live longer, that is.
Why calorie restriction appears to have such an impact on the lifespan of some creatures has been considered for decades. In the 1970s, the gerontologist Tom Kirkwood attacked the problem with particular gusto. Far from being about death, Kirkwood saw flexible longevity as an adaptation to do with sex. Though the discovery of gerontogenes was a long way off, Kirkwood made his argument based on economic grounds alone. He predicted that in situations where energy was limited, expensive investment in reproduction may become futile and that instead energy should be transferred into longevity, maintaining cells and sustaining life in the hope of good times ahead when the opportunities for sex reappear. This economic approach is something we have come to know only too well in recent years. Consider bankers. It's the same with them. In hard times bankers don't invest – they shrivel up and maintain their own interests. They sit and wait. They age. So, it turns out, it's probably the same with bodies. It is in the good times that they can afford to be more frivolous; they spread their influence and grow; they breed. They live faster lives. The vast majority of animals on Earth may be capable of the same trick as C. elegans.
But C. elegans is just one of a number of animals to be pulled apart by gerontologists in such a way; there are other animals that are similarly being picked apart by geneticists and gerontologists eager to expose other tricks organisms may be capable of to slow down death and prolong life. Two close competitors to C. elegans in the genetic search for the elixir of life are jellyfish and Hydra. Both, like C. elegans, are simple multicellular animals whose cell development and genetic information can be readily mapped. For both, opposing camps of scientists have gathered around them.
The so-called 'immortal jellyfish', Turritopsis, is perhaps the most lauded by those in the jellyfish camp. It is capable, they say, of ageing in reverse. Most jellyfish species begin life as tiny tentacle-covered polyps, glued to rocks, which then 'birth' free-swimming life stages (medusae) which will grow into adults, at which point they produce eggs and sperm and promptly die. But the immortal jellyfish flouts these normal jellyfish rules in the most remarkable way. The immortal jellyfish, as a post-spawning medusa, doesn't die. Under certain conditions it can sink to the seafloor, fold in on itself and take on the polyp form once again. It lives and lives again, in other words, while everything else lives and dies. Some people call it the Benjamin Button jellyfish for this very reason.
How the immortal jellyfish manages this is still up for grabs. They are difficult animals to study – immortal jellyfish are incredibly difficult to keep and breed in labs, for a start. The only scientist to do so for any significant period of time is Shin Kubota, a Kyoto University scientist who for the last 15 years has spent three hours each day caring for a brood of just 100 jellyfish. Kubota is a man wedded to an idea: 'Turritopsis application for human beings is the most wonderful dream of mankind,' he told The New York Times in 2012. 'Once we determine how the jellyfish rejuvenates itself, we should achieve very great things.'
So there's C. elegans and there's the immortal jellyfish – both being poked and prodded and probed by research scientists eager to uncover their secrets to slow ageing. And then there are others. Hydra, a genus that belongs to the same group as jellyfish, is another important player in the anti-ageing scene. Hydra win points for being much more common than immortal jellyfish (they exist in most unpolluted freshwater lakes, ponds and rivers on Earth, predating passing food rather like anemones do), and because they can be cultured and manipulated in labs very easily. Since 1998, when the gerontologist Daniel Martinez declared to the world (in a paper in Experimental Gerontology) that 'Hydra may have indeed escaped senescence and may be potentially immortal', many gerontologists have gathered around the Hydra camp, sticking with them even though other scientists have questioned their supposed miraculous ability to limit ageing. Hydra are of particular interest for the regenerative abilities of their stem cells (the body's master cells, capable of dividing into any one of hundreds of cell types). It seems that Hydra stem cells may have an unlimited capacity for self-renewal, which makes them different to most other creatures. This buys Hydra a place at the gerontology table, and then some.
Undoubtedly the interest in this trio of animals – nematodes, jellyfish and Hydra – is growing. And so, with them, grows the rhetoric about the impact that such studies could one day have on our own bodies. Anti-ageing is a real thing. It's a real movement. And it's only a matter of time before we can wield and manipulate lifespans more in line with what we wish, potentially living well over a century rather than mere decades. The question is when...
And then there is yeast. Yeast has become another classic study creature. Within yeast there has been discovered an unusual class of enzymes called sirtuins, which have been implicated in many of the cellular processes described in this book: apoptosis, stress resistance and the role of mitochondria in ageing. Incredibly, in 2014, by experimentally manipulating the sirtuin-like enzymes in mice, scientists managed to extend lifespan significantly and improve health in the process. The next step, one expects, is clinical trials; one day with people. This really is happening right now. The anti-ageing industry is evolving; an industry that is eyeing up the potential in enzymes and in our genes; a world where jellyfish and tiny worms unlock our wildest fantasies of living forever. Whether this amazes or terrifies you depends on your attitude to death, I guess. Me? I'm undecided. I wanted an opportunity to see this industry up close. I wanted to observe what it might look like, and where it might go, and the sorts of people that are enamoured with the idea of living longer. And that's when I saw it. An advert for an event like no other. The Anti-Ageing Show, taking place at London Olympia, was coming up the following week. So I bought tickets; I bought tickets and had my head blown off.
But before I tell you about what happened, I just want to reiterate something: I really meant it when I said that the anti-ageing industry is growing. According to The Times, in 2014 the global anti-ageing market reached $150 billion. Now it is approaching $200 billion. Where once facelifts were vogue, anti-ageing therapies now involve diets, exercise, hormones and all sorts of energising rubs and creams as well as the enzymes, the antioxidants and the possibilities that genetics throws into the mix, care of worms and jellyfish and, possibly, yeast. It really is big business. In September 2013, Google's CEO Larry Page announced Calico (the California Life Company). Calico's aim is to eliminate age-related diseases, like Alzheimer's and cancer, through a $1.5 billion life-extension research centre. Though some argue that Google are flag-flying for their 'Don't be evil' mantra (remember that?), there's a good chance they've spotted the market trend: in 2025, there will be twice the number of over-sixties as there were in 1995. The market is building itself, year on year, awaiting the products they are trying to produce.
Other institutions are also seeing the potential. There's the Age Reversal Fund ('Our plan is to achieve maximum advances in wellness, youthfulness, longevity and profits... in minimum time'). Then there's Larry Ellison, CEO of the tech company Oracle; the money man (according to Forbes) behind the Ellison Medical Foundation, another anti-ageing research centre. And there's also the SENS (Strategies for Engineered Negligible Senescence) Research Foundation, supported, in part, by Peter Thiel, co-founder of PayPal. There's no doubt about it – ageing is big business and for good reason: there's lives to be saved from the ravages of a host of age-related diseases, and there's bundles of money to be made. A planet of potential customers, few of whom seem ok with the idea of getting old and dying naturally. Anyway, on to the show...
Olympia, for those who have never had the pleasure on a warm day, is HOT. It's essentially a hangar-sized greenhouse-cum-oven. By the time I arrive, after a long walk from the Tube, I am a very sweaty man, completely overdressed, walking into a sauna. I arrive at about 10.30 am to find the show in full swing. The entrance going into the main hall is like an arrivals corridor in a country very much hotter than Britain. A gaggle of salespeople awaits us, handing us literature and free samples as we walk in; I am greeted with leaflets about facial acupuncture, 'bespoke advanced facials' and free samples of probiotic balancing cream which look and smell suspiciously like yoghurt. I flick open the exhibition magazine I have been handed and am met immediately with a half-page advert for something called 'gong therapy' where a man rings a gong and, to paraphrase, everyone feels much younger and better about things.
I decide it's best to sit down and have a coffee. I have decaffeinated coffee at events like this because I don't really like big crowds. Big crowds make me anxious; they make me nervy and a bit edgy. I need to sit down. I can't find a seat near the coffee stand so I sit on a set of big wide benches in front of an empty stage instead, and I look at the show guide. The Anti-Ageing Show magazine tells me about the stands that I should definitely spend time at. I scan through the company names: Aluminé, DermaNutri, Donna Bella New Look New You, EDM Therapy, Forever Living Products, iGrow Hair Laser Rejuvenation System, Maddisons Unique Gel, Queen of Oil, Rejuve Me, Megawhite, The Jane Plan. I am surprised to see that a popular cat rehoming charity is here, presumably because if we all live longer we might want access to cats for longer, too.
I scan the room. It is a place for beautiful people, none of whom I can estimate the age of. Many of the women wear tight black pencil skirts that go up past their navels. They are very busy, these women. They move fast. When they walk their hands move up and down in front of them like they're on a StairMaster. I can only see a handful of men. Each is toned. Tanned. Smiling with their teeth. Muscular. I feel a wave of insecurity as salespeople come toward me with clipboards and more free samples, but many of them steer away at the last minute as if they suddenly realise, by looking at my non-fashionable clothes, that I would probably prefer an early death. Maybe it's because I'm copiously sweating. Maybe it's that they spot that I have misapplied my face yoghurt.
The coffee here tastes awful. I feel really horrendous all of a sudden, sitting in front of the empty stage. A host of pencil-skirted women begin sitting down around me. They fill up the benches in preparation for a presentation that is about to take place. On the makeshift platform in front of us, two people arrange a dark leather dental chair. There are some cameras being set up and microphones are brought out. More people gather. A slim lady in a tight-fitting black dress is brought onto the stage and seats herself in the chair. Another woman, almost identically dressed, comes out from behind the stage and stands next to her. She has a microphone. A third lady comes out, this time in a tight-fitting red dress. All of these women have exactly the same kind of bodies. It's like they've come out of a box. A man with gorgeous hair and a dazzling smile comes out next. He kind of... zings... onto the stage. He tests his mic, then smiles to the audience and introduces his team before beginning a presentation about his company's range of 'dermal fillers'.
I sit through their presentation patiently. It's actually a very professional pitch. As it goes on I notice that more and more people turn up to stop and listen. By the end there is a bustling crowd. The presentation ends, and the gentleman invites the whole audience onto the stage to watch up close the lady in the chair have her face injected with fillers and other assorted 'rejuvenation sugars'. I assume no one would want to see this but I am wrong; the stage wobbles as almost every single person in the audience floods onto the stage for a closer look at the minor surgery that the poor woman on the chair is about to go through.
I decide that this is not for me. My disgusting coffee finished, I take this as my cue to have a walk around. In the dead zone between youth and agedness nobody here knows quite how to sell to me. Some try to attract me in by asking questions about my wife – when her birthday is, what I plan to get her for her birthday, and how I should celebrate it with a surprise photoshoot for her or a spa treatment or some gong therapy. I mumble and stutter my way out of these encounters, looking increasingly sweaty and like the sort of person you'd want to avoid on the next lap of the show, which they then do.
I really am not good in crowds. In my heavy coffee-drinking years I have had a number of panic attacks, a couple of which were rather intense. Many of these attacks involved crowds and I am sure they were driven partly by the fear that some situations would be mortally embarrassing to have a panic attack in, a thought which would promptly then give me a panic attack. I know others who have the same problem. The Tube, job interviews, sitting in the middle of a row in the theatre: these are the sorts of places it would happen. The thought strikes me that this would be a horrendous venue for a panic attack. I immediately try to crush this thought. It lives now. The sweat washes the yoghurt off my face and onto my collar. I start wondering whether the barista accidently gave me caffeinated coffee just now. It must have been caffeinated, I think. It must have been. I hadn't looked at whether he'd ticked the little box on the cup that says 'DECAF' (maybe he didn't tick the little box on the cup that says 'DECAF'?). I spin a tiny bit. I look for another place to sit down and spot another empty stage. A big banner hangs over it: 'THE GRACE KELLY STAGE' it says. I sit down and enjoy being left alone for a few minutes.
I had come to the show wanting and rather expecting to immerse myself in the consumer side of the global anti-ageing industry and to see, maybe, whether the biology that I have been researching is nudging its way into the anti-ageing limelight. It seems that, on the whole, it isn't. Looking around there is no mention of mitochondria, for instance. No talk of free radicals. Nothing about Hydra or jellyfish or genetics or... well, gerontology at all. This struck me as odd, because the word NATURAL seems to feature on everything. Do these organisations not yet know of the potential for anti-ageing that lies within our DNA or within the worms or the birds or the bats or the jellyfish? It seems that, on the whole, they don't. A few people gather on the benches around me. Once again I flick through the free Anti-Ageing Show magazine. I keep seeing pictures of a Harley Street doctor called Dr Aamer Khan. He's on everything here. The leaflets, the banners, the website. In every shot he stands with arms crossed, with one hand suggestively on his chin. He has incredibly white teeth and looks intently professional and handsome. He has charisma. In fact many of the speakers at the show seem to have oodles of charisma just like him. People seem drawn to hearing them speak here, drawn to wanting to know what they know. Eager to hear from them the secret of looking beautiful for as long as possible.
Weirdly, I have noticed these charismatic personas in some of my research, too. Gerontologists are rather sexy and charismatic people, it seems. Take the immortal jellyfish scientist Shin Kubota, for instance. Kubota isn't only famous for his jellyfish lab. Kubota has an alter ego. In Japan, Kubota is also known as Mr Immortal Jellyfish Man – he has a costume and everything. Mr Immortal Jellyfish Man has released a number of pop songs and six albums in Japan. He is charismatic. And there are others like Kubota. Throughout my research I have come across pictures and interviews with a gerontologist called Aubrey de Grey (de Grey runs SENS), who likes to say that the first person to reach 1,000 has already been born. This is mentioned in many magazine and newspaper interviews. De Grey is charismatic and distinctive; he has a long pointed ginger beard, and in all his photos he looks intensely serious about things. De Grey photographs very well. These are famous gerontologists; experts and professionals who really know their stuff. People put a lot of trust in people like these.
The Grace Kelly stage starts filling up around me for a talk. As before, microphones and cameras are set up on the stage. The same familiar dentist's chair appears. I decide to stay for this talk too. It is about something called Dracula Therapy. A tall, serious-looking man with a chequered shirt jumps onto the stage and stands in front of us proudly. In his hands is a vial of blood plasma that he has recently taken from the woman who has come to recline on the shiny black leather dentist's chair in front of us. Barely giving us any warning at all, he proceeds to inject the blood plasma back into her body, deep into her muscle tissue. 'We have to inject near the bone,' he says to us over the loudspeaker, with a hard-to-pinpoint European accent. 'Not toooooo near the bone,' he says calmly. 'But deep... deeeeeeeeep... near the bone...' He concentrates, the needle going in deeper. It goes in as far as it will go, in fact. I wince and turn my head. The people to my right appear fine with what's going on; they lean in for a closer look. They love it. The lady next to me is actually eating an egg mayonnaise sandwich while watching. I wait a few moments and try to look again. He is now injecting the needle deep into her neck. I really don't like this. Incredibly, the lady is barely flinching. I don't like it at all. He pushes in deeper with the needle. Horrified, I flick my head to one side once again, involuntarily jerking my body so violently that... that...
And that was when it happened. The day took a turn for the worse. Things got bad. A fire like lightning ripped across my chest. A bolt of electricity. The whole front half of my body went immediately into an agonising spasm, from my neck and down into my torso, causing me, I was sure, imminently to die. I let out a low 'UHHHH' from deep within my body and momentarily pull a face like I am having a very painful and prolonged orgasm. The lady next to me stops eating her sandwich. 'You ok?' she asks dryly. 'I...' I let out another strange noise through gritted teeth. It sounds like I am about to cough something up. 'I... need to... UHHHHHHHH.' I stand up and swivel round, wincing, trying to get to my feet. 'I need to make an... UHHHHHHH,' I say. She carries on with her sandwich and goes back to watching the Dracula Therapy.
The pain is intense but I recognise it. I know this pain because I've had this before; it's a kind of neck spasm that refers pain right down the front left-hand side of my chest. It has every single hallmark of a heart attack but it isn't one. I haven't had one in four years. This one is sharper, though, like a hot pipe being stabbed into my chest and slowly rotated. I walk slowly, almost limping with the pain, my head locked, my neck at a weird angle. Every breath burns so I have to take quick shallow breaths as I walk. I must get out of here, I think. As I walk across the show I learn that it hurts slightly less when I say 'UHHHHH' when I exhale. I start saying 'UHHHHH' as I exhale. It helps. And so, in the middle of an Anti-Ageing Show, I become a man hobbling around with hunched shoulders and a grimacing face going 'uhhh... uhhh... uhhh...', on the verge of death.
I carry on regardless. I'll be alright, I think. I spot the signs of a panic attack coming on. I reassure myself that it probably isn't a heart attack. Probably. I think about asking for help (I can't tell you how annoying it is to be surrounded by people in white coats and not one of them is a proper bloody doctor). I decide to leave the show. I keep my head down and limp through the aisles of strange anti-ageing exhibitors. I walk past the people putting their heads into strange metal helmets attempting to regrow lost hair. I walk past a cubicle of women happily putting their mouths over a strange luminescent ball on the end of a plastic stick. I walk past the people lying in black leather dentist's chairs having their cheeks vibrated by strange probes and ladies having their lower halves covered in gel and yoghurt. I walk past the vibrating platforms. The tarot readers. The Cats Protection League. And then, finally, I make it out. Out into the fresh air; back into the world I had known before. A world where the normal rules of nature seem to play out. A world where death is natural and, on the whole, all things accept it. It took a week to recover.
Being at the show affected me more than I had expected. I was amazed that jellyfish, free radicals and calorie restriction hadn't featured much. This worried me a little, like I had witnessed the calm before the storm. I couldn't help but feel that it might only be a matter of time before the cosmetics industry is swamped by the potential of cellular and genetic therapies that we are now discovering and that I discovered earlier in my research into death.
For some reason I felt a bit of deep dread at the thought of this, which is strange because there are so many opportunities for these therapies to improve the world. It's incredible that we happen to be alive at a time when the diseases of old age could be realistically tackled and that we could live for longer than our bodies ever evolved to. Incredible that we happen to be alive at a time where global healthcare could be revolutionised; where diseases of old age become a thing of the past. So why was I feeling dread? Why had I essentially freaked out? I don't know. I can't really explain it. I guess all new and exploding areas of science fill the popular imagination with fear like this. Nuclear technology bred Godzilla; the IT revolution bred Terminator; the prospect of genetic engineering bred Jurassic Park. Weirdly, though, I don't see any public concern about the anti-ageing revolution which we are undoubtedly heading toward. I find this strange. It seems to be creeping up on us. I can't help but think that we're sleepwalking into a world where people can pay to live longer than others, and that feels strange. Unethical somehow. There are questions I have that no one can really answer because there are no answers yet. For instance, will such anti-ageing treatments be available free through healthcare plans or the National Health Service? If not, how will we make it so that the poor don't end up paying for the pensions of the age-endowed? How will we go about avoiding the creation of a two-tier society of late-lifers and early-lifers? I'm not sure anyone knows yet, and that's unsettling to me.
On the flip side, though, there seem to be such positives about the anti-ageing movement. It could be a great thing: imagine the billions of pounds of healthcare provision that could be saved if we tackled age-related diseases by tackling ageing itself. It could be incredible. In Britain, many argue that the NHS is in real danger of disappearing forever. Perhaps this could save it? So yes, it is exciting. And amazing. But then... still the doubt lingers in my mind. Does the world really need humans that live, and consume, for longer than they do currently? What happens if humans live regularly until they are 120? Will that be enough, or will the Silicon Valley elite still strive to push us to 125? Or 130? The truth is that we will always want to live longer. I'm sure of it. Always. For many people life is simply too wonderful to be happy with it ending. And that's a problem. A big problem. Because it will.
CHAPTER SEVENTEEN
No, This is a Dead Frog
Later, long after the Anti-Ageing Show, I discover that there is a stumbling block to Aubrey de Grey's notion that some humans born today may be the first to live for a thousand years or more. That problem is the brain. Or more specifically, that problem is the neurons within our brain. For neurons don't replicate or regenerate in the same manner as normal cells. And if they could be made to replicate, each would lose their 10,000 synaptic connections to other neurons; synapses that together make up the thing you and I call experiences and memories. Lose them and we lose ourselves ('And so the price of immortality is our humanity,' concludes Nick Lane in Life Ascending).
Maybe de Grey is right, though: if we can tackle bodily ageing, maybe in time we will learn to tackle ageing in the brain, too, just in ways we cannot yet imagine. It seems unfathomable, but then so did so much of gerontology 30 years ago. When considering ageing and the brain, we find ourselves on another scientific frontier: that of neurogenesis, the process by which new neurons are born. Here, the worms and the jellyfish can't really help – it is birds, and their songs, that offer us a glimpse of the impossible. But first, we must revisit what we were all told about neurons...
You know the story. We were all taught it in school – we were told that the brain is fully kitted out with neurons shortly after birth, which are then trimmed back over the early years of life and on into later life. We were taught this because it really was the popular thinking about brains for decades, until someone thought to look into the brains of birds and they realised that it was actually quite, but not totally, wrong. The birds proved it. Far from being a static module incapable of new growth, brains of some male songbirds (at least the parts associated with song) appear to shrink back in summer (as territorial conflict and sexual tensions ease), only to 'regrow' in autumn in time to learn and rehearse their songs for the following spring. Essentially, parts of their brains could die and were able to grow back. After thousands of cells died, thousands more were born. This was a genuinely ground-breaking discovery. The research, undertaken by Steven Goldman and Fernando Nottebohm of the Rockefeller University, buoyed the concept of neurogenesis and inspired other zoologists and neurologists to seek out more such cases in nature. And they found them. Marmosets, rats, tree shrews, rabbits – all seemed capable of small amounts of neurogenesis.
In 1998, humans joined this elite pack. It turned out that our brains are also capable of growth, at least in the hippocampus – the part of the brain that, interestingly, is involved in memory and information storage. In humans, what might these new neurons do? That's the big question. Do they offer extra space for memory as bodies grow old, or is this just an elaborate developmental glitch, a cosmic red herring somehow? Predictably, scientists appear split over this point. Natural selection hates waste, and wasted cells are expensive, so these regrown cells must have a purpose, surely, but... there's also a chance that this is a side-avenue which has little consequence or bearing on the way in which brains work at all.
One thing remains clear, though: birds that cut back and later regrow the parts of their brain associated with song have to relearn that song. Their songs don't come back fully formed. Their experience is extinguished. No matter how hard we try, the human 'YOU' may never live longer than your neurons will allow. So how long is that, you may ask. The truth is that once more (and I know this is getting tiresome) we don't know. In 2013, Italian neurosurgeons discovered that mouse neurons transplanted into a rat's brain didn't die after 18 months, which is the normal lifespan of a mouse. In fact the mouse neurons continued working fine in the rat – these neurons were still alive and kicking in rats living twice as long. Mouse brains live for longer than anyone ever gave them credit.
There's a chance it may be the same for our own brains. Dr Lorenzo Magrassi (the co-author of the research on mouse neurons outlined above) thinks 160 might not be a problem. Others disagree. Nick Lane, for instance, suspects 120 years may be the upper limit for the lifespan of our neurons. Whether our children will find this out for themselves is still anyone's guess. Either way, even the most enthusiastic (and most economically endowed) of life-extenders will still have to face up to that uncomfortable truth. You are your brain. As with birds, if you refresh your brain cells your tune will change. And you may lose yourself in the process.
Driving up the motorway on my way to Alison's house I spend rather a great deal of time deliberating whether we should shake hands when we meet again or whether we should hug. Although I've only met Alison twice (probably a handshake then) she has been really supportive in her role as deathsplainer during my journey. Through regular correspondence she has provided me with such things as contacts (she got me in with Peter to talk dead pigs), advice ('this is a dead frog') and dead magpies (dead magpies). Plus, with her showing me the ermine moths and their incredible silken construction, I got to see first-hand the splendour with which nature acts, particularly when parasites force life to dangle closely over the edge. And through the ermines I also got to see the misinformed barbaric acts that humanity is capable of, when thoughts of death are invoked. I owe Alison a great deal, actually.
When I arrive and when we finally meet we mutually opt for a hug, rather than a handshake (though I suspect this is partly the Canadian in her). Alison has a lovely house. I like looking in people's houses and at Alison's I continue this passion with aplomb. She and her partner have made this personal space a paradise. Everything is in bloom, inside and out. There are plants everywhere. As we sit and chat in the kitchen, blue tits and sparrows gossip on the garden fence, making fleeting forays back and forth to well-stocked feeders. There are seedlings growing on a drying rack on the draining board. Binoculars on the kitchen table. A large poster of a dragonfly, lifted straight out of a Victorian identification guide, covers a wall at the bottom of the stairs. At the bottom of the garden is a large homemade solar array which her partner has designed and built. There are bee nest-boxes. Bird boxes. More feeders. Trees. Green. The works. Alison is much more into life than I had given her credit for.
'So...' I ask with a grin. 'Any dead birds in the house?' She looks at me as if I've just asked the stupidest question in the world. 'Oh yes, course,' she says matter-of-factly. 'Of course. There's a dead blackbird drying out round the back.' We gather up our things and walk out to get a coffee somewhere. I decided a few weeks before, not long after the Anti-Ageing Show, to make the journey back up to see Alison in Birchwood after she started making subtle references on Twitter to the ermine caterpillars and the lost trees. 'OH MY GOD, ARE THEY BACK?' I'd asked. Then I had thought about it. I mailed Alison again straight away. 'ACTUALLY, DON'T TELL ME! I WANT IT TO BE A SURPRISE! I'M GOING TO COME AND VISIT!' I suspected that somehow, against all odds, the ermines were going to come back. I thought it would be a really fitting end to the book – a total cliché really – to have it finish off with me seeing the ermine caterpillars again and the trees on which they once feasted resurrected from the dead. A metaphor for how, no matter how hard we try not to think about it, life sprouts once more from out of the ashes of death. Perfect, I'd thought.
And so here I was, back in Birchwood. As we headed off to get our coffee, Alison took us on a detour so that we could go past the site of last year's chaos. We walked for 10 minutes or so through and along the twisting paths over roads and between streets. A minute later Alison stopped suddenly and looked at me expectantly. 'Look around,' she said. I stopped. We were standing in the middle of a wide-open pedestrian walkway with rows of terraced houses to our left and to our right. 'This?' I said, slowly coming to terms with where we were stood. 'This... was it?' I squeaked. 'This is where the trees were?' 'Yep,' said Alison gravely. 'This is the walkway where the trees were.' It looked totally different. It seemed so open and light and sunny and... not green in any way. Just brightly lit tarmac and bricks really.
Alison pointed to the stumps. There they were. Four neat little tree stumps in what was once an avenue. Each stump had about a 30cm girth. I approached the nearest one and tried to count the rings but they had sadly weathered away. The stumps felt terribly wet. Waterlogged somehow. They were starting to rot. 'Come over here,' called Alison from up the street. 'Look at this one...' She stood in front of a stump which had a tiny sprig coming out of it. From out of the sprig a tiny leaf had sprouted. This single leaf almost seemed to suckle on the sun's rays that beat down upon it. That single leaf, powering a whole tree stump now. A tree with delusions of grandeur. I inspected the other tree trunks. Nothing. No other leaves at all. Just stumps. I was a tiny bit downcast at the sight of what Alison had brought me to inspect: an empty street with a single green leaf. No ermine caterpillars anywhere. I had misread Alison's communications. I realised my brilliant metaphor was bust. I spent about five minutes trying to take an arty photo of that single twig with a leaf coming out of it, but that didn't work out, either.
After a while I noticed that Alison had walked off down the street toward the coffee shop. I ran to catch her up, but she suddenly stopped before I got to her. She stopped underneath another tree. As I jogged toward her she turned round to me and pointed a single finger upwards into the branches above her head. An enormous smile crossed her face. Bloody hell, I thought. I caught her up and there it was. A single bird cherry tree had been forgotten about by the men with chainsaws. Within the branches above our heads were six apple-sized pockets of silk from which tiny caterpillars were due to emerge. A forgotten nook now bred life again. The caterpillars, like my metaphor, had pulled themselves from out of the ashes. I cannot tell you how amazing it was. It was a splendid thing to have seen. Splendid. We agreed to keep news about the ermines quiet, in case the housing association should fire up the chainsaws once more. I couldn't stop smiling about it, though. I smiled and smiled and smiled.
At the coffee shop I unloaded a little bit on Alison about everything I'd seen and researched and everyone I'd talked to on my journey into death. The spiders, the spider scare stories, the pigs, the ants, distressed donkeys, African penguins, snowy owls, the grotto salamander, the red kites. The lot. I talked about how, over months and months and months, I had discovered that humans were closer than ever to having the keys to the city: close to having something nearer to eternal life, closer to immortality. At the very least, I explained breathlessly, we could realistically expect to see lifespan altered artificially in our own lifetimes. Some of us may live healthy lives right into old age, I explained. 'The first person to live to 1,000 may already have been born,' I relayed quite proudly.
But I also expressed a tinge of sadness. I talked with her about my panic attack at the Anti-Ageing Show and how strange it had all been. 'By the end of my journey, I... I guess I got a little bit fed up with going on and on about death...' I admitted, honestly. Death really had taken me over for a while. Mourning, grieving, consciousness; our desperate attempts at holding out for just a few years longer. The scare stories. The extinction stories. The Dracula Therapy. It all got... it all got a bit much, I explained. Alison nodded. 'I get that feeling too sometimes,' she said. She paused, sipping her coffee. 'I don't know if everyone who studies death gets it, but I think you reach a point where you have to find a balance. I study death – the science of death, the societal and cultural interactions of death – but my everyday life is surrounded by, well, life,' she said a bit more perkily. I'd noticed that about her. She continued. 'Yes, I research death,' she agreed. 'But I'm much more interested in what that tells us about life.'
I mentioned to Alison about the leaf-cutting ants and how they fling the corpses of their nest-mates off the bottom of the nest into the chasm below. We talked about funeral plans. I asked her if she had any requests for what happens to her body after death. 'Ohhhh, I'm very much a supporter of green burials,' she said. 'You know, put me in a hessian bag, stick me in a nice field with some trees and some flowers. That sort of thing.' I asked her if she was ok with the mental image of her body being pulled apart by invertebrates. 'It's fine if animals want to eat me.' She shrugged. 'I don't have a sense of attachment to my remains. I would feel much more comfortable knowing that, in 50 years' time, my body has become a field of flowers,' she said quite breezily. I thought about this. 'I quite like the idea of a tree growing out of my head,' I said quietly. 'I quite like the idea of a horse chestnut tree's roots pulling apart my skeleton, draining my atoms from the soil to make conkers that my great grandkids can collect and keep on their windowsills.'
But, even still, as I said this to Alison, something deep within me coiled up when I pictured my decaying body lying there in the soil. Embarrassed, I told Alison about my horror at imagining my own body lying there. 'The idea of it...' I heard myself utter. 'The idea of my body lying there... decomposing. I don't know, it just makes me... uncomfortable,' I said. 'I just... I just don't like the thought of it. It's irrational, I know.' Alison smiled. 'Well, we're all irrational when it comes to death,' she said. We looked out of the window. 'I'm irrational too. The thing that I consider all the time is that I'm a Canadian living in a country where I'm not from. Ideally, if I die, I'd like to be buried where I'm from. But I probably won't be.' This sounded strange coming from a death professional like Alison. 'Why?' I asked. 'Why would that matter to you? After all, you'll be dead, right?' This came out much more bluntly than I had anticipated, so I immediately rephrased it. 'It's strange that you care,' I said. 'I do care...' said Alison, pausing for a moment. 'I care because I'm leaving the people I care about behind.' We finished up our coffees.
'We're seriously messed up, aren't we?' I said to Alison on the walk back. 'As a species, I mean. We have some serious issues about death, don't you think?' 'Go on...' she said. 'Well,' I continued. 'I've been messing about with this bloody book for so long and I can't help but feel that we have such trouble grasping the whole concept of it. We understand death on paper, sure, but... but we struggle.' We talked about my experience with the whole 'mourning' label and how people had often been very interested in my opinion of whether or not animals grieve or mourn. I explained my unprovable theory that actually I think we're quite lonely sometimes being the only animal to rationally and realistically be able to ponder our own mortality, and that this loneliness comes out in all sorts of weird ways. I expressed to Alison my belief that the ermine moth caterpillars had been victims of our itchy trigger finger when it comes to death; that they reminded us of death so much that they had freaked us out and they had had to go. We talked about the spiders and maggots.
In fact, the more we walked, the more I think all of my thoughts just seemed to somehow pour out of me. It turned into a bit of a diatribe, and looking back I am very sorry that Alison had to hear it all without me having time to organise my thoughts a little more. I couldn't stop talking about death. 'Death strips our self-worth from us,' I said at one point. 'It makes our lives meaningless. I think the weirdness we have about death is an emergent property of our impressive cognition, and that sometimes we struggle with that and that's why death terrifies us.'
Alison listened patiently and then she offered up her own opinion on death, which was far more succinct than my own. 'If we didn't have this weirdness surrounding death,' she said, 'then we might be totally different as a society.' She paused for a few moments, making sure I took it in. 'I mean, if we didn't give a shit about death, then...' She raised her eyebrows, and shook her head. 'I don't know... that's what being human is all about, isn't it?' Ahh. Perhaps it really is as simple as that, I thought. Perhaps the best expression of being human and being alive in modern times is to be a bit weird about death. I think Alison was totally right. In a funny sort of way, I have come to really like that about many humans that I know. Many of my friends and family are very irrational, and completely spooked by their own mortality, and I wouldn't want to change that. I wouldn't want to change that... much.
**Epilogue: The Meaning of the Loa Loa**
The extraordinary noise caused by the horses' hoofs makes the fishes issue from the mud, and excites them into combat. These yellowish and livid eels, resembling large aquatic snakes, swim at the surface of the water, and crowd under the bellies of the horses and mules. The struggle between animals of so different an organisation affords a very interesting sight...
So wrote Alexander von Humboldt in his account of his 1799 to 1804 travels in South America.
The eels, stunned by the noise, defend themselves by repeated discharges of their electrical batteries, and for a long time seem likely to obtain the victory. Several horses sink under the violence of the invisible blows which they receive in the organs most essential to life, and, benumbed by the force and frequency of the shocks, disappear beneath the surface. Others, panting, with erect mane and haggard eyes expressive of anguish, raise themselves, and endeavour to escape from the storm which overtakes them.
Von Humboldt's words are graphic and almost haunting in their brutality. There is a dramatic style about these sentences which Darwin himself (in The Voyage of the Beagle) is said to have emulated. His observations of electric eels doesn't end there, either. On the fate of the horses he continues:
A few, however, [...] gain the shore, stumble at every step and stretch themselves out on the sand, exhausted with fatigue, and having their limbs benumbed by the electric shocks of the gymnoti [eels]. In less than five minutes two horses were killed. The eel, which is five feet long, presses itself against the belly of the horse, and makes a discharge along the whole extent of its electric organ. It attacks at once the heart, the viscera, and the cæliac plexus of the abdominal nerves. It is natural that the effect which a horse experiences should be more powerful than that produced by the same fish on man, when he touches it only by one of the extremities. The horses are probably not killed, but only stunned; they are drowned from the impossibility of rising amid the prolonged struggle between the other horses and eels.
Nature is savage. Savage and brutal and devastating in its apparent efficiency. Brutal in its chaos. Brutal, gory, visceral. Animals die by strangulation, through the ingestion of poisons, via venomous fangs and spines, through suffocation, starvation and evisceration; the fact that electrocution finds itself on the list of ways to die really comes as little surprise. But humans are brutal too. For the electrocution of horses described above was a staged act, undertaken by Indians to show von Humboldt, at his request, how the locals fished for eels. Once the electric eels had lost their charge after wasting it all on the horses, the fishermen entered the water and pulled them out with their hands. Simple as that. Nature is brutal, but more brutal are the humans that enact such horrors knowingly.
I am aware that suffering and death, whatever the cause, is a problem for many nature-lovers on a personal, religious and philosophical level. So gruesome can be the reality of nature that many, including Darwin, have seen their faith challenged through observations of the apparent pernicious barbarism that abounds there. In an 1860 letter to the American naturalist Asa Gray, Darwin famously questioned how an all-knowing and caring God would create parasitic ichneumonid wasps. He wrote: 'There seems to me too much misery in the world... I cannot persuade myself that a beneficent and omnipotent God would have designedly created the Ichneumonidae with the express intention of their feeding within the living bodies of caterpillars, or that a cat should play with mice.'
David Attenborough has his own version of the ichneumonid: the loa loa – a nematode transmitted to humans through fly bites. The worm makes its way through connective tissue and occasionally drills its way out of eyeballs. The loa loa has become Attenborough's philosophical weapon of choice when attacked by creationists for failing to credit God with his documentaries' many natural wonders. 'What God would create a loa loa?' Sir David asks with (what I imagine to be) a patient and good-natured grin.
I'm not sure where I stand on God now that my book is finished. I have never been very good at debating with others God's existence, to be honest with you. I get too sweaty when particularly enthusiastic religious people pepper me with probing philosophical questions and, often, an enormous big itchy rash creeps up my neck which everyone seems to spend a great deal of time staring at, which only serves to make it worse and even more itchy. I occasionally find myself bringing up the thorny subject of the loa loa in those discussions that I do have. From scientifically minded religious people I am often met with a response that natural selection is God's process for getting things moving on Earth. A kind of cosmic terraforming event He has planned to prepare a world in which we humans can live, even if it does take billions of years to really get going. To subscribers of this particular worldview, nematode worms, flies that infest livestock with their maggots, cloaca-burrowing mites and ichneumon wasps are simply emergent noise in this God machine. Software bugs (and sometimes literally they are bugs) that can't be removed without the whole system breaking down, which would expose the mind of the Creator who is desperate to remain hidden to make us show faith that he exists as a way to prove to Him that we all love him which is actually a very complicated and strangely self-conscious thing for Him to want from us that I've never understood.
Anyway. For me, in my early academic years, the existence of such creatures as the loa loa did make me question any faith I once had. But perhaps, for a while, I went too far the other way. I relished the brutal acts of nature as a means to display openly to others what I believed was the type of world in which we live. Tennyson's 'red in tooth and claw' became, for me, a Darwinian war cry. It was a badge of honour; a way to fit in with the scientific reality in which I had found myself in my twenties. A way to fit in with fellow academics, too.
But now, over the years and after writing this book, I have softened a little. For me now, nature isn't a brutal place. It isn't only a place red in tooth and claw. It's not only a place of death. To me nature has become a place of wild and unthinking possibility; a maker of diversity, variation and incessant creation. And death? Death is the process through which more life is created. New species owe their life to it. Existing species are sustained by it. Extinct species are remembered by it. Schrödinger asked 'What is Life?' With death, the answer seems quite simple to me now. Mostly death is what you make of it; an understanding through which we might make better use of the time we have.
One of my many worries about this book being published now that I am at the end is that someone accuses me of downplaying the nastiness and the suffering and the pain and the gore from which we, and all things, have sprung; the realities of which play out each day. Gore. Blood. Entrails. Extinction. Cancer. Pain. Loss. I have mentioned all these things in this book, but perhaps not enough. Conversely, you might have noticed how many times parasites have been mentioned. Why? Because we are so often troubled by the thought of them, as Darwin was. What Darwin didn't appreciate is that we are all parasites. Parasites of life. Parasites within food webs. Parasites of the sun or of deep-sea ocean vents. We all take stuff, make stuff, and give it back in a more accessible chaotic doggy-bag for the universe in a wide range of forms: hot air, through our faeces, or through our own stinking corpses when we fail to balance the gerontological books properly. We are all agents of chaos, equal in our aims. All of us. And that's worth celebrating.
Occasionally I am invited to give talks to audiences about evolution and how natural selection works. I babble on about this and that whilst showing slides of the Great Tree of Life; I talk about slugs, jellyfish, fruit bats, duck genitalia, peacock spiders, deep-sea wars between giant squid and sperm whales, and I talk about how lucky we are to be alive at a time where all these wonders can be studied and understood. I talk about how much we still have to understand about nature; the colours and songs of non-bird dinosaurs, for instance, the last universal common ancestor of all living things, where and how slug mites have sex, and the many unusual things to do with ageing outlined in this book. And then I talk about how far we've come as a grassland-adapted primate that came (mostly) good; a grassland ape that became us. Human.
Once, at the end of a talk, a young boy came up to me, looking rather solemn. The Tree of Life was up on the presentation screen. He looked at it and quietly asked me something. He mumbled it. 'What's the point?' he said. I couldn't quite hear... 'Sorry?' I said. 'What's the meaning of it all?' he asked again. I stuttered and coughed and bumbled on about natural selection and this and that and, well, totally failed to give a good enough response and the young boy walked away with a bit of a weak smile. I have always regretted not giving a better answer. Now, finishing this book I realise what I should have said. He asked where the meaning was in life and I should have said that he was one of the most privileged human beings on the planet because, unlike most, he gets to find the meaning. He gets to choose the meaning. He gets to do something meaningful with his life. I think if we all found meaning in our lives, we'd probably find ourselves dying a bit better. For me, science gives me that meaning. And I am now planning for a good death.
Human life is too short. For many of us it will always be too short. For many of us it will always be too short no matter how much we manage to manipulate it and no matter how much money we throw at the problem. That problem will always remain: where is the meaning? I hope you can choose it well. I really hope you find out.
Acknowledgements
Almost every word of every sentence that appears in this book is, in some way, down to someone else; particularly the scientists and 'death professionals' offering their time, allowing me to be part of their interesting and important research, but also those who helped in other ways through direction and comments on the text. I am enormously grateful to them all for their time and they are named here together. They are (in no particular order): Rhiannon Bates and Dave Clarke (ZSL, London Zoo), Carla Valentine (Barts Pathology Museum), Megan Rosenbloom (Death Salon), Paul Butler, Peter Cross, Louisa Preston, Becky Wragg Sykes, Anne Hilborn, Jonathan Green, Sue Armstrong, Ben Hoare, Alan Stubbs, Jolle Jolles, Melissa Harrison, Bruna Bezerra, John Walters, Paul Stancliffe, Simon Leather, John Hutchinson, Andrew Whitehouse and Jo Gilvear (Buglife), Chris Cathrine, Chris Faulkes, Alex Thornton, Andrew Dawes, Lloyd and Rose Buck, Adam Hart and Stace Fairhurst, Faith Burden and Suzi Cretney, Ben Garrod, Ed Yong, Matthew Cobb, Darren Naish, Kane Brides, Phil 'Lash' Ashton, Ben and Jane Barlow, Lawrence Foster, Katherine Allen, Kathy Wormald, Silviu Petrovan, Matthew Oates, Richard Jones, Richard Fox, Amin Khan (www.aminart.co.uk) and Marsha Day (and everyone at Clipston Book Club!). And 'John' of false widow spider fame. And, of course, an enormous thank you to my deathsplainer, Alison Atkin.
This book couldn't have come about without Nick Lane's fantastic books, Oxygen: The Molecule That Made the World (2002), Power, Sex, Suicide: Mitochondria and the Meaning of Life (2005) and the brilliant Life Ascending: The Ten Great Inventions of Evolution (2009). Read them. They are wonderful.
Enormous thanks must also go to my editor at Bloomsbury, Jim Martin. Even though Jim was uneasy at times about commissioning a book about death, he stuck with it. Jim's a brilliant editor and a lovely person, which helps in every way when you're writing a difficult book like this. Thanks also to the rest of the Bloomsbury family: Laura Brooke, Anthony LaSasso, Jacqueline Johnson, Debbie Robinson, Lucy Clayton and Julie Bailey among them, along with many others too. Enormous thanks to Liz Drewitt (natureedit.com) for all of her incredibly helpful comments and edits. Also a special thank you to Anna MacDiarmid at Bloomsbury for steering the project through its final stages. My literary agent Jane Turnbull, like Jim, was never anything but supportive. Thank you.
A great deal of this book was written in Market Harborough library – such a quiet and warm place (we are enormously privileged to have libraries, please use them!). Thank you to all of the staff there, particularly Emily Warren. Thank you to Ruth Kent, my faithful and very supportive cuttings editor. And an enormous thank you too to Sam Goodlet for her fantastic chapter headers (you can find out more about Sam at www.samdrawsthings.co.uk).
The 'What's the point?' anecdote given about the young person in the epilogue is a true story (it's actually happened to me more than once) but the response I should had given didn't come to me courtesy of my own ruminations. It came to my mind because of a similar anecdote I had once heard about Carl Sagan, who apparently encouraged young people to 'choose something meaningful to do with their lives' when they asked such questions. It's a touching response (my advice: if you want to live forever, be like Carl Sagan).
Thank you to my mum and dad for all their love and never-ending support. Thank you so much for everything. You've taught me so much about life and death. Thank you. And final thanks must go to my wife, Emma, who has offered me so much love and kindness and not once wrinkled her nose when I came home (only a few times) stinking of death. It's not easy being married to a penniless writer, but somehow she puts up with it. Thank you, thank you, thank you. We found meaning in life together and every part of this life has been made wonderful through you. I love you to death... and back. x
Index
adipocere here–here
Age Reversal Fund here
ageing here–here
anti-ageing industry here–here
free radicals here–here, here–here, here, here, here
gerontogenes here–here
starvation here–here
albatross, Laysan here–here
Alzheimer's disease here, here
amphibians here–here
Angell, Tony Gifts of the Crow here–here, here–here
Animal Behaviour here
Anning, Mary here
antechinus here–here
Anti-Ageing Show, Olympia, London here, here–here, here, here, here
antioxidants here–here, here–here, here
ants, leaf cutting here, here–here
disposing of their dead here–here
shitatites here–here
apoptosis here–here
Arctica islandica here
Atkin, Alison here–here, here, here–here, here–here, here, here–here, here, here–here
Attenborough, Sir David here
Audubon, John James here–here
Bachman, John here–here
bacteria here–here, here, here
baculovirus here–here
Barja, Gustavo here
bats here, here–here
BBC here, here, here
bdelloid rotifers here
bees here
Benchley, Peter Jaws here
bezoars here–here
biomass here, here
Birchwood, Warrington here–here, here–here, here, here, here
BirdLife International here
birds here–here, here–here
brain function here, here
interaction with dead birds here–here
bivalves here, here
blowflies here–here
bluebottles here, here–here
body farms here–here
bones 48. here
brain function here–here
brine shrimps here
brown recluse spider here–here
Buck, Lloyd and Rose here–here
Buckland, William here–here
Buddle, Chris here
Buglife here, here, here, here, here
Burden, Faith here–here
Butler, Paul here–here
butylated hydroxytoluene (BHT) here
Bwlch Nant yr Arian here
Caenorhabditis elegans here–here
Calico (California Life Company) here
calories here–here
calorie restriction here–here, here
Campbell, Sir Menzies here
cancer here, here–here, here, here
carrion beetles here–here
caspases here–here, here
cataracts here, here, here
cats here, here–here, here–here
centipedes here
chaos here–here
cheese flies here–here, here–here
cheetahs here–here, here, here
chequered beetles here
children here–here, here–here, here–here, here–here
spiders here–here
chimpanzees here–here
Clostridium botulinum here
clothes moths here
clown beetles here
cockatoo, Major Mitchell here
conservation here–here
corvids here–here, here, here, here–here, here, here–here
CPR here, here
Cretney, Suzi here–here
Cross, Peter here–here, here, here–here, here
crows here–here, here–here
Simba here–here
cryptobiosis here
cyanobacteria here–here
Daily Mail here, here
Daily Star here
Darwin, Charles here, here
On the Origin of Species here–here
The Expression of the Emotions in Man and Animals here–here
The Voyage of the Beagle here
De Grey, Aubrey here, here–here
death here–here, here–here, here–here, here–here
death and reproduction here–here, here–here
definitions here–here
human disposal of the dead here–here, here–here
human mourning here
science of death here–here
Death Salon here–here, here–here, here, here
decomposition here–here, here–here, here–here
bacteria here–here, here
fungi here, here
insect activity here–here, here–here
maggots here–here
marine life here–here
smell here–here, here
Democritus here
Descartes, René here
Devil's coach-horse beetles here
diclofenac here
dinosaurs here–here
disgust here–here, here–here
expression here–here
pathogen avoidance here–here
smell here–here
spiders here–here
Disney here–here, here
DNA here, here
ageing here–here, here
free radicals here
naked mole rats here
dogs here, here–here, here
dolphin, Maui's here
Donkey Sanctuary, Sidmouth here–here
donkeys here–here
dung beetles here
ecosystems here, here, here, here–here
electric eels here–here
elephants here–here
Ellison, Larry here–here
Elton, Charles here–here
Empedocles here–here
ermine caterpillars here–here, here–here, here, here, here, here–here
evolution here–here, here–here
Experimental Gerontology here
extinction here–here, here–here, here–here, here–here
mass extinctions here–here
faeces here, here–here
bats here–here
coprolites here–here
guano here–here
whales here–here
Fairhurst, Stace here–here, here–here, here
false widow spider here–here, here–here, here
Faulkes, Chris here–here
fertilisers here, here–here
Haber-Bosch process here
Fisher, Diana here
flesh here–here, here
food chains here, here, here–here
food webs here, here, here–here, here, here
Forbes here
forensics here–here, here–here
fossils here–here, here–here, here, here
foxes here–here, here–here
free radicals here–here, here–here, here
freezer specimens here
Frog Helpline here–here, here, here, here
Froglife here
funeral industry here–here
fungi here, here
Fusobacterium here
gerontology here–here, here–here, here
God here–here
Goldman, Steven here
Goodall, Jane here
Google here
Gould, Stephen Jay The Wheel of Fortune and the Wedge of Progress here
Gray, Asa here
ground beetles here
guano here–here
Guardian here, here
Haber, Fritz here
hagfish here–here
Harman, Denham here–here, here
Hart, Adam here–here
harvestmen here
Heinrich, Bernd Life Everlasting here
Henson, Jim here
Hilborn, Anne here–here, here–here, here–here
horrid ground-weaver here–here, here–here, here–here
hummingbirds here, here
Hutchinson, Evelyn here–here
Hydra here–here, here
Independent here–here
IUCN here, here
jay, western scrub here–here
jellyfish here–here, here, here, here
Johnson, T. J. Pieter here–here
Joyce, James here
Khan, Aamer here–here
Kirkwood, Tom here
kites, red here–here, here–here
persecution here–here
reintroduction here
Kubota, Shin here, here
Lane, Nick Life Ascending here, here, here
Oxygen here
Laurenson, Karen here
Leather, Simon here–here
lemmings here–here, here–here, here
life here, here–here
definitions here–here
life on Mars here, here–here
what is life? here–here
what is the point of life? here
lifespans here, here, here–here, here–here, here–here, here, here, here
C. elegans here–here
Lindeman, Raymond here–here
Linnaeus, Carl here–here
loa loa here–here
longevity here–here, here–here, here–here
Lorenz, Konrad King Solomon's Ring here
maggots here–here
disgust here–here, here–here
Malthus, Thomas Essay on the Principles of Population here
Margaritifera margaritifera here–here
Mars here, here–here
Martinez, Daniel here
Marzluff, John Gifts of the Crow here–here, here–here
McCarthy, James here–here
Medawar, Peter here–here, here–here
mercury pollution here
Ming here–here, here, here–here, here
Mirror here
mitochondria here, here, here–here, here, here–here, here, here
mole rats, naked here–here, here
disposing of their dead here–here
mosquitoes here
Moss, Cynthia here–here
mourning here–here, here–here, here–here
chimpanzees here–here
crows here–here
domestic animals here–here
donkeys here–here
elephants here–here
western scrub jays here–here
YouTube here–here
MRS GREN here
mussel, pearl here–here
Mutschmann, Frank here–here
National Health Service (NHS) here
Natural History Museum, London here
natural selection here–here, here–here
Nature here
nematode worms here–here
loa loa here–here
neurons here
neurogenesis here–here
New York Times, The here
Newton, Sir Isaac here, here
niches here, here, here, here, here, here
noble false widow spider here–here, here–here, here
Nottebohm, Fernando here
octopuses, reef here–here
Oracle here–here
otters here–here
owls, snowy here–here
Page, Larry here
parasites here–here, here, here
parasites as predators here–here
parasitic wasps here–here, here
toxoplasmosis here–here
pathogen avoidance here–here
PayPal here
penguins, African here–here, here, here–here
Philipp, Eva here
phobias here
pigeons here, here
Playfair, Lyon here
polychaete worms here
Preston, Daniel L. here–here
Preston, Louisa here–here
puffins here
pyramids of numbers here, here, here
quahog, ocean here, here
Radford Quarry, Plymouth here, here–here, here
rattail fish here
reproduction here
death and reproduction here–here, here–here
octopuses here–here
spiders here–here
rockfish, copper here–here, here, here
Roman, Joe here–here
rove beetles here–here, here–here
Rozin, Paul here–here
Rüppell, Eduard here
salmon, Pacific here
sockeye here
Santa Cruz Basin here
Schrödinger, Erwin What Is Life? here–here, here, here, here, here
Second Law of Thermodynamics here–here
semelparity here–here
senescence here–here
SENS (Strategies for Engineered Negligible Senescence) Research Foundation here, here
sepsids here
Sex on Earth here–here, here–here, here
sexton beetles here–here
Shakespeare, William Coriolanus here
The Winter's Tale here
shark, sleeper here
Shell Oil here
sirtuins here
skin beetles here
smell here–here, here
TAARs (trace amine-associated receptors) here–here
snotworms here
social wasps here
souls here
spiders here, here–here
bad press here–here
brown recluse spider here–here
horrid ground-weaver here–here, here–here, here–here
suicidal mating here–here
spirit here, here
Stewart, Potter here
suicide here
cell suicide here–here, here
lemmings here–here, here–here
spiders here–here
TAARs (trace amine-associated receptors) here–here
'tar-babying' here
Tennyson, Alfred Lord here
termites here–here
thermodynamics here–here
Thiel, Peter here
Thornton, Alex here–here, here, here
Times, The here
Tithonus here
toads here–here, here, here, here
toad patrollers here–here, here–here
Toxoplasmosis gondii here–here
TRACES here–here, here, here
trees here–here
Trichodesmium here–here
trophic levels here–here, here
Turner, William here
Turritopsis here
Vetter, Rick here–here
viruses here–here
Von Humboldt, Alexander here, here–here
Von Liebig, Baron here
vultures here–here
decline of Old World species here–here
digestive adaptations here
finding food here–here
Waltner-Toews, David The Origin of Faeces here
Warrington Guardian here
wasps, parasitic here–here, here
social here
Waterton, Charles here–here
whale pumps here–here
White Wilderness here–here
Wilkinson, Benjamin Joel here
Williams, George C. here–here
Wired here, here
Worm, Ole here
worms here, here, here–here, here–here
Caenorhabditis elegans here–here
death fluorescence here–here
WWF (World Wildlife Fund) here
yeast here, here–here
Yong, Ed here
YouTube here–here
Zimmer, Carl Parasite Rex here
zombie-worms here
Ermine caterpillars wield silk like a shield. This allows the caterpillars beneath to continue 'farming' the tree safely protected.
Western scrub jays respond in predictable ways to the sight of their dead. (a) mock–feathers; (b) a dead bird; (c) stuffed owl; (d) stuffed bird.
Nature at its most brutal: Loa Loa, a tiny worm known to infect eyeballs.
Pacific salmon are perhaps the most arresting example of semelparity. Hundreds of thousands die each year within days of spawning.
Elephants: our most celebrated animal mourner. But what, really, do they know of death?
A yellow–footed antechinus mouse. All twelve species in the marsupial genus _Antechinus_ practice semelparity. Males invest nothing in body maintenance and everything in sperm.
Cookie, a male Major Mitchell's cockatoo residing at Brookfield Zoo, Chicago, is the oldest bird in captivity. Cookie hatched from his egg in 1933.
Insect nutrients re–packaged within bat guano for human use.
150 million–yearold fossilised faeces, probably from an ichthyosaur.
A riot of rove beetles. Diverse, colourful, oftoverlooked.
Even riddled with free–radical damage, naked mole rats can live 30 years.
Caterpillars aren't agents of death ... they harbour new life. Within the cocoons spun on this hornworm, adult parasitic wasps are readying.
Common toads: thousands are squashed by cars on their long migrations to breeding ponds. Conservationists generally meet such losses with sadness. But were the lives of these toads wasted? Ask the scavengers, who make such losses their personal gain.
The googly–eyed rockfish ... post-cataract. Fish age like we do.
Dead frogs, post–copulation: victims of evolutionary and ecological circumstance.
_Hydra_ exist in most freshwaters across the world. Their stem cells show impressive capabilities for regeneration. Could we one day make use of their genetic trickery to influence our own ageing process?
Red kites, like vultures, offer a valuable death–removal service. They have been clearing up after us for thousands of years.
BEHOLD, THE OLDEST ANIMAL IN THE WORLD. Ming (inset) died at the ripe old age of 507 years. In the background, an Icelandic sea–floor packed with quahog shells.
Bloomsbury Sigma
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BLOOMSBURY and the Diana logo are trademarks of Bloomsbury Publishing Plc
First published 2016
Copyright © Jules Howard, 2016
Jules Howard has asserted his right under the Copyright, Designs and Patents Act, 1988, to be identified as Author of this work.
All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage or retrieval system, without prior permission in writing from the publishers.
Photo credits (t = top, b = bottom, l = left, r = right, c = centre)
Colour section: P. 1: Ullstein bild / Getty Images. P. 2: Teresa L. Iglesias (A, B, D) and Gail L. Patricelli (C) (t); BSIP Ducloux/ Brisou/ Science Photo Library (cl); RedTC/ Shutterstock (bl). P. 3: Beverly Joubert / Getty Images (t); Auscape/ UIG/ Getty Images (b). P. 4: Steve Russell/ Contributor/ Getty Images (t); Thierry Falise/ Contributor/ Getty Images (b). P. 5: Jules Howard (tr); Katarina Christenson/ Shutterstock (tl); Tomatito/ Shutterstock (cl); Kurt_G/ Shutterstock (bl); Henrik Larsson/ Shutterstock (cr,br). P. 6: Chicago Tribune/ Getty Images (t); / Shutterstock (cl); CreativeNature, R. Zwerver/ Shutterstock (bl). P. 7: Vancouver Aquarium Marine Science Centre (t); Silviu Petrovan/ Froglife (www.froglife.org) (cr); Barcroft/ Contributor/ Getty Images. P. 8: Barcroft/ Getty Images (t); Erlendur Bogason (b); Bangor University (inset)
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ISBN (hardback) 978-1-4729-1507-8
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ISBN (ebook) 978-1-4729-1510-8
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1. Cover
2. Half-Title
3. Series
4. Dedication
5. Title
6. Contents
7. Introduction
8. PART 1: THIS IS A DEAD FROG
1. 1 Life and Death in the Universe
2. 2 Senescence and What Waits for the Lucky Few
3. 3 Fear and Loathing in Birchwood
4. 4 Free Radicals and the Secrets Within
5. 5 This is a Dead Frog
9. PART 2: THE EXPERIMENTAL PIG PHASE
1. 6 The Circus under the Tent
2. 7 Sex and Death: The Contract Killer
3. 8 Coffee with the Widow-maker
4. 9 Suicide, Snowy Owls and the Executioner Inside
5. 10 This is Not a Sheep
6. 11 The Grotto Salamander and the Guano
7. 12 The Horrid Ground-weaver
8. 13 Dark Matters
10. PART 3: JOURNEY TO THE END OF THE SHITATITE
1. 14 Bring out your Dead Ants
2. 15 Mourning has Broken
3. 16 Who Wants to Live Forever?
4. 17 No, This is a Dead Frog
11. Epilogue: The Meaning of the Loa Loa
12. Acknowledgements
13. Index
14. Plates
15. Copyright
|
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is palm oil bad in skincare
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"Palm oil can be produced without having to ravage the environment, wildlife, or exploit farmers, but it is such a widely used ingredient that many … But did you know that according to the World Wildlife Fund, an area the equivalent size of 300 football fields of rainforest is cleared each hour to make way for palm oil production? In addition, our suppliers are in a select group of international NGO's and leading producers including the WWF and Rainforest Action Network that form the Palm Oil Innovation Group (POIG). So the key is to halt the use of palm products, and in the meantime use responsibly-grown palms that do not require deforestation. While we expect palm oil to remain part of the beauty industry, we want to do our part to reduce our dependence on it and help reduce beauty's environmental footprint. "Palm oil can be produced without having to ravage the environment, wildlife, or exploit farmers, but it is such a widely used ingredient that many companies, big and small, sometimes don't know where their palm oil originated from, or perhaps how much deforestation had to take place for that palm oil to get to them," said David Petrillo, cosmetic chemist and founder of skin-care brand Perfect Image. By signing up, I agree to the Terms & to receive emails from POPSUGAR. Can I sell Essential's products in my salon? Most palm oil comes from tropical regions in Southeast Asia. Rapeseed (brassica capestris sterols) is fabulous for skin and hair. Although we are moving away from palm products as quickly as possible, the palm products and palm oil we do use are sourced from the best available options. All of our palm suppliers collaborate with Greenpeace International (one of the suppliers was voted the #1 sustainable palm oil producer) and the Forest Trust. This leads to impressively destructive deforestation as palm farmers simply burn down rainforest to clear land. Have you changed your formulas? "This is occurring because, in products, there could be palm oil, but in derivative form. Q: Why can't I see my product review on your website? Q: Essential Wholesale is proud to announce that we are now a Leaping Bunny certified facility! http://awsassets.panda.org/downloads/palm_oil_innovators_group_poig_launch_statement_june2013.pdf, Your email address will not be published. Q: Can I Get my Label on your Skincare Sample Sets? Harvesting palm oil and other palm products can destroy whole ecosystems and produce smoke-based pollution. Happily there are a few reliable sources for sustainable palm oil. Find out what nutritionists say about palm oil and if it's healthy. To help you in your selection, we have begun indicating every product that is palm-free on our site. This devastates habitats and burns animals, like the already endangered orangutan, alive. Creating Custom Skincare Products – What to Expect from Your Manufacturer, Creating Custom Skincare Products Part 2 – Developing Your Bill of Material. Yahoo is part of Verizon Media. By now you probably know that palm oil is considered unsustainable and that its harvest and production have a devastating impact on our environment. Sign up for our Fashion & Beauty newsletter. Organic mango and shea butters are good alternatives, as are organic jojoba oil and sunflower oil. To enable Verizon Media and our partners to process your personal data select 'I agree', or select 'Manage settings' for more information and to manage your choices. Palm products in themselves are not destructive, but the method of growth and harvest is, and new land is constantly needed to plant new trees. This is a long process, but in the meantime you can read our ingredient decks and see if an item has any palm in it. Figuring out whether you're about to purchase a product with palm oil — which is used in cosmetics for its moisturizing, texturizing, emollient, and foaming effects, plus its ability to remove oil and dirt from the hair or skin — can prove tricky, but there are a few things to look out for. Palm oil is derived from the fruit of oil … There are lists of these other names online for palm oil or its derivatives, but it is a huge list.". Further, the palm industry is linked to major environmental issues including habitat degradation, climate change, animal cruelty, smoke-based pollution, child-labor, indigenous rights abuses and endangering species that rely on the rainforest, including orangutans, Sumatran tigers, elephants and birds. "There are organizations that certify palm oil as sustainable around the world, but many people question whether they are doing enough and whether companies are meeting past commitments to protect the environment and the species that live there.". Please select the topics you're interested in: Would you like to turn on POPSUGAR desktop notifications to get breaking news ASAP? Q. Find out more about how we use your information in our Privacy Policy and Cookie Policy. We and our partners will store and/or access information on your device through the use of cookies and similar technologies, to display personalised ads and content, for ad and content measurement, audience insights and product development. "Liquid oils can be alternatives; these can include grapeseed oil, sunflower oil, coconut oil, babassu oil, or soybean oil," he said. the full list of customer questions and our answers. Palm is in many, many food and skincare products on your grocer store shelves. What does that mean for us and for you? Q: Why is Essential no longer accepting returns? There are new ingredients listed in many products. Some of the more common names in cosmetics include Sodium Laureth Sulfate, Glyceryl, and Octyl palmitate. Palm oil and palm kernel oil are used in lotions, cremes, washes, serums and gels. Our buyers search high and low to find great palm-free options, only to find that something we were 'told' was coconut actually contained palm when we reviewed the technical specs, something we are rigorous about.
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{
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ACCEPTED
#### According to
Index Fungorum
#### Published in
Monogr. Biol. Soc. Pakistan 7: 162 (1978)
#### Original name
Aleurina pakistanica S. Ahmad
### Remarks
null
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{
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Life after Brexit
Inspirational women 'virtually projected' onto Cromarty Lighthouse Field Station
Images of women who have worked and studied at the University's Lighthouse Field Station in Cromarty are being 'virtually projected' onto the Lighthouse to celebrate their contribution to science, research and teaching there.
We are extremely proud of the work we do at the field station and feel privileged to follow in the footsteps of these inspirational women, as well as having such a wealth of nature on our doorstep. " Barbara Cheney, Research Fellow at the Field Station
The virtual screening can be viewed online and highlights a selection of the more than 120 women that have contributed to the field station since it opened in 1990.
The University of Aberdeen Lighthouse Field Station, in the small coastal community of Cromarty, celebrates over 30 years of teaching and research on the ecology of marine mammals and northern fulmars with an online exhibition shining a spotlight on the inspirational women who have worked and studied there over the years.
Since 1990 the Lighthouse Field Station has provided a Highland base for marine biologists from the University and research carried out on the ecology and conservation of marine top predators has impacted on the way scientists from all over the world understand and manage marine ecosystems.
In its short history, the research coming out of the field station has impacted on marine conservation projects all over the world. Recently, the team has led an interdisciplinary study to investigate the consequences of offshore windfarm construction on marine mammal populations, with the results used to reduce the impact on marine mammals and inform windfarm developments worldwide. More locally, early research on bottlenose dolphins on the east coast of Scotland underpinned the creation and management of the Moray Firth Special Area of Conservation to protect this small population. This study has shown that the bottlenose dolphin population is increasing, and recent research has provided rare evidence of increasing reproduction and early survival in wildlife using a marine protected area.
As part of the University's wider International Women's Day 2021 celebrations, the profiles of women who have worked and studied at the field station will be highlighted weekly on their website and are virtually screened onto the front of the Lighthouse.
The team at Cromarty linked up with International Women and Girls in Science Day to launch the screening on February 11 this year with the aim to inspire young women to pursue a career in science by highlighting the research and teaching at the Lighthouse.
Barbara Cheney, Research Fellow at the Field Station, who is curating the project explains: "We are extremely proud of the work we do at the field station and feel privileged to follow in the footsteps of these inspirational women, as well as having such a wealth of nature on our doorstep.
"Since the field station was established women have been integral to our teaching, research and conservation projects and this is something that we want to celebrate in the hope that it will inspire more women into science and conservation.
"International Women's Day and International Day of Women and Girls in Science are perfect opportunities for us to spotlight some of the many women who have driven the science, research and teaching at the Lighthouse Field Station for over 30 years and hopefully into the future.
"To learn more about the women who have come through the doors of the Lighthouse, the role this has played in their career paths and their advice for future scientists please visit our website https://www.abdn.ac.uk/lighthouse/staff/women-in-science/ , and stay tuned to Twitter @CromartyLH and Facebook @lighthousefieldstation for weekly updates."
The University will hold a programme of online events for International Women's Day from Monday 8 – Saturday 13 March including keynote speakers; Anna Whitehouse, Trailblazing, straight-talking best-selling author, presenter, campaigner, and co-founder of 'Mother Pukka', and Jeffery Tobias Halter, gender strategist, author and president of YWomen.
Virtual screening
Cromarty Field Station
IWD 2021 at the University
The Communications Team
Directorate of External Relations, University of Aberdeen, King's College, Aberdeen
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{
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Ormskirk and Burscough Police want to speak to the man in the CCTV after a woman in her seventies had her purse stolen at M&S in Ormskirk. At around 1.30pm, on Monday, 8 October, a man walked into the store and followed several older women round. When one of them was distracted for a moment he took her purse which was in her handbag on her trolley. He then also took items from the shop before leaving without paying.
Ormskirk and Burscough Police want to speak to the man in the CCTV in connection with what happened – we know the quality isn't the best but we think it's important to post them as part of the investigation and also to act as a warning for people to be vigilant. If you have older relatives or friends please, please remind them to be careful with their personal belongings and valuables and to keep them as safe as possible in closed bags.
In this case, a card from the purse was later used both locally and in Liverpool so if you have friends or relatives in Merseyside, please share this post with them. If you have any information at all, please e-mail 2615@lancashire.pnn.police.uk quoting reference SB1805636.
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{
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Screen Recorder Free No Ads v1.1.5.7 Full APK is an application help you simple Record Screen and Take Screenshot anyplace.
You should go to security – >choose authorization – > consent – > Screen Recorder and turn on fly up window. Development, you go to security – > Permission – > AutoStart – > turn on Screen Recorder.
+ Support spare a video in SD Card or anything area which you need.
+ Please clean cache and data of the app if you have a problem after updating.
0 Response to "Screen Recorder Free No Ads v1.1.5.7 Full APK"
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{
"redpajama_set_name": "RedPajamaC4"
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| 6,811
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{"url":"http:\/\/www.chegg.com\/homework-help\/questions-and-answers\/what-is-ionization-energy-why-are-the-second-and-subsequent-ionization-energies-higher-tha-q3472706","text":"## Chemistry Study Question\n\nWhat is ionization energy? Why are the second and subsequent ionization energies higher than the first ionization energy? i will rate this question later on","date":"2013-05-19 11:10:33","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8147944808006287, \"perplexity\": 1394.9136568072895}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2013-20\/segments\/1368697420704\/warc\/CC-MAIN-20130516094340-00058-ip-10-60-113-184.ec2.internal.warc.gz\"}"}
| null | null |
Komposition är ett begrepp inom musiken som kan syfta på dels ett musikverk och dels på handlingen att komponera musik.
Komposition – musikverk
Begreppet har uppstått inom den västerländska konstmusiken och förutsatte att skapande konstnärer noterade sina verk. I nutida språkbruk används begreppet även för icke noterad musik, d.v.s. musik som endast existerar i klingande form, som levande musik eller på fonogram.
Termen kommer av latinets componere, 'ställa samman' 'ordna', och innebar ursprungligen att man kompletterade gregorianska melodier med fler stämmor till en flerstämmig sats. Ur denna praxis föddes ett regelsystem som kom att innebära att en komposition skulle vara resultatet av personlig originalitet och musikalisk hantverksskicklighet.
Komposition – att komponera
Komposition är konsten att skriva musik. Detta kan betyda flera saker, men avser i allmänhet att på något sätt planera och nedteckna vissa förutbestämda aspekter av ett musikaliskt flöde. Man kan skilja kompositionen från improvisationen, som inte är planerad i förväg. Komposition syftar till att skapa melodier och notskrift med instruktioner till musiker genom handskrift eller numera speciella datorprogram via olika slags vedertagna symbolsystem. Vissa personer skriver musik genom att provspela melodier på ett piano, en gitarr eller annat instrument, medan andra skriver likt en författare direkt vid ett skrivbord utan användning av instrument.
För det mesta används traditionell notskrift, men inom främst elektroakustisk musik och viss experimentell så kallad konkret musik används olika grafiska specialformer, ibland med notskriften formad som grafisk bildkonst. Under 1900-talet har inom den konkreta musiken även särskilda matematiskt baserade kompositionsformer vuxit fram med annorlunda tonskalor, särskilda instrumentvarianter och serier av halvtoner, kvartstoner etc i till exempel tolvtonsmusik, atonal musik i motsats till traditionell harmonisk melodiskt baserad musik Dessa moderna experimentformer har ofta stått i ett motsatsförhållande till den traditionella melodiformen, då de mer syftar till ett vetenskapligt utforskande av existensen och ljudvärlden som fenomen.
Yrkesformer
Det är vanligt att dela in personer som skriver musik i två grupper:
Kompositör eller tonsättare, som oftast är utbildade och mycket insatta i olika former av musikteori, akustik och estetik, behärskar flera stilgrepp och tekniker som kontrapunkt, och instrumentation. De kommunicerar med främst likaledes utbildade musiker via någon form av den etablerade moderna notskriften, eller skapar elektroakustisk musik (EAM). Begreppet tonsättning används inte minst i betydelsen att "sätta toner" till ett diktverk eller annan text.
Låtskrivare, som ofta också är sångtextförfattare och ibland själv framför och spelar in skivor med sin egen musik. Dessa är ofta självlärda och arbetar med delvis improviserade gehörstraderade arrangemang.
Dessutom används beteckningen arrangör när en musikmänniska (ofta en kapellmästare eller dirigent) arrangerar om ett tidigare komponerat verk till en ny form, för andra instrument, ensemblesammansättningar eller genrer, alternativt transponerar en komposition till en annan tonart. Man kan också för konsertbruk sätta ihop delar av befintliga verk till samlade potpurrier, eller inom viss modern populärmusik göra liknande sammansatta samplingar eller omarrangerade remixar. För att (särskilt förr) skriva ut och kopiera en kompositörs notskrift används ofta särskilda assistenter till sådant tidskrävande arbete, även om detta numera oftast görs via maskinkopiering. Det samma gäller när ett orkesterverks samlade partitur ska fördelas på separat utskrivna stämmor för olika instrument eller sångare. Det finns även exempel på tonsättare utan egen kunskap inom notskrivande eller orkestrering, varför en särskild arrangör anlitas för att genomföra detta praktiska arbete efter tonsättarens anvisningar.
Musikskapande kan också ske kollektivt eller improviserat, framför allt i ensembler inom till exempel jazz, populärmusik och världsmusik. Inom klassisk musik är det mer ovanligt, med undantag som kvartetten We Like We. All komponerad musik har inte alltid en tradition av notation utan lagras i musikernas minne och överförs mer från musiker till musiker, inte ovanligt inom till exempel folkmusik. Tonsättare kan ibland även ge utrymmen för musikernas egna personliga improvisationer i delar av verken. Detta blev inom klassisk musik vanligt under 1700-1800-talens virtuosepok, där olika instrumentalister och sångare (till exempel violinisten Niccolò Paganini) kunde bli vida kända för sina speciella tillkomponerade improvisationer, kadenser. Detta slags improvisationsutrymme förekommer i dag främst inom jazzmusikformerna.
Kompositionsutbildning i Sverige
I Sverige finns renodlade tonsättarutbildningar vid musikhögskolorna i Göteborg, Malmö, Piteå och Stockholm. Musiklärarutbildning med inriktning mot komposition finns vid Musikhögskolan Ingesund, i Piteå samt i Malmö. På Musikhögskolan i Örebro finns påbyggnadsutbildningar i komposition.
De ämnesansvariga lärarna vid tonsättarutbildningarna bär titeln professor i komposition. För närvarande (2010) innehas professurerna av Ming Tsao i Göteborg, Luca Francesconi i Malmö, Jan Sandström i Piteå och Karin Rehnqvist i Stockholm.
Källor
Typer av musikstycken
Musikproduktion
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Johnny talks to Adam Carolla 09.13.18.
We're pretty sure that Adam Carolla doesn't sleep.
He saw success as co-host of "Love Line" and "The Man Show"...but he's gone on to release numerous books, hosting shows like "To Catch A Contractor", appearing on "Celebrity Apprentice". hosting his daily podcast...and NOW he's launched his own damn channel on the streaming service Pluto TV that's decdicated to cars, motorcycles, racing, vintage cars and all things motor, simply called "Chassy"!
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{
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Petr Hubáček (* 2. září 1979, Brno) je bývalý český profesionální hokejista, naposledy hrající českou nejvyšší soutěž Tipsport extraligu za tým HC Dynamo Pardubice. Nastupoval na pozici levého útočníka.
Hráčská kariéra
Petr Hubáček zahájil svou extraligovou kariéru v roce 1998 v týmu Vítkovic, v letech 2000–2002 se nepříliš úspěšně pokoušel prosadit v severoamerické NHL (odehrál pouze 7 zápasů za Philadelphia Flyers). V roce 2002 se vrátil do Vítkovic, kde se postupně vypracoval na jednu z opor týmu.V roce 2008 přestoupil do týmu KHL, po následující sezóně se vrátil zpět do České republiky. V roce 2010 přestoupil do brněnské Komety. V průběhu sezóny 2011/2012 odešel do nejvyšší finské ligy a s klubem JYP Jyväskylä získal mistrovský titul. Od roku 2005 pravidelně nastupoval v české hokejové reprezentaci, s níž vybojoval v letech 2006–2011 všechny tři cenné kovy na mistrovství světa.V roce 2014 ukončil svoji reprezentační kariéru. V sezóně 2017/2018 hrál nejvyšší francouzskou hokejovou soutěž v týmu Rouen Dragons, se kterým získal mistrovský titul.
Osobní život
Po ukončení profesionální kariéry v roce 2018 začal působit jako hokejový expert v České televizi, například spolukomentuje Mistrovství světa v ledním hokeji. S manželkou má dceru a syna.
V Prostějově působil od roku 2021 jako skills kouč a od sezony 2022/2023 bude působit jako asistent hlavního trenéra.
Ocenění a úspěchy
2004 ČHL - Nejtrestanější hráč v playoff
Prvenství
ČHL
Debut - 8. září 1998 (HC Vitkovice proti HC Železárny Třinec)
První asistence - 11. září 1998 (HC Velvana Kladno proti HC Vitkovice)
První gól - 10. září 1999 (HC Vitkovice proti HC Femax Havířov, brankáři Pavlu Cagašovi)
NHL
Debut - 5. října 2000 (Philadelphia Flyers proti Vancouver Canucks)
První gól - 5. října 2000 (Philadelphia Flyers proti Vancouver Canucks, brankáři Felix Potvin)
Klubová statistika
| 1997–98
| HC Kometa Brno
| 1.ČHL
| 48
| 6
| 10
| 16
| 22
| —
| —
| —
| —
| —
|-bgcolor="#f0f0f0"
| 1998–99
| HC Vitkovice
| ČHL
| 25
| 0
| 4
| 4
| 2
| 4
| 0
| 0
| 0
| 0
|-
| 1998–99
| HC Kometa Brno
| 1.ČHL
| 9
| 1
| 5
| 6
| 10
| 6
| 2
| 3
| 5
| 6
|-bgcolor="#f0f0f0"
| 1999–00
| HC Vitkovice
| ČHL
| 48
| 11
| 12
| 23
| 85
| —
| —
| —
| —
| —
|-
| 2000–01
| Philadelphia Phantoms
| AHL
| 62
| 3
| 9
| 12
| 29
| 9
| 0
| 1
| 1
| 6
|-bgcolor="#f0f0f0"
| 2000–01
| Philadelphia Flyers
| NHL
| 6
| 1
| 0
| 1
| 2
| —
| —
| —
| —
| —
|-
| 2001–02
| Philadelphila Phantoms
| AHL
| 22
| 1
| 6
| 7
| 8
| —
| —
| —
| —
| —
|-bgcolor="#f0f0f0"
| 2001–02
| Milwaukee Admirals
| AHL
| 14
| 2
| 0
| 2
| 2
| —
| —
| —
| —
| —
|-
| 2002–03
| HC Hamé Zlín
| ČHL
| 44
| 4
| 15
| 19
| 14
| —
| —
| —
| —
| —
|-bgcolor="#f0f0f0"
| 2002–03
| HC Vitkovice
| ČHL
| 7
| 1
| 4
| 5
| 10
| 6
| 1
| 0
| 1
| 16
|-
| 2003–04
| HC Vitkovice
| ČHL
| 46
| 7
| 14
| 21
| 26
| 6
| 1
| 0
| 1
| 53
|-bgcolor="#f0f0f0"
| 2004–05
| HC Vitkovice
| ČHL
| 51
| 13
| 11
| 24
| 38
| 9
| 0
| 1
| 1
| 33
|-
| 2005–06
| HC Vitkovice Steel
| ČHL
| 52
| 17
| 23
| 40
| 46
| 6
| 1
| 0
| 1
| 2
|-bgcolor="#f0f0f0"
| 2006–07
| HC Vitkovice Steel
| ČHL
| 49
| 17
| 19
| 36
| 62
| —
| —
| —
| —
| —
|-
| 2006–07
| SC Bern
| NLA
| —
| —
| —
| —
| —
| 5
| 0
| 2
| 2
| 2
|-bgcolor="#f0f0f0"
| 2007–08
| HC Vitkovice
| ČHL
| 40
| 10
| 7
| 17
| 89
| —
| —
| —
| —
| —
|-
| 2008–09
| CHK Neftěchimik Nižněkamsk
| KHL
| 35
| 3
| 6
| 9
| 8
| —
| —
| —
| —
| —
|-bgcolor="#f0f0f0"
| 2008–09
| HC Vitkovice
| ČHL
| 5
| 1
| 0
| 1
| 2
| 10
| 4
| 6
| 10
| 6
|-
| 2009–10
| HC Vitkovice
| ČHL
| 37
| 10
| 19
| 29
| 6
| —
| —
| —
| —
| —
|-bgcolor="#f0f0f0"
| 2009–10
| HC Kometa Brno
| ČHL
| 13
| 1
| 3
| 4
| 8
| —
| —
| —
| —
| —
|-
| 2010–11
| HC Kometa Brno
| ČHL
| 47
| 7
| 12
| 19
| 52
| —
| —
| —
| —
| —
|-bgcolor="#f0f0f0"
| 2011–12
| HC Kometa Brno
| ČHL
| 27
| 4
| 4
| 8
| 32
| —
| —
| —
| —
| —
|-
| 2011–12
| JYP
| SM-l
| 30
| 5
| 9
| 14
| 6
| 14
| 1
| 6
| 7
| 2
|-bgcolor="#f0f0f0"
| 2012–13
| JYP
| SM-l
| 29
| 5
| 10
| 15
| 8
| 11
| 1
| 3
| 4
| 4
|-
| 2013–14
| JYP
| Liiga
| 50
| 10
| 12
| 22
| 14
| 7
| 3
| 1
| 4
| 6
|-bgcolor="#f0f0f0"
| 2014–15
| JYP
| Liiga
| 60
| 8
| 16
| 24
| 14
| 12
| 4
| 6
| 10
| 2
|-
| 2015–16
| JYP
| Liiga
| 57
| 4
| 12
| 16
| 12
| 13
| 2
| 2
| 4
| 2
|-bgcolor="#f0f0f0"
| 2016–17
| HC Dynamo Pardubice
| ČHL
| 48
| 8
| 9
| 17
| 26
| —
| —
| —
| —
| —
|-
| 2017–18
| Dragons de Rouen
| LM
| 38
| 4
| 7
| 11
| 14
| 15
| 0
| 3
| 3
| 2
|- bgcolor="#e0e0e0"
! colspan="3" | Celkem v NHL
! 6
! 1
! 0
! 1
! 2
! —
! —
! —
! —
! —
|}
Reprezentace
Premiéra v reprezentaci: 11. dubna 2000 Česko–Slovensko (Žilina).
| 2006
| Česko
| MS
|9||1||0||1||6
|-bgcolor="#f0f0f0"
| 2007
| Česko
| MS
|7||0||0||0||2
|-
| 2010
| Česko
| MS
|9||2||0||2||0
|-bgcolor="#f0f0f0"
| 2011
| Česko
| MS
|9||0||2||2||2
|-
| 2013
| Česko
| MS
|8||0||4||4||4
|-bgcolor="#e0e0e0"
! colspan="3" | Seniorská kariéra celkově
!42!!3!!6!!9!!14
|}
Reference
Externí odkazy
Rozhovor s Petrem Hubáčkem na www.idnes.cz.
Čeští hokejoví útočníci
Čeští hokejoví reprezentanti
Hráči Philadelphia Phantoms
Hokejisté Milwaukee Admirals
Hokejisté KHL
Hokejisté Nationalligy A
Hráči HC Kometa Brno
Hráči Philadelphia Flyers
Mistři světa v ledním hokeji
Narození 2. září
Narození v roce 1979
Narození v Brně
Žijící lidé
Muži
Hráči draftovaní Philadelphií Flyers
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,381
|
Tiburon (Haïtiaans Creools: Tibiwon) is een stad en gemeente in Haïti met 23.000 inwoners. De plaats ligt op de westelijke punt van het gelijknamige schiereiland Tiburon, 72 km ten noordwesten van de stad Les Cayes. De gemeente maakt deel uit van het arrondissement Chardonnières in het departement Sud.
Er wordt voornamelijk cacao verbouwd. Verder is er industriële verwerking van hout en koffie.
Indeling
De gemeente bestaat uit de volgende sections communales:
Stad in Haïti
Gemeente in Sud (Haïti)
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 2,614
|
Biografia
Nata a Urbino, figlia di un maresciallo dei carabinieri, vive a Bologna.
Ha partecipato al Festival di Sanremo 1971 interpretando, in abbinamento con Edda Ollari, il brano L'ora giusta, che per un solo punto non è stato ammesso alla serata finale. In seguito per qualche tempo si dedicherà all'attività di fotomodella.
Discografia
Singoli
1971 – L'ora giusta/Pioggia (Dischi Ricordi, SRL 10634)
1971 – Io non so vivere/Col cuore (Dischi Ricordi, SRL 10650)
Bibliografia
Eddy Anselmi, Festival di Sanremo. Almanacco illustrato della Canzone Italiana, 2009, ed. Panini, Modena, alla voce Visconti Lorenza pag. 939
Collegamenti esterni
Gruppi e musicisti delle Marche
Partecipanti al Festival di Sanremo
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,920
|
Martha Hooper Blackler Kalopothakes (, Blackler; June 1, 1830 – December 16, 1871) was a 19th-century American missionary to Greece. She was also a journalist and translator. Kalopothakes died in 1871.
Biography
Martha Hooper Blackler was born in Marblehead, Massachusetts, June 1, 1830. She was the daughter of Captain Francis Blackler. Having been converted early in life, she felt a deep interest in the cause of missions.
In 1858, she married Rev. Michael Demetrius Kalopothakes (Μιχαήλ Δ. Καλοποθάκης; 1825–1911), M.D. of Athens, who had spent several years in the United States studying medicine and theology. After graduating as a Calvinist and Reformed theologian from the Union Theological Seminary, New York City, he returned, accompanied by his wife, as a Protestant missionary to his native land. They had at least one child, a son, Francis Demetrius Kalopothakes (b. 1867).
Kalopothakes became so proficient in the Greek language that she was able to correct the proof-sheets of the Star of the East, a weekly paper published by her husband who was the founder of the Greek Protestant church. She translated books from the English and wrote articles for the Child's Paper, published also in Greek, and aided him in his correspondence with friends in England and the U.S. Though naturally somewhat timid, her gentle disposition and devotion to her work drew the people to her, and her influence was widely felt among the Greek women. But her excessive labors affected her health so seriously that it became necessary for her to return with her husband and children to the U.S. for a brief respite. In August. 1871, she sailed again for her missionary field, but died in Athens, December 16, 1871, after a few months of labor.
References
Attribution
Sources
1830 births
1871 deaths
19th-century American non-fiction writers
19th-century American women writers
19th-century American newspaper editors
American Protestant missionaries
Female Christian missionaries
Protestant missionaries in Greece
Translators from English
People from Marblehead, Massachusetts
Calvinist and Reformed writers
19th-century Calvinist and Reformed Christians
Women newspaper editors
19th-century American translators
Missionary linguists
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,662
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\section{Introduction}
Fiber-reinforced composites are ubiquitous in aerospace, automotive, mechanical, and light-weight civil structures due to their high strength-to-weight ratios, good fatigue performance, and design flexibility. However, it is well known that composite structures are susceptible to matrix cracking, delamination, and fiber breakage. If left unchecked, these damage modes can accumulate and cause catastrophic failure. For structures in safety-critical applications such as aircraft and bridges, this may result in significant loss of life. Therefore, damage must be inspected and preventive measures taken before it reaches a critical level.
Traditional damage tolerant design approaches that rely on intermittent inspections via nondestructive evaluation (NDE) often prove insufficient for composites due to the complexity of their damage initiation and growth mechanisms. Structural health monitoring (SHM) \citep{sohn2003review, lynch2007overview} is a promising complement to traditional NDE as it allows for continuous, real-time monitoring of damage initiation and growth in composite structures. Conventional SHM methodologies rely on the use of external sensors to monitor the condition of the structure. Three common categorizations of conventional SHM are vibration-based SHM, guided wave-based SHM, and embedded sensor-based SHM.
Vibration-based SHM \citep{carden2004vibration, montalvao2006review} monitors changes in the modal parameters of the structure such as natural frequencies, mode shapes, and curvature changes. These methods have been used to detect delaminations \cite{zou2000vibration, valdes1999delamination} and matrix cracks \cite{kessler2002damage} in composite plates and also in circular cylindrical composite shells \cite{ip2002locating}. Guided wave-based SHM \cite{mitra2016guided, raghavan2007guided, croxford2007strategies} uses ultrasonic wave propagation to detect the presence of damage. The waves are dispersed or attenuated when they encounter a flaw or a crack. The most common types of waves used for detecting cracks and delaminations include Lamb waves \cite{su2006guided, paget2003damage} and Rayleigh waves \cite{chakrapani2014interaction, hughes2019comparative}. Embedded sensor-based SHM uses discrete sensors integrated within the structure to monitor its condition. The most common types of sensors used for composites are strain gauges \cite{ajovalasit2011advances, zike2014correction, zhou2017strain}, fiber-optic sensors \cite{leung2005delamination, lee2018distributed, ramakrishnan2016overview, leng2003structural}, and piezoelectric sensors \cite{giurgiutiu2011structural, kalhori2017inverse}.
Although conventional SHM methodologies are more widely used, they have certain limitations. Vibration-based SHM, for example, is often not sensitive enough to detect small-sized defects. Both guided wave-based and embedded sensor-based SHM require physical integration of the sensors and actuators within the structure which can sometimes weaken the material. Another overarching limitation is that these methods only provide localized, discrete, and often limited information about the condition of the structure. Consequently, recent research focus has shifted toward the development of composites with intrinsic self-sensing properties to alleviate the limitations of conventional SHM.
Self-sensing composites possess one or more properties that allow them to `sense' changes to their mechanical, thermal, or chemical state. That is, the material itself functions as a sensor. In this area, nanofiller-modified composites have received considerable attention \cite{li2019review, costa2017high, stassi2014flexible, groo2020laser, groo2021fatigue}. These materials exhibit changes in their electrical behavior due to deformations and damage. This self-sensing property, known as piezoresistivity, has been extensively studied for SHM in combination with conductivity-based spatial imaging techniques such as electrical impedance tomography (EIT) because this combination allows for the mapping of mechanical effects through conductivity changes.
Beyond just allowing for spatial mapping of mechanics in self-sensing composites, EIT has recently emerged as a potential SHM modality because it is low-cost, non-invasive, and has nearly real-time imaging capabilities. Broadly speaking, and as summarized in \citep{tallman2020structural}, EIT has been used for SHM in intrinsically and extrinsically self-sensing composites. Intrinsically self-sensing composites incorporate conductive nanofillers in the polymer matrix. For such materials, EIT has been used for detecting through-holes \cite{tallman2015damage}, impact damage \cite{gallo2016spatial}, matrix cracking \cite{dai2016novel}, delaminations \cite{haingartner2020improved}, and UV radiation damage \cite{rastogi2021structural, clausi2019direct} in composites incorporating carbon nanotubes (CNTs) \cite{dai2016novel}, carbon nanofibers (CNFs) \cite{tallman2017inverse, tallman2014damage, hassan2020failure,hassan2020comparison}, and carbon black (CB) \cite{tallman2015damage}. Although most research has focused on thin plates, there has been some work in using EIT for damage detection in non-planar structures as well \cite{thomas2019damage, jauhiainen2021nonplanar}. Extrinsically self-sensing composites do not incorporate nanofillers but make use of externally applied sensing media. In this area, EIT has been used for detecting strain and damage in composites using nanofiller-based thin films \cite{hou2007spatial, hou2007electrical} and paints \cite{lestari2016sensing, loyola2013spatial}. Aside from composites, EIT has been used extensively for detecting damage due to holes \cite{gupta2017self, nayak2019spatial}, cracks \cite{smyl2018detection}, and moisture flows \cite{hallaji2015electrical} in self-sensing cementitious materials \cite{hallaji2014electrical, hallaji2014new}.
From the preceding discussion, it is clear that EIT can effectively detect and localize numerous damage modes in self-sensing materials. However, a critical limitation is that it provides little-to-no information about precise damage shape, size, or mechanism. This information is crucial for accurate prognostication of structural health. For example, if the precise size and location of a delamination can be ascertained, structural failure can be predicted and averted. Herein, we recognize the opportunity to address this limitation and advance the state-of-the-art in SHM of self-sensing composites. We propose a novel methodology for precisely determining damage shape and size from electrical measurements in self-sensing composites. Our unique approach uses a genetic algorithm (GA) to inversely compute damage geometry based on imaged conductivity changes and boundary voltage measurements. We experimentally investigate the potential of this approach on two damage mechanisms---through-holes and delaminations---in CNF-modified GFRP laminates.
The remainder of this manuscript is organized as follows. First, we mathematically formulate the EIT forward and inverse problems. Second, we present and formulate the GA-enabled damage shaping problem. Third, we describe the composite manufacturing procedures. Fourth, we discuss the electrical, through-hole, and impact testing procedures. Fifth, we present the EIT results along with the results from our GA-enabled damage shaping methodology and discuss their significance. Finally, we end with a brief summary, conclusions, and possible paths for future work.
\section{Electrical Impedance Tomography}
\subsection{Forward Problem}
As discussed earlier, EIT is a non-invasive method of imaging the internal conductivity distribution of a domain. EIT works by minimizing the difference between a vector of experimentally measured voltages and a vector of voltages computed numerically. The experimental voltage collection procedure is illustrated in Figure \ref{eit-injection}. The domain to be imaged is lined with electrodes. Current is injected between the first pair of electrodes and voltage differences are measured between the remaining electrode pairs. The current injection is then moved to the next electrode pair and voltage differences are again measured between the remaining electrode pairs. This process is repeated until all electrode pairs have received one current injection and a vector of \(L(L-3)\) voltage differences has been obtained, where \(L\) is the total number of electrodes.
\begin{figure}
\centering
\includegraphics[width=0.75\textwidth]{figures/eit-image.png}
\caption{Illustration of first and second current injection and voltage measurement schemes. The periphery of the domain is instrumented with electrodes, indicated by the red rectangles. Current is injected between the first pair of electrodes and voltage differences are measured between the remaining electrode pairs. The current injection is then moved to the next electrode pair and voltage differences are again measured. This process repeats until all adjacent electrode pairs have received a current injection.}
\label{eit-injection}
\end{figure}
The numerical voltages are computed by solving the EIT forward problem. To formulate the forward problem, consider Laplace's equation for steady-state diffusion in the absence of internal current sources. This is shown in equation (\ref{eq1}), where \(\sigma\) is the internal conductivity of the domain and \(\phi\) is the domain potential. We enforce two complete electrode model boundary conditions on equation (\ref{eq1}). The first boundary condition, shown in equation (\ref{eq2}), assumes a voltage drop across the electrodes due to the contact impedance between the domain and the electrodes. The second boundary condition, shown in equation (\ref{eq3}), enforces conservation of charge. In these equations, \(z_l\) is the contact impedance between the \(l\)th electrode and the domain, \(\boldsymbol{n}\) is an outward pointing normal vector, \(E_l\) is the length of the \(l\)th electrode, and \(V_l\) is the voltage of the \(l\)th electrode.
\begin{equation}\label{eq1}
\nabla\cdot\sigma\nabla\phi=0
\end{equation}
\begin{equation}\label{eq2}
\phi + z_l\sigma\nabla\phi\cdot\boldsymbol{n}=V_l
\end{equation}
\begin{equation}\label{eq3}
\sum_{l=1}^{L}\int_{E_l}\sigma\nabla\phi\cdot\boldsymbol{n} \hspace{3pt} \mathrm{d}S_l=0
\end{equation}
Equations (\ref{eq1}) to (\ref{eq3}) are often solved via the finite element (FE) method, as shown in equation (\ref{eq4}). In this equation, \(\boldsymbol{\Phi}\) is a vector of domain potentials, \(\boldsymbol{V}\) is a vector of electrode voltages and \(\boldsymbol{I}\) is a vector of injected currents. The matrices \(\boldsymbol{A_M}\), \(\boldsymbol{A_Z}\), \(\boldsymbol{A_W}\), and \(\boldsymbol{A_D}\) are formed as shown in equations (\ref{eq5}) to (\ref{eq8}), where \(N_i\) is the \(i\)th FE basis function. For an explicit solution to these equations for linear elements, interested readers are directed to \citep{tallman2020structural}.
\begin{equation}\label{eq4}
\begin{bmatrix}
\boldsymbol{A_M} + \boldsymbol{A_Z} & \boldsymbol{A_W} \\
\boldsymbol{A_W^T} & \boldsymbol{A_D}\\
\end{bmatrix}
\begin{bmatrix}
\boldsymbol{\Phi}\\
\boldsymbol{V}
\end{bmatrix}=
\begin{bmatrix}
\boldsymbol{0}\\
\boldsymbol{I}
\end{bmatrix}
\end{equation}
\begin{equation}\label{eq5}
A^e_{M \hspace{3pt} ij} = \int_{\Omega_e}\frac{\partial N_i}{\partial x_k} \sigma_{kl} \frac{\partial N_j}{\partial x_l} \hspace{3pt} \mathrm{d}\Omega_e
\end{equation}
\begin{equation}\label{eq6}
A_{Z\hspace{3pt} ij} = \sum_{l=1}^L \int_{E_l}\frac{1}{z_l} N_i N_j \hspace{3pt} \mathrm{d}S_l
\end{equation}
\begin{equation}\label{eq7}
A_{W \hspace{3pt} li} = -\int_{E_l}\frac{1}{z_l} N_i \hspace{3pt} \mathrm{d}S_l
\end{equation}
\begin{equation}\label{eq8}
A_D = \text{diag}\bigg(\frac{E_l}{z_l}\bigg)
\end{equation}
\subsection{Inverse Problem}
The goal of the EIT inverse problem is to recover the conductivity distribution of the domain interior using the measured and numerically computed boundary voltages. Herein, we will make use of a one-step linearization scheme to solve the inverse problem. This involves collecting a set of pre-damage voltages, a set of post-damage voltages, and then finding the conductivity change distribution that minimizes the difference between the two sets of voltages. We begin by defining the vector \(\delta\boldsymbol{V}\) as the difference between voltages collected at times \(t_2\) and \(t_1\), as shown in equation (\ref{eq9}).
\begin{equation}\label{eq9}
\delta\boldsymbol{V} = \boldsymbol{V}(\sigma_2,t_2) - \boldsymbol{V}(\sigma_1,t_1)
\end{equation}
Next, we define an equivalent numerical vector, \(\boldsymbol{W}(\delta\boldsymbol{\sigma})\), as shown in equation (\ref{eq10}). Here, \(\boldsymbol{F}(\cdot)\) represent the voltages computed by solving the forward problem at the conductivity in the argument, \(\boldsymbol{\sigma_0}\) is the baseline or undamaged conductivity, and \(\delta\boldsymbol{\sigma}\) is the conductivity change vector we seek. The boldfaced symbols indicate vector quantities that have been discretized via finite elements.
\begin{equation}\label{eq10}
\boldsymbol{W}(\delta\boldsymbol{\sigma}) = \boldsymbol{F}(\boldsymbol{\sigma_0} + \delta\boldsymbol{\sigma}) - \boldsymbol{F}(\boldsymbol{\sigma_0})
\end{equation}
We then linearize the first term on the right-hand side of equation (\ref{eq10}) using a Taylor series expansion about \(\boldsymbol{\sigma_0}\) and retain only the linear terms, as shown in equation (\ref{eq11}).
\begin{equation}\label{eq11}
\boldsymbol{F}(\boldsymbol{\sigma_0} + \delta\boldsymbol{\sigma}) \approx \boldsymbol{F}(\boldsymbol{\sigma_0}) + \frac{\partial \boldsymbol{F}(\boldsymbol{\sigma_0})}{\partial \boldsymbol{\sigma}}\delta\boldsymbol{\sigma}
\end{equation}
Substituting equation (\ref{eq11}) into equation (\ref{eq10}) and defining \(\boldsymbol{J}\) = \(\partial \boldsymbol{F}(\boldsymbol{\sigma_0})/\partial\boldsymbol{\sigma}\) as the sensitivity matrix yields equation (\ref{eq12}). The one-step linearized inverse problem then seeks the conductivity change, \(\delta\boldsymbol{\sigma}^*\), that minimizes the difference between \(\boldsymbol{W}(\delta\boldsymbol{\sigma})\) and \(\delta\boldsymbol{V}\) in the constrained linear least squares sense, as shown in equation (\ref{eq13}).
\begin{equation}\label{eq12}
\boldsymbol{W}(\delta\boldsymbol{\sigma}) \approx \boldsymbol{J}\delta\boldsymbol{\sigma}
\end{equation}
\begin{equation}\label{eq13}
\delta\boldsymbol{\sigma}^* = \underset{\boldsymbol{-\sigma_0}\leq\delta\boldsymbol{\sigma}\leq0.01\boldsymbol{\sigma_0}}{\text{min}}\frac{1}{2}\Bigg(\Bigg|\Bigg|\begin{bmatrix}
\boldsymbol{J}\\
\alpha\boldsymbol{L}\\
\end{bmatrix}\delta\boldsymbol{\sigma} - \begin{bmatrix}
\delta\boldsymbol{V}\\
\boldsymbol{0}\\
\end{bmatrix}\Bigg|\Bigg|^2_2\Bigg)
\end{equation}
A regularization term, \(\boldsymbol{L}\), has been included in equation (\ref{eq13}) due to the ill-posed nature of the EIT inverse problem. Here, we will use the discrete Laplace operator as the regularization term. The amount of regularization is controlled by the scalar parameter \(\alpha\). Also, note that the search for \(\delta\boldsymbol{\sigma}^*\) is constrained. The constraints used here are based on realistic assumptions about the conductivity change. It is well understood that damage such as cracks, through-holes, and delaminations manifests as a decrease in conductivity. The maximum decrease that is physically possible has a magnitude equal to the baseline conductivity and we expect the maximum increase to be relatively small. Therefore, we use 100\% change for the lower bound and 1\% change for the upper bound. This is reflected in the limits shown in equation (\ref{eq13}).
\section{GA-Enabled Damage Shaping Problem}
As discussed earlier, EIT has been successfully used to detect various kinds of damage in self-sensing composites. However, due to the ill-posed nature of the inverse problem, the spatial resolution of EIT is somewhat indistinct inasmuch as precise geometric features of conductivity artifacts cannot be sharply reconstructed. Considerable research has aimed at developing methodologies for precise artifact shape reconstruction from EIT images \cite{liu2020shape, liu2020bool, fan2021new}. While these approaches are undoubtedly powerful, they are unaware of the underlying physics of the material and consequently cannot discern between various damage modes. Therefore, in order to accurately determine damage shape and size from EIT-imaged conductivity changes, specific damage mechanisms must be integrated with suitable inversion strategies.
The goal of the damage shaping problem presented here is to recover the geometry of specific damage modes from EIT-imaged conductivity changes and boundary voltages by building some knowledge about the damage physics into the shaping algorithm. However, recovering mechanics from electrical measurements is an ill-posed, multi-modal inverse problem. This is because there is no well-defined mathematical relationship between damage geometry and conductivity change. In the absence of a suitable inversion algorithm and realistic constraints on the search space, the search may converge to a locally optimum, non-physical solution. In order to address this problem we need a global search algorithm and constraints based on realistic damage physics.
Genetic algorithms (GAs) \cite{golberg1989genetic, mitchell1998introduction} are a family of global search algorithms inspired by natural evolution. GAs are widely used for optimizing multi-modal functions by generating and evolving a population of solutions dispersed inside a search space. The population of solutions evolves through a process analogous to natural selection. Herein, we do not aim to develop a new algorithm but to instead use a well-established GA to solve the multi-modal damage shaping problem. To that end, we will make use of a GA developed by WA Crossley and used by Raghavan et al. \cite{raghavan2008spectral} for jet engine turbine blade NDE.
In addition to a global search algorithm, we require geometric models that realistically describe how different damage modes affect material conductivity. These models will need to be integrated with the GA so that only physically viable solutions are generated and selected. We can now formulate the GA-enabled damage shaping problem. We begin by defining the vector \(\delta\boldsymbol{F}(s_{GA})\) as shown in equation (\ref{eq14}), where \(\boldsymbol{F}(\boldsymbol{\sigma}(s_{GA}))\) are the voltages predicted by solving the EIT forward problem for a domain containing damage described by the GA-generated parameter, \(s_{GA}\). This parameter describes the shape and location of a specific damage mode based on a geometric damage model.
\begin{equation}\label{eq14}
\delta\boldsymbol{F}(s_{GA}) = \boldsymbol{F}(\boldsymbol{\sigma}(s_{GA})) - \boldsymbol{F}(\boldsymbol{\sigma_0})
\end{equation}
The goal of the damage shaping problem then is to seek the optimum shape parameter, \(s_{GA}^*\), that minimizes the \(l_1\)-norm of the difference between \(\delta\boldsymbol{F}(s_{GA})\), given by equation (\ref{eq14}), and \(\delta\boldsymbol{V}\), given by equation (\ref{eq9}). This can be cast as the optimization problem shown in equation (\ref{eq15}). In this work, we will develop geometric models for two damage modes---through-holes and delaminations---and integrate them with the GA to solve equation (\ref{eq15}). These models are described later in \S\ref{results_and_discuss}.
\begin{equation}\label{eq15}
s_{GA}^* = \underset{s_{\text{min}} \leq s_{GA}\leq s_{\text{max}}}{\arg\min} (\underbrace{|\delta\boldsymbol{V} - \delta\boldsymbol{F}(s_{GA})|_1}_{f})
\end{equation}
In the above equation, the parenthetical term is the fitness function, \(f\). During a single search, as the population of solutions evolves, \(f\) decreases and finally attains a stable value. This occurs when the candidates in the population have achieved a certain level of genetic similarity. This is quantified as the bit-string affinity (BSA) and is a pre-specified value. When the BSA is achieved, further evolution ceases. The BSA is one of two convergence criteria that we will use herein. The second convergence criterion is the maximum number of generations. That is, after the population has evolved a pre-specified number of times, further evolution ceases. At this point the optimum solution, \(s^*_{GA}\), and minimum fitness function value, \(f^*\), are recorded and a second search initiates using updated values of \(s_{\text{min}}\) and \(s_{\text{max}}\). This is repeated until the following global convergence criterion is satisfied, where \(f_n^*\) is the minimum fitness function value obtained after the \(n\)th search.
\begin{equation}
|f_n^* - f_{n+1}^*| \leq 1\times10^{-3}
\end{equation}
At this point, no further searches are performed using the GA and the final solution attained is treated as the converged solution.
\section{Composite Manufacturing}
To experimentally validate the proposed GA-enabled damage shaping methodology, GFRP laminates with 1.0 wt.\% CNF-modified polymer matrices were manufactured based on the procedure described by Tallman et al. \cite{tallman2014damage}. The CNF-modified matrix was prepared by mixing epoxy resin (Fibre Glast 2000) with the appropriate amounts of Pyrograf III PR-24-XT-HHT CNFs (Applied Sciences), surfactant (Triton X-100), and acetone. Acetone aids mixing by lowering the viscosity and the surfactant facilitates dispersion of the CNFs by modifying the surface chemistry of the mixture. An epoxy-to-acetone volume ratio of 2:1 and a surfactant-to-CNF weight ratio of 0.76:1 were used. The modified epoxy was then mixed in a planetary centrifuge for 3 minutes and sonicated in a bath sonicator for 1 hour for every 10 g of the mixture. The bath sonicator operated at a power of 35 W and a frequency of 45 kHz. After sonication, the mixture was stirred on a magnetic hot plate stirrer for 24 hours at a temperature of 60 $^{\circ}$C and a stirring speed of 600 rpm. The epoxy was then allowed to cool to room temperature and hardener was added using an epoxy-to-hardener weight ratio of 100:27. Air release agent (BYK A-501) was also added using an air release agent-to-total mixture weight ratio of 0.001:1. The mixture was then stirred by hand for 5 minutes and degassed at room temperature for 20 minutes in a vacuum chamber.
Unidirectional glass fiber sheets (Fibre Glast Saertex) were impregnated with the degassed CNF-modified epoxy using hand lay-up to produce two 10" \(\times\) 10" laminates with stacking sequences of \([0/90]_{\text{s}}\) and thicknesses of 3 mm. We will refer to these as laminates 1 and 2. Both laminates were vacuum bagged and cured in an oven for 5 hours at 60 $^{\circ}$C. After curing, two square specimens measuring 3.25" \(\times\) 3.25" were cut from each laminate. using a water-cooled tile saw. This resulted in a total of four plate-like specimens, one of which is used for later through-hole tests and three of which are used for later impact tests. Additionally, ten smaller specimens measuring 0.25" \(\times\) 0.25" were cut out of the remaining material from the 10" \(\times\) 10" laminates for the purpose of measuring the average in-plane and through-thickness conductivity of each plate.
\section{Experimental Procedures}
\subsection{Electrical Testing}
The conductivities of CNF/GFRP were measured to estimate the baseline conductivity for EIT and also for the damage shaping algorithm. For this, conductivity measurements were collected from the ten 0.25" \(\times\) 0.25" specimens cut from each laminate. The conductivities of each square were measured in the principal (\(x\), \(y\), \(z\)) coordinate system, illustrated in Figure \ref{fig-cond-meas}. To measure the conductivity in the \(x\)-direction, electrodes were applied by painting colloidal silver patches on the faces of the square with normal vectors pointing in the \(\pm x\)-directions. The resistance, \(R\), between the electrodes was measured using a multi-meter and the conductivity was calculated as \(\sigma_x = l_x/RA_e\), where \(l_x\) is the length of the square in the \(x\)-direction and \(A_e\) is the area of an electrode. The conductivities in the \(y\)- and \(z\)-directions were measured similarly. The measurement scheme is illustrated in Figure \ref{fig-cond-meas} and the mean conductivities measured from both laminates are listed in Table \ref{tab-cond}.
\begin{figure}[h!]
\centering
\includegraphics[width=0.75\textwidth]{figures/cond-meas.png}
\caption{Illustration of conductivity measurement scheme and principal coordinate system. The ellipses represent the fiber cross-sections. Top: Schematic of a sub-section of the laminate showing the principal coordinate system and the layer orientations. Bottom: Conductivity measurement in the \(x\)-(left), \(y\)-(middle), and \(z\)-directions (right). The filled red rectangles represent electrodes on the front faces and the outlined red rectangles represent electrodes on the back faces.}
\label{fig-cond-meas}
\end{figure}
\begin{table}
\centering
\caption{Mean and standard deviations of conductivities in the \(x\)-, \(y\)-, and \(z\)-directions measured from laminates 1 and 2.}
\begin{tabular}{cccc}
\toprule
Laminate & \(\sigma_x\) [S/m] & \(\sigma_y\) [S/m] & \(\sigma_z\) [S/m] \\
\midrule
1 & \(0.024\pm0.003\) & \(0.023\pm0.004\) & \((3.5\pm1.8)\times10^{-4}\) \\
2 & \(0.054\pm0.003\) & \(0.057\pm0.004\) & \((5.6\pm2.2)\times10^{-4}\) \\
\bottomrule
\end{tabular}
\label{tab-cond}
\end{table}
\subsection{Through-Hole and Impact Testing}
The four 3.25" \(\times\) 3.25" specimens were used for through-hole and impact testing as follows. For the two specimens cut from laminate 1, one was used for through-hole testing and the other was impacted with 25 J. For the two specimens cut from laminate 2, one was impacted with 23 J and the other was impacted with 28 J. Note, however, that all specimens tested were made using the same procedure described above and used the same CNF weight fraction. In order to collect EIT data, electrodes were applied to each specimen by painting evenly spaced colloidal silver patches on each edge. Each specimen was then adhered to an acrylic base and additional colloidal silver patches were painted on the acrylic to act as extended electrode tabs. A representative specimen with electrodes painted is shown in Figure \ref{fig-specimen}. Each specimen was connected to a current source (Keithley 6221) and a DAQ system (National Instruments PXIe-6368) to measure the electrode voltages.
\begin{figure}
\centering
\subfloat{{\includegraphics[width=0.30\textwidth]{figures/spec1.jpg} }}%
\qquad
\subfloat{{\includegraphics[width=0.53\textwidth]{figures/spec3.jpg} }}%
\caption{Representative CNF/GFRP square laminate used for through-hole and impact testing. Left: Top-down view of laminate without electrodes. Right: Laminate with electrodes painted and adhered to acrylic base.}%
\label{fig-specimen}%
\end{figure}
For the through-hole testing specimen, a current magnitude of 0.25 mA was used. One set of voltages was collected from the specimen in its undamaged state. Next, three circular holes of radii 1.19 mm, 2.38 mm, and 3.18 mm were successively drilled and voltages were collected after drilling each new hole.
For the three impact testing specimens, the energies (23 J, 25 J, and 28 J) were chosen deliberately to induce a measurable delamination without completely perforating the specimens. A current magnitude of 0.25 mA was used for the 23 J and 28 J impact specimens while a current magnitude of 0.1 mA was used for the 25 J impact specimen. One set of voltages was collected from each specimen in its undamaged state. The specimens were then mounted on a 6" \(\times\) 4" aluminum plate with a centrally located 2" \(\times\) 2" window and impacted in a drop tower (CEAST 9340) using a steel hemispherical striking head with a diameter of 15.8 mm. Post-impact voltages were then collected from each specimen. All three specimens were then destructively evaluated in order to determine the true size and shape of the delaminations. This was done by making multiple cuts through each specimen using a water-cooled tile saw and examining the delamination length at the cross-section of each cut using a Zeiss Axioskop 2 MAT microscope. Several images along the length of the delamination at each cross-section were taken and were used to reconstruct the full delamination shape.
\section{Results and Discussion}\label{results_and_discuss}
\subsection{Through-Holes}
The mean conductivities measured from laminate 1, shown in Table \ref{tab-cond}, were used as the initial estimate for the baseline conductivity of the through-hole testing specimen. The initial estimate was then iteratively updated to find the optimal baseline conductivity that minimized the difference between the pre-damage voltages and the forward operator predicted voltages. Using this approach, the optimum in-plane baseline conductivities were found to be \(\sigma_{x0}\) = \(\sigma_{y0}\) = 0.025 S/m. EIT was then performed using this baseline on a mesh consisting of 5,670 linear triangular elements and the EIT-imaged conductivity changes are shown in the left column in Figure \ref{fig-eit-ga-holes}. It can be seen from Figure \ref{fig-eit-ga-holes} that EIT is able to successfully detect the presence of the holes. However, it provides little-to-no information about the precise shape and size of each hole. This information must be indirectly inferred from the magnitude of the observed conductivity change. That is, a larger conductivity change corresponds to a bigger hole.
In order to reconstruct the precise hole size using the damage shaping methodology, a geometric model for through holes must be integrated with the GA. In this case the model consisted of a circular hole inside the FE mesh and the damage shape parameter was specified as \(s_{GA}\) = \([x_c, y_c, r]\), where \(x_c\) and \(y_c\) are the \(x\)- and \(y\)-coordinates of the center of the hole, respectively, and \(r\) is the radius of the hole. The GA initiates the search by generating a population between the bounds \(s_{\text{min}}\) and \(s_{\text{max}}\), which are the lower and upper bounds, respectively, on the location and size of the hole. These are specified based on the size and location of the artifacts observed in the EIT images. For example, for the case of one hole, \(s_{\text{min}}\) was specified as [55, 55, 0.5] mm and \(s_{\text{max}}\) was [62, 62, 5] mm. An adaptive meshing algorithm \cite{engwirda2014locally} was used to integrate this geometric model with the GA. Additionally, a population size of 50, a BSA of 99\%, and a maximum of 30 generations were used for the GA. The results are shown in the right column in Figure \ref{fig-eit-ga-holes}.
\begin{figure}[h]
\centering
\includegraphics[width=0.60\textwidth]{figures/eit-ga-holes.png}
\caption{EIT and GA-enabled damage shaping results from through-hole testing. The black circles indicate the true hole sizes and locations. Left column: EIT-imaged conductivity change. We can see that EIT is able to detect the presence of the holes but the exact shape and location are not clear. Right column: GA-enabled damage shaping results. It can be seen that by integrating a realistic damage model with the GA, the shape and size of the holes can be determined much more precisely than standard EIT.}
\label{fig-eit-ga-holes}
\end{figure}
In the first case, the GA is able to reconstruct a hole with a radius of 1.33 mm. In the second case, the GA is able to reconstruct one hole with a radius of 1.34 mm and a second hole with a radius of 2.79 mm. And in the third case, the GA is able to reconstruct three holes with radii of 1.34 mm, 2.79 mm, and 3.43 mm. We can see that these results are considerably more accurate and provide much more precise information about the damage shape and size than standard EIT, which often suffers from background noise and stray artifacts. The average percent errors in the GA predicted hole sizes and locations are listed in Table \ref{tab-hole-error}.
\begin{table}[h]
\centering
\caption{Average percent error in GA-predicted solutions relative to actual hole sizes and locations. Here, \(e_{x_c}\) and \(e_{y_c}\) are the average percent errors in the \(x\)- and \(y\)-coordinates of the center of the hole and \(e_r\) is the average percent error in the hole radius.}
\begin{tabular}{cccc}
\toprule
Hole number & \(e_{x_c}\) [\%] & \(e_{y_c}\) [\%] & \(e_{r}\) [\%] \\
\midrule
1 & 1.67 & 3.33 & 11.76 \\
2 & 3.33 & 5.77 & 17.22 \\
3 & 9.52 & 3.70 & 7.86 \\
\bottomrule
\end{tabular}
\label{tab-hole-error}
\end{table}
The BSA convergence for the first search of each case and the fitness function convergence for all searches of each case are shown in Figure \ref{fig-holes-conv}. For one hole, we observe good convergence with one search. For two holes, we require a higher number of generations to reach the BSA stopping criterion. In this case, successive searches slightly improve the solution. For three holes, the maximum number of generations is reached before the BSA stopping criterion is met. In this case, successive searches significantly improve the solution. This is because as the number of holes increases, the number of variables in \(s_{GA}\) also increases and the GA requires more computations to achieve a genetically similar population.
\begin{figure}[h]
\centering
\includegraphics[width=0.75\textwidth]{figures/holes-conv.png}
\caption{Convergence plots for through-hole reconstruction. Left: BSA convergence for first search case of each case. Right: Fitness function convergence for all searches of each case.}
\label{fig-holes-conv}
\end{figure}
\subsection{Delaminations}
The optimum baseline conductivities of the impact testing specimens were estimated using a similar approach as the through-hole testing specimen. The conductivities of the 23 J and 28 J impact specimens (from laminate 2) were found to be \(\sigma_{x0}\) = \(\sigma_{y0}\) = 0.055 S/m, and \(\sigma_{z0} = 5\times10^{-4}\) S/m, and the conductivities of the 25 J impact specimen (from laminate 1) were found to be \(\sigma_{x0}\) = \(\sigma_{y0}\) = 0.02 S/m, and \(\sigma_{z0} = 3\times10^{-4}\) S/m. EIT was performed on a mesh of 5,670 linear triangular elements and the conductivity change results from each impact are shown in the top row in Figure \ref{fig-eit-ga-delams}. Note that EIT endeavored to reconstruct the in-plane conductivity, \(\sigma_{x0}\) = \(\sigma_{y0}\) = \(\sigma\), which is isotropic -- even though each lamina is mildly electrically anisotropic, the symmetric layup renders the in-plane conductivity of the entire laminate as very nearly isotropic. We can immediately observe that EIT is able to detect each of the impacts and as the impact energy increases the intensity of the conductivity change at the impact location also increases. This indicates that increasing the impact energy is increasing the amount of damage within the laminate. However, from the EIT image alone, the size and shape of the induced delamination cannot be obviously determined.
To compute the delamination shape and size, the GA was integrated with a geometric model for delaminations as follows. FE models of each laminate were constructed using \(\sigma_{x0}\), \(\sigma_{y0}\), and \(\sigma_{z0}\). These models represent homogenized or `effective' laminates that have the same bulk electrical behavior as the physical laminate. Each FE model consisted of one layer of 2,700 linear quadrilateral elements sandwiched between two layers of 2,700 linear hexahedral elements. The GA was then used to generate elliptical conductivity artifacts described by the shape parameter \(s_{GA}\) = \([x_c, y_c, r_x, r_y]\) inside the middle layer. A conductivity of \(\sigma_x\) = \(\sigma_y\) = \(\sigma_z\) = \(\sigma_d\) = \(1\times10^{-6}\) S/m was assigned to the elements within the elliptical artifact. This concept is based on the fact that a delamination can be modeled as a failure at the interface between two layers of the laminate. In this case, these are the two layers of hexahedral elements that represent the homogenized composite. The individual layers of the physical laminate were not explicitly modeled for the inversion. These were not modeled because the EIT electrodes spanned the thickness of the laminate thereby making it impossible to extract through-thickness information. As such, the GA-produced delamination was inserted at the mid-plane of the homogenized models. A schematic of the delamination modeling procedure is shown in Figure \ref{fig-delam-model}. For the GA, a population size of 20, a BSA of 65\%, and a maximum of 20 generations were used.
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth]{figures/delam-model.png}
\caption{Schematic of delamination model integrated with the GA. The experimentally measured bulk conductivities are used to build a homogenized FE model with three layers of hexahedral elements. The middle layer is then collapsed to infinitesimal thickness and the GA is used to generate elliptical conductivity artifacts within this layer of elements.}
\label{fig-delam-model}
\end{figure}
As described earlier, optical microscopy was used to destructively evaluate the specimens. Figure \ref{fig-micro-img} shows an optical micrograph of the cross-section of the 23 J laminate. A delamination is clearly visible between the third (\(0 ^{\circ}\)) and fourth (\(90 ^{\circ}\)) layers. In fact, it was observed that the delamination always occurred between the third and fourth layers for each impact. The full shape of the delamination was then reconstructed as follows. For each cut made through a specimen, the delamination length was recorded and images were taken at regular intervals along the cross-section. A new cut was then made, the delamination length recorded again, and more images taken. In other words, the delamination length was measured with the aid of an optical microscope for each slice. This was repeated until a delamination was no longer observed using the microscope. The recorded delamination lengths and cut thicknesses were then used to reconstruct the in-plane shape of the delamination. This process is illustrated for a single cut in Figure \ref{fig-micro-slices}.
\begin{figure}
\centering
\includegraphics[width=0.45\textwidth]{figures/micro-img-compressed.png}
\caption{Optical microscopy image of cross-section of 23 J impact specimen. A delamination is clearly visible between the third and fourth layers, as indicated by the white arrows. The fibers in the \(90 ^{\circ}\) layers are pointing out of the page.}
\label{fig-micro-img}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth]{figures/micro-slices.png}
\caption{Illustration of actual delamination shape reconstruction using optical microscopy. Left: A cut is made through the laminate to expose the cross-section. Middle: Optical microscopy is used to measure the delamination length at the cross-section. Right: The cut thickness and delamination length are used to piece together the delamination. This procedure is repeated until the full delamination shape is obtained.}
\label{fig-micro-slices}
\end{figure}
The GA-generated delamination shapes along with the actual delamination shapes reconstructed using optical microscopy are shown in the second and third rows, respectively, in Figure \ref{fig-eit-ga-delams}. We can see immediately that the GA-generated solutions agree very well with the actual delamination shapes. As the impact energy increases, the size of the delamination also increases, which is what we observe from both the GA results and optical microscopy. There are nonetheless some differences between the GA-generated solutions and the actual delamination shapes. This may be attributed to the fact that an impact does not cause a pure delamination but a combination of delamination, matrix cracking, and fiber breakage. However, the proposed model does not account for these additional damage modes. As such, the algorithm tries to compensate for the additional damage by increasing the size of the predicted delamination. Regardless, we can see from Figure \ref{fig-eit-ga-delams} that the GA-predicted solutions are a significant improvement over standard EIT in terms of damage shape.
\begin{figure}[h!]
\centering
\includegraphics[width=0.75\textwidth]{figures/eit-ga-delams.png}
\caption{EIT, delamination shaping, and optical microscopy results from impact testing specimens. First (top) row: EIT-imaged conductivity change. The magnitude of the conductivity change increases as the impact energy increases. Second row: GA-enabled delamination shaping results. Third row: Actual delamination shapes reconstructed using optical microscopy. Bottom row: Photos of post-impacted specimens. The silver circles indicate the actual impact locations. Note that damage caused by the impacts is barely visible on the surface of the specimens.}
\label{fig-eit-ga-delams}
\end{figure}
Lastly, we examine the convergence of the delamination shaping algorithm. The fitness function convergence for the first search and the minimum fitness function value for all searches are shown in Figure \ref{fig-delam-conv}. We can see that the fitness function attains its minimum value for a relatively small number of generations. Additionally, the change in the minimum fitness function value between successive searches is not significant. This indicates that successive searches may not necessarily produce better quality solutions for the delamination shaping problem.
\begin{figure}[h!]
\centering
\includegraphics[width=0.75\textwidth]{figures/delam-conv.png}
\caption{Fitness function convergence plots for GA-enabled delamination shaping algorithm. Left: Fitness function convergence for first search of each impact case. Right: Fitness function convergence for all searches of each case.}
\label{fig-delam-conv}
\end{figure}
\section{Summary and Conclusions}
In this article we have presented a new technique for more accurately determining the shape and size of damage in self-sensing composites via EIT. Our technique uses a GA to inversely determine the shape of particular damage modes from EIT-imaged conductivity changes and boundary voltages. This is a significant advancement to state-of-the-art conductivity-based SHM which seeks only to spatially localize damage and does not provide any information about the underlying mechanics. The technique proposed here addresses this limitation and can transform SHM and NDE in self-sensing structures from mere damage detection and localization to much more robust damage characterization.
We began by manufacturing self-sensing CNF-modified GFRP laminates. The laminates were damaged by drilling multiple through-holes and impacting with three different energies to cause a delamination. EIT was performed on each laminate to image the damage-induced conductivity change. Two physics-based geometric models for damage were then developed---one for through-holes and one for delaminations---and each was integrated with a GA. The GA-integrated damage shaping algorithms were then used to reconstruct the shape and size of the holes and delaminations based on the observed conductivity changes and boundary voltages. The inversely reconstructed through-holes showed good agreement with the actual hole sizes. Furthermore, the algorithm was able to accurately reconstruct multiple holes. The delamination shaping results also showed good agreement with the actual delamination shapes determined destructively using optical microscopy.
The work presented here has potential to improve the safety of self-sensing structures in safety-critical applications by providing precise information about damage condition. However, some limitations of this approach must be recognized and addressed in future work. First, the use of a GA adds significant computational burden to EIT. We anticipate that this can be overcome by using more efficient high-performance computing architecture. Second, although this approach seems to show much potential, this exploratory study was limited to through-holes and delaminations. Additional damage models should be developed to capture more realistic and complex damage scenarios. Appropriate damage models will have to developed for these cases too. Finally, machine learning and artificial neural networks have shown promise in solving damage inversion and categorization problems \cite{lin2020realtime}. These should also be explored in future work.
\section*{Acknowledgements}
The authors gratefully thank Professor WA Crossley at Purdue University for the use of his GA, and Professor W Chen and graduate research assistant Nesredin Kedir at the Impact Science Lab at Purdue University for their assistance with optical microscopy. The authors also thank the Purdue University Graduate School for providing financial support through the Bilsland Dissertation Fellowship.
\bibliographystyle{elsarticle-num}
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{
"redpajama_set_name": "RedPajamaArXiv"
}
| 8,671
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Hemp Rec. – hip-hopowa wytwórnia muzyczna założona w 2009 roku z inicjatywy warszawskich raperów Wilka oraz Bilona z grupy Hemp Gru. W wytwórni Hemp Rec. swoje albumy wydawali tacy artyści jak: Hemp Gru, Bilon, Bas Tajpan, Jasiek MBH, HZD czy Jongmen. Dystrybucją do 2015 roku zajmowała się Fonografika.
Wydane albumy
2009
DJ Steez - Steezmatic 1 Mixtape
Hemp Gru - W Hemp Armii
Hemp Gru - Droga
2011
Hemp Gru - Jedność
Steez & Fuso - Hemp Gru Remixtape Vol. 1
Hudy HZD & Jasiek MBH - Już Wkrótce
Jasiek MBH - Nazwij To Jak Chcesz
Hemp Gru - Lojalność
Hemp Gru - Live In Palladium
2012
Hazzidy - Historie Z Dna
Bas Tajpan - Made In Tajpan
Hemp Gru - Braterstwo
2013
Ryfa Ri - Puzzle
Jongmen - Kontrapunkt
Centrum Strona - Świadkowie Patologii
2014
V/A - ŻywyRap! Mixtape
Luksmamilion - Fundament
Cywil - Lęk wysokości
BRZ - Woda
2015
Bilon - 3xNie
Zobacz też
Przypisy
Linki zewnętrzne
Oficjalna strona wytwórni
Hip-hopowe wytwórnie muzyczne
Polskie wytwórnie hip-hopowe
Muzyka w Warszawie
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 135
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An historical town nestled in the prairies, Nanton is rich with quaint charm and rural heritage.
High River is a haven of peaceful living with a balance of urban and rural lifestyles just south of Calgary.
A superior quality of life is waiting in the Foothills, serving from Claresholm to Okotoks.
Providing Real Estate expertise for farms and acreages throughout the Alberta Grasslands.
Lorraine Boulton is a professional providing real estate expertise to Nanton, High River, Okotoks, Claresholm, Vulcan, Turner Valley, Black Diamond, Longview and all the smaller communities in between. Your realty expert serving southern Alberta.
You can trust that you have all available information when you are dealing with Lorraine. She will find you a new home, sell the house you are leaving or search for that perfect rural ranch house with acreage.
Copyright © 2019 Lorraine Boulton. All Rights Reserved.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 2,344
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This is just a straight shot with my cell phone, no apps used.
I like the color of the light, now that the days are getting shorter. It gives a whole new feeling to moving around in the world.
On another note, I could tell people were looking at me like I was crazy because I was taking pictures of this door and what was above me in the bus.
It's funny taking pics in public. But I suppose completely normal for a city like L.A.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 8,360
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{"url":"http:\/\/lara.epfl.ch\/web2010\/equivalence_of_finite_state_machine_and_regular_expression_languages","text":"\u2022 English only\n\n# Equivalence of finite state machines and regular expression languages\n\nWe next show that a language is given by a regular expression if and only if it is a language of some finite state machine.\n\nIf a language is given by one of these two ways, we can always convert to the other if this is more convenient.\n\n\u2022 regular expressions can be easier to specify textually\n\u2022 it is easier to check whether a string is accepted by a finite state machine\n\n## Every language given by a regular expression is accepted by some finite state machine\n\nBy induction on the structure of regular expressions, we construct the finite state machine that accepts this language.\n\nFor the base case, observe that we can easily construct finite state machines for empty language , and a finite state machine for a singleton language for .\n\nFor the inductive step, we use closure properties of finite state machines for the cases of union, concatenation, and iteration.\n\n## Every language accepted by a finite state machine is given by some regular expression\n\nFinite state machines with regular expression labels. We first generalize the notion of a finite state automaton so that we can label its edges not only with elements of as in the standard definition of finite state machine and with epsilon transitions as in finite state machine with epsilon transitions, but with arbitrary regular expressions.\n\nAn accepting execution for such a generalized finite state machine is a sequence of states and regular expressions with , and the accepted strings of that execution are all strings in the union of over all such accepting sequences.\n\nNote that if all regular expressions are elements of , the definition reduces to the standard definition of finite state machine.\n\nPreparing for conversion to regular expression. To convert a finite state machine into a regular expression, we first view it as a generalized finite state machine, and then eliminate states of the state machine one by one. We start the process by creating a fresh initial state and fresh final state and expressing all final states in by transitions to . We let be the new set of final states. For any pair of states, we then ensure that there is exactly one edge between them:\n\n\u2022 if there was no edge, we introduce an edge with the label is ;\n\u2022 if there are multiple edges with labels , we introduce instead one edge whose label is the regular expression .\n\nElimination step: We show how to eliminate a state (we assume is not initial and not a final state).\n\n\u2022 let the self-loop edge labelled be\n\u2022 for every two states and (possibly equal), distinct from :\n\u2022 suppose we have these regular expressions on edges:\n\u2022 extend label from to with\n\nAt the end, we are left with one non-empty edge from to , whose label is the desired regular expression.\n\n## Some consequences\n\n\u2022 Given an automaton that accepts , construct an automaton that accepts ?\n\u2022 Given a regular expression for , construct a regular expression for ?\n\u2022 Given two regular expressions, how to compute their intersection?\n\n#### Exercise\n\nConsider alphabet . A string is desperate if it contains \u2018aaa\u2019 as a substring. Construct a regular expression that describes the set of all strings that are not desperate.\n\nOne solution:","date":"2013-05-24 04:53:36","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8289250731468201, \"perplexity\": 373.86500556864564}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2013-20\/segments\/1368704179963\/warc\/CC-MAIN-20130516113619-00012-ip-10-60-113-184.ec2.internal.warc.gz\"}"}
| null | null |
Q: Can I get a mixture of := and = in Go if statements? Go newbie here...
If func returns a value and an error, can I write an if statement so the value stays in scope after the if statement, but the error does not? That is a common thing I want to do, and I work around it by just creating a var err error local variable and let err remain in scope after the if statement, but that is not really what I want. I only do it because I don't know how to avoid it. Can I somehow have different scopes for the two returned values?
Details:
Go has a common idiom that looks like this:
if val, err := func(); err != nil {
/* val and err are in scope */
...
}
/* val and err are no longer in scope */
and one can
var (
val SomeType
err error
)
if val, err = func(); err != nil {
/* val and err are in scope */
...
}
/* val and err are still in scope */
But how do I:
var val SomeType
// How do I write the XXXX operator?
if val, err XXXX func(); err != nil {
/* val and err are in scope */
...
}
/* Only val is in scope now */
How to write XXXX?
|
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| 6,309
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TIME to auction 3 NFT covers based on iconic 'Is God Dead?' design
The TIME NFTs will be auctioned individually and as a collection on SuperRare through March 24.
TIME Magazine is embracing the blockchain digital art movement by auctioning three non-fungible tokens, or NFTs, inspired by some of its most iconic covers throughout the decades.
The American news magazine announced Monday that the three NFTs will be sold both individually and as a collection on SuperRare, a digital-art trading platform, through March 24. The collection is based on the theme, "Is ___ Dead?" which refers to a series of provocative typological covers inspired by the original April 8, 1966 rendition, "Is God Dead?" As TIME notes, this was the first cover in the magazine's history to include only typography with no image.
The NFT rendition of "Is God Dead?" is now available on SuperRare, alongside TIME's April 3, 2017 cover, "Is Truth Dead?" and the forthcoming March 29/April 5 cover, "Is Fiat Dead?"
The question "Is Fiat Dead?" references the meteoric decline in purchasing power of government-controlled currencies like the U.S. dollar. As TIME noted, a cryptocurrency like Bitcoin (BTC) is challenging present-day monetary norms through its fixed supply and transparent monetary policy.
"I love the idea that its meaning isn't clear to the casual viewer – much like the crazy, lucrative world of NFTs," says TIME Creative Director D.W. Pine, who designed the forthcoming "Is Fiat Dead?" cover.
The NFT market has exploded in popularity over the past year, with sales quadrupling in 2020 alone. As Cointelegraph recently reported, everyone from social media influencers to celebrities have embraced NFTs.
Investors are also taking notice. Just last week, NFT marketplace OpenSea raised $23 million in Series A funding led by Andreessen Horowitz and angel investors including Mark Cuban, Tim Ferriss and Naval Ravikant.
Previous Mining firm aims to go public through merger with Nasdaq-listed company
Next Number-two gaming DApp raises $2 million in private utility token sale
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
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| 1,107
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xyvrsbdzuwrxszztfvvvebuaccfewec
Real Milwaukee men can enjoy pink, umbrella-laden drinks.
Are you man enough for frou-frou drinks?
By Royal Brevvaxling
Special to OnMilwaukee.com
E-mail author | Author bio
More articles by Royal Brevvaxling
Published Feb. 9, 2012 at 9:10 a.m.
"Bar Month" at OnMilwaukee.com – brought to you by Hornitos, OR-G, Party Armor, Red Stag, Absolut, Fireball and Malibu – is back for another round! The whole month of February, we're serving up intoxicatingly fun articles on bars and clubs – including guides, the latest trends, bar reviews and more. Grab a designated driver and dive in!
Supposedly, the frou-frou drink was created to appeal mainly to women, relative newcomers to the public consumption of cocktails in the 20th century. Drinks with colorful liqueurs and fruity flavors are the basic foundation of the frou-frou.
Although ultimately subjective, the category tends to include drinks such as the mojito, screaming orgasm and anything with "tini" at the end of its name, as well as all frozen drinks like daiquiris and certainly any drink served with an umbrella.
"My current favorite is the Apartment 137 at Distil – like a glass full of melted dreamsicles," says Paul Piaskoski, CBS 58 news anchor.
Steve Kabelowsky, a strategist for an area marketing firm and OnMilwaukee.com blogger, is also a proud male imbiber of frou-frou drinks.
"I enjoy the occasional sex on the beach and sangria, but I order vodka cranberry all the time. I get looks sometimes, but never comments to my face. Those probably happen behind my back," says Kabelowsky.
In addition to sex on the beach, Kabelowsky has an appreciation for the theater, art, antiques, history and design and can also speak to the virtues of an NFL 3-4 defense and break down college hoops match-ups.
"I understand the differences with where I am in the stereotypical spectrum here. I'm comfortable with who I am," says Kabelowsky.
It would seem that men are finally becoming men, less afraid to be publicly outed for lots of reasons. While social stigmas remain for a host of things, liking romantic comedies and listening to and enjoying Tori Amos, to name a few, being called out at the bar for enjoying the sweeter side of the finer things in life can still be challenging.
"I was at dinner with a bunch of people that I was on the road with and ordered a sangria. Someone piped up, saying I should order a real drink. I just looked at him," says David Webb, a corporate airline pilot and self-described "lover of the sweeter drinks."
Etymology of the word "frou-frou" to designate drinks traditionally, if not stereotypically, appealing to women doesn't seem very straightforward at first. It's a French word used to indicate the noise made by a dress as someone is walking. (But perhaps this only makes sense in French; this author has a tough time imagining this sound. Maybe primary research is in order? Gather your skirts and digital voice recorders.)
Frou-frou also means the ornamentation on women's clothing, and this is probably where its use arises in designating a drink light or frilly, overly feminine if not downright girlie – and in questioning the masculinity of a fella as he moves his drink umbrella so his mustachioed lips can fully grasp his fruity cocktail glass.
"I never feel silly. I'm comfortable in my masculinity, the same way I feel about wearing pink in support of breast cancer awareness," says Kabelowsky, who enjoys the orange dreamsicle (also called a creamsicle, any kind of drink made with orange liqueur or Absolut orange).
"I love those. But I also like Beam and Cokes, and the occasional shot or two. I guess those would be considered more 'manly.' I'd never consider myself a metrosexual, and I'm not a homosexual, not that – here's a 'Seinfeld' reference – there's anything wrong with that," he says.
Matters of taste are always shaped by social forces; therefore, it's understandable that when personal preferences are deemed feminine in a homophobic society that people will get cagey. When interviewed, a lot of men make it clear that they're heterosexual frou-frou drinkers, but maintain that they're comfortable with how their drink preferences intersect their sexuality.
"I like pina coladas. I don't like sports, but I like women," says Mike Becher, a 47-year-old retail industry worker.
Becher was on vacation in Mexico when he had his first pina colada, and he prefers them served in a coconut.
"I am 45 years-old and as straight as they come. I fell in love with sangria at a Brazilian bar / restaurant just outside of Sarasota, Fla.," says Webb.
Webb enjoys the "island lifestyle"; this is when he can wear his Tommy Bahamas shirt and shorts and ride with the top down on a convertible. Drinking certain frou-frou drinks seems right in line with this way of life.
Other lifestyle demands often accompany changes in drink preferences – like those associated with age.
"I am a total sweet drink junkie. It wasn't always that way, but the older you get, the harder it gets – know what I mean? I'm 45, and at this point, beer makes me feel bloated and sleepy, and hard liquor has a tendency to wipe out the whole next day," says Piaskoski.
Piaskoski has the benefit of being married to a shot-and-a-beer kind of girl. He says this saves him from some potential embarrassment because people often assume the pink drink he ordered is for her.
But that's in public. Piaskoski says his "pink drink preference is well established amongst those who know me" and that he hasn't lost any friends or family over it, not that he'd care too much.
"I still pee standing up, park myself in front of the TV every Sunday for Packers games and served in the military, so I think I still have my man card. I just occasionally use it as a coaster for my cosmo," says Piaskoski.
Tags: frou-frou drinks, steve kabelowsky, david webb, mike becher, paul piaskoski, cosmopolitan, sangria, sex on the beach, apartment 137, pina colada, distil, jim beam
mkeforlife | Feb. 9, 2012 at 10:39 a.m. (report)
The notion that sangria is a frou-frou drink is misplaced. Real sangria has fruit but is not as sweet as the garbage that most places serve around here. When made right, it is divine and strong. As to the other drinks, only men with small units are afraid to drink whatever, whenver they want.
1 comment about this article.
White Claw Hard Seltzer craze creates pining consumers
New booze Natty Rush to challenge Four Loko, MillerCoors' Steel Reserve
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 8,574
|
You are here: Home > Features
From front line to bottom line
Features Posted 28/02/20
Specialist accountant who enjoyed his army years says there are important lessons that business can learn from service life.
By Christine Rayner
As a veteran of the First Gulf War, Duncan Cochrane-Dyet has seen his share of action under fire. Now with several decades of experience within the financial sector under his belt, he can see the benefits of life as both soldier and civilian. "The army teaches you confidence, leadership and how to act in extreme conditions," Duncan tells me. "I thoroughly enjoyed my six years in the service, but it was a single person's life and I needed to move on." That "moving on" led him into accountancy and a life dedicated to the financial sector.
A few minutes into our conversation, it becomes clear that the army left Duncan with very decided views on people skills – and how they could be incorporated into business.
"I am concerned that there is no comprehensive leadership training for newcomers to business, unlike the army," he tells me. "We teach our people managing, but not leading and I think business is the poorer for it."
Duncan wrote a blog on the issue soon after he joined MHA MacIntyre Hudson (MHA), a national Top 15 firm of accountants, in 2015. It's still available on the company website and makes interesting reading.
The piece begins: "It probably goes without saying that the foundation of the success of our Armed Forces is leadership, at all levels. The army trains its officers at the Royal Military Academy Sandhurst, where leadership is taught formally. "Odd, then, that we in the business world do not place the same emphasis on leadership as a discrete skill that can be developed and disregard the huge and beneficial impact that effective leadership at all levels can have. There is virtually no formal leadership training, although this is starting to appear as a component in management courses."
Duncan joined MHA's Kent team after several years in the financial sector in London – with firms Ernst and Young (EY) and PricewaterhouseCoopers (PwC). He looks back with affection on those days, and on lessons learned in how the profession worked.
Now, as a specialist audit and assurance partner with MHA, Duncan divides his time between the firm's Kent offices in Canterbury and Maidstone and is responsible for a fast-developing team.
"When I started, we had 27 people, now we have more than 100," he tells me proudly. And it won't stop there, the company has plans to double the size of its workload in the next five years, so Duncan is going to be busy.
We chat about his management style and he pauses to consider the answer. "This is about empowering people, and allowing them to make mistakes and to learn from them. This is a very complex world and I could not do my job without regular discussions with the team. I operate very much an open door policy – anyone is welcome to pop into my office at any time, to chat about an issue."
Life at home is similarly hectic for Duncan, who is married to a GP who is also an assistant director with NHS England. Their three children are aged 22, 20 and 19 and are all pursuing their career dreams. His elder son is in the education sector, his daughter is in vet's school and his younger son is embarking on medical studies, following his mother. Despite all these responsibilities, Duncan still finds time to walk the family's two cocker spaniels and goes to the gym when he can.
Last edited 09/04/20
Aim high, always
Persistence paid off
Tweets from @SEBmagazine
Tweets by @SEBmagazine
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 3,078
|
{"url":"https:\/\/forum.allaboutcircuits.com\/threads\/aircraft-wont-turn.1055\/","text":"# Aircraft wont turn\n\n#### nanobyte\n\nJoined May 26, 2004\n120\nI am trying to make a program on Borland C++ Builder that will draw a aircraft(a simple concaved triangle with a line going through) and make the triangle be able to turn or spin 1 to 360 degrees(or negative angles). My problem is with making the aircraft turn. The function I'm using isn't working. I used this function to make a previous object( a circle with a line going through it to turn). So I figure that since the shape I'm using is different, I may need to changed the whole function. Check out the code and me what you think(it include the function to draw, erase, and turn the aircraft). I also have a attachment showing how I want the aircraft to be able to turn.\n\nRich (BB code):\n\/\/Draws Aircraft\nvoid Aircraft::constructAircraft(void)\n{\nForm1->Canvas->Pen->Color=clBlue;\nForm1->Canvas->Pen->Width=1;\nForm1->Canvas->MoveTo(x,y);\nForm1->Canvas->LineTo(x-size,y+size); \u00a0\/\/left side\nForm1->Canvas->LineTo(x,y+(size\/2)); \/\/The base\nForm1->Canvas->LineTo(x+size,y+size);\nForm1->Canvas->LineTo(x,y);\n\nForm1->Canvas->Pen->Color=clBlack;\nForm1->Canvas->LineTo(x,y);\nForm1->Canvas->LineTo(x,y+(size\/3));\n}\n\n\/\/Erases Aircraft\nvoid Aircraft::scrapAircraft(void)\n{\nForm1->Canvas->Pen->Color=clBtnFace;\nForm1->Canvas->Pen->Width=1;\nForm1->Canvas->MoveTo(x,y);\nForm1->Canvas->LineTo(x-size,y+size); \u00a0\/\/left side\nForm1->Canvas->LineTo(x,y+(size\/2)); \/\/The base\nForm1->Canvas->LineTo(x+size,y+size);\nForm1->Canvas->LineTo(x,y);\n\nForm1->Canvas->Pen->Color=clBtnFace;\nForm1->Canvas->LineTo(x,y);\nForm1->Canvas->LineTo(x,y+(size\/3));\n}\n\nRich (BB code):\n\/\/turns the aircraft\n\/*void Aircraft::turn(int t)\n{\nfor(int i=0; i<abs(t); i++)\n{\nscrapAircraft();\nif(t>0)\nangle+=1;\nelse\nangle-=1;\nconstructAircraft();\nSleep(T);\n}\n\n}*\/\n\n#### Brandon\n\nJoined Dec 14, 2004\n306\nWhat is Form1, Canvas, Pen, Color, etc?\n\nAre they defined classes or something from a header?\n\nI've never done any form of drawing in C++ yet, I usually only deal with console apps.\n\nWouldn't mind trying to help and learning a little more at the same time.","date":"2022-05-22 08:14:27","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.33495640754699707, \"perplexity\": 4367.552607723935}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-21\/segments\/1652662545090.44\/warc\/CC-MAIN-20220522063657-20220522093657-00518.warc.gz\"}"}
| null | null |
Spree::Product.class_eval do
# Returns only products that are in stock or backorderable
add_search_scope :on_hand do
where(
<<-SQL
#{table_name}.id IN
(
SELECT product_id FROM #{Spree::Variant.table_name} v
JOIN #{Spree::StockItem.table_name} i
ON v.id = i.variant_id
WHERE v.deleted_at IS NULL
AND i.deleted_at IS NULL
GROUP BY product_id
HAVING SUM(count_on_hand) > 0
OR MAX(CASE backorderable
WHEN #{ActiveRecord::Base.connection.quoted_true} THEN 1
ELSE 0
END) > 0
)
SQL
)
end
end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 9,902
|
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love gives us a fairy tale. "
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 9,030
|
Howard Gordon discusses 24: Live Another Day with IGN
By 24 Spoilers , February 19th, 2014 · 5 comments
IGN TV: Obviously, at this point, you have so much on your plate. What was it about this show that made you say, "I need to make time for this. I want to go back to this" and return for 24: Live Another Day?
Howard Gordon: Honestly, it was almost like a bad joke — or a good joke. I had dinner with [Fox Networks Group Chairman and Chief Executive Officer] Peter Rice, who mentioned very off-hand, "Are you doing the [24] movie?" He's the boss, so he would know! I said, "You know, probably not…" It didn't look like it was going to happen. He said, "Would you ever think of doing it as a limited series?" I said, "That's a really interesting idea. I'm coincidentally having dinner with Kiefer on Wednesday" — it was, like, a Saturday night. I go, "I'll talk about it with Kiefer." Over dinner, we both said, "Nah, nah." Then both of us, the next day, called each other. We just riffed like, "If we both did it, it would be this. What if it's that?" Then I went to [20th Century Fox Television CEOs] Dana Walden and Gary Newman, and Dana and Gary said, "Let's go over to [FOX Chairman of Entertainment] Kevin Reilly." I just mulled on the idea for a little bit. Literally, she called Kevin, and Kevin said, "Come over!" And they said yes! But I said, "I'll only do it if Evan and Manny [are involved] — and I can assemble the team." We're friends, so I knew their deals were coming up.
It was one of those things where, coming back to your question, everyone missed Jack and this show so much, even though four years ago, I would have bet the house that there was no way this moment would ever come. I was so happy, and we were all happy that we got out with our integrity. We were all very, very proud of the show. We had our bumps, we had our good seasons and our less good seasons, but by and large I think it was a very successful run creatively and one that ended fulfilling the promise that the show had in the beginning. We know we're tempting fate at some level, but f**k it!
IGN: [Laughs] Right, right. That would help! When it comes to the Jack and Chloe dynamic, the final scene of the show was very tragic, but also touching and Jack was open with her in a way he usually isn't. But it sounds like when we meet them again, it's going to be very much the opposite of when we last saw them.
Gordon: It's the first time between seasons that four years have elapsed. That's a long time. Even between seasons [with the time jumps] — if you did the math, it's probably 2027 or something like that! [Laughs] But all the characters have to progress along their own continuum, and Chloe's had the kind of tragic upshot. Current events kind of gave us inspiration there too. We liked the idea of Chloe being a cross between Lisbeth Salander and Edward Snowden. That idea really got us psyched.
Check out the full interview at IGN which also discusses Audrey's return, the writers being surprised that Heller was still alive, whether Aaron Pierce will return, and some juicy new details about Yvonne Strahovski's character Kate Morgan. The Yvonne/Kate paragraph has some spoilers on the characters backstory.
Related Topics · 24: Live Another Day, Interview, Aaron Pierce, Audrey Raines, Howard Gordon, Kate Morgan, Kevin Reilly, Yvonne Strahovski
Jack is Back Special – 20 minute preview of 24: Live Another Day
By 24 Spoilers , April 7th, 2014 · 40 comments
FOX has released an incredible 20 minute special preview for 24: Live Another Day titled "Jack is Back." The video has loads of brand new footage and interviews with just about the entire cast and includes the first footage of Michelle Fairley as the main villain Margot (in what looks to be a standout role)…. View Article
Yvonne Strahovski on Kate Morgan's storyline: "It's dark"
By 24 Spoilers , April 30th, 2014 · 11 comments
New York Post has a nice piece on Yvonne Strahovski. Most of it is about her personal life but here's the 24 related info. "You meet Kate at a point in her life when she's feeling dejected and doesn't have a lot to hold onto," Strahovski says. "When Jack Bauer comes into the picture, and… View Article
Getting to Know Kate Morgan
By 24 Spoilers , June 2nd, 2014 · 5 comments
Yvonne Strahovski talks about her role as the brilliant but impulsive CIA agent Kate Morgan.
Follow @24spoilers
I'd like to read about Audrey's return but I don't want the rest spoiled for me….. But I'm glad that came about the way it did. & there & his answer was simple they all missed Jack!!! That's great cause I did to as I'm sure most of the fans did. This show needed another season I can't believe they seemed to be okay with leaving season 8 as is. Sounds like up until that conversation they were going to leave fans hanging with season 8's ending. & hopefully they will do more seasons & it will re-energize there creative idea's & hopefully have 24 get this franchisablity they all keep suggesting. Including fox who has also suggested this. So maybe this will be the start of some new ideas for storylines among other possibility's as well.
Very interesting about possible Aaron Pierce return!
Yeah Aaron needs to be in it
Absolutely right!
Kiefer's character on Touch, and the long-faced terrorist on Homeland just weren't cutting it (besides, ginger blokes have no business being leading men). People want to see Jack Bauer.
24bauerfan
^The hell?
Anyway, I didn't read the whole interview, but he does give some interesting answers. So excited the show is back!
Comment Policy b i u spoiler
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24 Spoilers » 24: Live Another Day » Howard Gordon discusses 24: Live Another Day with IGN
24 Spoilers Comment Policy
Our comment policy is very simple - be civil and respectful. This means no personal attacks, racism, sexism, homophobia, excessive language, and obviously no spamming, excessive self-promotion, or overly repetitive comments.
Everyone is welcome and encouraged to voice their opinion as long as it adds constructively to the conversation. Please be respectful of other people's viewpoints even if you personally disagree.
We do not tolerate intentional attempts to hijack, derail, or bait others into an emotional response. Failure to comply with these rules will result in a warning and repeat offenders may be permanently banned.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,857
|
Q: Use cache in auth middleware I'd like to write own auth route middleware to use user cache. If I will simple check with cache in DB user then I see
Call to a member function setCookie() on null
I should use UserProvider probably. But then I don't use cache.
Does it any way to return same result like original auth but set cache inside?
My current code is:
<?php
namespace Sakuicms\Auth\Middleware;
use Closure;
use Illuminate\Contracts\Auth\Factory as Auth;
use Illuminate\Auth\AuthenticationException;
class Authenticate
{
protected $auth;
public function __construct(Auth $auth)
{
$this->auth = $auth;
}
protected function getName()
{
return 'login_'.config('auth.defaults.guard').'_'.sha1('Illuminate\Auth\SessionGuard');
}
public function handle($request, Closure $next, ...$guards)
{
$id = session($this->getName());
if($id>0){
$model = config('auth.providers.users.model');
return \Cache::rememberForever('db.users.'.$id, function() use($model,$id){
return $model::select(['id'])->where('id',$id)->first();
});
}
throw new AuthenticationException('Unauthenticated.', $guards);
return $next($request);
}
}
EDIT
I solve this problem. Of course it was my wrong. I always return not $next($request) but clear user object
Below is code which work
<?php
namespace Sakuicms\Auth\Middleware;
use Closure;
use Illuminate\Contracts\Auth\Factory as Auth;
use Illuminate\Auth\AuthenticationException;
use Sakuicms\Auth\SessionGuard;
class Authenticate
{
protected $auth;
public function __construct(Auth $auth)
{
$this->auth = $auth;
}
protected function getName()
{
return 'login_'.config('auth.defaults.guard').'_'.sha1('Illuminate\Auth\SessionGuard');
}
public function handle($request, Closure $next, ...$guards)
{
$this->authenticate($guards);
return $next($request);
}
protected function authenticate(array $guards)
{
if(empty($guards)){
$id = session($this->getName());
if($id>0){
$model = config('auth.providers.users.model');
return \Cache::rememberForever('db.users.'.$id, function() use($model,$id){
return $model::select(['id'])->where('id',$id)->first();
});
}
}
foreach ($guards as $guard) {
if ($this->auth->guard($guard)->check()) {
return $this->auth->shouldUse($guard);
}
}
throw new AuthenticationException('Unauthenticated.', $guards);
}
}
Probably exists better/more elegant solution but for now it's ok for me. I'll refactor it in next stage.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 621
|
using System.Text.RegularExpressions;
using NLog.Targets;
namespace Reusable.Utilities.NLog
{
public static class DatabaseParameterInfoExtensions
{
// https://regex101.com/r/wgoA3q/1
// h t t ps://regex101.com/delete/BDmR7fAqwYQiT5DW5PKAJFAm
private static readonly Regex ParamRegex = new Regex("^(?<Prefix>.)(?<Name>[a-z0-9_-]+)(?:[:](?<Null>null))?", RegexOptions.IgnoreCase);
public static string Prefix(this DatabaseParameterInfo parameter) => ParamRegex.Match(parameter.Name).Groups["Prefix"].Value;
public static string Name(this DatabaseParameterInfo parameter) => ParamRegex.Match(parameter.Name).Groups["Name"].Value;
public static string FullName(this DatabaseParameterInfo parameter) => $"{parameter.Prefix()}{parameter.Name()}";
public static bool Nullable(this DatabaseParameterInfo parameter) => ParamRegex.Match(parameter.Name).Groups["Null"].Success;
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 6,434
|
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May 19, 2008, 06:10pm EDT |
In Pictures: The Billionaire Universities
© Daniel Cardiff/iStockphoto
Studying hard pays well. Most of the 469 Americans on Forbes' most recent list of the world's billionaires received a college education. Certain schools have been particularly adept at training future billionaires. Ten schools have graduated 192 members of the group.
© Darren McCollester/Newsmakers
Top 5 Billionaire Universities
A look at which schools have graduated the most of America's richest.
1. Harvard University
50 billionaire graduates
The oldest institution of higher learning in the U.S. has also graduated the most current billionaires. It has awarded 53 degrees to this affluent group. Notable grads include Microsoft Chief Executive Steve Ballmer and New York City's mayor, Michael Bloomberg.
More on Harvard University
2. Stanford University
It's fitting that Stanford University was founded by the wealthy railroad tycoon Leland Stanford. The California school has handed more diplomas to living billionaires than any school except one. Notable alumni include Google's Sergey Brin and Larry Page.
More on Stanford University
© Steven Minicola
3. University of Pennsylvania
University of Pennsylvania ranks high on the list of billionaire schools thanks to its prestigious Wharton business school. Twenty billionaires have graduated from that school alone. Wharton graduates include junk bond king Michael Milken and SAC Capital founder Steven Cohen.
More on the University of Pennsylvania
© AP Photo/Bob Child
4. Yale University
Nineteen billionaires received an undergraduate degree from Yale, but none have received a graduate degree from the school. Not helping is that Yale's business school consistently receives much lower rankings than its undergraduate school. Billie Yalies include private equity whiz Stephen Schwarzman and Sears Chairman Eddie Lampert.
More on Yale University
© AP Photo/Diane Bondareff
5. Columbia University
The football team is a consistent loser, but they must be doing something right in the classrooms at Morningside Heights. Columbia has awarded 17 degrees to future billionaires. Best known is Warren Buffett; the world's richest man attended Columbia Business School to study under legendary investor Benjamin Graham.
More on Columbia University
© Mahlon Lovett
6. Princeton University
Princeton's 13 billionaire alumni include financier Carl Icahn, Amazon founder Jeff Bezos and former eBay Chief Executive Meg Whitman. Getting accepted to the school's undergraduate program is notoriously hard: It only accepts about 10% of applicants.
More on Princeton University
© Mario Tama/Getty Images
7. New York University (tie)
An unusual distinction goes to New York University. The school has five dropouts who have gone on to become billionaires. One is Carl Icahn. After receiving a degree in philosophy from Princeton, Icahn enrolled in NYU's medical school. Bored by all the memorization required, he jumped ship to be a stockbroker.
More on New York University
© Steve Geer/iStockphoto
7. University of Chicago (tie)
University of Chicago is the top billionaire producer of the Midwest. It narrowly edges out Northwestern University, which has 9 billionaire alumni. Notable University of Chicago billionaire grads include Morningstar founder Joseph Mansueto.
More on the University of Chicago
9. Cornell University; Massachusetts Institute of Technology; Northwestern University; University of California, Berkeley; University of California, Los Angeles; University of Southern California (tie)
Nine billionaire graduates each
Six schools tie for ninth with nine billionaire graduates each. The most famous wealthy alum of any of these schools might be USC's George Lucas. He directed his first film, THX 1138, while he was still a student there. The Star Wars creator is now worth $3.9 billion.
More on Cornell University
More on Massachusetts Institute of Technology
More on Northwestern University
More on the University of California, Berkeley
More on the University of California, Los Angeles
More on the University of Southern California
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 1,180
|
var Storage = require('../src/wrapper'),
store;
module.exports = {
setUp: function (callback) {
Storage.local();
store = Storage.create();
callback();
},
'tests store find method': function(test) {
var KEY = 'FIND_KEY',
VALUE = 'waldo';
test.equal(store.size(), 0, 'Store is empty');
test.equal(store.find(KEY), undefined, 'Found nothing for ' + KEY);
store.store(KEY, VALUE);
test.equal(store.find(KEY), VALUE, 'found ' + VALUE + ' at ' + KEY);
test.equal(store.size(), 1, 'Store is not empty');
test.done();
},
tearDown: function (callback) {
store.clear();
callback();
}
};
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,060
|
Q: Issues Using Redux-Observable With Axios I'm trying to learn redux-observables but I seem to be having an issue getting my app to return data. I keep getting the error below and I'm not sure where I'm going wrong or what the error actually means.
Error: TypeError: axios__WEBPACK_IMPORTED_MODULE_3___default.a.get(...).map is not a function
Actions:
import { FETCH_DATA, FETCH_DATA_FAIL } from './constants';
export const fetchData = exampleData => ({
type: FETCH_DATA,
payload: { exampleData }
});
export const fetchDataFail = () => ({
type: FETCH_DATA_FAIL
});
EPIC:
import 'rxjs';
import { FETCH_DATA, FETCH_DATA_FAIL } from './constants';
import { fetchData } from './actions';
import axios from 'axios';
import { Observable } from 'rxjs';
import { mergeMap } from 'rxjs/operators';
import { ofType } from 'redux-observable';
export const exampleEpic = action$ =>
action$.pipe(ofType(FETCH_DATA),
mergeMap(action =>
axios.get('https://jsonplaceholder.typicode.com/todos/1')
.map(response => fetchData(response))
.catch(error => Observable.ofType(FETCH_DATA_FAIL)))
);
REDUCER:
import { FETCH_DATA, FETCH_DATA_FAIL } from './constants';
import { combineReducers } from 'redux';
const initialState = {};
export const exampleData = (state = initialState, action) => {
switch (action.type) {
case FETCH_DATA:
return action.payload
case FETCH_DATA_FAIL:
return {};
default:
return state;
}
};
export default combineReducers({
exampleData
});
EXAMPLE COMPONENT:
import React, { Component } from 'react';
import { connect } from 'react-redux';
import { fetchData } from './actions';
class App extends Component {
onClick = ()=>{
this.props.fetchData();
}
render() {
return (
<div>
<button onClick={this.onClick}><h1>Hello World</h1></button>
{JSON.stringify(this.props.data) }
</div>
);
}
}
const mapStateToProps = (state) => {
return {
data: state
}
};
function mapDispatchToProps(dispatch) {
return {
fetchData: () => dispatch(fetchData())
}
};
export default connect(
mapStateToProps,
mapDispatchToProps
)(App);
A: Using .then would have solved the issue, by the right way of doing it is using rxjs's from function, like below
import 'rxjs';
import { FETCH_DATA, FETCH_DATA_FAIL } from './constants';
import { fetchData } from './actions';
import axios from 'axios';
import { Observable, from } from 'rxjs';
import { mergeMap, map } from 'rxjs/operators';
import { ofType } from 'redux-observable';
export const exampleEpic = action$ =>
action$.pipe(ofType(FETCH_DATA),
mergeMap(action =>
from(axios.get('https://jsonplaceholder.typicode.com/todos/1'))
.map(response => fetchData(response))
.catch(error => Observable.ofType(FETCH_DATA_FAIL)))
);
Also, make sure you import .map operator from rxjs
Update: syntax using the .pipe operator
export const exampleEpic = action$ =>
action$.pipe(
ofType(FETCH_DATA),
mergeMap(action => from(axios.get('https://jsonplaceholder.typicode.com/todos/1/'))
.pipe(
map(response => fetchData(response)),
catchError(() => of(fetchDataFailure()))
)
)
)
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,600
|
\section{\textbf{Introduction}}
Fujita \cite{Fujita} considered the initial-boundary problem for a semilinear parabolic equation
\begin{equation}\label{Fu}
\left\{\begin{aligned}
&\frac{\partial u}{\partial t}=\Delta u+u^{1+\alpha}, \ t>0, \ x\in \mathbb{R}^{d}, \\
&u(x,0)=a(x),\ x\in \mathbb{R}^{d},\\
\end{aligned}\right.
\end{equation}
Fujita showed that there does not exist a global solution for any nontrivial nonnegative initial data when $0<d\alpha<2$, and there exists a global solution for sufficiently small initial data when $d\alpha>2$. Hayakawa \cite{Hayakawa} proved that (\ref{Fu}) has no global solution for any nontrivial nonnegative initial data in the critical case $d\alpha=2$ if the dimension $d$ equals 1 or 2. \\
Fujita \cite{Fu} studied the initial-boundary problem for a semilinear parabolic equation in domain $D\subset \mathbb{R}^{d}$:
\begin{equation}\label{Fujita}
\left\{\begin{aligned}
&\frac{\partial u}{\partial t}=\Delta u+f(u), \ t>0, \ x\in D, \\
&u(x,0)=a(x),\ x\in D,\\
&u(x,t)=0, \ x\in \partial D,
\end{aligned}\right.
\end{equation}
Denote $\lambda_{0}$ as the smallest eigenvalue of $-\Delta$ and the corresponding eigenfunction $\phi_{0}>0$, satisfies $\int_{D}\phi_{0}(x)dx=1$ and
\begin{equation*}
\left\{\begin{aligned}
&-\Delta \phi_{0}=\lambda_{0}\phi_{0} \ \ \ \mbox{in} \ D,\\
&\phi_{0}|_{\partial D}=0.
\end{aligned}\right.
\end{equation*}
Assume that $f$ satisfies the following \\
(\mbox{f.1}) $f$ is locally Lipschitz continuous. \\
(\mbox{f.2}) $f(0)\geq 0$ and $f(r)>0$ for $r>0$. \\
(\mbox{f.3}) $1/f$ is integrable at $t=+\infty$. \\
(\mbox{f.4}) $f$ is convex in $[0,\infty)$. \\
(\mbox{f.5}) $f(r)-\lambda_{0}r>0 \ \mbox{for} \ \ r>\int_{D}a_{0}\phi_{0}dx$, where $a_{0}=\exp(-k|x|^{2})$, $k>0$, $x\in \mathbb{R}^{d}$.\\
Fujita \cite{Fu} showed that if $D$ is bounded, $a(x)\geq 0$ in $D$ and $f$ satisfies (\mbox{f.1})- (\mbox{f.5}), then the solution of (\ref{Fujita}) blows up in finite time. As a special case that $f(r)=r^{1+\alpha}(\alpha> 0)$, the solution of (\ref{Fujita}) blows up in finite time if
\begin{equation*}
\int_{D}a(x)\phi_{0}(x)dx\geq \lambda^{1/\alpha}_{0}.
\end{equation*}
We refer to \cite{GV} about the many developments on solutions of nonlinear parabolic equations may blow up in finite time.
Recent years, stochastic partial differential equations has attracted the attention of many researchers. It is of interest to study the non-existence of global solutions to parabolic stochastic partial differential equations perturbed by random noise as follows:
\begin{equation}\label{multiplicative}
\left\{\begin{aligned}
&du=\Delta u+f(u)+\sigma(u)dW_{t}, \ t>0, \ x\in D, \\
&u(x,0)=g(x),\ x\in D,\\
&u(x,t)=0, \ x\in \partial D.
\end{aligned}\right.
\end{equation}
When $f(u)\equiv0$, $\sigma(u)=u^{\gamma}\ (\gamma\geq 1)$,
Mueller \cite{Mueller} considered the equation
\begin{equation}\label{gamma}
\left\{\begin{aligned}
&\frac{\partial u}{\partial t}=\Delta u+u^{\gamma}\dot{W}, \ \gamma\geq 1, \ t>0, \ 0\leq x\leq J,\\
&u(t,0)=u(t,J)=0,
\end{aligned}\right.
\end{equation}
where $\dot{W}=\dot{W}(t,x)$ is 2-parameter white noise and $u(x,0)$ is nonnegative and continuous. The conclusion is that for $1\leq \gamma<\frac{3}{2}$, $u$ exists for all time. Mueller \cite{M} showed that when $u(x,0)$ is a continuous nonnegative function on $[0,J]$, vanishing at the endpoints, but not identically zero, then there is a positive probability that the solution $u$ of (\ref{gamma}) blows up in finite time if $\gamma>3/2$. When $\sigma(u)\equiv 1$ and the Laplacian operator $\Delta$ is replaced by the infinitesimal generator of a $C_{0}$ semigroup, Prato and Zabczyk \cite{PZ} considered the stochastic semilinear equation
\begin{equation}\label{prato}
\left\{\begin{aligned}
&du=(Au+F(u))dt+dW\\
&u(0)=\xi,
\end{aligned}\right.
\end{equation}
where $A$ is the generator of semmigroup $S(t)=e^{At}$ on a Banach space $E$, and $F$ is a mapping from $E$ into $E$. $W$ is a Wiener process defined on a probability space $(\Omega, \mathcal{F}_{t}, P)$. $\xi$ is an $\mathcal{F}_{0}$-measurable $E$-valued random variable. They assumed that $F$ satisfies the Lipschitz condition on bounded sets of $E$. This property of $F$ together with some other conditions ensure that (\ref{prato}) has a unique non-exploding solution. When $\sigma(u)=\sigma$ (positive constant), $W$ is a 2-dimensional Brownian sheet, $f$ is a nonnegative, convex function such that $\int_{0}^{\infty}1/f<\infty$, Bonder and Groisman \cite{BG} proved that the solution to (\ref{multiplicative}) blows up in finite time with probability one for every nonnegative initial datum $u(x,0)\geq 0$. Dozzi and L$\acute{\mbox{o}}$pez-Mimbela \cite{DL} considered the equation (\ref{multiplicative}) with $\sigma(u)=\kappa u$, where $\beta, \kappa$ are given positive numbers, $W_{t}$ is a standard one-dimensional Brownian motion. They proved that the solution of (\ref{multiplicative}) blows up in finite time with positive probability if $f(u)\geq Cu^{1+\beta}$ ($u>0$, $C>0$ ).
Chow \cite{Chow,Ch} considered the initial-boundary value problem for the parabolic It$\hat{\mbox{o}}$ equation
\begin{equation}\label{Ito}
\left\{\begin{aligned}
&\frac{\partial u}{\partial t}=Au+f(u,x,t)+\sigma(u,\nabla u,x,t)\partial_{t}W(x,t)\\
&u(x,0)=g(x),\ x\in D,\\
&u(x,t)=0, \ t\in (0,T),x\in \partial D,
\end{aligned}\right.
\end{equation}
where $D\subset \mathbb{R}^{d}$, $A=\sum_{i,j=1}^{d}\frac{\partial}{\partial x_{i}}[a_{ij}(x)\frac{\partial}{\partial x_{j}}]$ is a symmetric, uniformly elliptic operator with smooth coefficients, $f$ and $\sigma$ are given functions. For $x\in \mathbb{R}^{d}, \ t\geq 0$, $W(x,t)$ is a continuous Wiener random field defined in a complete probability space $(\Omega, \mathcal{F}, P)$ with a filtration $\mathcal{F}_{t}$. $W(x,t)$ has mean $\mathbb{E}W(x,t)=0$ and covariance function $q(x,y)$ defined by
\begin{equation*}
\mathbb{E}\{W(x,t)W(y,t)\}=(t \wedge s)q(x,y), \ x,y\in \mathbb{R}^{d},
\end{equation*}
where $t \wedge s=\min\{t,s\}$ for $0\leq t,s\leq T$. Let $H=L^{2}(D)$, $H^{1}=H^{1}(D)$ be the $L^{2}$-Sobolev space of first order and $H^{1}_{0}$ the closure in $H^{1}$ of the space of $C^{1}$-functions with compact support in $D$. Under the usual conditions, such as coercivity conditions, Lipschitz continuity and boundedness conditions, Eq.(\ref{Ito}) has a a unique global strong solution $u\in C([0,T];H)\cap L^{2}([0,T]; H^{1})$ (see \cite[Theorem 3-7.2]{C}). To consider positive (nonnegative) solutions, the author assume that the following conditions hold: \\
$\mbox{(P1)}$ There exists a constant $\delta\geq 0$ such that
\begin{equation*}
\frac{1}{2}q(x,x)\sigma^{2}(r,\xi,x,t)-\sum_{i,j=1}^{d}a_{ij}(x)\xi_{i}\xi_{j}\leq \delta r^{2},
\end{equation*}
for all $r\in \mathbb{R}$, $x\in \overline{D}$, $\xi\in \mathbb{R}^{d}$ and $t\in [0,T]$.\\
$\mbox{(P2)}$ The function $f(r,x,t)$ is continuous on $\mathbb{R}\times \overline{D}\times [0,T]$ such that $f(r,x,t)\geq 0$ for $r\leq 0$ and $x\in \overline{D}$, $t\in [0,T]$.\\
$\mbox{(P3)}$ The initial datum $g(x)$ on $\overline{D}$ is positive and continuous. \\
Chow \cite{Chow} proved that the solution of Eq.(\ref{Ito}) is positive. Under some suitable conditions, Chow \cite{Chow, Ch} showed that the positive solutions of a class of stochastic reaction-diffusion equations will blow up in the $L^{p}$-norm sense, $p\geq 1$. Chow and Liu \cite{CL} considered the problem of explosive solutions in mean $L^{p}$-norm sense of semilinear stochastic functional parabolic differential equations of retarded type.
Lv and Duan \cite{Lv} considered the Eq.(\ref{Ito}) with $A=\triangle$, the Laplacian operator, the nonlinear term $f$ is assumed to be satisfied by an inequality, which is weaker than the condition $\mbox{(P2)}$, the noise intensity $\sigma$ allows to be higher nonlinear than the square nonlinear (see \cite[formula (3.2)]{Lv}). They proved that the noise could induce finite time blow up of solutions.
Recent years, stochastic partial differential equations driven by L$\acute{\mbox{e}}$vy noise have attracted many attentions (see, for example, \cite{ZJ, W, Y, L, PZ, D, LZ, RZ, SH}). But there are few results about the existence of explosive solutions to stochastic partial differential equations with L$\acute{\mbox{e}}$vy noise in the literature. Bao and yuan \cite{Bao} considered the stochastic reaction-diffusion equations with jumps
\begin{equation}\label{jump}
\left\{\begin{aligned}
&\frac{\partial u}{\partial t}=Au+b(t,u,x)+\sigma(t,u,\nabla u,x)\partial_{t}W(x,t)\\
&\quad\quad\quad+\int_{\mathbb{Y}}\Upsilon(t,u,x,y)\partial_{t}\widetilde{N}(t,dy), \ t>0,\\
&u(x,0)=\phi(x),\ x\in \mathcal{O}, \ u(t,x)|_{\partial \mathcal{O}}=0, \ t>0,
\end{aligned}\right.
\end{equation}
where $\mathcal{O}\subset \mathbb{R}^{n}$ is a bounded domain with $C^{\infty}$ boundary $\partial \mathcal{O}$, $A=\sum_{i,j=1}^{n}\frac{\partial}{\partial x_{i}}(a_{i,j}(x)\frac{\partial}{\partial x_{j}})$ be a symmetric, uniformly elliptic operator with smooth coefficients, $W(x,t)$ is a Wiener random defined on the completed probability space $(\Omega,\mathcal{F},\{\mathcal{F}\}_{t\geq 0}, \mathbb{P})$, $\widetilde{N}(dt,du)$ is the compensated Poisson measure. Under some conditions, they showed that the solution of (\ref{jump}) blows up in finite time. It should be pointed out that the nonlinear term $b:[0,\infty)\times \mathbb{R}\times \overline{O}\mapsto \mathbb{R}$ is assumed to be locally Lip-continuous w.r.t the second variable such that $b(t,r,x)\geq 0$ for any $r\leq 0$, however, there are many functions don't satisfy this condition, for example, $b(r)=r(1-r^{2})$. And $\mathcal{O}\subset \mathbb{R}^{n}$ is assumed to be bounded, the proof of Theorem 2.1 in \cite{Bao} depends on the boundedness of volume of $\mathcal{O}$. The results of \cite{Bao} can't be generalized to the case for unbounded domain, such as $\mathcal{O}=\mathbb{R}^{n}$.
In this paper, we study the problem of explosive solutions to a class of semilinear stochastic parabolic differential equations driven by L$\acute{\mbox{e}}$vy noise. The paper is organized as follows. In Section 2, we recall some basic results for semilinear stochastic parabolic equations with L$\acute{\mbox{e}}$vy noise. In Section 3, under some assumptions, we prove that the existence of positive solutions of a semilinear stochastic reaction-diffusion equation. In Section 4, under some suitable conditions on the drift or diffusion term, we prove that the solutions of stochastic parabolic differential equations will blow up in a finite time in mean $L^{p}$-norm sense, $p\geq 1$. Some examples are presented to illustrate the theory. In Section 5, we establish a global existence theorem based on a Lyapunov functional. We show that the existence of global solution to stochastic Allen-Cahn equation driven by L$\acute{\mbox{e}}$vy noise.
\section{\textbf{Preliminaries}}
Let $D$ be a domain in $\mathbb{R}^{d}$, which has a smooth boundary if it is bounded. Denote $L^{2}(D)$ by $H$, the usual $L^{2}$ real Hilbert space with the inner product $(\cdot,\cdot)$ and norm $\|\cdot\|$, respectively. Let $H^{1}=H^{1}(D)$ be the $L^{2}$-Sobolev space of first order. Denote $H_{0}^{1}$ the closure in $H^{1}$ of the space of $C^{1}$-functions with compact support in $D$. Denote by $D([0,T],H)$ the space of all c$\grave{a}$dl$\grave{a}$g paths from $[0,T]$ into $H$.
Let $W(x,t)$ be a continuous Wiener random field defined on a complete probability space $(\Omega, \mathcal{F}, \mathbb{P})$ with a filtration $\mathcal{F}_{t}$. $W(x,t)$ has mean zero and covariance function $q(x,y)$ such that
\begin{equation*}
\mathbb{E}W(x,t)=0, \ \ \mathbb{E}\{W(x,t)W(y,t)\}=(t\wedge s)q(x,y),\ s,t\in [0,T], x,y\in \mathbb{R}^{d}.
\end{equation*}
The associated covariance operator $Q$ in $H$ with kernel $q(x,y)$ is defined by
\begin{equation*}
(Q\phi)(x)=\int_{D}q(x,y)\phi(y)dy, \ \ x\in D,\ \phi\in H.
\end{equation*}
In this paper, we assume that the covariance function $q(x,y)$ is bounded, continuous and there is $q_{0}>0$ such that
\begin{equation*}
\sup_{x,y\in D}|q(x,y)|\leq q_{0}\ \ \mbox{and} \ \mbox{Tr}\ Q=\int_{D}q(x,x)dx<\infty.
\end{equation*}
Let $(Z, \mathcal{B}(Z)$ be a measurable space. Denote by $N(dt,dz)$ the Poisson random measure with intensity measure $dt\nu(dz)$ on $\mathbb{R}_{+}\times Z$, here $\mathbb{R}_{+}=[0,\infty)$, $dt$ is the Lebesgue measure on $\mathbb{R}_{+}$, $\nu(dz)$ is a $\sigma$-finite measure on $(Z, \mathcal{B}(Z))$. Denote by $\widetilde{N}(dt,dz)=N(dt,dz)-dt\nu(dz)$ the compensated Poisson measure. Assume that $W$ and $N$ are independent.
Consider the initial-boundary problem of a semilinear stochastic reaction-diffusion equation in domain $D\subset \mathbb{R}^{d}$:
\begin{equation}\label{rd}
\left\{\begin{aligned}
&\frac{\partial u}{\partial t}=Au+f(u,x,t)+\sigma(u,\nabla u,x,t)\partial_{t}W(x,t)\\
&\quad\quad+\int_{Z}\varphi(u,x,z,t)\partial_{t}\widetilde{N}(t,dz),\\
&u(x,0)=g(x),\ x\in D,\\
&u(x,t)=0, \ t\in (0,T),x\in \partial D,
\end{aligned}\right.
\end{equation}
where $A=\sum_{i,j=1}^{d}\frac{\partial}{\partial x_{i}}[a_{ij}(x)\frac{\partial}{\partial x_{j}}]$ is a symmetric, uniformly elliptic operator with smooth coefficients, that is, there exists a constant $c>0$ such that $b(x,\xi):=\sum_{i,j=1}^{d}a_{ij}(x)\xi_{i}\xi_{j}\geq c|\xi|^{2}$ for all $x\in \overline{D}$ and $\xi=(\xi_{1},\ldots, \xi_{d})\in \mathbb{R}^{d}$.
Let $u_{t}=u(\cdot,t)$, $F_{t}(u)=f(u,\cdot,t)$, $\Sigma_{t}(u)=\sigma(u,\nabla u, \cdot,t)$, \ $\Gamma_{t}(u,z)=\varphi(u,\cdot,z,t)$ and $W_{t}=W(\cdot,t)$, then we can rewrite the equation (\ref{rd}) as
\begin{equation}\label{parabolic}
\left\{\begin{aligned}
&du_{t}=[Au_{t}+F_{t}(u_{t})]dt+\Sigma_{t}(u_{t})dW_{t}+\int_{Z}\Gamma_{t}(u_{t},z)\widetilde{N}(dt,dz),\\
&u_{0}=g,
\end{aligned}\right.
\end{equation}
where $A$ is regarded as a linear operator from $H^{1}$ into $H^{-1}$ with domain $D(A)=H_{0}^{1}\cap H^{2}$, $F_{t} :H\rightarrow H$ is continuous.
If $A$ satisfies the coercivity condition, $f$ and $\sigma$ satisfy the Lipschitz continuity and boundedness conditions, the equation (\ref{parabolic}) has a unique global strong solution $u\in L^{2}([0,T]; H^{-1})\cap D([0,T]; H)$( see Theorem 3.2, \cite{RZ}).
To consider the positive solutions, we assume that (\ref{rd}) has a unique (strong) solution. In addition, we assume that
$\mbox{(A1)}$
\begin{equation*}
f(u,x,t)\geq a_{1}u^{\beta}+a_{2}u,
\end{equation*}
where $a_{1},a_{2}\in \mathbb{R}$, $\beta>1$, $(-1)^{\beta}\in \mathbb{R}$ and
\begin{equation}
a_{1}\left\{\begin{aligned}
&>0, \ \mbox{if}\ (-1)^{\beta}=1,\\
&<0, \ \mbox{if}\ (-1)^{\beta}=-1.
\end{aligned}\right.
\end{equation}
$\mbox{(A2)}$ There exist constants $b_{1},b_{2}\geq 0$ such that
\begin{equation*}
\frac{1}{2}q(x,x)\sigma^{2}(u,\xi,x,t)-\sum_{i,j=1}^{d}a_{ij}(x)\xi_{i}\xi_{j}\leq b_{1}|u|^{m}+b_{2}u^{2},
\end{equation*}
for all $u\in \mathbb{R}$, $x\in \overline{D}$, $\xi\in \mathbb{R}^{d}$ and $t\in [0,T]$, where $2< m<\beta+1$.
$\mbox{(A3)}$ There exist a a constant $\mu\in [2,\beta+1)$ and mappings $\psi: \overline{D}\rightarrow \mathbb{R}_{+}$ with $\int_{Z}\psi(z)\nu(dz)<+\infty$, such that
\begin{equation}
\varphi^{2}(u,x,z,s)\leq \psi(z)|u(x,s)|^{\mu}.
\end{equation}
$\mbox{(A4)}$ the initial datum $g(x)$ on $\overline{D}$ is positive and continuous.
As in \cite{Chow}, let $\eta(r)=r^{-}$ denote the negative part of $r$ for $r\in \mathbb{R}$, or $\eta(r)=0$, if $r\geq 0$ and
$\eta(r)=-r$ if $r<0$. Set $k(r)=\eta^{2}(r)$ so that $k(r)=0$ for $r\geq 0$ and $k(r)=r^{2}$ for $r<0$. For $\varepsilon>0$, let $k_{\varepsilon}(r)$ be a $C^{2}$-regularization of $k(r)$ defined by
\begin{equation}\label{kr}
k_{\varepsilon}(r)=\left\{\begin{aligned}
&r^{2}-\frac{\varepsilon^{2}}{6}, &r<-\varepsilon,\\
&-\frac{r^{3}}{\varepsilon}(\frac{r}{2\varepsilon}+\frac{4}{3}), \ &-\varepsilon\leq r<0,\\
&0, &r\geq 0.
\end{aligned}\right.
\end{equation}
It is easy to see that $k_{\varepsilon}(r)$ has the following properties. \\
\textbf{Lemma 2.1.} (see \cite{Chow}). The first two derivatives $k'_{\varepsilon}$, $k''_{\varepsilon}$ of $k_{\varepsilon}$ are continuous and satisfy the conditions: $k'_{\varepsilon}(r)=0$ for $r\geq 0$; and $k''_{\varepsilon}(r)\geq 0$ for any $r\in \mathbb{R}$. Moreover, as $\varepsilon\rightarrow 0$, we have
\begin{align}\label{convergence}
k_{\varepsilon}(r)\rightarrow k(r),\ k'_{\varepsilon}(r)\rightarrow -2\eta(r)\ \ \mbox{and} \ k''_{\varepsilon}(r)\rightarrow 2\theta(r),
\end{align}
where $\theta(r)=0$ for $r\geq 0$, $\theta(r)=1$ for $r<0$, and the convergence is uniform for $r\in \mathbb{R}$.
\section{\textbf{Positive solutions}}
In this section, we will consider the existence of positive solution of Eq. (\ref{rd}).
\textbf{Theorem 3.1} Suppose that the conditionss $\mbox{(A1)-(A4)}$ hold. Then the solution of initial-boundary value problem (\ref{rd}) with nonnegative and continuous data remains positive so that $u(x,t)\geq 0$, a.s. for almost every $x\in D$ and for all $t\in [0,T]$. \\
\textbf{Proof.} Let $u_{t}=u(\cdot,t)$ and
\begin{equation*}
\Phi_{\varepsilon}(u_{t})=(1,k_{\varepsilon}(u_{t}))=\int_{D}k_{\varepsilon}(u(x,t))dx.
\end{equation*}
From It$\hat{\mbox{o}}$'s formula, it follows that
\begin{align*}
\Phi_{\varepsilon}(u_{t})&=\Phi_{\varepsilon}(g)+\int_{0}^{t}\int_{D}k'_{\varepsilon}(u(x,s))A u(x,s)dxds\\
&\quad+\int_{0}^{t}\int_{D}k'_{\varepsilon}(u(x,s))f(u(x,s),x,s)dxds\\
&\quad+\int_{0}^{t}\int_{D}k'_{\varepsilon}(u(x,s))\sigma(u(x,s),\nabla u(x,s),x,s)dW(x,s)dx\\
&\quad+\frac{1}{2}\int_{0}^{t}\int_{D}k''_{\varepsilon}(u(x,s))q(x,x)\sigma^{2}(u(x,s),\nabla u(x,s),x,s)dxds\\
&\quad+\int_{0}^{t}\int_{Z}\int_{D}\big(k_{\varepsilon}(u(x,s)+\varphi(u,x,z,s))-k_{\varepsilon}(u(x,s))\big)dx\widetilde{N}(dsdz)\\
&\quad+\int_{0}^{t}\int_{Z}\int_{D}\big(k_{\varepsilon}(u(x,s)+\varphi(u,x,z,s))-k_{\varepsilon}(u(x,s))-\varphi(u,x,z,s)k'_{\varepsilon}(u(x,s)))dx\nu(dz)ds\\
&\quad=\Phi_{\varepsilon}(g)+\int_{0}^{t}\int_{D}k''_{\varepsilon}(u(x,s))\big(\frac{1}{2}q(x,x)\sigma^{2}(u(x,s),\nabla u(x,s),x,s)-b(x,\nabla u(x,s))\big)dxds\\
&\quad+\int_{0}^{t}\int_{D}k'_{\varepsilon}(u(x,s))f(u(x,s),x,s)dxds\\
&\quad+\int_{0}^{t}\int_{D}k'_{\varepsilon}(u(x,s))\sigma(u(x,s),\nabla u(x,s),x,s)dW(x,s)dx\\
&\quad+\int_{0}^{t}\int_{Z}\int_{D}\big(k_{\varepsilon}(u(x,s)+\varphi(u,x,z,s))-k_{\varepsilon}(u(x,s))\big)dx\widetilde{N}(dsdz)\\
&\quad+\int_{0}^{t}\int_{Z}\int_{D}\big(k_{\varepsilon}(u(x,s)+\varphi(u,x,z,s))-k_{\varepsilon}(u(x,s))-\varphi(u,x,z,s)k'_{\varepsilon}(u(x,s)))dx\nu(dz)ds.
\end{align*}
By taking expectations of both sides of the above equality, we have
\begin{align*}
\mathbb{E}\Phi_{\varepsilon}(u_{t})&=\Phi_{\varepsilon}(g)+\mathbb{E}\int_{0}^{t}\int_{D}k''_{\varepsilon}(u(x,s))\big(\frac{1}{2}q(x,x)\sigma^{2}(u(x,s),\nabla u(x,s),x,s)-b(x,\nabla u(x,s))\big)dxds\\
&\quad+\mathbb{E}\int_{0}^{t}\int_{D}k'_{\varepsilon}(u(x,s))f(u(x,s),x,s)dxds\\
&\quad+\mathbb{E}\int_{0}^{t}\int_{Z}\int_{D}\big(k_{\varepsilon}(u(x,s)+\varphi(u,x,z,s))-k_{\varepsilon}(u(x,s))-\varphi(u,x,z,s)k'_{\varepsilon}(u(x,s)))dx\nu(dz)ds.
\end{align*}
From $\mbox{(A1)}$ and Lemma 2.1, it follows that
\begin{align}\label{inequality}
\mathbb{E}\Phi_{\varepsilon}(u_{t})&\leq \Phi_{\varepsilon}(g)+\mathbb{E}\int_{0}^{t}\int_{D}k''_{\varepsilon}(u(x,s))\big(b_{1}|u(x,s)|^{m}+b_{2}|u(x,s)|^{2}\big)dxds\nonumber\\
&\quad+\mathbb{E}\int_{0}^{t}\int_{D}k'_{\varepsilon}(u(x,s))(a_{1}u^{\beta}(x,s)+a_{2}u(x,s))dxds\nonumber\\
&\quad+\mathbb{E}\int_{0}^{t}\int_{Z}\int_{D}\big(k_{\varepsilon}(u(x,s)+\varphi(u,x,z,s))-k_{\varepsilon}(u(x,s))-\varphi(u,x,z,s)k'_{\varepsilon}(u(x,s)))dx\nu(dz)ds.
\end{align}
By Taylor's theorem, in view of the integral form of the remainder, we have
\begin{align}\label{Taylor}
k_{\varepsilon}(u(x,s)+\varphi(u,x,z,s))-k_{\varepsilon}(u(x,s))-(k'_{\varepsilon}(u(x,s)),\varphi(u,x,z,s))\nonumber\\
=\int_{0}^{1}(1-\tau)k''_{\varepsilon}(\varphi(u,x,z,s)\tau+u(x,s))\varphi^{2}(u,x,z,s)d\tau
\end{align}
Substitute (\ref{Taylor}) into (\ref{inequality}), we get
\begin{align}\label{integral}
\mathbb{E}\Phi_{\varepsilon}(u_{t})&\leq \Phi_{\varepsilon}(g)+\mathbb{E}\int_{0}^{t}\int_{D}k''_{\varepsilon}(u(x,s))\big(b_{1}|u(x,s)|^{m}+b_{2}|u(x,s)|^{2}\big)dxds\nonumber\\
&\quad+\mathbb{E}\int_{0}^{t}\int_{D}k'_{\varepsilon}(u(x,s))(a_{1}u^{\beta}(x,s)+a_{2}u(x,s))dxds\nonumber\\
&\quad+\mathbb{E}\int_{0}^{t}\int_{Z}\int_{D}\int_{0}^{1}(1-\tau)k''_{\varepsilon}(\varphi(u,x,z,s)\tau+u(x,s))\varphi^{2}(u,x,z,s)d\tau dx\nu(dz)ds.
\end{align}
Since $\lim_{\varepsilon\rightarrow 0}\mathbb{E}\Phi_{\varepsilon}(u_{t})=\mathbb{E}\|\eta(u_{t})\|^{2}$, taking the limits on both sides of (\ref{integral}) as $\varepsilon\rightarrow 0$, by (\ref{convergence}) we obtain
\begin{align}\label{limit}
\mathbb{E}\|\eta(u_{t})\|^{2}&\leq \int_{D}|\eta(g(x))|^{2}dx+2\mathbb{E}\int_{0}^{t}\int_{D}\theta(u(x,s))\big(b_{1}|u(x,s)|^{m}+b_{2}|u(x,s)|^{2}\big)dxds\nonumber\\
&\quad-2\mathbb{E}\int_{0}^{t}\int_{D}\eta(u(x,s))(a_{1}u^{\beta}(x,s)+a_{2}u(x,s))dxds\nonumber\\
&\quad+2\mathbb{E}\int_{0}^{t}\int_{Z}\int_{D}\int_{0}^{1}(1-\tau)\theta(\varphi(u,x,z,s)\tau+u(x,s))\varphi^{2}(u,x,z,s)d\tau dx\nu(dz)ds.
\end{align}
By the definition of $\eta$, it follows that $\eta(g)=0$. This together with $\mbox{(A4)}$, Lemma 2.1 and $(-1)^{\beta}a_{1}=|a_{1}|$ yield
\begin{align}\label{u}
\mathbb{E}\|\eta(u_{t})\|^{2}
&\leq 2\mathbb{E}\int_{0}^{t}\int_{D}\big(b_{1}|u(x,s)|^{m}+b_{2}|u(x,s)|^{2}\big)dxds\nonumber\\
&\quad-2\mathbb{E}\int_{0}^{t}\int_{D}\eta(u(x,s))(a_{1}u^{\beta}(x,s)+a_{2}u(x,s))dxds\nonumber\\
&\quad+\int_{Z}\psi(z)\nu(dz)\ \mathbb{E}\int_{0}^{t}\int_{D}|u(x,s)|^{\mu}dxds\nonumber\\
&= 2\mathbb{E}\int_{0}^{t}\int_{D}[b_{1}{(u^{-})}^{m}(x,s)+b_{2}{(u^{-})}^{2}(x,s)]dxds\nonumber\\
&\quad-2\mathbb{E}\int_{0}^{t}\int_{D}[|a_{1}|{(u^{-})}^{\beta+1}(x,s)-a_{2}{(u^{-})}^{2}(x,s)]dxds\nonumber\\
&\quad+\int_{Z}\psi(z)\nu(dz)\ \mathbb{E}\int_{0}^{t}\int_{D}{(u^{-})}^{\mu}(x,s)dxds.
\end{align}
It is known that the following $L^{p}$ interpolation inequality and Young inequality hold (see \cite{GT})
\begin{align}\label{alpha}
\|u\|_{L^{r}}\leq \|u\|^{\alpha}_{L^{p}}\|u\|^{1-\alpha}_{L^{q}},
\end{align}
\begin{align}\label{rpq}
ab\leq \varepsilon a^{\delta}+\varepsilon ^{-\frac{\omega}{\delta}}b^{\omega},
\end{align}
where $\alpha\in (0,1)$, $\varepsilon>0$, $\delta>0$, $\omega>0$, $a>0$, $b>0$,
\begin{align*}
&\frac{1}{r}=\frac{\alpha}{p}+\frac{1-\alpha}{q}, \ 1\leq p \leq r\leq q \leq \infty,\\
&\frac{1}{\delta}+\frac{1}{\omega}=1.
\end{align*}
Since $2< m<\beta+1$, it follows that from (\ref{alpha}) and (\ref{rpq})
\begin{align}\label{beta}
2b_{1}\int_{D}(u^{-})^{m}(x,t)dx&=2b_{1}\|u^{-}\|^{m}_{L^{m}}\nonumber\\
&\leq C\|u^{-}\|^{m\alpha}_{L^{2}}\|u^{-}\|^{m(1-\alpha)}_{L^{\beta+1}}\nonumber\\
&\leq \varepsilon \|u^{-}\|_{L^{\beta+1}}^{m(1-\alpha)\frac{2}{2-m\alpha}}+C(\varepsilon, m, \beta)\|u^{-}\|^{2}_{L^{2}}\nonumber\\
&=\varepsilon \|u^{-}\|^{\beta+1}_{L^{\beta+1}}+C(\varepsilon, m, \beta)\|u^{-}\|^{2}_{L^{2}},
\end{align}
where $\alpha=\frac{2(\beta+1-m)}{m(\beta-1)}$. \\
Similarly, for $\mu\in [2,\beta+1)$, we obtain
\begin{align}\label{levy}
\int_{Z}\psi(z)\nu(dz)\ \int_{D}{(u^{-})}^{\mu}(x,s)dxds&\leq C\|u^{-}\|^{\mu}_{L^{\mu}}\nonumber\\
&\leq C\|u^{-}\|^{\mu\alpha'}_{L^{2}}\|u^{-}\|^{\mu(1-\alpha')}_{L^{\beta+1}}\nonumber\\
&\leq \varepsilon \|u^{-}\|_{L^{\beta+1}}^{\mu(1-\alpha')\frac{2}{2-\mu\alpha'}}+C(\varepsilon, \mu, \beta)\|u^{-}\|^{2}_{L^{2}}\nonumber\\
&=\varepsilon \|u^{-}\|^{\beta+1}_{L^{\beta+1}}+C(\varepsilon, \mu, \beta)\|u^{-}\|^{2}_{L^{2}},
\end{align}
where $\alpha'=\frac{2(\beta+1-\mu)}{\mu(\beta-1)}$. \\
Putting (\ref{beta}) and (\ref{levy}) into (\ref{u}), we obtain
\begin{align*}
\mathbb{E}\|\eta(u_{t})\|^{2}&\leq \int_{0}^{t}(2\varepsilon-2|a_{1}|)\mathbb{E}\|u^{-}_{s}\|^{\beta+1}_{L^{\beta+1}}ds+(2b_{2}+2a_{2}+C(\varepsilon, m, \beta)+C(\varepsilon, \mu, \beta))\int_{0}^{t}\mathbb{E}\|u_{s}^{-}\|^{2}_{L^{2}}ds
\end{align*}
Let $\varepsilon \in (0, |a_{1}|)$. Then
\begin{align*}
\mathbb{E}\|\eta(u_{t})\|^{2}\leq C \ \int_{0}^{t}\mathbb{E}\|\eta(u_{t})\|^{2}ds,
\end{align*}
From Gronwall's inequality, it follows that $\mathbb{E}\|\eta(u_{t})\|^{2}=0$. This implies that $\eta(u_{t})=u^{-}(x,t)=0$ a.s. for a.e. $x\in D$ and $t\in [0,T]$. The proof is complete. \ \ \ $\Box$ \\
\textbf{Remark 3.1.} The assumption $\mbox{(A1)}$ is weaker than the assumption $\mbox{(H1)}$ in \cite{Bao}. For example, if we consider the Allen-Cahn type equation, $f(u)=u-u^{3}$ doesn't satisfy $\mbox{(H1)}$, but $f$ satisfies $\mbox{(A1)}$. \\
\textbf{Remark 3.2.} Since $A=\sum_{i,j=1}^{d}\frac{\partial}{\partial x_{i}}[a_{ij}(x)\frac{\partial}{\partial x_{j}}]$ is more general than the Laplacian operator $\triangle$, Theorem 3.1 is the generalization of Theorem 3.1 in \cite{Lv}. \\
\textbf{Remark 3.3.} If it is assumed that $\beta\in (0,1)$, for the case $1+\beta\leq m<2$ and $1+\beta\leq q <2$, by the $L^{p}$ interpolation inequality and Young inequality, we can get the corresponding results.\\
\section{\textbf{Explosive solutions}}
In this section, we consider the unbounded solutions of the equation (\ref{rd}). \\
For the elliptic equation:
\begin{equation}\label{elliptic}
\left\{\begin{aligned}
&A\vartheta=-\lambda\vartheta,\ \mbox{in}\ D,\\
&\vartheta=0, \ \mbox{on}\ \partial D,
\end{aligned}\right.
\end{equation}
it is well known that all the eigenvalues of $-A$ are strictly positive, increasing and the eigenfunction $\phi$ corresponding to the smallest eigenvalue $\lambda_{1}$ does not change sign in the domain $D$ (see p. 355, \cite{LE}). We can normalize it in such a way that
\begin{equation}\label{norm}
\phi(x)\geq 0, \ \ \ \int_{D}\phi(x)dx=1.
\end{equation}
\textbf{Theorem 4.1.}
Suppose the initial-boundary value problem (\ref{rd}) has a unique local solution and the conditions $\mbox{(A1)-(A4)}$ hold. In addition, we assume that $\lambda_{1}> a_{2}$, $a_{1}>0$, and
\begin{equation*}
\int_{D}g(x)\phi(x)dx> \big(\frac{\lambda_{1}-a_{2}}{a_{1}}\big)^{\frac{1}{\beta-1}},
\end{equation*}
and if $\lambda_{1}<a_{2}$, we assume that $\int_{D}g(x)\phi(x)dx>0$, where $\lambda_{1}$ is the smallest eigenvalue of $-A$ and $\phi$ is the corresponding eigenfunction. Then, for any $p\geq 1$, there exists a constant $T_{p}>0$ such that
\begin{equation}\label{lp}
\lim_{t\rightarrow T^{-}_{p}}\mathbb{E}\|u_{t}\|_{L^{p}}=\lim_{t\rightarrow T^{-}_{p}}\mathbb{E}\big\{\int_{D}|u(x,t)|^{p}dx\big\}^{1/p}=\infty.
\end{equation}
That is, the solution explodes in mean $L^{p}$-norm sense. \\
\textbf{Proof.} By Theorem 3.1, Eq. (\ref{rd}) has a unique positive solution. We will prove the theorem by contradiction. We suppose (\ref{lp}) is false. Then there exists a global positive solution $u$ such that
\begin{equation*}
\sup_{0\leq t\leq T}\mathbb{E}\big\{\int_{D}|u(x,t)|^{p}dx\big\}^{1/p}<\infty,
\end{equation*}
for any $T>0$. Let $\phi$ be the the eigenfunction defined in (\ref{elliptic}). Define
\begin{equation}\label{hat}
\hat{u}(t):=\int_{D}u(x,t)\phi(x)dx\geq 0.
\end{equation}
By (\ref{norm}), $\phi$ can be regarded as the probability density function of a random variable $\xi$ in $D$, independent of $W_{t}$. The equality (\ref{hat})
can be interpreted as an expectation $\hat{u}(t)=\mathbb{E}_{\xi}\{u(\xi,t)\}$. From (\ref{rd}), (\ref{hat}) and the self-adjointness of $A$, it follows that
\begin{align}\label{multiply}
\hat{u}(t)&=(g,\phi)+\int_{0}^{t}\int_{D}[Au(x,s)]\phi(x)dxds+\int_{0}^{t}\int_{D}f(u,x,s)\phi(x)dxds\nonumber\\
&\quad+\int_{0}^{t}\int_{D}\sigma(u,\nabla u,x,s)\phi(x)dxdW(x,s)\nonumber\\
&\quad+\int_{0}^{t}\int_{Z}\int_{D}\varphi(u,x,z,s)\phi(x)dx\widetilde{N}(ds,dz)\nonumber\\
&=(g,\phi)-\lambda_{1}\int_{0}^{t}\int_{D}u(x,s)\phi(x)dxds+\int_{0}^{t}\int_{D}f(u,x,s)\phi(x)dxds\nonumber\\
&\quad+\int_{0}^{t}\int_{D}\sigma(u,\nabla u,x,s)\phi(x)dxdW(x,s)\nonumber\\
&\quad+\int_{0}^{t}\int_{Z}\int_{D}\varphi(u,x,z,s)\phi(x)dx\widetilde{N}(ds,dz).
\end{align}
Taking the expectation to both sides of (\ref{multiply}) and by Fubini's theorem, we have
\begin{align*}
\mathbb{E}\hat{u}(t)=(g,\phi)-\lambda_{1}\int_{0}^{t}\mathbb{E}\hat{u}(s)ds+\int_{0}^{t}\mathbb{E}\int_{D}f(u,x,s)\phi(x)dxds,
\end{align*}
or, in the differential form,
\begin{equation}\label{differential}
\left\{\begin{aligned}
&\frac{d\xi(t)}{dt}=-\lambda_{1}\xi(t)+\mathbb{E}\int_{D}f(u,x,s)dx\\
&\xi(0)=\xi_{0},
\end{aligned}\right.
\end{equation}
where $\xi(t)=\mathbb{E}\hat{u}(t)$, $\xi_{0}=(g,\phi)$. By $(\mbox{A1})$ and Jensen's inequality, we obtain
\begin{equation}\label{Jensen}
\left\{\begin{aligned}
&\frac{d\xi(t)}{dt}\geq-\lambda_{1}\xi(t)+a_{1}\xi^{\beta}(t)+a_{2}\xi(t),\\
&\xi(0)=\xi_{0},
\end{aligned}\right.
\end{equation}
If $\lambda_{1}\geq a_{2}$, for $\xi_{0}> \big(\frac{\lambda_{1}-a_{2}}{a_{1}}\big)^{\frac{1}{\beta-1}}$, we can show that $\xi(\cdot)$ is strictly increasing. It follows from (\ref{Jensen}) that
\begin{align}\label{contra}
T&\leq \int_{\xi_{0}}^{\xi(T)}\frac{ds}{a_{1}s^{\beta}-(\lambda_{1}-a_{2})s}\leq \int_{\big(\frac{\lambda_{1}-a_{2}}{a_{1}}\big)^{\frac{1}{\beta-1}}}^{\infty}\frac{ds}{a_{1}s^{\beta}-(\lambda_{1}-a_{2})s}< \infty.
\end{align}
If $\lambda_{1}< a_{2}$, for $\xi_{0}> 0$, we can show that $\xi(\cdot)$ is strictly increasing. We have
\begin{align}\label{contradict}
T=\int_{0}^{T}dt&\leq \int_{0}^{T}\frac{d\xi(t)}{a_{1}\xi^{\beta}(t)}=\int_{\xi_{0}}^{\xi(T)}\frac{ds}{a_{1}s^{\beta}}< \infty.
\end{align}
Since $T$ is arbitrary, either (\ref{contra}) or (\ref{contradict}) results in a contradiction. Therefore, for $\lambda_{1}\geq a_{2}$, $\xi_{0}> \big(\frac{\lambda_{1}-a_{2}}{a_{1}}\big)^{\frac{1}{\beta-1}}$, $\xi(t)$ must blow up at a time $T_{p}\leq \int_{\xi_{0}}^{\xi(T)}\frac{ds}{a_{1}s^{\beta}-(\lambda_{1}-a_{2})s}$. For $\lambda_{1}< a_{2}$, $\xi(t)$ must blow up at a time $T_{p}\leq \int_{\xi_{0}}^{\xi(T)}\frac{ds}{a_{1}s^{\beta}}$. \\
Since $\phi$ is bounded and continuous on $\overline{D}$, by H$\ddot{\mbox{o}}$lder's inequality, we have
\begin{align}
\xi(t)\leq \big(\int_{D}|\phi(x)|^{q}dx \big)^{1/q}\big(\mathbb{E}\int_{D}|u(x,t)|^{p}dx \big)^{1/p},
\end{align}
where $q=p/(p-1)$, $p\geq 1$. So the positive solution explodes at some time $T'\leq T_{e}$ in the mean $L^{p}$-norm for each $p\geq 1$. The proof is complete. \ \ \ $\Box$ \\
\textbf{Example 4.1.}
Consider the following problem in a spherical domain $D=B(R)$ in $\mathbb{R}^{3}$:
\begin{equation}\label{example}
\left\{\begin{aligned}
&\frac{\partial u}{\partial t}=\triangle u+u^{\frac{8}{3}}-u+\gamma_{0}(u^{3}+|\nabla u|^{2})^{1/2}\partial_{t}W(x,t)+c_{0}\int_{0}^{\infty}zu^{3}\partial_{t}\widetilde{N}(t,dz),\
t>0,x\in D,\\
&u(x,0)=a_{0}e^{-\alpha |x|},\ x\in D,\\
&u(x,t)|_{|x|=R}=0, \ t>0,
\end{aligned}\right.
\end{equation}
where $\widetilde{N}(dt,dz)=N(dt,dz)-dt\nu(dz)$ is a compensated Poisson measure corresponding to the Poisson random measure $N(dt,dz)$, $W(x,t)$ is a continuous Wiener random field with the covariance function
\begin{align*}
q(x,y)=b_{0}\exp\{-\rho(x\cdot y)\}, \ \ x,y\in \mathbb{R}^{3}.
\end{align*}
The constants $\sigma_{0}$, $c_{0}$, $a_{0}$, $\alpha$ are strictly positive and $x\cdot y=\sum_{i=1}^{3}x_{i}y_{i}$. Here $A=\triangle$, $f=u^{\frac{8}{3}}-u$, $\sigma=\gamma_{0}(u^{3}+|\nabla u|^{2})^{1/2}$, $\varphi=c_{0}zu^{3}$, $Z=(0,\infty)$.
It is obvious that conditions $\mbox{(A1)}$ and $\mbox{(A4)}$ are satisfied. If $\frac{1}{2}b_{0}\gamma^{2}_{0}<1$,
since
\begin{align*}
\frac{1}{2}b_{0}\gamma^{2}_{0}\exp\{-\rho|x|^{2}\}(u^{3}+|\xi|^{2})-|\xi|^{2}\leq (\frac{1}{2}b_{0}\gamma^{2}_{0}-1)|\xi|^{2}+\frac{1}{2}b^{2}\gamma^{2}_{0}u^{3}.
\end{align*}
then condition $\mbox{(A2)}$ is satisfied.
If $\int_{0}^{\infty}z^{2}\nu(dz)<\infty$, take $\mu=6$ and $\psi(z)=c^{2}_{0}z^{2}$, then the condition $\mbox{(A3)}$ is satisfied.
From Theorem 3.1, it follows that the solution of Eq. (\ref{example}) is positive. The smallest eigenvalue of the elliptic equation (\ref{elliptic}) is $\lambda_{1}=(\frac{\pi}{R})^{2}$ and the corresponding normalized eigenfunction is $\phi(x)=\frac{1}{4R^{2}|x|}\sin\frac{\pi|x|}{R}$, $0<|x|<R$.
If $a_{0}$ is sufficiently large, then we have
\begin{align}\label{a0}
\int_{D}g(x)\phi(x)dx=\int_{0}^{R}\frac{a_{0}e^{-\alpha r}}{4R^{2}r}\sin \frac{\pi r}{R}dr >\frac{a_{0}}{4R^{3}}\int_{0}^{R}e^{-\alpha r}\sin\frac{\pi r}{R}dr>(\frac{\pi^{2}}{R^{2}}+1)^{\frac{3}{5}},
\end{align}
Therefore, by Theorem 4.1, the solutions to the Eq. (\ref{example}) will blow up in finite time in mean $L^{p}$-norm for any $p\geq 1$.
Note that Theorem 3.1 in \cite{Bao} is not suitable for Eq. (\ref{example}).
To discuss the noise-induced explosion, we consider the following stochastic reaction-diffusion equation:
\begin{equation}\label{noise-induced}
\left\{\begin{aligned}
&\frac{\partial u}{\partial t}=Au+f(u,x,t)+\sigma(u,x,t)\partial_{t}W(x,t)\\
&\quad\quad\quad+\int_{Z}\varphi(u,x,z,t)\partial_{t}\widetilde{N}(t,dz),\
t>0,x\in D\\
&u(x,0)=g(x),\ x\in D,\\
&u(x,t)=0, \ t>0,x\in \partial D,
\end{aligned}\right.
\end{equation}
which is a special case of Eq. (\ref{rd}), where $\sigma$ is independent of $\nabla u$. We assume that the noise terms satisfy the following conditions: \\
$(\mbox{A1}')$ The correlation function $q(x,y)$ is continuous and positive for $x,y\in \overline{D}$ such that
\begin{align*}
\int_{D}\int_{D}q(x,y)v(x)v(y)dxdy\geq \kappa \big (\int_{D}v(x)dx\big)^{2}
\end{align*}
for any non-negative $v\in H$ and some constant $\kappa>0$. \\
$(\mbox{A2}')$ The function $f(u,x,t)$ is continuous on $\mathbb{R}\times \overline{D} \times [0,\infty)$ such that $f(u,x,t)\geq 0$ for $u\geq 0$ and $x\in \overline{D}$, $t\in [0,\infty)$. \\
$(\mbox{A3}')$ There exist continuous functions $\sigma_{0}$, $G$ such that they are both positive, convex and satisfy
\begin{align*}
\sigma(u,x,t)\geq \sigma_{0}(u), \ \ \sigma^{2}_{0}(u)\geq G(u^{2}),
\end{align*}
for $x\in \overline{D}$, $u\geq 0$, $t\in [0,\infty)$. \\
$(\mbox{A4}')$ There exist continuous functions $\varphi_{0}$, $K$ such that they are both positive, convex and satisfy
\begin{align*}
&\int_{Z}\big(\int_{D}\varphi(u,x,z,t)\phi(x)dx\big)^{2}\nu(dz)\geq \int_{Z}\big(\int_{D}\varphi_{0}(u,z)\phi(x)dx\big)^{2}\nu(dz), \\ &\int_{Z}\varphi^{2}_{0}(u,z)\nu(dz)\geq K(u^{2}),
\end{align*}
for $x\in \overline{D}$, $z\in Z$, $u\geq 0$, $t\in [0,\infty)$. \\
$(\mbox{A5}')$ There exists a constant $M>0$ such that
$\kappa G(u)+K(u)> 2\lambda_{1}u$ for $u>M$, and
\begin{align*}
\int_{M}^{\infty}\frac{du}{\kappa G(u)+K(u)-2\lambda_{1}u}< \infty.
\end{align*}
$(\mbox{A6}')$ The initial datum satisfies the following
\begin{align*}
(g,\phi)=\int_{D}g(x)\phi(x)dx>M.
\end{align*}
\textbf{Theorem 4.2.} Assume that the initial-boundary value problem (\ref{rd}) has a unique positive local solution and the conditions $(\mbox{A1}')-(\mbox{A6}')$ hold. Then for each $p\geq 2$, there exists a constant $T_{p}$ such that
\begin{equation}\label{noise}
\lim_{t\rightarrow T^{-}_{p}}\mathbb{E}\|u_{t}\|_{L^{p}}=\lim_{t\rightarrow T^{-}_{p}}\mathbb{E}\big\{\int_{D}|u(x,t)|^{p}dx\big\}^{1/p}=\infty.
\end{equation}
That is, the solution explodes in mean $L^{p}$-norm sense. \\
\textbf{Proof.} We assume the conclusion is false. Then there exists the solution $u$ and for some $p\geq 2$, $\mathbb{E}\|u_{t}\|^{p}<\infty$, $t\in [0,T]$, for any $T>0$.
Let $\hat{u}(t)=(\phi,u_{t})$ be defined as before. By (\ref{noise-induced}),
\begin{align}\label{gradient}
\hat{u}(t)&=(g,\phi)+\int_{0}^{t}\int_{D}[Au(x,s)]\phi(x)dxds+\int_{0}^{t}\int_{D}f(u,x,s)\phi(x)dxds\nonumber\\
&\quad+\int_{0}^{t}\int_{D}\sigma(u,x,s)\phi(x)dW(x,s)dx\nonumber\\
&\quad+\int_{0}^{t}\int_{Z}\int_{D}\varphi(u,x,z,s)\phi(x)dx\widetilde{N}(ds,dz)\nonumber\\
&=(g,\phi)-\lambda_{1}\int_{0}^{t}\int_{D}u(x,s)\phi(x)dxds+\int_{0}^{t}\int_{D}f(u,x,s)\phi(x)dxds\nonumber\\
&\quad+\int_{0}^{t}\int_{D}\sigma(u,x,s)\phi(x)dW(x,s)dx\nonumber\\
&\quad+\int_{0}^{t}\int_{Z}\int_{D}\varphi(u,x,z,s)\phi(x)dx\widetilde{N}(ds,dz).
\end{align}
By (\ref{gradient}), we apply the It$\hat{\mbox{o}}$'s formula to $\hat{u}^{2}(t)$ to get
\begin{align}\label{square}
\hat{u}^{2}(t)&=(g,\phi)^{2}-2\lambda_{1}\int_{0}^{t}\hat{u}^{2}(s)ds+2\int_{0}^{t}\int_{D}\hat{u}(s)f(u,x,s)\phi(x)dxds\nonumber\\
&\quad+2\int_{0}^{t}\int_{D}\hat{u}(s)\sigma(u,x,s)\phi(x)dxdW(x,s)\nonumber\\
&\quad+\int_{0}^{t}\int_{D}\int_{D}q(x,y)\phi(x)\phi(y)\sigma(u,x,s)\sigma(u,y,s)dxdyds\nonumber\\
&\quad+\int_{0}^{t}\int_{Z}\big[\big(\hat{u}(s)+\int_{D}\varphi(u,x,z,s)\phi(x)dx\big)^{2}-\hat{u}^{2}(s)\big]\widetilde{N}(ds,dz)\nonumber\\
&\quad+\int_{0}^{t}\int_{Z}\big[\big(\hat{u}(s)+\int_{D}\varphi(u,x,z,s)\phi(x)dx\big)^{2}-\hat{u}^{2}(s)\nonumber\\
&\quad-2\hat{u}(s)\int_{D}\varphi(u,x,z,s)\phi(x)dx\big]\nu(dz)ds.
\end{align}
Let $\eta(t)=\mathbb{E}\hat{u}^{2}(t)$. Taking expectations of both sides of (\ref{square}), we obtain
\begin{align*}
\eta(t)&=(g,\phi)^{2}-2\lambda_{1}\int_{0}^{t}\eta(s)ds+2\mathbb{E}\int_{0}^{t}\int_{D}\hat{u}(s)f(u,x,s)\phi(x)dxds\nonumber\\
&\quad+\mathbb{E}\int_{0}^{t}\int_{D}\int_{D}q(x,y)\phi(x)\phi(y)\sigma(u,x,s)\sigma(u,y,s)dxdyds\nonumber\\
&\quad+\mathbb{E}\int_{0}^{t}\int_{Z}\big(\int_{D}\varphi(u,x,z,s)\phi(x)dx\big)^{2}\nu(dz)ds,
\end{align*}
or, in the differential form,
\begin{equation}\label{form}
\left\{\begin{aligned}
&\frac{d\eta(t)}{dt}=-2\lambda_{1}\eta(t)+2\mathbb{E}\hat{u}(t)\int_{D}f(u,x,t)\phi(x)dx\\
&\quad\quad\quad+\mathbb{E}\int_{D}\int_{D}q(x,y)\phi(x)\phi(y)\sigma(u,x,t)\sigma(u,y,t)dxdy\\
&\quad\quad\quad+\mathbb{E}\int_{Z}\big(\int_{D}\varphi(u,x,z,t)\phi(x)dx\big)^{2}\nu(dz), \\
&\eta(0)=\eta_{0}=(g,\phi)^{2}.
\end{aligned}\right.
\end{equation}
By $(\mbox{A2}')$, we have $\mathbb{E}\hat{u}(t)\int_{D}f(u,x,t)\phi(x)dx\geq 0$. By $(\mbox{A1}')$, $(\mbox{A3}')$, Jensen's inequality, we have
\begin{align}\label{Schwarz}
&\int_{D}\int_{D}q(x,y)\phi(x)\phi(y)\sigma(u,x,t)\sigma(u,y,t)dxdy\nonumber\\
&\geq \kappa\big(\int_{D}\phi(x)\sigma(u,x,t)dx\big)^{2}\nonumber\\
&\geq \kappa\big(\int_{D}\phi(x)\sigma_{0}(u)dx\big)^{2}\nonumber\\
&\geq \kappa\sigma^{2}_{0}(\hat{u}(t))\nonumber\\
&\geq \kappa G(\hat{u}^{2}(t)).
\end{align}
By $(\mbox{A4}')$, Jensen's inequality, we get
\begin{align}\label{dz}
&\int_{Z}(\int_{D}\varphi(u,x,z,t)\phi(x)dx)^{2}\nu(dz)\nonumber\\
&\geq\int_{Z}\big(\int_{D}\varphi_{0}(u,z)\phi(x)dx\big)^{2}\nu(dz)\nonumber\\
&\geq\int_{Z}\varphi^{2}_{0}(\hat{u}(t),z)\nu(dz)\nonumber\\
&\geq K(\hat{u}^{2}(t)).
\end{align}
From (\ref{Schwarz}), (\ref{dz}), (\ref{form}) and Jensen's inequality, it follows that
\begin{align}\label{deduce}
\frac{d\eta(t)}{dt}&\geq -2\lambda_{1}\eta(t)+\kappa\mathbb{E}G(\hat{u}^{2}(t))+\mathbb{E}K(\hat{u}^{2}(t))\nonumber\\
&\geq -2\lambda_{1}\eta(t)+\kappa G(\eta(t))+K(\eta(t)).
\end{align}
Similar to (\ref{contra}), for $\eta_{0}>M$, we obtain
\begin{align*}
T\leq \int_{\eta_{0}}^{\eta(T)}\frac{du}{\kappa G(\eta(t))+K(\eta(t))-2\lambda_{1}u}\leq\int_{M}^{\infty}\frac{du}{\kappa G(\eta(t))+K(\eta(t))-2\lambda_{1}u}<\infty.
\end{align*}
Since $T$ is arbitrary, this results in a contradiction. Therefore, the mean square $\eta(t)=\mathbb{E}\hat{u}^{2}(t)$ must blow up at some finite time $T_{\ast}>0$. Applying the H$\ddot{\mbox{o}}$lder inequality, we see that (\ref{noise}) holds for each $p\geq 2$. \ \ $\Box$ \\
\textbf{Remark 4.1.} In \cite{Ch}, \cite{CL}, the correlation function $q(x,y)$ is assumed to satisfy the inequality
\begin{equation}\label{remark}
\int_{D}\int_{D}q(x,y)v(x)v(y)dxdy\geq q_{1}\int_{D}v^{2}(x)dx
\end{equation}
for any positive $v \in H$ and for some $q_{1}>0$.
In fact, this assumption is not suitable. If the domain $D$ is bounded and $q\in (0,1]$, by the Cauchy-Schwarz inequality, we have
\begin{equation}\label{correlation}
\int_{D}\int_{D}q(x,y)v(x)v(y)dxdy\leq \big(\int_{D}v(x)dx\big)^{2}\leq \mu(D)\int_{D}v^{2}(x)dx,
\end{equation}
where $\mu(D)$ is the volume of $D$. By (\ref{remark}), (\ref{correlation}), we have $\mu(D)\geq q_{1}$. If the bounded domain $D$ is small enough, then we get a contradiction. \\
\textbf{Remark 4.2.} We consider the problem (\ref{noise-induced}) with a Levy-type noise, and the coefficient operator $A$ is more general than the Laplacian, it is easy to see that Theorem 4.2 is the generalization of Theorem 4.3 in \cite{Lv}. \\
\textbf{Example 4.2.}
Consider the following problem in a spherical domain $D=B(R)$ in $\mathbb{R}^{3}$:
\begin{equation}\label{noise explosion}
\left\{\begin{aligned}
&\frac{\partial u}{\partial t}=\triangle u+u^{1+\alpha}+\mu u^{4}\partial_{t}W(x,t)+c_{0}\int_{0}^{\infty}zu^{6}\partial_{t}\widetilde{N}(t,dz),\
t>0,x\in D,\\
&u(x,0)=a_{0}e^{-\beta |x|},\ x\in D,\\
&u(x,t)|_{|x|=R}=0, \ t>0,
\end{aligned}\right.
\end{equation}
where $\widetilde{N}(dt,dz)=N(dt,dz)-dt\nu(dz)$ is a compensated Poisson measure corresponding to the Poisson random measure $N(dt,dz)$, $W(x,t)$ is a continuous Wiener random field with the covariance function
\begin{align*}
q(x,y)=b_{0}\exp\{-\rho(x\cdot y)\}, \ \ x,y\in \mathbb{R}^{3}.
\end{align*}
The constants $\mu$, $c_{0}$, $a_{0}$, $\alpha$, $\beta$ are strictly positive and $x\cdot y=\sum_{i=1}^{3}x_{i}y_{i}$. Here $A=\triangle$, $f=u^{1+\alpha}$, $\sigma=\mu u^{4}$, $\varphi=c_{0}zu^{6}$, $Z=(0,\infty)$.\\
For $x,y\in B(R)$, we have
\begin{align*}
q(x,y)\geq \kappa=b_{0}\exp\{-\rho R^{2}\}.
\end{align*}
Then for any non-negative $v\in H$,
\begin{align*}
\int_{D}\int_{D}q(x,y)v(x)v(y)dxdy\geq \kappa \big (\int_{D}v(x)dx\big)^{2}.
\end{align*}
The condition $(\mbox{A1}')$ holds. It is obvious that $f=u^{1+\alpha}> 0$ for $u>0$, the condition $(\mbox{A2}')$ holds.
Let $G(u)=\mu^{2} u^{4}$, $\sigma_{0}(u)=\mu u^{4}$. Then $\sigma(u,x,t)=\mu u^{4}=\sigma_{0}(u)$ and $\sigma^{2}_{0}(u)=G(u^{2})$. $\sigma_{0}$ and $G$ are both continuous, positive and convex. The condition $(\mbox{A3}')$ is satisfied. Let $\varphi_{0}(u,z)=c_{0}zu^{6}$. Assume $\int_{0}^{\infty}z^{2}\nu(dz)<\infty$, let $K(u)=\big(c_{0}\int_{0}^{\infty}z^{2}\nu(dz)\big)u^{6}$. Then $\varphi(u,x,z,t)=c_{0}zu^{6}=\varphi_{0}(u,z)$. $\varphi_{0}$ and $K$ are both positive and convex. The condition $(\mbox{A4}')$ holds. The smallest eigenvalue of the elliptic equation (\ref{elliptic}) is $\lambda_{1}=(\frac{\pi}{R})^{2}$. If $b_{0}$ or $c_{0}$ is large enough, it is easy to see that $b_{0}\exp\{-\rho R^{2}\}\mu^{2}u^{4}+\big(c_{0}\int_{0}^{\infty}z^{2}\nu(dz)\big)u^{6}>2(\frac{\pi}{R})^{2}u$ for $u> M$, and
\begin{align*}
\int_{M}^{\infty}\frac{du}{b_{0}\exp\{-\rho R^{2}\}\mu^{2}u^{4}+\big(c_{0}\int_{0}^{\infty}z^{2}\nu(dz)\big)u^{6}-2(\frac{\pi}{R})^{2}u}< \infty.
\end{align*}
The condition $(\mbox{A5}')$ is satisfied. If $a_{0}$ is sufficiently large, simliar to (\ref{a0}),we have $\int_{D}g(x)\phi(x)dx>M$.
By Theorem (4.2), the solution of (\ref{noise explosion}) will blow up in finite time in $L^{p}$-norm for any $p\geq 2$.
Now we consider the explosive solution problem for (\ref{rd}), when the domain $D$ is unbounded, for example, $D=\mathbb{R}^{d}$. Let $B(R)=\{x\in \mathbb{R}^{d}: |x|< R\}$. \\
\textbf{Theorem 4.3.} Assume that the initial-boundary value problem (\ref{rd}) has a unique local solution and the conditions $\mbox{(A1)-(A3)}$ hold, where $D=\mathbb{R}^{d}$. Then for any $R>0$, there exists a constant $T_{p}(R)>0$ such that
\begin{align*}
\lim_{t\rightarrow T_{p}(R)-}\mathbb{E}\big\{\int_{B(R)}|u(t,x)|^{p}\big\}^{1/p}=\infty,
\end{align*}
provided that the conditions of Theorem 4.1 holds for $p\geq 1$ or the conditions of Theorem 4.2 holds for $p\geq 2$, where $D=\mathbb{R}^{d}$. \\
\textbf{Proof.} The proof follows the spirit of the one for Theorem 3.3 in \cite{CL}. For the sake of completeness, we present it. We only consider the case under the conditions of Theorem 4.1, since the proof under the conditions of Theorem 4.2 is similar.
By restricting the solution $u$ to $\overline{B(R)}$, let $\hat{u}(t)=\int_{B(R)}u(x,t)\phi(x)dx\geq 0$ as defined by (\ref{hat}). Since $u\geq 0$ on the boundary $\partial B(R)$, by Green's identity,
\begin{align}\label{normal}
(Au_{t},\phi)=-\lambda_{1}\phi+\int_{\partial B(R)}u(x,t)\big(-\frac{\partial \phi(x)}{\partial \nu}\big)dS.
\end{align}
Denote $n=(n_{1},n_{2},\ldots,n_{d})$ as the unit outward normal vector to the boundary $\partial B(R)$. Since there exists a constant $c>0$ such that $\sum_{i,j=1}^{d}a_{ij}(x)\xi_{i}\xi_{j}\geq c|\xi|^{2}$ for all $x\in \overline{D}$ and $\xi=(\xi_{1},\ldots, \xi_{d})\in \mathbb{R}^{d}$. We have $\nu\cdot n=\sum_{i,j}^{d}a_{ij}n_{i}n_{j}\geq 0$. This implies that the conormal $\nu(x)$ is an exterior direction field. Since $\phi>0$ in $B(R)$ and $\phi=0$ on $\partial B(R)$, we have
\begin{align}\label{direction}
\frac{\partial \phi(x)}{\partial \nu}\leq 0.
\end{align}
Putting (\ref{normal}) into (\ref{multiply}), by (\ref{direction}), we obtain the inequality (\ref{Jensen}). The rest of proof can be completed as in Theorem 4.1. \ \ $\Box$ \\
\textbf{Remark 4.3.} In \cite{Bao}, when the domain $D=\mathbb{R}^{d}$, it seems impossible to consider the existence of the position solution of initial-boundary value problem (\ref{rd}) and the explosionn of the position solution. The reason is that the proof of Theorem 2.1 in \cite{Bao} relies on the fact that the volume $V(D)$ of domain $D$ is bounded. In \cite{Bao}, the proofs of Theorem 3.1 and Theorem 4.1 are both rely on Theorem 2.1. So for $D=R^{d}$, they are not valid.
\section{\textbf{Global solutions for a stochastic Allen-Cahn equation driven by a L$\acute{\mbox{e}}$vy type noise}}
In this section, we consider the following stochastic Allen-Cahn equation driven by a L$\acute{\mbox{e}}$vy type noise,
\begin{equation}\label{AC}
\left\{\begin{aligned}
&du=(\triangle u+u(1-u^{2}))dt+bu^{m}dW_{t}+cu^{n}\int_{Z}z\widetilde{N}(dt,dz), \ t>0, \ x\in D,\\
&u(x,0)=h(x),\ x\in D,\\
&u(x,t)=0, \ t>0,x\in \partial D,
\end{aligned}\right.
\end{equation}
where $1<m<2$, $1<n<2$, $b,c\in \mathbb{R}$, $D\subset \mathbb{R}^{3}$, $Z=(0,\infty)$.
Let $V$ be a real separable Hilbert space. We first consider the more general equation
\begin{equation}\label{general}
\left\{\begin{aligned}
&du_{t}=(Au_{t}+F_{t}(u_{t})dt+\Sigma_{t}(u_{t})dW_{t}+\int_{Z}\Gamma_{t}(u_{t},z)\widetilde{N}(dt,dz),\ t\geq 0,\\
&u_{0}=h(x),
\end{aligned}\right.
\end{equation}
where the coefficients $A$, $F_{t}$, $\Sigma_{t}$ and $\Gamma_{t}$ are assumed to be non-random or deterministic. $W(x,t)$ is a Wiener random field, $(Z,\mathcal{B}(Z))$ is a measurable space. $\widetilde{N}(dt,dz)$ is the compensated Poisson measure. Here we say that an $\mathcal{F}_{t}$-adapted $V$-valued process $u_{t}$ is a \emph{strong solution}, or a \emph{variational solution}, of the equation (\ref{general}) if $u\in L^{2}([0,T]; V)$, and for any $\varphi\in V$, the following equation
\begin{align*}
(u_{t},\varphi)&=(h,\varphi)+\int_{0}^{t}(Au_{s}, \varphi)ds+\int_{0}^{t}(F_{s}(u_{s}), \varphi)ds+\int_{0}^{t}(\varphi, \Sigma_{s}(u_{s})dW_{s})\\
&\quad+\int_{0}^{t}(\int_{Z}\Gamma_{s}(u_{s},z)\widetilde{N}(ds,dz), \varphi)
\end{align*}
holds for each $t\in [0,T]$ a.s.
Denote $L_{1}(V)$ the space of nuclear (trace class) operators on $V$. Let $U\subset V$ be a open set and let $U\times [0,T]=U_{T}$. Here a functional $\Phi: U_{T}\rightarrow \mathbb{R}$ is said to be a \emph{strong It$\hat{\mbox{o}}$ functional} if it satisfies the following (see \cite[pp. 226]{C}): \\
(1) $\Phi: U_{T}\rightarrow \mathbb{R}$ is locally bounded and continuous such that its first two partial derivatives $\partial_{t}\Phi(v,t)$, $\Phi'(v,t)$ and $\Phi''(v,t)$ exist for each $(v,t)\in U_{T}$.\\
(2) The derivatives $\partial _{t}\Phi$ and $\Phi'\in V$ are locally bounded and continuous in $U_{T}$.\\
(3) For any $\Gamma\in \mathcal{L}_{1}(V)$, the map: $(v,t)\rightarrow Tr[\Phi''(v,t)\Gamma]$ is locally bounded and continuous in $(v,t)\in U_{T}$.\\
(4) $\Phi'(\cdot,t): U\rightarrow V$ is such that $(\Phi'(\cdot,t), v)$ is continuous in $t\in [0,T]$ for any $v\in V$ and
\begin{align*}
\|\Phi'(v,t)\|\leq \kappa(1+\|v\|), \ (v,t)\in U\times [0,T],
\end{align*}
for some $\kappa>0$.
Let $U\subset V$ be a neighborhood of the origin. By a similar statement to that in \cite[pp. 228]{C}, we present the definition of Lyapunov functional.
Define the operator $\mathcal{L}_{t}$ as follows:
\begin{align*}
\mathcal{L}_{t}\Phi(v,t)&=\frac{\partial}{\partial t}\Phi(v,t)+\frac{1}{2}Tr[\Phi''(v,t)\Sigma_{t}(v)Q\Sigma^{\ast}_{t}(v)]+(Av, \Phi'(v,t))\\
&\quad+(F_{t}(v), \Phi'(v,t))+\int_{Z}[\Phi(v+\Gamma_{t}(v,z),t)-\Phi(v,t)-\big(\Gamma_{t}(v,z), \Phi'(v,t)\big)]\nu(dz),
\end{align*}
where $Q$ is the covariance operator.
A strong It$\hat{\mbox{o}}$ functional $\Phi: U\times \mathbb{R}^{+}\rightarrow \mathbb{R}$ is said to be a
\emph{Lyapunov functional }for the equation (\ref{general}), if \\
(1) $\Phi(0,t)=0$ for all $t\geq 0$, and, for any $\varepsilon>0$, there is a $\delta>0$ such that
\begin{align*}
\inf_{t\geq 0, \|h\|\geq \varepsilon}\Phi(h,t)\geq \delta, \ \mbox{and}
\end{align*}
(2) for any $t\geq 0$ and $v\in U$,
\begin{align*}
\mathcal{L}_{t}\Phi(v,t)\leq 0.
\end{align*}
Let $u^{h}_{t}$ be a strong solution of the equation (\ref{AC}) with $u^{h}_{0}=h$. \\
\textbf{Definition 5.1.} The solution $u^{h}_{t}$ is said to be nonexplosive if
\begin{equation*}
\lim_{r\rightarrow \infty} P\{\sup_{0\leq t\leq T}\|u^{h}_{t}\|\geq r\}=0,
\end{equation*}
for any $T>0$. If the above holds for $T=\infty$, the solution is said to be ultimately bounded. \\
\textbf{Lemma 5.1.} Let $\Phi:U\times \mathbb{R}^{+}\rightarrow \mathbb{R}^{+}$ be a Lyapunov functional and let $u^{h}_{t}$ denote the strong solution of (\ref{general}). For $r>0$, let $B_{r}=\{h\in V: \|h\|<r\}$ such that $B_{r}\subset U$. Define
\begin{align*}
\tau=\inf\{t>0: u^{h}_{t}\in B^{c}_{r}, \ h\in B_{r}\},
\end{align*}
with $ B^{c}_{r}=V\backslash B_{r}$. We put $\tau=T$ if the set is empty. Then the process $\phi_{t}=\Phi(u^{h}_{t\wedge \tau}, t\wedge \tau)$ is a local $\mathcal{F}_{t}$-supermartingale and the following Chebyshev inequality holds
\begin{align*}
P\{\sup_{0\leq t \leq T}\|u^{h}_{t}\|\geq r\}\leq \frac{\Phi(h,0)}{\Phi_{r}},
\end{align*}
where
\begin{align*}
\Phi_{r}=\inf_{0\leq t \leq T, h\in U\cap B^{c}_{r}} \Phi(h,t).
\end{align*}
\textbf{Proof.} From It$\hat{\mbox{o}}$'s formula, it follows that
\begin{align*}
\Phi(u^{h}_{t\wedge \tau})&=\Phi(h,0)+\int_{0}^{t\wedge \tau}\mathcal{L}_{s}\Phi(u^{h}_{s},s)ds+\int_{0}^{t\wedge \tau}(\Phi'(u^{h}_{s},s),\Sigma_{s}(u^{h}_{s}))dW_{s}\\
&\quad+\int_{0}^{t\wedge \tau}\int_{Z}(\Phi(v+\Gamma_{s}(v,z),s)-\Phi(v,s))\widetilde{N}(ds,dz)\\
&\leq \Phi(h,0)+\int_{0}^{t\wedge \tau}(\Phi'(u^{h}_{s},s),\Sigma_{s}(u^{h}_{s}))dW_{s}\\
&\quad+\int_{0}^{t\wedge \tau}\int_{Z}(\Phi(v+\Gamma_{s}(v,z),s)-\Phi(v,s))\widetilde{N}(ds,dz),
\end{align*}
therefore, $\phi_{t}=\Phi({u^{h}_{t\wedge \tau}}, t\wedge \tau)$ is a local supermartingale and
\begin{align*}
\mathbb{E}\phi_{t}\leq \mathbb{E}\phi_{0}=\Phi(h,0).
\end{align*}
By definition,
\begin{align*}
\mathbb{E}\phi_{T}&=\mathbb{E}\Phi(u^{h}_{T\wedge \tau}, T\wedge \tau)\\
&\geq \mathbb{E}\{\Phi(u^{h}_{\tau}; \tau\leq T)\}\\
&\geq \inf_{0\leq t\leq T, \|h\|=r}\Phi(h,t)P\{\tau\leq T\}\\
&\geq \Phi_{r}P\{\sup_{0\leq t\leq T}\|u^{h}_{t}\|\geq r\},
\end{align*}
the proof is complete. \ \ $\Box$ \\
\textbf{Theorem 5.1.} If there exists an It$\hat{\mbox{o}}$ functional $\Psi: V\times \mathbb{R}^{+}\rightarrow \mathbb{R}^{+}$ and a constant $\alpha>0$ such that
\begin{align*}
\mathcal{L}_{t}\Psi\leq \alpha \Psi(v,t)\ \ \mbox{for any} \ v\in V,
\end{align*}
and the infimum $\inf_{t\geq 0, \|h\|\geq r}\Psi(h,t)=\Psi_{r}$ exists such that $\lim_{r\rightarrow \infty}\Psi_{r}=\infty$, then the solution $u^{h}_{t}$ does not explode in finite time. \\
\textbf{Proof.} Let $\Phi(v,t)=e^{-\alpha t}\Psi(v,t)$. We have
\begin{align*}
\mathcal{L}_{t}\Phi(v,t)&=\frac{\partial}{\partial t}\Phi(v,t)+\frac{1}{2}\mbox{Tr}[\Phi''(v,t)\Sigma_{t}(v)Q\Sigma^{\ast}_{t}(v)]+(Av, \Phi'(v,t))\\
&\quad+(F_{t}(v), \Phi'(v,t))+\int_{Z}[\Phi(v+\Gamma_{t}(v,z),t)-\Phi(v,t)-\Phi'(v,t)\Gamma_{t}(v,z)]\nu(dz)\\
&=-\alpha e^{-\alpha t}\Psi(v,t)+e^{-\alpha t}\frac{\partial}{\partial t}\Psi(v,t)+e^{-\alpha t}\big(\frac{1}{2}Tr[\Psi''(v,t)\Sigma_{t}(v)Q\Sigma^{\ast}_{t}(v)]+(Av, \Psi'(v,t))\\
&\quad+(F_{t}(v), \Psi'(v,t))+\int_{Z}[\Psi(v+\Gamma_{t}(v,z),t)-\Psi(v,t)-\Psi'(v,t)\Gamma_{t}(v,z)]\nu(dz)\big)\\
&=-\alpha e^{-\alpha t}\Psi(v,t)+e^{-\alpha t}\mathcal{L}_{t}\Psi\leq 0.
\end{align*}
Therefore $\Phi$ is a Lyapunov functional. By Lemma 5.1, we have
\begin{align*}
P\{\sup_{0\leq t \leq T}\|u^{h}_{t}\|>r\}\leq \frac{\Phi(h,0)}{\Phi_{r}}=\frac{\Psi(h,0)}{\Psi_{r}}\rightarrow 0
\end{align*}
as $r\rightarrow \infty$, for any $T>0$. \ \ $\Box$ \\
\textbf{Theorem 5.2.} Let $1<m<2$, $1<n<2$ and the initial datum $h(x)$ on $\overline{D}$ is positive and continuous. Suppose that $\int_{0}^{\infty}z^{2}\nu(dz)< \infty$ and there is $q_{0}>0$ such that $\sup_{x,y\in D}|q(x,y)|\leq q_{0}$. Then the equation (\ref{AC}) has a global strong solution. \\
\textbf{Proof.} In view of the proof of Theorem 3-6.5 in \cite[pp. 86]{C} and the proof of Theorem 3.2 in \cite{RZ}, we can show that the equation (\ref{AC}) has a local strong solution. By Theorem 3.1, the solution is positive. Define $\Phi(v,t)=\|v\|^{2}_{L^{2}}$. The infimum $\inf_{t\geq 0, \|h\|\geq r}\Phi(h,t)\rightarrow \infty$ as $r\rightarrow \infty$. We have
\begin{align}\label{Lyapunov}
\mathcal{L}_{t}\Phi(v,t)&=\frac{\partial}{\partial t}\Phi(v,t)+\frac{b^{2}}{2}\mbox{Tr}[\Phi''(v,t)v^{m}Qv^{m}]+(\Delta v, \Phi'(v,t))\nonumber\\
&\quad+(v-v^{3}, \Phi'(v,t))+\int_{Z}[\Phi(v+cv^{n}z,t)-\Phi(v,t)-(cv^{n}z, \Phi'(v,t))]\nu(dz)\nonumber\\
&\leq b^{2}\int_{D}q(x,x)v^{2m}(x)dx-2\int_{D}|\nabla v|^{2}dx+2\int_{D}(v^{2}-v^{4})dx\nonumber\\
&\quad+\int_{0}^{\infty}(cv^{n}z,cv^{n}z)\nu(dz)\nonumber\\
&\leq b^{2}q_{0}\|v\|^{2m}_{L^{2m}}+2\|v\|^{2}_{L^{2}}-2\|v\|^{4}_{L^{4}}+c^{2}\|v\|^{2n}_{L^{2n}}\int_{0}^{\infty}z^{2}\nu(dz).
\end{align}
By (\ref{alpha}) and (\ref{rpq}), we have
\begin{align}\label{rpqv}
\|v\|^{2m}_{L^{2m}}&\leq \|v\|^{2m\alpha}_{L^{2}}\|v\|^{2m(1-\alpha)}_{L^{4}}\nonumber\\
&\leq \varepsilon\|v\|^{\frac{2m(1-\alpha)}{1-m\alpha}}_{L^{4}}+\varepsilon^{-\frac{1-m\alpha}{m\alpha}}\|v\|^{2}_{L^{2}}\nonumber\\
&\leq \varepsilon\|v\|^{4}_{L^{4}}+\varepsilon^{-\frac{1-m\alpha}{m\alpha}}\|v\|^{2}_{L^{2}},
\end{align}
where $\alpha=\frac{2-m}{m}$. Similarly,
\begin{equation}\label{n}
\|v\|^{2n}_{L^{2n}}\leq \varepsilon \|v\|^{4}_{L^{4}}+\varepsilon^{-\frac{1-n\beta}{n\beta}}\|v\|^{2}_{L^{2}},
\end{equation}
where $\beta=\frac{2-n}{n}$. By (\ref{Lyapunov}), (\ref{rpqv}) and (\ref{n}),
\begin{align*}
\mathcal{L}_{t}\Phi(v,t)&=\big(b^{2}q_{0}\varepsilon+c^{2}\varepsilon\int_{0}^{\infty}z^{2}\nu(dz)-2\big)\|v\|^{4}_{L^{4}}\nonumber\\
&\quad+\big(b^{2}q_{0}\varepsilon^{-\frac{1-m\alpha}{m\alpha}}+c^{2}\varepsilon^{-\frac{1-n\beta}{n\beta}}\int_{0}^{\infty}z^{2}\nu(dz)+2\big)\|v\|^{2}_{L^{2}}.
\end{align*}
Choose $\varepsilon$ sufficiently small, we have
\begin{align*}
\mathcal{L}_{t}\Phi(v,t)\leq C\Phi(v,t).
\end{align*}
Therefore, by Theorem 5.1, the equation (\ref{AC}) has a global strong solution. \ \ $\Box$ \\
|
{
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Crest Trail - FR 357 to Junction Saddle #270
There is a day use fee to park at the Rustler Park trailhead just outside of the campground. Follow signage appropriately.
Current Trail Conditions
As of October 2020, the Crest Trail is clear of deadfall from Fly Saddle to Junction Saddle. Between Rustler Park and Fly Saddle there is a report of at least one tree down. North of Rustler Park, the trail was cleared over the summer but may have new deadfall. The tread is intermittently narrow and in poor quality in places, but passable to hikers.
The Crest Trail is accessible from many locations along the Chiricahua crest. Major access points for this leg of the Crest include:
The northern terminus (31.91693, -109.26827) is along the Barfoot Park Road (FR 357), 0.14 mile north of its junction with the Rustler Park Road (FR 42D). This trailhead is signed, but there is no parking immediately across from it, so it is better to park at the junction and walk there.
The Barfoot Park Trail climbs half a mile starting from the southwest corner of the meadow at Barfoot Park (31.91697, -109.27995) to meet the Crest at Barfoot Lookout Saddle. (31.91479, -109.27410)
The primary trailhead exists just outside the Rustler Park gate. (31.90686, -109.27724) There is a large parking lot across the road from the trailhead with dual vault toilets. A 0.26 mile spur trail climbs to the southwest and connects into the Crest at the Rustler Park Junction. (31.90552, -109.28077) As of April 2017, there is a $5 day use fee to park here.
The Bootlegger Trail climbs steeply to the Crest at a signed junction above Rustler Park. (31.90162, -109.28226)
A 450 foot spur trail meets the Crest at the north edge of Bootlegger Saddle (31.89305, -109.28318) from a bend in the Long Park Road (FR 42D). (31.89389, -109.28211) The Rock Creek Trail connects in at the south edge of the saddle, and as of early May 2016, it has a new trail sign visible from the Crest. (31.89246, -109.28368)
The 0.68 mile long Long Park Trail connects to the Crest at Fly Saddle (31.87965, -109.28665) from the end of the Long Park Road (FR 42). (31.88653, -109.27931)
The Saulsbury Trail climbs steeply from its trailhead in West Turkey Creek to meet the Crest a little over a quarter mile northwest of Round Park. (31.87195, -109.28715)
The Greenhouse Trail connects in from the east at Cima Park. (31.86141, -109.28739)
The southern terminus is at Junction Saddle, (31.84959, -109.28897) which can be reached via the other two legs of the Crest Trail or the Chiricahua Peak Trail. This junction is marked with multiple signs, though some are currently incorrectly numbered.
Barfoot Park Road (FR 357) to Barfoot Lookout Saddle
280 ft ↑
13.3% slope
The Crest Trail climbs immediately away from the Barfoot Park Road, cutting up the south slope of Buena Vista Peak heading west-southwest. This area, once heavily forested, was badly burned by the 2011 Horseshoe 2 fire and while many trees remain standing, nearly all are dead. At the end of this segment, the trail reaches Barfoot Lookout Saddle directly south of Buena Vista Peak, a signed junction with the Barfoot Park Trail and Barfoot Lookout Trail. (31.91479, -109.27410) The Crest Trail continues south via the leftmost fork in the junction.
Barfoot Lookout Saddle to Rustler Park Junction
Largely remaining at a level elevation, this segment of the Crest heads southwest and stays on the southeastern side of the crest itself and dropping slightly in elevation as it approaches Rustler Park.
Rustler Park Junction to Bootlegger Trail
Two spur trails connect in at this signed junction, (31.90551, -109.28077) one from the upper loop of the Rustler Park Campground and the other from the parking lot outside Rustler Park, just in front of the locked gate along the Rustler Park Road (FR 42D). Those two trails have their own junction a short distance to the southeast and combine into a single trail which continues to this junction.
The Crest Trail heads west from here and curves around to the south as it ascends the slope of the actual crest of the Chiricahuas, at times only a short distance from the top. A little over two tenths of a mile after beginning to head south, and a very short distance after curving again towards the southwest, the Bootlegger Trail climbs away to the ridgetop off the right side of the trail. (31.90162, -109.28226) This junction is marked with a brand new sign as of spring 2013.
Bootlegger Trail to Bootlegger Saddle
The trail heads along the northwest face of the hill south of Rustler Park, visible along the Rustler Park Road in places. After two tenths of a mile, with a short but steep stretch or two along the way, there is a point directly beneath the prominent rock cliffs on the hill's face which frequently washes out or has debris from above drop onto the trail for a short stretch. Crossing this is usually not especially difficult, but care should be taken as there is a significant drop to one side of the trail.
From here, the trail continues southeast a short distance before swinging south. Within a tenth of a mile you should be able to see the Long Park Road (FR 42D) not far below the trail, following the same basic route for a while. Three tenths of a mile further and the trail passes through a gate of sorts and 200 feet after that, a 60 foot spur trail leaves to the east and drops to Hillside Spring. (31.89531, -109.28149) Note that the sign at the spring lists this segment of the Crest Trail as being the Bootlegger Trail, which is no longer the case.
It's nearly two tenths of a mile further to the north edge of the meadow at Bootlegger Saddle, where two junctions occur. The first is a 450 foot spur trail which drops away northeast to the Long Park Road (31.89305, -109.28318) and the second, the southern terminus of the Bootlegger Trail, lies 200 feet beyond along the Crest Trail at the southern edge of Bootlegger Saddle. (31.89255, -109.28339) There is not a visible trail junction here, but head west approximately 80 feet through the meadow and a trail sign with "257"and an arrow should be found. It may be lying on the ground. (31.89256, -109.28367) The Bootlegger Trail drops away to the south and begins a steep, switchbacking descent from here.
Bootlegger Saddle to Fly Saddle
270 ft ↑ / 105 ft ↓
The Crest Trail leaves Bootlegger Saddle heading south, and widens for a stretch, climbing along the way. The earlier spur trail down to the Long Park Road shows evidence of having once been a road, and this portion of the Crest Trail may have been as well. 0.18 miles south of Bootlegger Saddle, the Long Park Connector Trail, an unmaintained old roadbed, forks off to the east, (31.88910, -109.28394) bending to the southeast along the way and ending up at Long Park. The Crest Trail narrows to a proper trail width again here and curves to the west for a short stretch, leveling out somewhat for a time. A bit of an S-curve follows over the next tenth of a mile before the trail emerges from under pine canopy to cross a barren stretch. The lack of trees here at least provides an excellent view out over the west side of the Chiricahuas.
0.15 miles beyond, the trail re-enters forested terrain, though this does not last and another barren slope must be crossed shortly after, this one extending the remaining distance to Fly Saddle with only a few patches of living trees between. New aspen growth is occurring, however—and threatening to encroach on the trail in places. This area can provide a fantastic view of Fly Peak in the fall with its aspen turning color.
250 feet before Fly Saddle, the Wilderness boundary is crossed, a brand new sign marking its position. (31.88030, -109.28692) The saddle itself is a five-way signed junction in the middle of a raspberry patch. (31.87965, -109.28665) The Crest Trail comes in from the northwest and departs to the southwest, the Long Park Trail heads northeast to the end of the Long Park Road, the Centella Trail east out to Centella Point and the Fly Peak Trail southeast to climb up and back down the other side of that peak to Round Park.
Fly Saddle to Saulsbury Junction
Patchy burns remain the norm through here as the Crest Trail passes to the west of Fly Peak. After a quarter mile, the trail turns southwest and shortly after enters a thicker stretch of pines before swinging around to the southeast, exiting onto another barren and very steep slope and coming to Saulsbury Junction, where the Saulsbury Trail leaves on the right side of the trail, heading northwest, almost paralleling the Crest Trail for a short while as it drops away steeply. (31.87195, -109.28714) This junction is marked with a sign, but it is on the left side of the trail and may not be immediately obvious, and the Saulsbury Trail is faint at this point and can be easy to miss.
Saulsbury Junction to Round Park
95 ft ↑ / 10 ft ↓
Continuing along the barren slope with a very steep drop off the right side, the trail maintains its southeasterly course the remaining short distance to Round Park, which is nestled in a saddle on the south side of Fly Peak. This area has been hit badly by fire and while there are still living trees in the area immediately around the Park's meadow, they are fairly limited in number. The trail cuts diagonally across the meadow and after approximately 60 feet, the Fly Peak Trail connects in. (31.86884, -109.28508) That trail is not visible immediately at this point, but there is a sign for it about 35 feet to the northwest (31.86892, -109.28506), from which point it heads north for a time before beginning its switchbacking ascent.
Nearly 200 feet beyond, at the southeastern edge of Round Park, (31.86842, -109.28480) the Bear Wallow Trail connects in, heading northeast to pass along the east side of Fly Peak and connect midway along the Centella Trail. The Booger Spring Trail forks off the Bear Wallow Trail a short distance to the north.
Round Park to Cima Saddle
Continuing its southeasterly heading, the trail exits Round Park almost immediately after the last junction and begins climbing to a saddle between Ward Peak and Wattmid Ridge. This stretch has a large number of aspen saplings mixed in among the sparse pines. Shortly before the saddle, the pines become thicker, and approximately a quarter mile beyond Round Park a faint trail junction can be seen on the left. (31.86524, -109.28290) This is the abandoned southern half of the Booger Spring Trail.
150 feet beyond, you will exit the trees onto the saddle. The patch of fire damage here makes it possible to look down into Greenhouse Canyon to the south. The trail swings to the southwest and begins its four tenths of a mile descent to Cima Saddle, which was hit by the fire but still has many standing trees—but almost as many fallen ones. The Greenhouse Trail descends to the east from here. (31.86141, -109.28739) There is a sign at this junction, but it is disconnected from the ground and may have fallen over. The Ward Canyon Trail once dropped down the ridge to the northwest to Helispot 31, but this trail has been abandoned and due to the extensive fire damage and erosion along the slope it once passed across, it is unlikely there is any trace of it remaining. The Crest Trail continues to the southwest.
Cima Saddle to Anita Park Junction
Exiting the southern edge of Cima Saddle, the trail heads southwest and passes through a grove of saplings on an otherwise barren slope. There are almost no large standing trees along the trail through this entire segment, largely as a result of the 1994 Rattlesnake Fire. After a quarter mile, you will swing around to the southeast, and 0.16 miles beyond that bend you pass the point where a connector trail to the Mormon Ridge Trail once descended to the south. (31.85704, -109.28947) This trail has been completely lost to erosion on this steep slope and had been abandoned. To reach the Mormon Ridge Trail now you will need to continue on the Crest Trail beyond Junction Saddle to Chiricahua Saddle and then descend from there to Mormon Saddle.
Back to the Crest Trail—you will gradually swing around to the south and after nearly three tenths of a mile the trail enters a more recent burn, where the Horseshoe 2 fire took out what was untouched by the Rattlesnake. A few trees do remain, but the majority here were obliterated, only their blackened stumps remaining. After passing under a rock ledge after about a tenth of a mile, the Anita Park Trail climbs away to the northwest on the left side of the trail. (31.85127, -109.28848)
Anita Park Junction to Junction Saddle
5 ft ↑ / 10 ft ↓
This extremely short segment continues south from Anita Park and swings around gently to the right until it reaches Junction Saddle, (31.8496, -109.28898) a four-way junction with the Chiricahua Peak Trail to the southwest, the western leg of the Crest Trail (#270B) heading west (before swinging southwest towards to its terminus at Monte Vista Peak), and the eastern leg of the Crest Trail (#270C) to the south (before swinging southeast to its terminus at Sentinel Peak).
Last updated October 12, 2020.
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\section{Introduction}
Over a billion people worldwide currently suffer from poor vision that could be improved with prescription eyeglasses \cite{Durr2014}. A major barrier to providing eyeglasses to this population is access to the trained personnel and expensive equipment required for a comprehensive eye examination. Economic restrictions, a lack of clinical providers, and distance to healthcare settings all limit access to effective ocular diagnosis and treatment \cite{Durr2014,Resnikoff2012,Fletcher1999}. To overcome these barriers, eye care providers, such as Aravind Eye Care System and L V Prasad Eye Institute, are implementing an approach that relies heavily on point-of-care screening provided by trained residents at the community level \cite{Rao2004, Rangan2007, Rao2012}. This strategy alleviates issues with transportation and reduces cultural barriers that prevent uptake of services \cite{Rao2012}. For these minimally-trained workers to be effective, there is a need for low-cost, portable, and easy-to-use devices capable of the objective assessment of a wide variety of ophthalmic diseases.
A comprehensive eye examination includes both refraction to provide eyeglass prescriptions and inspection to screen for abnormalities. Numerous inexpensive, point-of-care tools for managing ophthalmic conditions have recently been developed. With the widespread adoption of mobile phones and rapid advancement of their camera technology, the potential of smartphone-based ophthalmic imaging has been recognized \cite{Lord2010,Giardini2014,Mamtora2018,Kim2018,Arima2019}. Other portable techniques have been demonstrated with an inexpensive point-and-shoot camera \cite{Tran2012} and with a Raspberry Pi \cite{Shen2017}. A computational single-pixel ophthalmoscope was recently demonstrated for increased visibility through opacities \cite{Lochocki2016}.
To improve efficiency and quality of prescribing eyeglasses, accurate, low-cost ocular aberrometry has been demonstrated with both handheld \cite{Durr2015,Durr2019} and smartphone-based autorefractors \cite{Ciuffreda2015}. It is likely that many such devices will be required to tackle the diverse causes of global visual impairment such as age-related macular degeneration, glaucoma, and uncorrected refractive error \cite{Bourne2020}. A simple device that combines funduscopy and aberrometry, two essential parts of a comprehensive eye exam, could reduce costs and training time while increasing efficiency.
Diffuser cameras have been explored as an attractive alternative to conventional approaches to measure lightfield information \cite{Antipa2016,platt2001history,ng2005light,li2019fast,levoy2006light,xue2020singleshot,chen2020design}.
With a thorough characterization of the diffuser's caustic point-spread-function (PSF) under incoherent illumination, plenoptic analysis \cite{ng2005light} allows view synthesis and digital refocusing \cite{Antipa2016}.
Lens-free diffuser-based imaging can also be implemented by formulating the reconstruction as an inverse problem, enabling single-shot volumetric photography \cite{Waller2018} and microscopy \cite{kuo2020chip}.
Further, utilizing temporal multiplexing by the rolling shutter of a CMOS sensor, video reconstruction is possible from a single diffuser image \cite{antipa2019video}.
Extended depth-of-field photography has been demonstrated by deconvolving with the invariant far-field diffuser PSF \cite{Cossairt2010}.
Diffuser-based phase imaging under spatially partially coherent illumination \cite{LuL2019,Wang2020} is possible by solving the transport-of-intensity equation \cite{teague1983deterministic,petruccelli2013transport}.
Wavefront sensing \cite{Erto2017} and ocular aberrometry \cite{McKay2019} have also recently been demonstrated with diffusers.
In each instance, the diffuser can be treated as a randomly distributed microlens array with slightly varying foci~\cite{Antipa2016}.
However, compared to the spot pattern formed by a microlens array, the caustic pattern formed by the diffuser is more structured that produces a better evenly distributed transfer function.
This in turn makes the deconvolution problem better conditioned and minimizes the reconstruction artifacts~\cite{kuo2020chip}.
Diffuser imaging is enabled by computational imaging, which synergistically combines optics and algorithms~\cite{mait2018computational}.
It belongs to the class of computational imaging architectures that reduce the overall optics complexity by computation, including coded aperture imaging~\cite{adams2017single,shin2019minimally}, lens-free holography~\cite{mcleod2016unconventional}, compound imager~\cite{tanida2001thin,xue2020singleshot}, and lightfield/integral imager~\cite{levoy2006light,stern2006three}.
Diffuser imaging is attractive because it uses a simple and cheap optical element, does not require any special alignment between the diffuser and the image sensor~\cite{Antipa2016,McKay2019}, and achieves the imaging capability by a single-shot under both spatially coherent~\cite{McKay2019} and incoherent illumination~\cite{Antipa2016,kuo2020chip}.
In this paper, we develop and demonstrate funduscopy of a model eye with a diffuser-based computational imager.
Our diffuser-imager design is particularly inspired by the work by Antipa, et al.~\cite{Antipa2016}.
In~\cite{Antipa2016}, the diffuser is used in a ``finite-conjugate'' configuration, in which each object point projects a spherical wavefront to the diffuser, similar to the standard ``single-lens'' imager.
In funduscopy, due to the presence of the ocular lens, the {\it ``infinite-conjugate''} configuration is better suited, in which each in-focus object point on the retina projects a {\it planar} wavefront to the diffuser.
In this configuration, the diffuser can be treated as the second lens in a telecentric 4F system, which provides both shift-invariance across the field-of-view (FOV) and an invariant magnification under defocus.
Conveniently, this configuration is identical to that used in the diffuser-based ocular aberrometry~\cite{McKay2019}.
Taken together, we believe this diffuser-based sensing framework has exciting potential advantages in ocular imaging, and could enable simultaneous funduscopy and ocular aberrometry on the same platform.
The diffuser-imager is integrated with an illumination module based on an annular ring of LEDs, which provides flood-illumination across a 33$^{\circ}$ FOV.
We demonstrate the imaging capability of the proposed device by reconstructing various incoherent objects, including patterns on a self-emitting OLED screen and incoherently illuminated printed patterns through a simple model eye, as well as through a commercial model eye fundus.
In addition, we assess image reconstruction quality, and demonstrate robustness of the reconstruction algorithm to refractive error imparted on the object or the PSF used for reconstruction.
This work shows promise for the future development of a device that could perform funduscopy and aberrometry through a single diffuser camera.
\begin{figure}[t]
\centering\includegraphics[width = 0.9\linewidth]{overview}
\caption{Overview of the proposed diffuser ocular imaging workflow, including: (a) PSF calibration, (b) diffuser-image acquisition, and (c) imaging reconstruction. The PSF is a highly structured caustic pattern. During acquisition, the sensor captures a 2D image resulting from the PSF convolved with the remitted light of the fundus. A high-quality retinal image is reconstructed by solving a regularized deconvolution problem.}
\label{overview}
\end{figure}
\section{Methods}
We image the fundus with a ``DiffuserCam'', which consists of an iris placed adjacent to a holographic diffuser, separated $f_d$ from the image sensor.
To achieve large FOV ocular imaging, we jointly designed the optical hardware, calibration procedures, acquisition methods, and reconstruction algorithms.
Our workflow consists of three stages as summarized in Fig.~\ref{overview}, including an initial and {\it single-time} system PSF calibration, image acquisition, and computational reconstruction.
In the PSF calibration stage, the system response is captured by displaying a point source on an OLED screen placed at the front focal plane of a simple eye model.
In the acquisition stage, the image sensor captures a measurement of the flood-illuminated fundus through the diffuser.
In the reconstruction stage, we solve a regularized deconvolution problem to recover a high-quality fundus image.
In this section, we first describe our general optical design, then we lay out the specific experimental implementations for optimizing the system performance, and lastly we outline the theoretical principles and formulation of our reconstruction algorithm.
\begin{figure}[t]
\centering\includegraphics[width = 0.9\linewidth]{method1}
\caption{Zemax ray-tracing of the (a) imaging and (b) illumination paths of the diffuser imager. (a) The cornea image is relayed to the diffuser so that each point on the retina produces a shifted caustic PSF. (b) Ring LEDs are also relayed to the cornea to avoid central illumination and reduce specular reflection. The FOV of the system is currently limited by the numerical aperture of the illumination optics.}
\label{method1}
\end{figure}
\subsection{Optical design}
Existing fundus cameras use lens-based imaging, where high image quality is achieved by optimizing lens design, typically resulting in multi-element, bulky, and expensive systems \cite{Shen2017}.
We propose the use of a thin diffuser as an alternative for the imaging lens, which would significantly reduce size, weight, and cost of the whole system, in addition to being compatible with diffuser-based aberrometry.
In this system (Fig.~\ref{overview}(b)), the eye is illuminated with an LED ring through a beam splitter.
The reflected light from the fundus first passes through a 4F relay lens system.
The diffuser is placed at the conjugate plane of the eye lens, which captures parallel beams from an emmetropic eye.
The image sensor is placed at the ``back-focal plane'' of a diffuser, where sharp caustic patterns form \cite{Waller2018}.
To achieve large-FOV imaging and illumination, a carefully designed optical system is required.
In the following, we describe our design of the imaging path and the illumination path, as shown in Fig.~\ref{method1}(a) and (b), respectively.
To simulate an eye in a Zemax model, we use a curved retinal surface ($R$ = 14 mm), a bi-convex lens ($f = 25$ mm, Thorlabs LB1761-A), and an iris ($d = 7.7$ mm) (Fig.~\ref{method1}(a)).
This results in collimated light exiting the pupil from any spot on the fundus.
A relay system images the cornea to the diffuser, so that each point on the fundus produces a parallel beam with a distinct angle impinging on the same region on the diffuser within the desired FOV.
This increases the linear shift-invariance (LSI) of the system over a large FOV, which in turn simplifies the reconstruction algorithm.
To further reduce large-angle distortions, we use the Double-Gauss design \cite{mandler1980design}.
In our design, two lens groups (Lens 1 and Lens 2) each containing two doublets are inserted.
Lens~1 has a short focal length $f_1=37.5$ mm and can collect a large angle of reflected light leaving the eye.
The light is relayed by Lens 2 through the beam splitter (Thorlabs BSW16) and onto the diffuser.
To avoid the beam splitter limiting the large field angle, Lens 2 should also have a short focal length $f_2=50$ mm to achieve a small magnification.
However, the volume of the beam splitter limits the minimum length of $d_4+d_5$ to larger than 40mm.
The relay system was designed by taking all of these constraints into consideration.
Lens~1 consists of two $f=75$ mm doublets (Thorlabs AC508-075-A) and Lens~2 consists of two $f=100$ mm doublets (Thorlabs AC508-100-A).
The Zemax simulation, in which we modeled the system with the actual lenses used, shows that the reflected angle within $\pm15^{\circ}$ can be well imaged to the diffuser plane without shift.
For reflected angle between $15^{\circ}$ and $25^{\circ}$, the collimated light exiting the pupil can still fully illuminate the iris adjacent to the diffuser despite the beam shift due to aberrations, indicating that the LSI condition is approximately maintained.
For the field angle larger than $25^{\circ}$, the beam shift passes beyond the edge of the iris, which results in a different caustic PSF shape and violation of the LSI condition. For $30^{\circ}$ field angles, the shift is significant--only $6.3\%$ of the area of the entrance aperture to the DiffuserCam is illuminated by the collimated beam.
We model the thin diffuser as an array of randomly distributed microlenses with approximately the same focal length $f_d$, similar to~\cite{Antipa2016}.
By placing the camera $f_d$ away from the diffuser, the PSF contains high-contrast caustic patterns.
Precise control of this distance is not required because the caustic patterns from the diffuser are intrinsically more robust to defocus than a standard lens.
Intuitively, this is because each diffuser feature can be treated as a low numerical aperture (NA) lens that provides a large depth-of-field (DOF), which removes the need for precise focus control.
Under the LSI condition, the PSF size is set by the size $d$ of the iris placed in front of the diffuser.
The extent of the diffuser-image is approximately $d+2s$, where the maximum displacement, $s$, is related to the imaging-path FOV $\theta_{\mathrm{imag}}$ by $s = (f_1/f_2)f_d\theta_{\mathrm{imag}}/2$.
In practice, one needs to choose an image sensor size $D > d+2s$.
We found this condition is achievable using off-the-shelf components with a $0.5^{\circ}$ holographic diffuser (Edmunds Optics 47-989, $f_d\approx 6$ mm), the relay system described above to provide >$50^{\circ}$ FOV, which is within the range found in high-end commercial fundus cameras.
As shown in Fig.~\ref{method1}(b), the off-axis LED ring is conjugate to eye lens through the same beam splitter and relay system.
The achievable FOV is further limited by the illuminated area on the fundus, which approximately spans an angular FOV: $\theta_{\mathrm{illum}} = (f_2/f_1)\theta_{\mathrm{LED}}$.
The emitting angular range of the LED $\theta_{\mathrm{LED}}$ needs to be optimized to maximize the measurement contrast.
Our preliminary prototype uses a ring LED to minimize specular reflection with a limited $\theta_{\mathrm{LED}}$ that achieved a $33^{\circ}$ FOV.
The ring diameter was designed to be 8 mm for approximately matching the pupil size after being demagnified by the relay system, and practically constrained by the coarse LED grid in the prototype.
By adjusting the distance between the LED ring and Lens 2, the illumination FOV can be further fine tuned.
\begin{figure}[t]
\centering\includegraphics[width = 0.75\linewidth]{method2}
\caption{Experimental setup of the diffuser-based funduscope. (a) Overhead view of the imaging and illumination paths, (b) details of compact components including the LED ring, a pair of polarizers crossed between the LED array and diffuser, and the diffuser camera, (c) a 3D-printed cap to confine the divergence angle of the illumination, and (d) diffuser camera components including a 3D printed iris placed in front of the diffuser to limit the size of the PSF.}
\label{method2}
\end{figure}
\subsection{Hardware design $\&$ implementation}
An overview of the diffuser-based funduscope is shown in Fig.~\ref{method2}(a).
The setup is compact, especially for the illumination and DiffuserCam parts, as shown in Fig.~\ref{method2}(b).
To increase the contrast and reduce the stray-light background, a pair of crossed polarizers are placed in front of the LED and the diffuser imager.
The LED ring is implemented with an off-the-shelf LED matrix (Spacing = 2 mm, SparkFun LuMini LED Matrix - $8\times 8$ (64 $\times$ APA102-2020)).
Due to the discrete grid of the array, the actual diameter of the ring is 9.5 mm in our prototype (Fig.~\ref{method2}(c)).
In addition, the LED array is covered by a 3D-printed cap to limit the illumination angle (Fig.~\ref{method2}(c)) in order to block the stray-light from entering the sensor directly.
For the diffuser imager, the diffuser and a 3D-printed iris with 3.2 mm diameter are placed adjacent to one another and $\sim$6 mm before a monochromatic sCMOS image sensor (Thorlabs Quantalux, 5.04 $\mu$m pixel size, 1920 $\times$ 1080 pixels, full-well capacity 23000 e$^-$, dynamic range 87 dB).
\subsection{Algorithm}
The final fundus images are reconstructed following the general inverse problem framework that combines two complementary sources of information: the forward model describing the imaging process with the pre-calibrated PSF, and the prior describing the structural or statistical information about fundus images.
Specifically, we used a 2D LSI model that assumes the raw measurements are the convolution of the object and a single invariant PSF that is pre-captured with an on-axis point source.
With this LSI model, our preliminary experiments show high-resolution reconstruction in the central FOV region of a diffuser image of the retinal object.
However, the direct deconvolution algorithm is inevitably sensitive to noise due to the poor conditioning of the inverse problem using the non-conjugate imaging geometry. We mitigated this poor-conditioning by incorporating priors in the deconvolution algorithm. The prior we used is through the L-2 norm regularizer. Accordingly, we formulate the regularized inverse problem through the minimization of:
\begin{equation*}
\hat{\mathbf{x}}=\argmin_\mathbf{x}||\mathbf{y}-\mathbf{h}*\mathbf{x}||^{2}_{2}+\mu||\mathbf{x}||^{2}_{2},
\end{equation*}
where $\mathbf{y}$ denotes the measurement, $\mathbf{x}$ the object, $\mathbf{h}$ is the PSF, and $\mu||\mathbf{x}||^{2}_{2}$ is the L-2 regularization term with weight $\mu$. This Tikhonov regularized solution is conveniently calculated by first performing the Fourier transform, then Fourier domain filtering, and lastly inverse Fourier transforming. The optimal regularization parameter $\mu$ is found by picking the visually-optimal reconstruction when varying $\mu$ in a predefined small range.
\begin{figure}[t]
\centering\includegraphics[width = \linewidth]{result1}
\caption{Experimental FOV characterization of the imaging path of our prototype by using a self-illuminated retina. The design in (a) provides $\sim50^\circ$ FOV, as demonstrated on (b) a dot-array object and (c) a retinal object. The raw diffuser image acquired from each object is shown in the green-outlined inset. The direct reconstructed images in (b)(i) and (c)(i) and the ones with flat field post-correction in (b)(ii) and (c)(ii) are compared. Cutlines are compared between the flat-field corrected reconstruction and the displayed object. The PCC, SSIM, and PSNR of each reconstructed image are computed against the original displayed object.}
\label{fig:result1}
\end{figure}
\section{Results}
In this section, we assess the diffuser funduscope in three scenarios.
First, we conducted PSF calibration and FOV analysis of the imaging system using a simple model eye with a self-illuminated OLED screen for its retina.
Second, we replaced the self-illuminated OLED screen with various objects printed on paper, and projected the system's off-axis, ring illumination to the simple model eye for reconstruction.
The first two experiments show the effect of the system's illumination on the FOV.
Last, we use a commercial model eye to assess the image quality of the diffuser funduscope with a physiologically realistic object.
\subsection{Simple model eye with self-illuminating object}
\label{sec:result1}
For analyzing the FOV of the imaging system in the absence of illumination limitations, we measured a self-illuminated simple model eye (Fig.~\ref{fig:result1}(a)).
The simple model eye is composed of an object placed at the focal plane of a biconvex lens ($f = 25$ mm) and a 7.7 mm aperture, which provides a crude model of the human eye~\cite{McKay2019}.
We used an OLED screen as a self-illuminated object, placed at the focal plane.
The PSF was measured first by displaying an on-axis point source (diameter 275 $\mu$m) on the screen, which produced the caustic pattern, shown in Fig.~\ref{fig:result1}(a).
Next, the screen displayed an array of equally spaced point sources for calibrating the FOV as shown in Fig.~\ref{fig:result1}(b).
Here, the green outlined insert is our raw measurement and the right-hand-side is the regularized reconstruction.
We observe in this setting that the system is able to reconstruct over a 51.2$^\circ$ angular FOV.
Figure~\ref{fig:result1}(c) shows our reconstruction from displaying an image of a retina with diabetic retinopathy \cite{budai2013robust} on the screen, which demonstrated a relatively wide FOV of 48.3$^\circ$.
The directly reconstructed images are shown in Figs.~\ref{fig:result1}(b)(i) and (c)(i).
We observe uneven intensity distribution in these images possibly due to the mismatch between the model curved retina (in Fig.~\ref{method1}) and the flat OLED screen used for displaying the object.
To compensate for this effect, we applied an additional flat-field post-correction to the reconstruction, as shown in Figs.~\ref{fig:result1}(b)(ii) and (c)(ii).
Cutlines are made across characteristic feature regions to compare the reconstruction and the original displayed object.
The reconstruction quality is further quantified by comparing the recovered image with the original displayed object using the Pearson correlation coefficient (PCC), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM).
For the dot array object in Fig.~\ref{fig:result1}(b), the flat-field correction leads to reconstruction quality improvement, in particular--the SSIM improves from 0.59 to 0.85.
This can be understood from an improvement in the luminance agreement between points at large FOV angles. For the retinal image object in Fig.~\ref{fig:result1}(c), the loss of contrast reduces the SSIM.
Looking at the cutlines, though the vascular features are blurred in the reconstruction, the major features are captured, and both bright and dark edges are followed.
\begin{figure}[h]
\centering\includegraphics[width = \linewidth]{result2}
\caption{Experimental FOV characterization of external illumination and imaging. (a)~Test objects are printed on paper and placed at the focal plane of the simple model eye. The PSF used is the same as was acquired previously from the OLED screen. (b,c) Our design provides $\sim$33$^\circ$ FOV, as demonstrated with (b) ruler patterns with both positive and negative contrast, and (c) a retinal image. All reconstructions are flat-field corrected. Cutlines of the raw images are shown to compare the measurement contrast from the positive and negative contrasted ruler patterns.
Cutlines are compared between the reconstruction and the printed pattern. The PCC, SSIM, and PSNR of each reconstructed image are computed against the original printed pattern.}
\label{fig:result2}
\end{figure}
\subsection{Simple model eye with external illumination}
Next, we tested diffuser imaging with an external illumination system.
In this experiment, the simple model eye was also used, however we substituted the OLED screen with a printed paper object, as shown in Fig.~\ref{fig:result2}(a).
The same PSF measured from the on-axis point source on OLED screen (from section~\ref{sec:result1}) was used for the reconstruction, as illustrated in Fig.~\ref{fig:result2}(a).
We first analyzed the FOV by imaging a printed ruler with both positive and negative contrast (Fig.~\ref{fig:result2}(b)).
The imaging system reconstructed an image of the ruler 15 mm in length, equivalent to a 33.4$^\circ$ angular FOV.
We then printed and imaged the same retinal image displayed in Fig. \ref{fig:result1}(c).
In this printed fundus, the FOV was moved to three locations by translating the model eye laterally.
Due to the planar object and uneven illumination, non-uniform intensity distribution in the direct reconstruction was also observed.
We applied the same flat-field correction to each reconstruction in the results shown in Fig.~\ref{fig:result2}(b) and (c).
Cutlines are made across characteristic features to compare the reconstruction and the corresponding printed pattern.
Similar to our previous observation, aside from minor reduced contrast, we show major features are faithfully recovered.
In particular, in each FOV of Fig.~\ref{fig:result2}(c), vessels and other small features can clearly be resolved.
The reconstruction quality is further inspected by PCC, PSNR and SSIM.
As highlighted by the comparison for the ruler pattern with the positive and negative contrast in Fig.~\ref{fig:result2}(b), while the PCC remains similar, the PSNR and SSIM are much reduced for the positive contrast case (Fig.~\ref{fig:result2}(b)(ii)).
This degradation indicates a potential challenge in reconstructing an object with sparse negative-contrasted features with an otherwise uniform bright background since it results in a less structured measurement with low contrast, as evident by comparing the cutlines from the raw measurements between the two cases in Fig.~\ref{fig:result2}(b).
For the printed retina object, the cutlines again show that important clinical features like the vessels, hemorrhages, and optic disk are captured by the reconstruction at all three FOVs explored in Fig.~\ref{fig:result2}(c).
\begin{figure}[h]
\centering\includegraphics[width = \linewidth]{result3}
\caption{Diffuser imaging of a commercial model eye. (a) Left: The data acquisition and PSF calibration are individually performed on different setups. Right: The reconstruction from both the measurement and the PSF taken with no refractive error (0D). (b) The reconstruction results using fundus measurements under different refractive errors with a 0D PSF.
(c) The reconstruction results of a 0D fundus measurement using aberrated PSFs.
Cutlines are shown in each reconstructed images and demonstrate consistent contrast with different refractive errors or defocused PSFs.}
\label{fig:result3}
\end{figure}
\subsection{Commercial model eye with external illumination}
To investigate the performance of our combined imaging and illumination system in a physiologically-realistic scenario, we next imaged a commercial model eye (HEINE Ophthalmoscope Trainer), which has realistic retinal structures and allows varying amounts of refractive error.
Figure \ref{fig:result3}(a) shows the overall procedure of this experiment.
First, raw data is acquired (green insert) without refractive error (0D), and reconstructed using the same PSF calibrated in the previous experiments (from Fig.~\ref{fig:result1}(a)).
Next, to assess the robustness of the system to refractive error, we tested two scenarios: (1) reconstruction of fundus images with varying refractive errors using a single emmetropic PSF acquired at 0D refractive error, and (2) reconstruction of the fundus of an emmetropic model eye using ametropic PSFs acquired at a range of different retinal positions.
Figure~\ref{fig:result3}(b) shows that when the refractive error is within a range of -4D to 4D, no significant degradation of image quality occurs.
In Fig.~\ref{fig:result3}(c), the distance at which the PSF was acquired was varied by $\pm$4 mm.
This simulates PSFs acquired in eyes that are too short or too long, thus testing the sensitivity of the reconstruction to changes in the PSF that could result if calibration is done in an eye with refractive error.
Using a thin-lens approximation, this spans refractive error from -5.5D to +7.6D.
The reconstruction results indicate that when the refractive error is as high as -5.5D or +7.6D, we observe slight degradation of image quality in both contrast and resolution.
All reconstructed images are flat-field corrected to compensate for uneven illumination.
A cutline across the optic disk region for each reconstructed image is shown, indicating consistent contrast is achieved across the defocus range investigated.
\section{Discussion}
\subsection{Self-illuminated object}
The initial set of experiments with a self-illuminated OLED screen used as the retina in a simple model eye provided insight into the fundamental operation and potential performance of the diffuser-based funduscope in the absence of illumination constraints.
For initial calibration and subsequent deconvolution, the system PSF was measured by illuminating an on-axis point source on the OLED screen.
As seen in Fig.~ref{fig:result1}(a), the PSF is a highly structured caustic pattern, which is the fundamental signal used in both DiffuserCam~\cite{Waller2018} and diffuser-based ocular aberrometry~\cite{McKay2019}.
Next, a point source array was illuminated on the screen (Fig.~\ref{fig:result1}(b)), and the acquired image (green insert) is deconvolved with the system PSF to reconstruct the object.
From this result, we can determine that the imaging path is able to provide a 51$^{\circ}$ angular FOV. Interestingly, when looking at the acquired signal before reconstruction (Fig.~\ref{fig:result1}(b), green insert), a structured pattern is observed, consistent with the expected appearance of the PSF convolved with a point array.
When the image of a retina with diabetic retinopathy is displayed on the OLED screen (Fig.~\ref{fig:result1}(c)), a similar 48.3$^{\circ}$ FOV is reconstructed.
Many important features of the retina are visible, including the optic disk and healthy vasculature, as well as retinal scarring and hemorrhage.
The detection FOV is similar to the 45$^{\circ}$ FOV typically achieved by non-mydriatic fundus photography~\cite{Mackay2015}.
The reconstructed structures at large field angles are more blurred and have lower contrast, due to distortion of a flat screen being projected by a single bi-convex lens.
When exiting the simple model eye lens, these rays are not parallel, which changes their PSF, making it no longer spatially invariant. When applying our deconvolution algorithm with a fixed PSF, the reconstruction performance of structure at high field angle decreases.
\subsection{External illumination with a simple model eye}
In the next set of experiments, we used external illumination via a ring LED, and demonstrated simple model eye reconstructions of test objects printed on paper (Fig.~\ref{fig:result2}).
We first used printed rulings of known size for calibration (Fig.~\ref{fig:result2}(b)).
From these objects, we observed a high contrast reconstruction over a 33.4$^{\circ}$ FOV.
Comparing these results with the 51$^{\circ}$ FOV demonstrated with the OLED retina (Fig.~\ref{fig:result1}(b)), it is apparent that the current system FOV is limited by the extent of the LED illumination.
This can be mitigated by improving the illumination numerical aperture.
Using the same two printed ruler patterns in Fig.~\ref{fig:result2}(b) with opposite contrast demonstrates the impact of signal sparsity on measurement contrast and reconstruction quality.
The sparse-printed rulings (white rulings and black background, left) were captured with higher contrast and reconstructed with better quality, as compared to its counterpart, the dense-printed rulings (black rulings on white background, right).
Lastly, we printed the same retina pattern used on the OLED screen (Fig.~\ref{fig:result1}(c)) for imaging and reconstruction using the ring LED illumination (Fig.~\ref{fig:result2}(c)).
Again we observe a similar FOV as observed with the ruler, less than when we used the displayed retina on the OLED screen, further indicating our FOV is limited by the illumination extent.
However, despite a more limited FOV, we still observe the same clinical retinal features reconstructed in the self-illuminated pattern.
\subsection{Commercial model eye reconstruction}
In the last set of experiments, we replaced the simple model eye with a commercial model eye to test a more physiologically realistic object in the presence of refractive error and aberrated PSFs (Fig.~\ref{fig:result3}).
Reconstructions of the commercial model eye fundus were performed with LED illumination, using the same PSF acquired from the on-axis point source in the calibration step (Fig.~\ref{fig:result1}(a)), and with 0D refractive error.
The initial result of the commercial model eye fundus reconstruction is shown in Fig. \ref{fig:result3}(a), where the optic disk and blood vessels are clearly visible.
A similar angular FOV was observed here with the commercial model eye as was previously demonstrated with the simple model eye.
The FOV, though limited by the extent of illumination provided by the ring LED, still reveals a greater FOV than conventional direct ophthalmoscopy~\cite{Mackay2015}.
After reconstructing an initial image of the commercial model eye fundus with emmetropia, a refractive error of between -4D and 4D was introduced (Fig.~\ref{fig:result3}(b)).
Despite the refractive error, the diffuser funduscope still produced fundus images of similar quality to the emmetropic case.
Importantly, fundus images were reconstructed using the same PSF as applied in the 0D case and in the reconstructions of Fig. \ref{fig:result2}, and no re-calibration was required.
Finally, we evaluated the image reconstruction quality produced if the PSF were acquired from locations other than the focal point of the model eye lens (Fig.~\ref{fig:result3}(c)).
PSFs were acquired as the OLED screen was translated from -4mm to +4mm, to simulate the PSF acquired from eyes that are too long (myopia), and too short (hyperopia), respectively.
Next, the raw data acquired from the 0D refractive error case was reconstructed with these varied PSFs.
Again the fundus was reconstructed successfully over a similar 33$^{\circ}$ FOV, though some degradation of contrast and resolution begin to appear at the extreme refractive errors.
Together, these results demonstrate that the diffuser funduscope is robust to refractive error over a range of myopia and hyperopia large enough to cover a substantial range of clinical cases~\cite{Schwiegerling}.
This is because the 0.5$^{\circ}$ holographic diffuser used in this study can be modeled as a random array of irregular lenslets, each with a very large f/\# and large depth-of-focus.
Further, the reconstruction quality is similar to that achieved by other computational ophthalmoscope techniques~\cite{Lochocki2016}.
Overall, we believe our imaging system is robust and stable to refractive error within a reasonable range, and shows promise for improving the accessibility of medical diagnosis of retinal disease.
\subsection{Special considerations in diffuser-based computational imaging}
The diffuser-imaging follows a ``non-focal'' imaging geometry -- the PSF spreads over an extended area.
Accordingly, each pixel on the image sensor measures mixed signals from multiple object points.
This generally reduces the image contrast in the raw measurements as compared to traditional ``focused'' imaging systems.
Consequently, image sensors with low read-noise, large well capacity, and high dynamic range are desired to better capture the encoded information.
In our prototype, we chose an sCMOS camera that provides <1 e$^-$ median read-noise, 23000 e$^-$ full-well capacity and 87 dB dynamic range.
Image quality can be further improved with better image sensor, as shown in~\cite{Antipa2016}.
The image contrast can also be significantly improved by using a properly-designed microlens array~\cite{xue2020singleshot} or customized aperiodic microlens array~\cite{kuo2020chip}.
Our future work will investigate these strategies with the additional considerations of keeping the platform low-cost and compatible to ocular aberrometry.
Our reconstruction was implemented by the Tikhonov regularization algorithm, which has the advantage that it provides a closed-form solution, is computationally efficient and fast.
In our implementation, reconstructing a 1080$\times$1920-pixel image using MATLAB on Mac OS machine takes about 0.26 seconds.
However, this L-2 regularization strategy suffers from a fundamental trade-off between the reconstructed resolution, image contrast, and ringing artifacts~\cite{bertero1998introduction}.
This limited the reconstruction quality, especially for complex objects, e.g. Fig.~\ref{fig:result1}(c).
The reconstruction quality is further affected by the presence of a strong background, e.g. Fig.~\ref{fig:result2}(b).
It has been shown that these limitations can be alleviated by incorporating advanced image priors, such as sparsity~\cite{Antipa2016} and deep neural network learned priors~\cite{monakhova2019learned}, using an iterative algorithm.
However, these algorithms typically require significantly larger computational cost and longer execution time.
Recently, end-to-end task-specific deep learning models emerge to be an appealing solution for achieving both high-quality image reconstruction and highly efficient inference implementation~\cite{barbastathis2019use,sinha2017lensless,li2018deep,xue2019reliable}.
Given the recent achievements in automatic analysis of retinal images~\cite{gulshan2016development,gargeya2017automated}, combining our diffuser-funduscopy and data-driven deep learning models may be a promising future direction to pursue.
\section{Conclusion}
Visual impairment is a pressing global health concern, and many of its causes are avoidable. This problem can be improved by the development and distribution of robust, low-cost diagnostic devices that require minimal training to operate. In this paper we develop and demonstrate one such approach for retinal imaging by developing and characterizing a compact diffuser funduscope. We demonstrate high-quality funduscopy of a model eye that is robust to a large range of refractive error. Further, the point spread function used for deconvolution is a caustic pattern produced by the same holographic diffuser from which ocular aberrometry has been previously demonstrated. In future work, we envision these two techniques working synergistically, allowing simultaneous measurement of refractive error and funduscopy in one compact, inexpensive device.
\section*{Funding}
This work was partially supported by a Johns Hopkins Medical Scientist Training Program Fellowship, an NIH NIBIB R21 grant (R21 EB024700), and NSF grants (1711156, 1813848).
\section*{Acknowledgments}
We thank Shivang R. Dave and Ahhyun Stephanie Nam from PlenOptika, Inc., for fruitful discussions on funduscopy.
\section*{Disclosures}
GNM and NJD are listed as co-inventors on a provisional patent application assigned to Johns Hopkins University that is related to the technologies described in this article. They may be entitled to future royalties from this intellectual property.
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{
"redpajama_set_name": "RedPajamaArXiv"
}
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Q: How to get multiple copies of a UIView loaded from a nib? I want to use a UIView hierarchy multiple times (the nib object is a template). Unfortunately, UIView does not conform to <NSCopying> so
[cell.contentView addSubview: [[templEditCellView copy] autorelease]];
does not work.
I wasn't surprised, since I want a deep copy of the view hierarchy.
Currently the view is one of several top-level objects in the nib it is loaded from. Is there a way to reload a single specified top-level object from the nib? Should I split out the view to a single NIB which can be reloaded on demand? Or is there another way to make a deep copy of a view?
Thanks!
A: Easiest way to make a deep copy of a view is to archive and unarchive it.
id copyOfAView =
[NSUnarchiver unarchiveObjectWithData:
[NSArchiver archivedDataWithRootObject:aView]];
Putting the view in its own nib works too. You can create an NSNib object and reload it as many times as you want.
A: You can't load it directly to the cell's content view, but you can create a class with outlets for the view(s) and load it with
[[NSBundle mainBundle] loadNibNamed:@"TheNib" owner:anObject options:nil];
There is more info around SO and the 'net about loading table view cells from nibs. I really like Bill Dudney's approach but the method described by Jeff LaMarche is easier and great for many situations.
A: This seems to be working well at the moment for what I need:
if (! templEditCellView) {
[[NSBundle mainBundle] loadNibNamed:@"TextEditCellView" owner:self options:nil];
if (! templEditCellView) {
abort(); // !!
}
}
[cell.contentView addSubview: templEditCellView];
templEditCellView = nil;
The table controller is placing the same customized view heirarchy in the content of each cell in this case.
I'd love to see an approach that doesn't multiply nib files if I have lots of different cell customizations (as I might).
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
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About the NCC ›
Report to Members ›
Major activities carried out during 2005.
Trade policy's impact on the U.S. cotton industry increased in 2005 as international trade negotiations, free trade agreements and even international public opinion influenced the industry's future as never before.
WTO Doha Round
NCC Chairman Woods Eastland and American Cotton Producers (ACP) Chairman John Pucheu were joined by senior NCC staff in Geneva to share concerns with World Trade Organization officials regarding the Doha Round of trade talks. Support was declared for a balanced and comprehensive agreement, but one that would not single out cotton for treatment that is different from agriculture as a whole, including an "early harvest." Eastland and NCC staff also shared that concern with the U.S. Trade Representative's office.
Likewise, NCC Vice Chairman Allen Helms told the Senate Agriculture Committee that the U.S. cotton industry was willing to support U.S. negotiators and fully participate in the Doha Round, provided cotton is treated equitably and not singled out and if meaningful improvements are made in market access.
Helms and Eastland were joined by NCC President/CEO Mark Lange in another Geneva meeting with Crawford Falconer. The newly appointed WTO chair of the agricultural negotiations and of the special cotton subcommittee expressed his desire to keep the subcommittee in a monitoring capacity only.
The NCC joined with the USTR and Congressional members in reacting against European Commission for Trade Peter Mandelson's call for singling out cotton for an early harvest. NCC responded to a similar proposal by a group of African countries saying, "The U.S. cotton program is not the source of economic hardship for farmers in African countries."
NCC staff, attending the WTO ministerial meeting in Hong Kong, conveyed industry concerns to U.S. negotiators about the continued efforts to single out cotton from the broader agricultural negotiations. Upon conclusion of the ministerial, NCC Chairman Eastland expressed appreciation to Ambassador Rob Portman and Agriculture Secretary Mike Johanns for their diligent efforts, but also noted the industry's extreme disappointment at the ministerial's declaration that calls for larger and quicker cuts for cotton.
Lange joined representatives of several commodity groups and general farm organizations in a roundtable discussion aimed at closing a loophole whereby the Subsidies Code rules can undermine the WTO negotiations.
U.S.-Brazil Dispute
The NCC expressed its disappointment with the WTO appellate body's ruling in the Brazil/U.S. cotton dispute – a decision that upheld the dispute panel's determinations regarding the upland cotton program's Step 2 component, the export credit guarantee program, classification of direct payments and serious prejudice.
Following the ruling, NCC staff met with the USTR's office, key Congressional members and other commodity and general farm organizations regarding the NCC's plans for a response. Later, NCC Chairman Woods Eastland stressed to USTR and USDA officials the importance of their consulting with the U.S. cotton industry on a U.S. response and its implementation.
The NCC registered its opposition with USDA's proposal submitted to Congress in early July that called for the immediate elimination of Step 2. That move, the NCC pointed out, would alter a fundamental piece of the sales and marketing structure for U.S. cotton in mid-stream, harming many U.S. cotton producers, merchants and textile manufacturers. Eventually, a budget reconciliation package that included an August 1, 2006 termination of the Step 2 program passed the Congress and was signed into law.
Participants from the C-4 West African countries, accompanied by leadership from Tuskegee University, hear about advances in cotton biotechnology during a stop in Mississippi as part of an integrated pest management training program.
U.S. Cotton Policy and Africa
The NCC lauded the USDA and the USTR's office for their launch of "The West Africa Cotton Improvement Program" in November. The program, aimed at helping African cotton farmers improve farm income, emanated from a year of preparatory work by USDA and US AID working cooperatively with the U.S. cotton industry.
Among the 2005 activities was a U.S. delegation accompanied by ACP Chairman Pucheu that talked with officials from five West African cotton-producing countries on ways to improve their cotton yields and quality. A follow-up conference in Mali enabled U.S. officials to discuss other technologies that could improve the Africans' crops. Later, West African officials participated in Cotton Incorporated's Engineered Fiber Selection conference, observed the Universal Cotton Standards conference and participated in three NCC co-sponsored training programs covering fiber classification, entomology, soil conservation and fertility.
Immediately following the Board's decision to support the Dominican Republic-Central America Free Trade Agreement (CAFTA), the NCC began an extensive effort to help secure the legislation's passage. Working in cooperation with the National Council of Textile Organizations (NCTO), the NCC pressed the Bush Administration on implementation issues such as cumulation and limiting third country participation.
Later, NCC Vice Chairman Allen Helms participated in an NCTO news conference that provided the NCC with the opportunity to publicly join with the Administration in urging Congress to adopt CAFTA. NCC leaders promoted the trade pact's passage through Congressional contacts, which included distribution of state CAFTA fact sheets for industry members to relay to their respective Congressmen. NCC staff and leaders also conducted meetings with the USTR office, generated letters to the editor, participated in other news conferences and offered Congressional testimony. That included former NCC Chairman Bob McLendon's appearance before the Senate Agriculture Committee and Southeast producers Sam Spruell's and Jimmy Webb'sparticipation in a news conference of five Republican Congressmen from textile districts, who announced their CAFTA support.
Early in 2005, the NCC joined with the National Council of Textile Organizations and several other textile, fiber and labor organizations in support of a 2005 "platform" that called for actions to strengthen domestic manufacturing and the preservation of American jobs. That platform included a commitment to the continuation of WTO-consistent restraints on imports of Chinese textile and apparel through either a bilateral agreement with China or special safeguards.
The NCC also participated with key textile, trade and labor organizations in a news briefing that shed light on the tremendous surge of Chinese apparel/textile products after quotas were lifted January 1, 2005. The NCC notified the USTR and the Committee for the Implementation of Textile Agreements (CITA) of government data, including U.S. Customs documents. The NCC then worked closely with the U.S. textile industry and the Administration to ensure appropriate safeguards be imposed against surging China imports.
Chinese combed yarn (301) was among several textile and apparel products on which safeguard petitions were affirmed by the Committee for the Implementation of Textile Agreements.
Throughout the year, the NCC supported the U.S. textile industry's filing of petitions to limit textile/apparel imports from China. Data provided by NCC's Economic Services Department was instrumental in convincing CITA of the need to implement safeguards, including the importance of self-initiating "threat-based" safeguards in product categories where U.S. market disruption was imminent. CITA reached affirmative decisions on the following petitions that were filed in 2004: 338/339 (Cotton Knit Shirts), 347/348 (Cotton Trousers), 352/652 (Cotton & MMF Underwear), 638/639 (MMF Knit Shirts), 301 (Combed Cotton Yarn), 340/640 (M&B Cotton & MMF Shirts, Not Knit), 647/648 (MMF Trousers), 349/649 (Cotton & MMF Brassieres) and 620 (Other Synthetic Filament Fabric).
In November, the United States and China signed a broad agreement on Chinese textile imports that went into effect on January 1, 2006 and is slated to end on December 31, 2008. The pact placed quotas on a broader range of textile and apparel products (34) than were covered by safeguards (19). This agreement was widely seen as constructive by U.S. textile and fiber leaders. The NCTO also called for a separate textile sectoral negotiation in the WTO Doha Round to deny another opportunity for China to dominate trade in textile and apparel products.
The NCC was vigorous on additional activities related to China.
It worked with the Administration, which conducted numerous meetings with Chinese officials about the way China allocates its raw cotton import quotas. An additional concern has arisen with the variable duty announced by China on imports in excess of its WTO commitment. This duty places the price of imported cotton above that of Chinese domestic polyester.
The NCC capitalized on two opportunities to provide Congressional testimony on China trade issues. Bobby Weil testified before the House Ways and Means Committee and Tom Stallings appeared before the House Small Business Committee. In addition to quota allocation and textile safeguard issues, the testimony conveyed concerns regarding China's WTO raw cotton accession agreement compliance, including market access, contract sanctity, quality standards and evolving trade terms. Industry concerns also were shared about the cooperative efforts with the Chinese government as it endeavors to reform its cotton classification system.
In June, NCC Chairman Eastland participated in a Cotton Council International-sponsored trip to China. He addressed the China Cotton Association's third international conference on the importance of global cotton promotion. The presentation also explained the advantages of U.S. cotton and fostered a better understanding of the U.S. cotton research and promotion program, as well as the need for China and other cotton-producing countries to establish similar self-help programs.
NCC staffers went to China in the fall to interact with the China Cotton Association, an NCC-modeled organization. This endeavor was aimed at helping China reform its processing and classing systems but also to promote U.S. cotton with this important trading partner.
The Coalition for a Sound Dollar, of which the NCC is a member, commended President Bush and Treasury Secretary John Snow for assertions that China should act immediately on currency reform. The Coalition also urged the Treasury Department to cite China for currency manipulation and expedite negotiations for putting it to an end. The NCC also remained active in the Fair Currency Alliance that urged the U.S. government to insist that China revalue and ultimately float its currency.
In other trade-related issues:
NCC Chairman Woods Eastland exhorted China and other major cotton-producing and consuming countries to join together in promoting cotton and increasing demand for the fiber on a global basis. Eastland stressed this need in two key presentations, the China International Cotton Conferences and the International Cotton Advisory Committee's plenary session.
NCC President/CEO Mark Lange was named to the Agricultural Policy Advisory Committee for Trade. Named to the Tobacco, Cotton, Peanuts, and Planting Seeds Agricultural Technical Advisory Committee for Trade were: Mississippi producer Kenneth Hood, Texas producers Dale Artho and Kenneth Dierschke, Missouri producer Chuck Earnest, and Alabama merchant Robert Weil, II. Also named to that ATAC panel were Billy Carter, Jr., North Carolina Cotton Producers Assoc.; Thomas W. Smith, AMCOT; Gary Adams, NCC's vice president, Economics and Policy Analysis; and Bill Gillon, NCC's counsel and advisor on trade issues.
NCC Report to Members Archive Joint Message from the Chairman and the President Legislative Affairs Trade Communications Technical Cotton Council International The Cotton Foundation Video Staff Report Download this Report (PDF)
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
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Q: Pass API Text Data to other Page Flutter I'm facing an issue regarding API datas,
I want the pass the texts, Image generated by API to another screen screen
Here is the
String _name(dynamic user){
return user['name']['title'];
}
String _description(dynamic user){
return user['name']['description'];
}
I want to pass these texts to the next screen using Provider or MaterialRoute Page,
How can I do so in a real example
Thanks
A: You can do this by 2 ways:
*
*Pass a data to screen as arguments. For example:
class SecondScreen extends StatelessWidget {
final String title;
final String description;
SecondScreen(this.title, this.description);
}
And in routing:
Navigator.push(
context,
MaterialPageRoute(builder: (context) => SecondScreen(title, description)),
);
*Create a model class in Provider and add data to it before moving to another screen and access this data in the second screen.
A Provider basically allows you to access data belonging to class from any widget. Here is a link to the Provider package. You'll find examples over there.
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
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//////////////////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2014-2015, Egret Technology Inc.
// All rights reserved.
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
// * Neither the name of the Egret nor the
// names of its contributors may be used to endorse or promote products
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//
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// EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
//////////////////////////////////////////////////////////////////////////////////////
class Main extends egret.DisplayObjectContainer {
/**
* 加载进度界面
* Process interface loading
*/
private loadingView: LoadingUI;
public constructor() {
super();
this.addEventListener(egret.Event.ADDED_TO_STAGE, this.onAddToStage, this);
}
private onAddToStage(event: egret.Event) {
//设置加载进度界面
//Config to load process interface
this.loadingView = new LoadingUI();
this.stage.addChild(this.loadingView);
//初始化Resource资源加载库
//initiate Resource loading library
RES.addEventListener(RES.ResourceEvent.CONFIG_COMPLETE, this.onConfigComplete, this);
RES.loadConfig("resource/default.res.json", "resource/");
}
/**
* 配置文件加载完成,开始预加载preload资源组。
* configuration file loading is completed, start to pre-load the preload resource group
*/
private onConfigComplete(event: RES.ResourceEvent): void {
RES.removeEventListener(RES.ResourceEvent.CONFIG_COMPLETE, this.onConfigComplete, this);
RES.addEventListener(RES.ResourceEvent.GROUP_COMPLETE, this.onResourceLoadComplete, this);
RES.addEventListener(RES.ResourceEvent.GROUP_LOAD_ERROR, this.onResourceLoadError, this);
RES.addEventListener(RES.ResourceEvent.GROUP_PROGRESS, this.onResourceProgress, this);
RES.addEventListener(RES.ResourceEvent.ITEM_LOAD_ERROR, this.onItemLoadError, this);
RES.loadGroup("preload");
}
/**
* preload资源组加载完成
* Preload resource group is loaded
*/
private onResourceLoadComplete(event: RES.ResourceEvent): void {
if (event.groupName == "preload") {
this.stage.removeChild(this.loadingView);
RES.removeEventListener(RES.ResourceEvent.GROUP_COMPLETE, this.onResourceLoadComplete, this);
RES.removeEventListener(RES.ResourceEvent.GROUP_LOAD_ERROR, this.onResourceLoadError, this);
RES.removeEventListener(RES.ResourceEvent.GROUP_PROGRESS, this.onResourceProgress, this);
RES.removeEventListener(RES.ResourceEvent.ITEM_LOAD_ERROR, this.onItemLoadError, this);
this.createGameScene();
}
}
/**
* 资源组加载出错
* The resource group loading failed
*/
private onItemLoadError(event: RES.ResourceEvent): void {
console.warn("Url:" + event.resItem.url + " has failed to load");
}
/**
* 资源组加载出错
* The resource group loading failed
*/
private onResourceLoadError(event: RES.ResourceEvent): void {
//TODO
console.warn("Group:" + event.groupName + " has failed to load");
//忽略加载失败的项目
//Ignore the loading failed projects
this.onResourceLoadComplete(event);
}
/**
* preload资源组加载进度
* Loading process of preload resource group
*/
private onResourceProgress(event: RES.ResourceEvent): void {
if (event.groupName == "preload") {
this.loadingView.setProgress(event.itemsLoaded, event.itemsTotal);
}
}
private textfield: egret.TextField;
/**
* 创建游戏场景
* Create a game scene
*/
private createGameScene(): void {
/*//添加地图
var map: TileMap = new TileMap();
this.addChild(map);
//this.astarPath(9,0);
var chara: Character = new Character(this);
this.addChild(chara);
chara.idle();
//添加点击监听
this.stage.addEventListener(egret.TouchEvent.TOUCH_TAP, function (e: egret.TouchEvent): void {
var startx: number = Math.floor((chara._body.x) / 50);
var starty: number = Math.floor(chara._body.y / 50);
var endx: number = Math.floor(e.localX / 50);
var endy: number = Math.floor(e.localY / 50);
var path: Point[] = map.astarPath(startx - 1, starty, endx, endy);
if (path.length > 0) {
chara.move(e.localX, e.localY, path);
}
}, this);*/
TaskService.init();
for(var i:number = 0;i<NPCManager.NPCList.length;i++){
this.addChild(NPCManager.NPCList[i]);
}
var panel = new TaskPanel();
panel.x = 0;
panel.y = 0;
this.addChild(panel);
TaskService.addObserver(panel);
}
private createBitmapByName(name: string): egret.Bitmap {
var result = new egret.Bitmap();
var texture: egret.Texture = RES.getRes(name);
result.texture = texture;
return result;
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,662
|
{"url":"https:\/\/codegolf.meta.stackexchange.com\/questions\/18269\/january-2020-moderator-election-community-interest-check\/18294","text":"# January 2020 Moderator Election \u2014 Community Interest Check\n\nThis community last had an election last year, and has recently seen their moderator team reduced by two.\n\nAs such, by request of the remaining two moderators on the team, and to find replacements for Mego and Dennis, we're looking at scheduling an election to start somewhere in January 2020. To avoid finding ourselves in a situation where an election would fail due to an insufficient number of candidates, though, I'm posting this to try to assess the community members' willingness to step up and nominate themselves, when the actual election's nomination period starts.\n\nPlease leave an answer if you'd be willing to run for a moderator position, should we decide to run an election. Like I mentioned, we're looking at scheduling the nomination period to start some time in January '20.\n\nNOTE: This is not an official election nomination thread, just a \"pulse check\" to get a notion of how many people here would be willing to step up, so you don't have to put up your whole election nomination.\n\n\u2022 That largely depends on whether you've resolved the situation with Monica or not, and given you've started censoring links to the gofundme, the magic 8 ball says... \"Very Doubtful\"\n\u2013\u00a0Jo King Mod\nNov 14 '19 at 21:27\n\u2022 Dennis and Mego stepped down for a reason. Judging for the vote counts in their annoucements, many people agree with their motives and respect their decision. Running for moderator now would feel, to a large extent, like going against that cause Nov 14 '19 at 23:59\n\u2022 Given that many people, in addition to Mego and Dennis, have stated that they would stop or greatly decrease their participation to Code Golf, I doubt we even need new mods given the current activity. Nov 15 '19 at 7:38\n\u2022 If you're going to check our pulse, you're going to find the community alive and incredibly angry at the SE administration. Your recalculation of reputation will not appease us. Nov 18 '19 at 20:35\n\u2022 Note that DJMcMayhem, in their post stepping down as moderator indicated that they wanted the community to find a replacement moderator: codegolf.meta.stackexchange.com\/q\/18476\/20080 Jan 24 '20 at 3:10\n\u2022 A site could be shut down if there are not enough people to moderate it. This makes me qualify my comment above. If we reach a point where the site's continuity is at stake I'm sure people will want to run as moderators to keep this community going Jan 27 '20 at 15:42\n\nI would run. I fundamentally disagree with many of Stack Exchange's policies. And, should I run and on the off-chance, actually get elected, I would not endorse all of SE's individual decisions, but I still have faith in the community, and if the community needs moderators, and especially since doubling the load on the other two moderators is understandably hard, I'm willing to help, for the community.\n\nI still do not agree with how SE handled this, and I never will. A true apology or a peaceful resolution is well overdue and not sufficient, at this point. But, and maybe I'm too optimistic\/loyal or have too much faith, I still believe the merit of this platform comes from the community. If an election were held sooner than now, or now, I wouldn't run, because after the whole community was damaged by these events and we lost two amazing moderators, it would feel like a hurried attempt to silence and patch over the problem, but January 2020 will be enough time to make a decision. I probably would run, but of course that's under the condition that nothing even worse happens.\n\nBut please, do not call it \"replacing\". Nobody can replace the hole left by Mego and Dennis, certainly not me. Their presence and support for our community will forever be missed, and I can only hope to start a time that grows to as great as their legacy, but never to replace it.\n\n\u2022 This is the only reason, in my opinion, for why we need an election however, it does seems like the community has also lessened, which compensates for the lack of moderators. I wouldn't know, a current moderator could probably answer this better but I think the question that needs asking is Do we need more moderators? rather than Are people willing to be moderators?. Nov 22 '19 at 19:48\n\u2022 @totallyhuman Well I specifically requested JNat to post this because I feel like we do. Nov 22 '19 at 22:38\n\u2022 I'm curious. What's your stance now, after the firing of community managers (Shog9 and Robert Cartaino)? Does that count as something \"even worse\"? Jan 16 '20 at 11:02\n\u2022 @StewieGriffin I've seen the two Goodbye posts for them, but I'm not exactly sure what happened and where to find that information. Could you send me a link or a quick rundown of what happened? It sounds like it might count as that, unfortunately...\n\u2013\u00a0hyper-neutrino Mod\nJan 16 '20 at 12:52\n\nI would run. However, if I am elected, I'll step down. I don't think it is right to replace Mego and Dennis, who are clearly better candidates than me.\n\n\u2022 You aren't eligible to run without the required badges (Civic Duty, Strunk & White, Deputy, Convention) Nov 15 '19 at 3:50\n\u2022 @RedwolfPrograms I'm aware but I'm trying to make a statement not actually become a moderator. Nov 15 '19 at 4:11\n\u2022 @RedwolfPrograms as far as I know, that's only the case on Stack Overflow\n\u2013\u00a0Doorknob Mod\nNov 15 '19 at 5:11\n\u2022 RedwolfPrograms, Doorknob, further, it seems only 300 rep is needed for a self-nomination: \"In the nomination phase, any community member in good standing with at least 300 reputation may nominate themselves \u2014 and only themselves \u2014 as a candidate in the moderator election.\" Nov 15 '19 at 6:21\n\u2022 So if you're not actually interested in the position, what's the point of this answer? Nov 15 '19 at 6:38\n\u2022 @DJMcMayhem Sounds like abstentionism. Nov 15 '19 at 13:30\n\u2022 @gerrit correct. Nov 15 '19 at 19:27","date":"2021-09-18 17:24:28","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.23553097248077393, \"perplexity\": 1554.6333217381873}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-39\/segments\/1631780056548.77\/warc\/CC-MAIN-20210918154248-20210918184248-00604.warc.gz\"}"}
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{"url":"http:\/\/mathoverflow.net\/revisions\/14334\/list","text":"3 corrected direction of some arrows\n\nIn the category of sets there is no such thing as the initial local ring into which R maps, i.e. a local ring L and a map f:R-->L such that any map from R into a local ring factors through f.\n\nBut a ring R is a ring object in the topos of Sets. Now if you are willing to let the topos vary in which it should live, such a \"free local ring on R\" does exist: It is the ring object in the topos of sheaves on Spec(R) which is given by the structure sheaf of Spec(R). So the space you were wondering about is part of the solution of forming a free local ring over a given ring (you can reconstruct the space from the sheaf topos, so you could really say that it \"is\" the space).\n\nEdit: I rephrase that less sloppily, in response to Lars' comment. So the universal property is about pairs (Topos, ring object in it). A map (T,R)-->(T',R') between such is a pair\n\n(adjunction $f_:T \\leftrightarrow T':f^$ , morphism of ring objects $f^*R'\\rightarrow R$).\n\nNote that by convention the direction of the map is the geometric direction, the one corresponding to the direction of a map topological spaces - in my \"universal local ring\" picture I was stressing the algebraic direction, which is given by $f^*$.\n\nNow for a ring R there is a map $(Set,R)\\rightarrow(Sh(Spec(R)), O_{Spec(R)})$(Sh(Spec(R)), O_{Spec(R)})\\rightarrow(Set,R)$:$f^* R$is the constant sheaf with value R on Spec(R), the map$f^* R \\rightarrow O_{Spec(R)}$is given by the inclusion of R into its localisations which occur in the definition of$O_{Spec(R)}$. This is the initial terminal map (Set,R)-->(T,L) into T,L)-->(Set,R) from pairs with L a local ring. For a simple example you might want to work out how such a map factors, if the target domain pair happens to be of the form (Set,L). This universal property of course determines the pair up to equivalence. It thus also determines the topos half of the pair up to equivalence, and thus also the space Spec(R) up to homeomorphism.(end of edit) An even nicer reformulation of this is the following (even more high brow, but to me it gives the true and most illuminating justification for the Zariski topology, since it singles out just the space Spec(R)): A ring R, i.e. a ring in the topos of sets, is the same as a topos morphism from the topos of sets into the classifying topos T of rings (by definition of classifying topos). There also is a classifying topos of local rings with a map to T (which is given by forgetting that the universal local ring is local). If you form the pullback (in an appropriate topos sense) of these two maps you get the topos of sheaves on Spec(R) (i.e. morally the space Spec(R)). The map from this into the classifying topos of local rings is what corresponds to the structure sheaf. Isn't that nice? See Monique Hakim's \"Schemas relatifs et Topos anelles\" for all this (the original reference, free of logic), or alternatively Moerdijk\/MacLane's \"Sheaves in Geometry and Logic\" (with logic and formal languages). 2 included a more detailed explanation Edit: I rephrase that less sloppily, in response to Lars' comment. So the universal property is about pairs (Topos, ring object in it). A map (T,R)-->(T',R') between such is a pair (adjunction$f_:T \\leftrightarrow T':f^ $, morphism of ring objects$f^*R'\\rightarrow R$). Now for a ring R there is a map$(Set,R)\\rightarrow(Sh(Spec(R)), O_{Spec(R)})$:$f^* R$is the constant sheaf with value R on Spec(R), the map$f^* R \\rightarrow O_{Spec(R)}$is given by the inclusion of R into its localisations which occur in the definition of$O_{Spec(R)}\\$.This is the initial map (Set,R)-->(T,L) into pairs with L a local ring. For a simple example you might want to work out how such a map factors, if the target pair happens to be of the form (Set,L).\n\nThis universal property of course determines the pair up to equivalence. It thus also determines the topos half of the pair up to equivalence, and thus also the space Spec(R) up to homeomorphism.(end of edit)\n\nAn even nicer reformulation of this is the following (even more high brow, but to me it gives the true and most illuminating justification for the Zariski topology)topology, since it singles out just the space Spec(R)):\n\n1\n\nIn the category of sets there is no such thing as the initial local ring into which R maps, i.e. a local ring L and a map f:R-->L such that any map from R into a local ring factors through f.\n\nBut a ring R is a ring object in the topos of Sets. Now if you are willing to let the topos vary in which it should live, such a \"free local ring on R\" does exist: It is the ring object in the topos of sheaves on Spec(R) which is given by the structure sheaf of Spec(R). So the space you were wondering about is part of the solution of forming a free local ring over a given ring (you can reconstruct the space from the sheaf topos, so you could really say that it \"is\" the space).\n\nAn even nicer reformulation of this is the following (even more high brow, but to me it gives the true and most illuminating justification for the Zariski topology):\n\nA ring R, i.e. a ring in the topos of sets, is the same as a topos morphism from the topos of sets into the classifying topos T of rings (by definition of classifying topos). There also is a classifying topos of local rings with a map to T (which is given by forgetting that the universal local ring is local). If you form the pullback (in an appropriate topos sense) of these two maps you get the topos of sheaves on Spec(R) (i.e. morally the space Spec(R)). The map from this into the classifying topos of local rings is what corresponds to the structure sheaf.\n\nIsn't that nice? See Monique Hakim's \"Schemas relatifs et Topos anelles\" for all this (the original reference, free of logic), or alternatively Moerdijk\/MacLane's \"Sheaves in Geometry and Logic\" (with logic and formal languages).","date":"2013-05-24 15:31:48","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9369574785232544, \"perplexity\": 570.6866048944112}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2013-20\/segments\/1368704713110\/warc\/CC-MAIN-20130516114513-00088-ip-10-60-113-184.ec2.internal.warc.gz\"}"}
| null | null |
{"url":"http:\/\/newhouseinmobiliaria.com\/dpovpf\/modulus-and-conjugate-of-a-complex-number-b4d8fa","text":"# modulus and conjugate of a complex number Home \/ modulus and conjugate of a complex number\n\n## modulus and conjugate of a complex number\n\n'https:\/\/':'https:\/\/') + \"vmss.boldchat.com\/aid\/684809033030971433\/bc.vms4\/vms.js\"; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(vms, s); }; if(window.pageViewer && pageViewer.load) pageViewer.load(); else if(document.readyState==\"complete\") bcLoad(); else if(window.addEventListener) window.addEventListener('load', bcLoad, false); else window.attachEvent('onload', bcLoad); Sign-In. It has the same real part. Summary. There is a very nice relationship between the modulus of a complex number and its conjugate.Let\u2019s start with a complex number z =a +bi z = a + b i and take a look at the following product. Modulus of a Conjugate: For a complex number z\u2208Cz\u2208\u2102. If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. |z| = 0. 5. \u2022 \u2223z\u2223 = \u2223 z\u0304 \u2223 2. Approach: A complex number is said to be a conjugate of another complex number if only the sign of the imaginary part of the two numbers is different. Modulus of a Complex Number Contact an Academic Director to discuss your child\u2019s academic needs. Let us see some example problems to understand how to find the modulus and argument of a complex number. z \u2013 = 2i Im(z). This fact is used in simplifying expressions where the denominator of a quotient is complex. A complex number z=a+bi is plotted at coordinates (a,b), as a is the real part of the complex number, and bthe imaginary part. |7| = 7, |\u2013 21| = 21, | \u2013 \u00bd | = \u00bd. It's really the same as this number-- or I should be a little bit more particular. If you are on a personal connection, like at home, you can run an anti-virus scan on your device to make sure it is not infected with malware. The complex conjugate of a + bi is a \u2013 bi, and similarly the complex conjugate of a \u2013 bi is a + bi.This consists of changing the sign of the imaginary part of a complex number.The real part is left unchanged.. Complex conjugates are indicated using a horizontal line over the number or variable. Complex number calculator: complex_number. Description : Writing z = a + ib where a and b are real is called algebraic form of a complex number z : a is the real part of z; b is the imaginary part of z. They are the Modulus and Conjugate. Misc 13 Find the modulus and argument of the complex number ( 1 + 2i)\/(1 \u2212 3i) . From this product we can see that. Common Core: HSN.CN.A.3 Beginning Activity. How do you find the conjugate of a complex number? If we add a complex number and it\u2019s conjugate, we get Thus, we have a formula for the real part of a complex number in terms of its conjugate: Similarly, subtracting the conjugate gives and so . Formulas for conjugate, modulus, inverse, polar form and roots Conjugate. \u00afz = (a +bi)(a\u2212bi) =a2 +b2 z z \u00af = ( a + b i) ( a \u2212 b i) = a 2 + b 2. The conjugate of a complex number z=a+ib is denoted by and is defined as . z\u00af. modulus of conjugate. Modulus or absolute value of z = |z| |z| = a 2 + b 2 Since a and b are real, the modulus of the complex number will also be real. \u2223z\u2223 = 0 iff z=0. SchoolTutoring Academy is the premier educational services company for K-12 and college students. An Argand diagram has a horizontal axis, referred to as the real axis, and a vertical axis, referred to as the imaginaryaxis. In this situation, we will let $$r$$ be the magnitude of $$z$$ (that is, the distance from $$z$$ to the origin) and $$\\theta$$ the angle $$z$$ makes with the positive real axis as shown in Figure $$\\PageIndex{1}$$. whenever we have to show a complex number purely real we use this property. The modulus of a number is the value of the number excluding its sign. Select one of SchoolTutoring Acedemy\u2019s premier Test Prep programs. \u00af. |z| = |3 \u2013 4i| = 3 2 + (-4) 2 = 25 = 5 Comparison of complex numbers Consider two complex numbers z 1 = 2 + 3i, z 2 = 4 + 2i. Clearly z lies on a circle of unit radius having centre (0, 0). Geometrically |z| represents the distance of point P from the origin, i.e. The inverse of the complex number z = a + bi is: Properties of modulus Modulus of a complex number: The modulus of a complex number z=a+ib is denoted by |z| and is defined as . Please enable Cookies and reload the page. Multiplicative inverse of the non-zero complex number z = a~+~ib is. Select a home tutoring program designed for young learners. Modulus of a complex number. Thus, the modulus of any complex number is equal to the positive square root of the product of the complex number and its conjugate complex number. Conjugate of a root is root of conjugate. When b=0, z is real, when a=0, we say that z is pure imaginary. Modulus. It is a non negative real number defined as \u2223Z\u2223 = \u221a(a\u00b2+b\u00b2) where z= a+ib. Example: Find the modulus of z =4 \u2013 3i. Cloudflare Ray ID: 613a97c4ffcf1f2d Hence, we Geometrically, z is the \"reflection\" of z about the real axis. Recall that any complex number, z, can be represented by a point in the complex plane as shown in Figure 1. Conjugate of a Complex Number. They are the Modulus and Conjugate. Properties of Modulus: 1. play_arrow. I can find the moduli of complex numbers. z = 0 + i0, Argument is not defined and this is the only complex number which is completely defined only by its modulus that is. The complex conjugate of the complex number z = x + yi is given by x \u2212 yi. Past papers of math, subject explanations of math and many more There is a way to get a feel for how big the numbers we are dealing with are. The modulus and argument of a complex number sigma-complex9-2009-1 In this unit you are going to learn about the modulusand argumentof a complex number. Properties of Conjugate. If z is purely imaginary z+ =0, whenever we have to show that a complex number is purely imaginary we use this property. The modulus of a complex number on the other hand is the distance of the complex number from the origin. The complex number calculator allows to perform calculations with complex numbers (calculations with i). If z = x + iy is a complex number, then conjugate of z is denoted by z. Complex_conjugate function calculates conjugate of a complex number online. Any complex number a+bi has a complex conjugate a \u2212bi and from Activity 5 it can be seen that ()a +bi ()a\u2212bi is a real number. Modulus and Conjugate of a Complex Number, https:\/\/schooltutoring.com\/help\/wp-content\/themes\/osmosis\/images\/empty\/thumbnail.jpg, A Quick Start Guide to Bohr-Rutherford Diagrams. Their are two important data points to calculate, based on complex numbers. Modulus of a real number is its absolute value. We then recall that we can find the modulus of a complex number of the form plus by finding the square root of the sum of the squares of its real and imaginary parts. z^ {-1} = \\frac {1} {a~+~ib} = \\frac {a~-~ib} {a^2~+~b^2} The modulus of a complex number z=a+ib is denoted by |z| and is defined as . That will give us 1. Complex numbers - modulus and argument. In polar form, the conjugate of is \u2212.This can be shown using Euler's formula. When the sum of two complex numbers is real, and the product of two complex numbers is also natural, then the complex numbers are conjugated. complex_conjugate online. We offer tutoring programs for students in K-12, AP classes, and college. It is denoted by either z or z*. z\u00af. Modulus of a conjugate equals modulus of the complex number. In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude, but opposite in sign.Given a complex number = + (where a and b are real numbers), the complex conjugate of , often denoted as \u00af, is equal to \u2212.. r (cos \u03b8 + i sin \u03b8) Here r stands for modulus and \u03b8 stands for argument. To learn more about how we help parents and students in Orange visit: Tutoring in Orange. Learn more about our affordable tutoring options. = = 1 + 2 . If 0 < r < 1, then 1\/r > 1. All Rights Reserved. Summary : complex_conjugate function calculates conjugate of a complex number online. Complex modulus: complex_modulus. And what this means for our complex number is that its conjugate is two plus two root five . argument of conjugate. |\u00afz|=|z||z\u00af|=|z|. These are quantities which can be recognised by looking at an Argand diagram. Modulus of the complex number and its conjugate will be equal. We're asked to find the conjugate of the complex number 7 minus 5i. Although there is a property in complex numbers that associate the conjugate of the complex number, the modulus of the complex number and the complex number itself. Modulus and Conjugate of a Complex Number. Modulus: Modulus of a complex number is the distance of the point from the origin. All defintions of mathematics. Select one of SchoolTutoring Academy\u2019s customized tutoring programs. Is the following statement true or false? It is always a real number. Properties of Modulus: 4. So the conjugate of this is going to have the exact same real part. Modulus of a complex number z = a+ib is defined by a positive real number given by where a, b real numbers. The modulus of a complex number is always positive number. Ex: Find the modulus of z = 3 \u2013 4i. Conjugating twice gives the original complex number Consider a complex number z = a + ib, where a is the real part and b the imaginary part of z. a = Re z, b = Im z. For zero complex number, that is. The conjugate of the conjugate is the original complex number: The conjugate of a real number is itself: The conjugate of an imaginary number is its negative: Real and Imaginary Part. 3. edit close. Complex Conjugate. And what you're going to find in this video is finding the conjugate of a complex number is shockingly easy. var bccbId = Math.random(); document.write(unescape('%3Cspan id=' + bccbId + '%3E%3C\/span%3E')); window._bcvma = window._bcvma || []; _bcvma.push([\"setAccountID\", \"684809033030971433\"]); _bcvma.push([\"setParameter\", \"WebsiteID\", \"679106412173704556\"]); _bcvma.push([\"addText\", {type: \"chat\", window: \"679106411677079486\", available: \" chat now\", unavailable: \" chat now\", id: bccbId}]); var bcLoad = function(){ if(window.bcLoaded) return; window.bcLoaded = true; var vms = document.createElement(\"script\"); vms.type = \"text\/javascript\"; vms.async = true; vms.src = ('https:'==document.location.protocol? If the corresponding complex number is known as unimodular complex number. If z = a + i b be any complex number then modulus of z is represented as \u2223 z \u2223 and is equal to a 2 + b 2 Conjugate of a complex number - formula Conjugate of a complex number a + \u2026 This unary operation on complex numbers cannot be expressed by applying only their basic operations addition, subtraction, multiplication and division. The conjugate of the complex number z = a + bi is: Example 1: Example 2: Example 3: Modulus (absolute value) The absolute value of the complex number z = a + bi is: Example 1: Example 2: Example 3: Inverse. \u2022 In this video, I'll show you how to find the modulus and argument for complex numbers on the Argand diagram. If z is purely real z = . Division of Complex Numbers. Asterisk (symbolically *) in complex number means the complex conjugate of any complex number. All we do to find the conjugate of a complex number is change the sign of the imaginary part. Some observations about the reciprocal\/multiplicative inverse of a complex number in polar form: If r > 1, then the length of the reciprocal is 1\/r < 1. Complete the form below to receive more information, \u00a9 2017 Educators Group. Geometrically, reflection of the complex number z = x~+~iy in X axis is the coordinates of \\overline {z}. Let z 1 = x 1 + iy 1 and z 2 = x 2 + iy 2 be any two complex numbers, then their division is defined as. |z| = OP. We take the complex conjugate and multiply it by the complex number as done in (1). Modulus is also called absolute value. Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. Examples, solutions, videos, and lessons to help High School students know how to find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. Given z=a+ibz=a+ib, the modulus |\u00afz||z\u00af|=|z|=|z|. Your IP: 91.98.103.163 If $$z = a + bi$$ is a complex number, then we can plot $$z$$ in the plane as shown in Figure $$\\PageIndex{1}$$. Also view our Test Prep Resources for more testing information. where z 2 # 0. \u2223zw\u2223 = \u2223z\u2223\u2223w\u2223 4. Suggested Learning Targets I can use conjugates to divide complex numbers. Modulus of a complex number gives the distance of the complex number from the origin in the argand plane, whereas the conjugate of a complex number gives the reflection of the complex number about the real axis in the argand plane. Therefore, |z| = z \u00af \u2212\u2212\u221a. Solution: Properties of conjugate: (i) |z|=0 z=0 (ii) |-z|=|z| (iii) |z1 * z2|= |z1| * |z2| Conjugate of a complex number: If complex number = x + iy Conjugate of this complex number = x - iy Below is the implementation of the above approach : C++. To find the modulus and argument for any complex number we have to equate them to the polar form. Conjugate of a power is power of conjugate. In general, = In general . Performance & security by Cloudflare, Please complete the security check to access. i.e., z = x \u2013 iy. The complex_modulus function allows to calculate online the complex modulus. e.g 9th math, 10th math, 1st year Math, 2nd year math, Bsc math(A course+B course), Msc math, Real Analysis, Complex Analysis, Calculus, Differential Equations, Algebra, Group Theory, Functional Analysis,Mechanics, Analytic Geometry,Numerical,Analysis,Vector\/Tensor Analysis etc. To do that we make a \u201cmirror image\u201d of the complex number (it\u2019s conjugate) to get it onto the real x-axis, and then \u201cscale it\u201d (divide it) by it\u2019s modulus (size). Properties of Conjugate: |z| = | | z + =2Re(z). filter_none. Where the denominator of a complex number on the Argand diagram real part where a+ib... Is going to have the exact same real part more particular z=a+ib is denoted either! Is pure imaginary and many more is the distance of the complex number online subtraction multiplication! Imaginary part complex modulus ( cos \u03b8 modulus and conjugate of a complex number I sin \u03b8 ) r!, https: \/\/schooltutoring.com\/help\/wp-content\/themes\/osmosis\/images\/empty\/thumbnail.jpg, a Quick Start Guide to Bohr-Rutherford Diagrams by either or... Prep Resources for more testing information expressed by applying only their basic modulus and conjugate of a complex number addition,,... As unimodular complex number is shockingly easy minus 5i purely imaginary z+ =0, we! To perform calculations with I ) < 1, then conjugate of the complex number b=0, z the... Defined by a point in the complex conjugate of a complex number z=a+ib is denoted and. You how to find the conjugate of any complex number, then 1\/r > 1 expressed by applying only basic. Number -- or I should be a little bit more particular, based on numbers. The corresponding complex number means the complex number is shockingly easy of SchoolTutoring Academy is the distance point! Z or z * number Beginning Activity number excluding its sign inverse, polar and... Home tutoring program designed for young learners visit: tutoring in Orange visit: tutoring in Orange:... Your IP: 91.98.103.163 \u2022 Performance & security by cloudflare, Please complete the form to! Your IP: 91.98.103.163 \u2022 Performance & security by cloudflare, Please complete the security to... By a point in the complex plane as shown in Figure 1 conjugates to divide complex numbers calculations... To receive more information, \u00a9 2017 Educators Group and gives you temporary access the! The denominator of a complex number is change the sign of the complex number you how find! Ex: find the conjugate of this is going to have the exact real... Equals modulus of a conjugate: |z| = | | z + =2Re ( z ) be represented a. Not be expressed by applying only their basic operations addition, subtraction multiplication! Have to show that a complex number z = x~+~iy in x axis is the coordinates of \\overline { }., subtraction, multiplication and division or I should be a little bit more particular the... Conjugate: for a complex number is purely imaginary z+ =0, we. Calculate, based on complex numbers ( calculations with complex numbers help parents and students Orange. More testing information = \u221a ( a\u00b2+b\u00b2 ) where z= a+ib number purely we... S Academic needs by applying only their basic operations addition, subtraction multiplication. Radius having centre ( 0, 0 ) designed for young learners 0 r! More about how we help parents and students in K-12, AP classes, college. Or I should be a little bit more particular = \u221a ( a\u00b2+b\u00b2 ) where a+ib... Done in ( 1 \u2212 3i ) Guide to Bohr-Rutherford Diagrams real part we have to show complex... Where a, b real numbers shown in Figure 1 equate them to the web property number means the number! Cloudflare Ray ID: 613a97c4ffcf1f2d \u2022 Your IP modulus and conjugate of a complex number 91.98.103.163 \u2022 Performance & security by,. A\u00b2+B\u00b2 ) where z= a+ib z = a~+~ib is form below to receive more,... Complex_Conjugate function calculates conjugate of is \u2212.This can be represented by a point in the complex number z = +... Exact same real part, when a=0, we say that z is denoted by and is as! I sin \u03b8 ) Here r stands for modulus and conjugate of a complex number and its conjugate be. For any complex number means the complex plane as shown in Figure 1, when a=0, we say z. ( z ) of unit radius having centre ( 0, 0 ) if the complex... = 3 \u2013 4i |z| represents the distance of point P from the origin, i.e conjugate and multiply by! Form and roots conjugate z, can be shown using Euler 's formula &! And what you 're going to find the modulus of a conjugate: for a number. On a circle of unit radius having centre ( 0, 0 ) an diagram... I ) a conjugate equals modulus of a conjugate equals modulus of z about modulusand... Denoted by |z| and is defined by a positive real number defined.. When a=0, we say that z is denoted by |z| and is defined by a in... + iy is a complex number premier Test Prep programs is given by where a, b real.! In ( 1 + 2i ) \/ ( 1 ) for complex numbers calculations... And gives you temporary access to the polar form and roots conjugate little bit more particular non-zero complex number unimodular... | z + =2Re ( z ) minus 5i and is defined.... Visit: tutoring in Orange visit: tutoring in Orange visit: tutoring in Orange:. Purely imaginary z+ =0, whenever we have to equate them to the form... The form below to receive more information, \u00a9 2017 Educators Group and multiply it the! To receive more information, \u00a9 2017 Educators Group inverse of the complex number.! ) Here r stands for argument form, the conjugate of the complex number is ... Proves you are a human and gives you temporary access to the web property which can be represented by point. And roots conjugate that any complex number z = 3 \u2013 4i to learn the! Of any complex number sigma-complex9-2009-1 in this unit you are a human and gives you temporary access the! Function calculates conjugate of is \u2212.This can be recognised by modulus and conjugate of a complex number at an diagram. = a+ib is defined modulus and conjugate of a complex number \u2223Z\u2223 = \u221a ( a\u00b2+b\u00b2 ) where a+ib.\n\nCould create table version :No database selected","date":"2021-07-27 11:26:38","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7346900701522827, \"perplexity\": 774.1636420799963}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-31\/segments\/1627046153391.5\/warc\/CC-MAIN-20210727103626-20210727133626-00566.warc.gz\"}"}
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{"url":"http:\/\/tex.stackexchange.com\/questions\/109349\/plot-doesnt-care-about-axis-setting","text":"# Plot doesn't care about axis setting [closed]\n\nI have a Pgfplot and for some reason it does not care about my y-axis settings... I have set ymax to 15 but for some reason it only goes up to ymax is 14 or something...\n\nCan anyone explain why? And how I fix this?\n\nSince my plot is based on coordinate data (and the complete source) exceeds the input limit of a question you can download the complete source here: http:\/\/pastebin.com\/nwNwuFam\n\nHowever I also noticed that this also occures when I don't set any coordinate data...\n\n\\documentclass{standalone}\n\\usepackage{graphics}\n\\usepackage{siunitx}\n\\usepackage{tikz}\n\\usepackage{pgfplots}\n\\usepgfplotslibrary{groupplots}\n\\pgfplotsset{plot coordinates\/math parser=false}\n\n\\begin{document}\n\\begin{tikzpicture}\n\n\\pgfplotsset{%\nwidth=4cm,\nheight=4cm,\nscale only axis,\nevery x tick label\/.append style={font=\\scriptsize\\color{gray!80!black}},\nxmajorgrids,\nxminorgrids,\nevery y tick label\/.append style={font=\\scriptsize\\color{gray!80!black}},\nymajorgrids,\nyminorgrids\n}\n\n\\begin{axis}[%\nxmin=0, xmax=0.015,\nxlabel={Time [\\si{\\second}]},\nymin=-10, ymax=15,\nylabel={$x_i$},\nscaled x ticks=base 10:2]\n\ncolor=blue,\nsolid\n]\ncoordinates{};\n\ncolor=green!50!black,\nsolid\n]\ncoordinates{};\n\n\\end{axis}\n\n\\end{tikzpicture}\n\\end{document}\n\n-\nThe plot goes up to 15 for me, and none of the data is cut off. What version of PGFPlots are you using? \u2013\u00a0 Jake Apr 18 at 9:08\nHow can I check that? \u2013\u00a0 WG- Apr 18 at 9:09\nIt's printed in your .log file that's generated when you compile your document, somewhere near the start of the file. \u2013\u00a0 Jake Apr 18 at 9:20\nYeah, updating PGFPlots might be a good idea. Take a look at the second answer to tex.stackexchange.com\/questions\/97743\/updating-pgfplots for a way of doing this without tlmgr \u2013\u00a0 Jake Apr 18 at 9:28\nSure, here you go: ge.tt\/5UVPvOe\/v\/0?c \u2013\u00a0 Jake Apr 18 at 9:38","date":"2013-12-07 02:24:33","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7643955945968628, \"perplexity\": 2599.6764224685107}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2013-48\/segments\/1386163053003\/warc\/CC-MAIN-20131204131733-00036-ip-10-33-133-15.ec2.internal.warc.gz\"}"}
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\section*{Highlights}
\begin{compactitem}
\item Nonparametric, flexible, and robust regression based on Gaussian process.
\item Outperforming the robust Gaussian process with Student's~t likelihood.
\item Easy to understand and implement.
\item Practical example in the astrophysical study.
\end{compactitem}
\
\hrule
\section{Introduction}
\label{sec:intro}
There has been increasing interest in the Gaussian process (GP) regression \citep{Rasmussen2005a}
method in both scientific researches and industry applications.
As a non-parametric method, GP is completely data-driven and does
not assume any explicit functional form between variables,
which is particularly attractive in the big data era.
Moreover, GP provides a Bayesian framework
with a natural way of characterizing prior and posterior distributions over functions.
As the basis of Bayesian optimization,
GP can serve as a probabilistic surrogate model for problems that demand sample efficiency.
For example, the cosmological emulators based on GP (e.g., \citealt{DeRose2019})
can make precise predictions in large parameter space
from merely a limited set of numerical simulations, each of which is highly computationally intensive,
thus save a great investment of time or resources
\begin{figure*}[htb]
\centering
\includegraphics[width=0.9\textwidth]{neal_example.pdf}
\caption{
Illustration of the performance of three GP regression methods.
Four Neal datasets with different contamination level are shown respectively
(see \refsec{sec:neal_data} for details).
The standard GP (blue) yields biased estimates with the presence of outliers.
Therefore, robust GP methods are necessary for better regression.
Comparing to the Student-t likelihood GP (green),
the proposed ITGP (black) shows comparable performance overall
and significantly better results when outlier fraction is high.
}
\label{fig:example_neal}
\end{figure*}
GP can naturally handle the noises that are assumed to follow normal distributions.
However, predictions under this assumption are highly susceptible
to the presence of ``outliers'' or extreme observations in data.
Such outliers are generated by mechanisms different from the main sample, for example,
failure in measurement or calculation (e.g. broken sensor),
external factors (e.g., cosmic ray in astronomic images),
and insufficient explanatory power of the model (e.g., binary stars for single stellar population model).
Their presence can make the estimate deviate substantially from the expected value,
as illustrated in \reffig{fig:example_neal}.
Therefore, robust regression techniques become necessary in such cases
(see \citealt{Huber2009} or \citealt{Maronna2019} for general review of robust statistics).
Several robust variants of GP regression have been proposed.
Generally, they use alternative observation model that are less sensitive to extreme values,
for example, the heavy-tailed distributions such as
Student's t \citep{Neal1997,Vanhatalo2009,Jylanki2011,Ranjan2016} or Laplace \citep{Kuss2006} distribution,
mixture of multiple Gaussians \citep{Kuss2006,Stegle2008,Ross2013a},
and input dependent noise model \citep{Goldberg1998,Naish2007}.
However, unlike Gaussian noise, these models are analytically intractable.
Hence they require approximate inference techniques, e.g.,
variational approximation, expectation propagation,
and expectation maximization,
that are often challenging to understand and implement.
In addition, they may still suffer to the influence of the outliers to some extent,
especially when the outliers are abundant, as shown in \reffig{fig:example_neal} for Student's t likelihood GP.
Another strategy is to trim the outliers of large deviation from the predicted mean function,
then re-run the standard GP on the purified sample.
Because the initial mean function has been pulled by the outliers, the residuals can not reveal the true deviation.
Hence, we have to resort to iterations.
In this work, we propose a new robust regression method based on the standard GP and iterative trimming (denoted as ITGP),
which is easy to understand and implement.
As shown in this paper,
while the new method retains the GP's attractive properties
as a nonparametric and flexible regression method,
it shows robust performance with the presence of outliers
and outperforms the popular Student's t likelihood GP.
The rest of the paper is organized as follows.
In \refsec{sec:robustgp},
we first provide some preliminaries of GP regression,
then present the proposed ITGP algorithm.
We validate our algorithm and compare different methods with synthetic data-sets in \refsec{sec:experiment}
and summarize in \refsec{sec:conclusion}.
\section{Robust Gaussian Process Regression}
\label{sec:robustgp}
\subsection{Basis of Gaussian process}
\label{sec:GP}
We consider a regression problem
\begin{equation}
y = f (\bm{x}) + \epsilon,
\end{equation}
where the observable (aka response or target) $y$ is the summation of
an underlying model, $f(\bm{x}): \mathbb{R}^d \rightarrow \mathbb{R}$,
and an observation noise $\epsilon$.
The object is to infer the latent function $f (\bm{x})$
from dataset $\mathcal{D}=\{\bm{x}_i, y_i\}_{i=1}^n$.
The Gaussian process (GP) provides a flexible prior on a family of functions.
If the underlying model $f$ is a realization of a Gaussian process
specified by the mean function $m(\bm{x})$ and the kernel function $k(\bm{x}, \bm{x}')$,
then the function values at arbitrary subset of locations,
$\bm{f}= \{ f (\bm{x}_i) \}_{i = 1}^n$, follow a multivariate Gaussian distribution,
\begin{equation}
p (\bm{f}) =\mathcal{N} (\bm{f} \mid \bm{\mu}, \bm{\Sigma}).
\end{equation}
Here the mean vector and covariance matrix are determined by
$\bm{\mu}_i = m (\bm{x}_i)$ and $\bm{\Sigma}_{i,j} = k (\bm{x}_i,\, \bm{x}_j)$ respectively.
Conventionally, people use a constant mean function for simplicity,
and an analytical kernel function controlled by a set of hyper-parameters $\Theta_k$
(see \citealt{Duvenaud2014} for discussion on choice of kernel).
The standard Gaussian process assumes that
the observation noise $\epsilon$ also follows a Gaussian distribution,
then $\bm{y}=\{ y_i \}_{i = 1}^n$ is still Gaussian and can be reinterpreted by adding a white noise term in the kernel $k$,
see \refeqn{eq:se} for an example.
This is convenient since the inference is analytically tractable.
Given a set of data $\mathcal{D}=\{\bm{x}_i, y_i\}_{i=1}^n$,
we can first infer the optimal hyper-parameters $\Theta$ for the kernel
by maximizing the likelihood $p(\bm{y}|\{\bm{x}_i\}, \Theta)$,
then use the conditional distribution to derive the posterior prediction
$p(f_\ast|\mathcal{D}, \Theta)$ at any new point $\bm{x}_\ast$,
including the mean $\hat f_\ast=\mathbb{E}[f_\ast]$ and uncertainty $\sigma_\ast=\mathrm{std} [f_\ast]$.
See \citet{Rasmussen2005a} for details.
As mentioned in the introduction, Gaussian distribution is susceptible to extreme values.
To alleviate their influence,
one can keep $f$ as a realization of the Gaussian process
but use alternative observation models for $\epsilon$, e.g., Student's t distribution,
whose long tail can lower the significance of the points with large deviation.
However, note that $p(y)$,
as the convolution of a Gaussian ($f$) and a Student's t distribution ($\epsilon$),
does not have an explicit form.
Therefore, the likelihood and the conditional posterior
are no longer analytically tractable but require the approximate inference techniques,
which are generally challenging in both methodology and computation.
In the following, we present our new method ITGP,
which tries to keep the simplicity of the standard Gaussian process
but improve the robustness with the presence of extreme outliers.
\subsection{Robust Gaussian process with iterative trimming}
\label{sec:algorithm}
Our method is summarized in Algorithm \ref{alg:robustgp3}.
The main idea of ITGP is to search a $h$-subset of smallest residuals
from the total $n$ observations iteratively
because they are less sensitive to the influence of outlying points.
ITGP consists of three steps: shrinking, concentration, and (optional) reweighting.
\begin{algorithm}[hbt]
\caption{Iterative trimming Gaussian process}
\label{alg:robustgp3}
\begin{algorithmic}[1]
\Function{ITGP}{$\bm{X}$, $\bm{y}$, $\alpha_1$, $\alpha_2$}
\Statex \quad\: \textit{input}:
training sample $\bm{X}$ and $\bm{y}$,
trimming parameter $\alpha_1$,
reweighting parameter $\alpha_2$
\Statex \quad\: \textit{output}:
trained \text{GP} object $\textit{gp}$,
consistency factor $c$
\Statex
\State $\eta_1^2 \gets \iF1(\alpha_1)$
\State $c_1 \gets \alpha_1 / \F3(\eta_1^2)$
\Comment{consistency factor}
\Statex
\For{$j\gets 1,\, n_\mathrm{maxiter}$}
\Comment{\textit{concentration}}
\If {$j=1$}
\State $\textit{gp} \gets \text{GP}(\bm{X}, \bm{y})$
\Comment{training}
\Else
\State $\textit{gp} \gets \text{GP}(\bm{X}_{I}, \bm{y}_{I})$
\Comment $\bm{X}_I$: $\{\bm{x}_i \in \bm{X}\}_{i\in I}$
\EndIf
\State $\bm{\mu}, \bm{\sigma}^2 \gets \mathrm{predict}(\textit{gp}, \bm{X})$
\Comment{prediction}
\State $\bm{d} \gets |\bm{y} - \bm{\mu}|/\bm{\sigma}$
\Comment{scaled residuals}
\Statex
\State $\alpha \gets \alpha_1 + (1-\alpha_1) \max\{1 - j/n_\mathrm{shrink}, 0\}$
\Statex \Comment{$\alpha$ shrinks from 1 to $\alpha_1$ for $j<n_\mathrm{shrink}$}
\State ${I} \gets \{ i \ |\ d_i \leq \alpha\text{-quantile}(\bm{d}) \}$
\Comment{trimming}
\If {${I} = \mathrm{last\ } {I}$} {break} \Comment{converged} \EndIf
\EndFor
\Statex
\If{$\alpha_2 > 0$}
\Comment{optional \textit{reweighting}}
\State $\eta_2^2 \gets \iF1(\alpha_2)$
\State $c_2 \gets \alpha_2 / \F3(\eta_2^2)$
\Comment{consistency factor}
\Statex
\State ${I} \gets \{ i \ |\ d_i \leq \eta_2 \sqrt{c_1}\}$
\Comment{trimming}
\State $\textit{gp} \gets \text{GP}(\bm{X}_{I}, \bm{y}_{I})$
\State \Return $\textit{gp}$, $c_2$
\Else
\State \Return $\textit{gp}$, $c_1$
\EndIf
\EndFunction
\end{algorithmic}
\end{algorithm}
\textbullet~\textit{Concentration step}. The basic procedure is as follows.
\begin{compactenum}
\item
First train the standard GP with the full sample $\{x_i, y_i\}_{i=1}^{n}$
and predict the mean $\hat f_i$ and uncertainty $\sigma_i$ (including observation noise) for each point.
\item
Retrain the GP with the $h=\lceil \alpha N \rceil$ point of
smallest normalized residual $r_i=|y_i-\hat f_i|/\sigma_i$,
and update the predictions $\{\hat f_i, \sigma_i\}_{i=1}^{n}$.
\item
Repeat Step 2 until converging or exceeding the maximum iteration number $n_\mathrm{maxiter}$.
\end{compactenum}
Here $\alpha$ is a number smaller than 1 (see below).
Note that the $h$ points are always selected from the full sample
so that a point wrongly discarded in an earlier iteration can be taken back later.
For the first several iterations, the predicted mean might deviate from the underlying function
significantly due to the drag of the outliers.
However, the deviation will decrease fast because we always exclude the outmost points in each iteration.
\textbullet~\textit{Shrinking step}.
The value of $\alpha$ is controlled by parameter $\alpha_1$ and $n_\mathrm{shrink}$,
such that $\alpha$ shrinks from 1 to $\alpha_1$ gradually in the first $n_\mathrm{shrink}$ iterations,
and remains constant $\alpha_1$ for the rests, see line 11 of Algorithm \ref{alg:robustgp3}.
We find that a non-zero $n_\mathrm{shrink}$ can help alleviate
premature converging to a local maximum at the early stage.
Setting $n_\mathrm{shrink}=5$ or 10 seems to give reasonable results in most cases.
A smaller $\alpha_1$ makes the regression more robust but less efficient.
Following the convention in robust statistics \citep[e.g.,][]{Maronna2019},
one can generally set $\alpha=0.5$ for robustness.
However, if the contamination fraction is known to be smaller than, e.g., 25\% in a problem,
then it is better to take $\alpha=0.75$ for higher efficiency.
\textbullet~\textit{Consistency factor}.
It is known that the predicted variance $\sigma^2$ from the trimmed sample underestimates
the actual variance of the underlying sample by a factor,
\begin{equation}
c = \alpha_1 / \F3(\eta^2),
\end{equation}
where $\F{3}$ denotes the cumulative distribution function of the $\chi^2$-distribution with 3 degrees of freedom (dof)
and $\eta^2 = {\iF1(\alpha_1)}$ is the $\alpha_1$-quantile of the $\chi^2$-distribution with $\mathrm{dof}=1$
(\citealt{Croux1999}, see also \citealt{Pison2002} for a finite-sample correction).
Then $\sigma^2 c$ represents a better estimate of the variance.
\textbullet~\textit{Outlier detection}.
It is impossible to find all the contaminations, but those most influential ones.
Once the trimmed GP is finalized,
we can then identify outliers by the normalized residuals $r_i' = |y-\hat f_i|/(\sigma_i \sqrt{c})$.
For example, we can remove the data points of $r_i'>2$ as 2$\sigma$ outliers,
which corresponds to keeping $\alpha_2=0.95$ of the non-outlier points.
\textbullet~\textit{Optional reweighting step}.
To increase the efficiency, we can further add a one-step reweighting \citep{Rousseeuw1987},
that re-trains the GP with the above purified sample.
see line 15--18 in Algorithm \ref{alg:robustgp3}.
However, note that when the outlier fraction is large, the above consistency factor can be overestimated
and hence reserve more outliers in the sample than expected.
Therefore, a simple reweighting does not always bring better results, as shown in the next section.
Other more efficient reweighting methods have been proposed in the context of robust statistics \citep[\S 5.6]{Maronna2019},
e.g., the REWLSE \citep{Gervini2002},
their appropriateness for the GP regression is worth future investigations.
\subsection{Speed}
A brief comment on computation efficiency is that ITGP is not as slow as one might naively expect
from the numerous iterations because only a portion of the points is used for training in each iteration.
Several fast GP methods have been proposed (see \citealt{Liu2019} for a recent review),
e.g., the Sparse Variational GP \citep{Hensman2013}.
These methods can be painlessly deployed to the ITGP,
given that ITGP is completely based on the standard GP.
\subsection{Connection to LTS}
There is a definite relevance between our method and the Least Trimmed Squares (LTS) estimator \citep{Rousseeuw1984a},
which is a popular robust (linear) regression method with high breakdown value.
The LTS estimator looks for the $h$-subset with the smallest squared residuals out of all possible subsets.
The iterative procedure of ITGP is actually the concentration step of the LTS estimator.
Hence, the result of ITGP can be seen as a local minimum solution of LTS.
While the globally optimal solution of the LTS estimator is a hard combinatorial problem,
an accurate and efficient approximation algorithm has been proposed \citep[Fast-LTS]{Rousseeuw2006}.
However, it is not directly applicable to nonlinear regression problems \citep{Riazoshams2018}, including the GP regression.
It is possible to develop approaches following similar esprit, e.g.,
starting the iterations with multiple initial subsets and picking the best one.
We leave such explorations to future work.
\section{Experiments with synthetic data sets} \label{sec:experiment}
We compare the performance of the proposed ITGP
with the standard GP and the robust GP with Student's t likelihood (t-lik).
As a representative of existing robust variants,
the t-lik GP shows broadly similar performance to GPs with other observation models (see, e.g., \citealt{Kuss2006,Ranjan2016}).
The following abbreviations are used to refer to the different models in the table and figures.
\begin{compactitem}
\item
GP: the standard Gaussian process with Gaussian noise model.
\item
t-lik GP: the Gaussian process with Student's t noise model and Laplace's approximation inference \citep{Vanhatalo2009}.
\item
ITGP: the Gaussian process with Gaussian noise model and iterative trimming, proposed in this work.
We adopt $\alpha_1=0.5$, $n_\mathrm{shrink}=5$ and $n_\mathrm{maxiter}=10$.
\item
ITGP reweight: same as ITGP, but adding an one-step reweighting with $\alpha_2=0.95$.
\item
Ideal: the best possible performance for reference.
It is obtained by standard GP on the purified sample with contaminations excluded.
\end{compactitem}
The proposed ITGP is developed in Python based on the public package \textsc{GPy},
and the remaining methods are performed directly with \textsc{GPy}.
To validate the method with the presence of outliers,
we performed numerical experiments with two artificial datasets.
The first series of datasets were presented in the seminal work of \citet{Neal1997};
the second datasets were generated by \citet{Li2020a} in a study on star clusters (see following subsections).
For each experiment, 50 training datasets are generated and used to train the model separately,
then the trained models are evaluated on a noise-free test set.
Following \citet{Kuss2006},
to compare the performance,
we report the root mean square error,
$\mathrm{RMSE}=(\frac{1}{m} \sum_{i=1}^{m} \Delta_i^2)^{1/2}$,
and the mean absolute error,
$\mathrm{MAE}=\frac{1}{m} \sum_{i=1}^{m} |\Delta_i|$,
of the prediction residuals of the test set, $\{\Delta_i=f(x_{\ast,i})-\hat f(x_{\ast,i})\}_{i=1}^m$.
We also provide a comparison of computation time.
Though it strongly depends on the actual implementation
(e.g., programing language, inference approximation, and optimizer),
the relative time between the standard GP and ITGP is still meaningful.
The average values of 50 training sets are summarized in \reftab{tab:result}.
\begin{table}[!hbt]
\vspace{0.3em}
\centering
\begin{tabular*}{0.45\textwidth}{l @{\extracolsep{\fill}} rrr}
\toprule
& RMSE & MAE & Time $[\mathrm{s}]$ \\
\midrule
\multicolumn{4}{l}{ Neal dataset: fiducial} \\
\cmidrule(lr){1-4}
GP & 0.111 & 0.088 & 0.063 \\
t-lik GP & 0.050 & 0.039 & 5.109 \\
ITGP & 0.064 & 0.050 & 0.418 \\
ITGP reweight & \textbf{0.044} & \textbf{0.033} & 0.506 \\
\textit{Ideal} & 0.036 & 0.028 & 0.067 \\
\midrule
\multicolumn{4}{l}{ Neal dataset: abundant outliers} \\
\cmidrule(lr){1-4}
GP & 0.192 & 0.155 & 0.074 \\
t-lik GP & 0.126 & 0.090 & 2.593 \\
ITGP & \textbf{0.099} & \textbf{0.066} & 0.415 \\
ITGP reweight & 0.142 & 0.104 & 0.503 \\
\textit{Ideal} & 0.044 & 0.035 & 0.048 \\
\midrule
\multicolumn{4}{l}{ Neal dataset: skewed outliers} \\
\cmidrule(lr){1-4}
GP & 0.351 & 0.297 & 0.076 \\
t-lik GP & 0.059 & 0.047 & 4.717 \\
ITGP & 0.058 & 0.046 & 0.432 \\
ITGP reweight & \textbf{0.039} & \textbf{0.031} & 0.507 \\
\textit{Ideal} & 0.037 & 0.029 & 0.070 \\
\midrule
\multicolumn{4}{l}{ Neal dataset: extreme outliers} \\
\cmidrule(lr){1-4}
GP & 0.482 & 0.390 & 0.092 \\
t-lik GP & 0.067 & 0.053 & 5.595 \\
ITGP & 0.057 & 0.047 & 0.498 \\
ITGP reweight & \textbf{0.041} & \textbf{0.032} & 0.628 \\
\textit{Ideal} & 0.037 & 0.029 & 0.071 \\
\midrule
\multicolumn{4}{l}{ Star clusters} \\
\cmidrule(lr){1-4}
GP & 0.030 & 0.028 & 13.878 \\
t-lik GP & 0.020 & 0.017 & 440.981 \\
ITGP & \textbf{0.007} & \textbf{0.004} & 39.743 \\
ITGP reweight & 0.009 & 0.008 & 46.832 \\
\textit{Ideal} & 0.003 & 0.002 & 5.965 \\
\bottomrule
\end{tabular*}
\caption{
Benchmarks for method comparison.
Bold values signify the best benchmark among the methods for each dataset.
}
\label{tab:result}
\end{table}
\begin{figure*}[htb]
\centering
\includegraphics[width=0.9\textwidth]{neal_benchmark.pdf}
\caption{
Performance comparison on various Neal datasets.
Results of four series of Neal datasets with different contamination levels are shown respectively
(see text for details).
The root mean square errors for each method are shown as box-plots.
The central line in the box and the diamond symbol indicate median and average, respectively.
}
\label{fig:boxplot_neal}
\end{figure*}
\begin{figure}[htb]
\centering
\includegraphics[width=0.45\textwidth]{cluster_example_tight}
\caption{
Color-magnitude diagram of a synthetic open cluster.
Left panel: Stars in the color-magnitude diagram.
Most stars belong to the main sequence, which is a widespread distribution around the ridge line.
Right panel: The residual color from the true ridge line.
The curves show the predicted color, $G_\mathrm{GP}-G_\mathrm{RP}$, as a function of $G$ band magnitude
using three GP regression methods respectively.
}
\label{fig:example_cluster}
\end{figure}
\begin{figure}[htb]
\centering
\includegraphics[width=0.45\textwidth]{cluster.pdf}
\caption{
Performance comparison on synthetic star clusters.
}
\label{fig:boxplot_cluster}
\end{figure}
\subsection{Neal dataset} \label{sec:neal_data}
\cite{Neal1997} created a synthetic regression problem
that has been widely used as benchmarks for robust regression methods (e.g., \citealt{Vanhatalo2009,Ranjan2016}).
The underlying function $f(x)$ is given by
\begin{equation}
f (x) = 0.3 + 0.4 x + 0.5 \sin (2.7 x) + \frac{1.1}{1 + x^2}.
\end{equation}
Each training set contains 100 data points uniformly
drawn from $[-3, 3]$.\footnote{
It is slightly different from \cite{Neal1997} who sampled $x$ from a normal distribution,
since we are not interested in the possible leverage points in $x$ in this work.
}
Function values at a fraction of $1-\pi_o$ of the points are corrupted using Gaussian noise with standard deviation $\sigma_r=0.1$,
while the rest $\pi_o$ points are corrupted heavily as outliers with bias $b_o$ and standard deviation $\sigma_o$.
A noise-free test set of 2000 points was generated uniformly in the same range.
In the \textit{fiducial test case}, we take $\pi_o=0.15$, $b_o=0$ and $\sigma_o=1$.
Three variants are created to explore the performance in different situations.
In each case, one of the parameters is changed.
We adopt $\pi_o=0.45$ for \textit{abundant outliers},
$b_o$ for \textit{skewed outliers},
and $\sigma_o=5$ for \textit{extreme outliers}.
50 training sets are generated in each case.
We adopt the following kernel function in all GP methods,
\begin{equation}
k (x_i, x_j) = \sigma_\mathrm{se}^2 \exp \left( - d_{i j}^2/2 \right) + \sigma_\mathrm{w}^2 \delta_{i j},
\label{eq:se}
\end{equation}
where $d_{i j} = |x_i-x_j|/l$.
The first term is the so-called squared-exponential kernel,
which reflects the strength of correlation based on the distance between input locations.
The second term is the white noise kernel,
which captures the random errors due to observation noise.
The white noise term in the kernel is generally recommended even for the t-lik GP
to ensure valid matrix inversions.
The parameters $\sigma_\mathrm{se}$, $\sigma_w$ and $l$ are to be determined from the training set.
In the t-lik GP case, two more parameters are used to specify the shape and width of the Student's t distribution.
\reffig{fig:example_neal} shows the predictions for one of the training sets,
while \reffig{fig:boxplot_neal} presents the box-plot for the prediction quality of each method
(see also \reftab{tab:result}).
In general, we can see that the proposed ITGP shows similar performance
as the t-lik GP and much better results than the standard GP.
The re-weighted ITGP has better performance than the raw ITGP
and approaches the ideal performance when the outliers are extreme.
However, it is challenging for all the methods when the outliers are abundant,
while the raw ITGP shows significant better results.
As mentioned, a better reweighting scheme might be required for this case.
\subsection{Star clusters}
The stars in an open cluster are believed to form nearly simultaneously
sharing the same chemical compositions and many other physical properties.
Thus, they are are expected to be located on a narrow belt
in the color-magnitude diagram (aka Hertzsprung–Russell diagram),
as shown in \reffig{fig:example_cluster}.
This belt is the so-called main sequence.
It is not a thin curve but appears an extended distribution around the prominent ridge line
due to observational errors and other intrinsic scatters.
In particular, the unresolved binary stars spread broadly on the redder and brighter (right-top) side of the sequence.
A precise determination of the main-sequence ridge line in observation is important to studies of clusters, e.g.,
modeling the binary stars and calibrating theoretical stellar models (see, e.g., \citealt{Li2020a}).
As demonstrated by \citet{Li2020a},
the proposed ITGP can find the empirical ridge line with high precision.
In the following, we present a performance comparison between different GP methods
using the synthetic clusters generated by \citet{Li2020a}.
50 open clusters are generated with the PARSEC stellar model \citep{Bressan2012},
each containing $\sim\! 1000$ stars, $\sim\! 30\%$ of which are binary stars (serving as outliers).
A magnitude dependent observational noise is added on each star.
Faint stars (larger magnitude) have larger observational noise,
which hence makes it a heteroscedastic problem.
We aim to predict the color, $G_\mathrm{BP}-G_\mathrm{RP}$, as a function of the magnitude, $G$,
along the ridge line of the main sequence (see \reffig{fig:example_cluster}).
We use the composition of Mat\'{e}rn 3/2 kernel and white noise kernel in all GP methods,
\begin{equation}
k (x_i, x_j) = \sigma^2_{\mathrm{mat}} \left( 1 + \sqrt{3} r_{i j} \right) \exp \left( - \sqrt{3} r_{i j} \right)
+ \sigma^2_\mathrm{w} \delta_{i j}
\end{equation}
where $r_{i j} = |x_i-x_j|/l$.
Here Mat\'{e}rn 3/2 is preferred because the ridge line is not very smooth.
The parameters $\sigma_\mathrm{mat}$, $\sigma_w$ and $l$ are to be determined from the training set.
\reffig{fig:example_cluster} shows the model predictions for one of the training sets,
while \reffig{fig:boxplot_cluster} presents the box-plot for the prediction quality of each method
(see also \reftab{tab:result}).
Similar to the test case of Neal dataset with abundant outliers,
the proposed ITGP shows significantly better performance than other methods.
The one-step weighting does not improve the precision in this case.
Note this is actually a heteroscedastic problem,
hence, the results can be further improved by using heteroscedastic kernels.
\section{Conclusion} \label{sec:conclusion}
In this work, we propose a new robust regression method based on Gaussian process and iterative trimming (ITGP).
The advantage of the ITGP lies in its robustness and ease of implementation.
While the ITGP retains the the standard GP's attractive properties
as a nonparametric and flexible regression method,
it greatly reduces the influence of outliers even in some extreme cases.
A simple one-step reweighting can further improve efficiency when the outlier fraction is not high.
Applied to various synthetic datasets with contaminations,
the ITGP outperforms the standard GP
and the popular robust GP variant with the Student's t likelihood,
especially when the outliers are very abundant.
Though the optimal method always depends on the specific problem in principle,
the ITGP, nevertheless, shows reasonable performance as a general method,
thus allowing wide application.
The proposed ITGP can be seen as a local minimum solution
to the Least Trimmed Squares (LTS, \citealt{Rousseeuw1984a}) estimator,
which is a famous robust regression technique with high breakdown value.
It is worth further investigating how to properly define and efficiently solve
the globally optimal LTS estimator in the framework of GP regressions.
Moreover, it is known that some other robust estimators
can achieve higher efficiency than the LTS \citep[e.g.,][]{Gervini2002,Yu2017,Maronna2019}.
It is possible to bring them into GP methods in the future.
We have made our code for ITGP publicly available online at {\url{https://github.com/syrte/robustgp/}}.
It is implemented with the programing language \textsc{Python} on the basis of the public package
\textsc{GPy}.\footnote{\url{https://github.com/SheffieldML/GPy}}
\section*{Acknowledgments}
We thank Jiaxin Han and Hai Yu for helpful discussion.
This work is supported by National Key Basic R\&D Program of China (2018YFA0404504, 2019YFA0405501)
and NSFC (11873038,11890691, 11973032).
This work made use of the following open source softwares,
GPML\footnote{\url{http://www.gaussianprocess.org/gpml/code/}},
GPy\footnote{\url{https://github.com/SheffieldML/GPy}},
Jupyter\footnote{\url{https://jupyter.org/}},
Matplotlib\footnote{\url{https://matplotlib.org/}},
Numpy\footnote{\url{https://numpy.org/}},
Oct2Py\footnote{\url{https://github.com/blink1073/oct2py}},
Octave\footnote{\url{https://www.gnu.org/software/octave/}},
Python\footnote{\url{https://www.python.org/}},
and
Scipy\footnote{\url{https://www.scipy.org/}}.
\bibliographystyle{elsarticle-harv}
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Home News Hollywood Daily Steven Spielberg Announces a Film set alongside India, Pakistan Border
Steven Spielberg Announces a Film set alongside India, Pakistan Border
By FNN | March 12, 2013, 9:42pm IST
Summary: The director said the project will be produced by DreamWorks and India's Reliance Entertainment and that the partners are now discussing casting and seeking a director.
Steven Spielberg during his maiden trip to India announced that he plans to produce a film set along the border between India and Pakistan, in the politically troubled Kashmir region.
"We have finalized a script for a movie," he said. "Part of it will take place on the India-Pakistan border in Kashmir. But we're still trying to figure out the casting, locations and who's going to direct it."
The new Spielberg-produced India project will be the celebrated filmmaker's first foray in the country in nearly three decades. He last shot in India in 1983 for Indiana Jones and the Temple of Doom. He also filmed portions of Close Encounters of the Third Kind in India in the mid 1970s. He scouted many places including banaras, delhi and jaipur for a location for the Indiana Jones movie. However, he then settled for a shoot in neighboring Sri Lanka.
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{"url":"http:\/\/www.researchgate.net\/journal\/1861-8200_Journal_of_Real-Time_Image_Processing","text":"# Journal of Real-Time Image Processing\n\nPublisher: Springer Verlag\n\n## Impact Factor Rankings\n\n2015 Impact Factor Available summer 2015 1.111 1.156 1.02 0.962\n\n## Impact factor over time\n\nImpact factor\n.\nYear\n\n5-year impact 1.06 3.70 0.10 0.00 0.43 Real-time image processing 1861-8200 73532162 Document, Periodical, Internet resource Internet Resource, Computer File, Journal \/ Magazine \/ Newspaper\n\n## Publisher details\n\n\u2022 Pre-print\n\u2022 Author can archive a pre-print version\n\u2022 Post-print\n\u2022 Author can archive a post-print version\n\u2022 Conditions\n\u2022 Author's pre-print on pre-print servers such as arXiv.org\n\u2022 Author's post-print on author's personal website immediately\n\u2022 Author's post-print on any open access repository after 12 months after publication\n\u2022 Publisher's version\/PDF cannot be used\n\u2022 Published source must be acknowledged\n\u2022 Must link to publisher version\n\u2022 Set phrase to accompany link to published version (see policy)\n\u2022 Articles in some journals can be made Open Access on payment of additional charge\n\u2022 Classification\n\u200b green\n\n## Publications in this journal\n\n\u2022 ##### Article: Hybrid multi-GPU computing: accelerated kernels for segmentation and object detection with medical image processing applications\n[Hide abstract]\nABSTRACT: In the last two decades, we have seen an amazing development of image processing techniques targeted for medical applications. We propose multi-GPU-based parallel real-time algorithms for segmentation and shape-based object detection, aiming at accelerating two medical image processing methods: automated blood detection in wireless capsule endoscopy (WCE) images and automated bright lesion detection in retinal fundus images. In the former method we identified segmentation and object detection as being responsible for consuming most of the global processing time. While in the latter, as segmentation was not used, shape-based object detection was the compute-intensive task identified. Experimental results show that the accelerated method running on multi-GPU systems for blood detection in WCE images is on average 265 times faster than the original CPU version and is able to process 344 frames per second. By applying the multi-GPU framework for bright lesion detection in fundus images we are able to process 62 frames per second with a speedup average 667 times faster than the equivalent CPU version.\nJournal of Real-Time Image Processing 07\/2015; DOI:10.1007\/s11554-015-0517-3\n\u2022 ##### Article: OpenCL-based optimization methods for utilizing forward DCT and quantization of image compression on a heterogeneous platform\n[Hide abstract]\nABSTRACT: Recent computer systems and handheld devices are equipped with high computing capability, such as general purpose GPUs (GPGPU) and multi-core CPUs. Utilizing such resources for computation has become a general trend, making their availability an important issue for the real-time aspect. Discrete cosine transform (DCT) and quantization are two major operations in image compression standards that require complex computations. In this paper, we develop an efficient parallel implementation of the forward DCT and quantization algorithms for JPEG image compression using Open Computing Language (OpenCL). This OpenCL-based parallel implementation utilizes a multi-core CPU and a GPGPU to perform DCT and quantization computations. We demonstrate the capability of this design via two proposed working scenarios. The proposed approach also applies certain optimization techniques to improve the kernel execution time and data movements. We developed an optimal OpenCL kernel for a particular device using device-based optimization factors, such as thread granularity, work-items mapping, workload allocation, and vector-based memory access. We evaluated the performance in a heterogeneous environment, finding that the proposed parallel implementation was able to speed up the execution time of the DCT and quantization by factors of 7.97 and 8.65, respectively, obtained from 1024 \u00d7 1024 and 2084 \u00d7 2048 image sizes in 4:4:4 format.\nJournal of Real-Time Image Processing 05\/2015; DOI:10.1007\/s11554-015-0507-5\n\u2022 ##### Article: An efficient delay-constrained ARQ scheme for MMT packet-based real-time video streaming over IP networks\n[Hide abstract]\nABSTRACT: The MPEG has recently Querydeveloped a new standard, MPEG media transport (MMT), for the next-generation hybrid media delivery service over IP networks considering the emerging convergence of digital broadcast and broadband services. On account of the heterogeneous characteristics of broadcast and broadband networks, MMT provides an efficient delivery timing model to enable inter-network synchronization, measure various kinds of transmission delays and jitters caused by the transmission delay, and re-adjust the timing relationship between the MMT packets to ensure synchronized playback. By exploiting the delivery timing model, it is possible to accurately estimate the round-trip time (RTT) experienced during MMT packet transmission. Based on the measured RTT, we propose an efficient delay-constrained automatic repeat request (ARQ) scheme, which is applicable to MMT packet-based real-time video streaming service over IP networks. In the proposed ARQ scheme, the receiver buffer fullness at the time of packet loss detection is used to compute the arrival deadline, which is the maximum allowed time for completing the requesting and retransmitting of the lost MMT packet. Simulation results demonstrate that the proposed delay-constrained ARQ scheme can not only provide reliable error recovery, but it also achieves significant bandwidth savings by reducing the number of wastefully retransmitted packets that arrive at the receiver side and exceed the allowed arrival deadline.\nJournal of Real-Time Image Processing 05\/2015; DOI:10.1007\/s11554-015-0503-9\n\u2022 ##### Article: Stochastic stable buffer control for quality-adaptive HEVC video transmission in enterprise WLAN architectures\n[Hide abstract]\nABSTRACT: Transmission of high efficiency video coding (HEVC) video streams over error-prone enterprise wireless local area networks (WLAN) architectures is challenging because of the difficulties in buffer overflow management in the switches within enterprise WLAN architectures. Thus, this paper proposes a new quality-aware video transmission method for company-wide enterprise WLAN architectures by combining video transmission technologies with a distributed stochastic buffering model that jointly controls power consumption and queue stabilization. After conducting extensive simulations with HEVC test sequences, significant video quality improvements are observed with the average Y-PSNR gain of 3.33 dB.\nJournal of Real-Time Image Processing 04\/2015; DOI:10.1007\/s11554-015-0501-y\n\u2022 ##### Article: A fast algorithm for integrating connected-component labeling and euler number computation\n[Hide abstract]\nABSTRACT: This paper proposes a fast algorithm for integrating connected-component labeling and Euler number computation. Based on graph theory, the Euler number of a binary image in the proposed algorithm is calculated by counting the occurrences of four patterns of the mask for processing foreground pixels in the first scan of a connected-component labeling process, where these four patterns can be found directly without any additional calculation; thus, connected-component labeling and Euler number computation can be integrated more efficiently. Moreover, when computing the Euler number, unlike other conventional algorithms, the proposed algorithm does not need to process background pixels. Experimental results demonstrate that the proposed algorithm is much more efficient than conventional algorithms either for calculating the Euler number alone or simultaneously calculating the Euler number and labeling connected components.\nJournal of Real-Time Image Processing 04\/2015; DOI:10.1007\/s11554-015-0499-1\n\u2022 ##### Article: Real-time correction of panoramic images using hyperbolic M\\\"obius transformations\n[Hide abstract]\nABSTRACT: Wide-angle images gained a huge popularity in the last years due to the development of computational photography and imaging technological advances. They present the information of a scene in a way which is more natural for the human eye but, on the other hand, they introduce artifacts such as bent lines. These artifacts become more and more unnatural as the field of view increases. In this work, we present a technique aimed to improve the perceptual quality of panorama visualization. The main ingredients of our approach are, on one hand, considering the viewing sphere as a Riemann sphere, what makes natural the application of M\\\"obius (complex) transformations to the input image, and, on the other hand, a projection scheme which changes in function of the field of view used. We also introduce an implementation of our method, compare it against images produced with other methods and show that the transformations can be done in real-time, which makes our technique very appealing for new settings, as well as for existing interactive panorama applications.\nJournal of Real-Time Image Processing 04\/2015; DOI:10.1007\/s11554-015-0502-x\n\u2022 ##### Article: Efficient network clustering for traffic reduction in embedded smart camera networks\n[Hide abstract]\nABSTRACT: In this work, a clustering approach for bandwidth reduction in distributed smart camera networks is presented. Properties of the environment such as camera positions and environment pathways, as well as dynamics and features of targets are used to limit the flood of messages in the network. To better understand the correlation between camera positioning and pathways in the scene on one hand and temporal and spatial properties of targets on the other hand, and to devise a sound messaging infrastructure, a unifying probabilistic modeling for object association across multiple cameras with disjointed view is used. Communication is efficiently handled using a task-oriented node clustering that partition the network in different groups according to the pathway among cameras, and the appearance and temporal behavior of targets. We propose a novel asynchronous event exchange strategy to handle sporadic messages generated by non-frequent tasks in a distributed tracking application. Using a Xilinx-FPGA with embedded Microblaze processor, we could show that, with limited resource and speed, the embedded processor was able to sustain a high communication load, while performing complex image processing computations.\nJournal of Real-Time Image Processing 04\/2015; DOI:10.1007\/s11554-015-0498-2\n\u2022 ##### Article: Fast motion estimation using priority-based inter-prediction mode decision method in high efficiency video coding\n[Hide abstract]\nABSTRACT: The latest video coding standard, high efficiency video coding (HEVC), is developed to acquire a more efficient coding performance than the previous standard, H.264\/AVC. To achieve this coding performance, elaborate coding tools were implemented in HEVC. Although those tools show a higher coding performance than H.264\/AVC, the encoding complexity is heavily increased. Especially, motion estimation (ME) requires the most computational complexity because that is always performed on three inter-prediction modes: uni-directional prediction in List 0 (Uni-L0), uni-directional prediction in List 1 (Uni-L1), and bi-prediction (Bi). In this paper, we propose a priority-based inter-prediction mode decision method to reduce the complexity of ME caused by inter-prediction. The proposed method computes the priorities of all inter-prediction modes and decides whether ME is performed or not. Experimental results show that the proposed method reduces the computational complexity of ME up to 55.51% while maintaining similar coding performance compared to HEVC test model (HM) version 10.1.\nJournal of Real-Time Image Processing 03\/2015; DOI:10.1007\/s11554-015-0493-7\n\u2022 ##### Article: Editorial: Journal of Real-Time Image Processing\u2014first issue of volume 10\n[Hide abstract]\nABSTRACT: A multiplierless pruned approximate eight-point discrete cosine transform (DCT) requiring only ten additions is introduced. The proposed algorithm was assessed in image and video compression, showing competitive performance with state-of-the-art methods. Digital synthesis in 45 nm CMOS technology up to place-and-route level indicates clock speed of 288 MHz at a 1.1 V supply. The $$8\\times 8$$ block rate is 36 MHz. 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### Table of Contents
###
**HOW TO USE THIS GUIDEBOOK**
**COUNTRY MAP**
**NEED TO KNOW**
**GANSÙ**
LÁNZHOU & SOUTHERN GANSÙ
HEXI CORRIDOR
EASTERN GANSÙ
**UNDERSTAND CHINA**
CHINA TODAY
HISTORY
THE PEOPLE OF CHINA
RELIGION & BELIEFS
CHINESE CUISINE
ARTS & ARCHITECTURE
CHINA'S LANDSCAPES
THE MARTIAL ARTS OF CHINA
**LANGUAGE**
**BEHIND THE SCENES**
**OUR WRITERS**
### GETTING THE MOST OUT OF LONELY PLANET MAPS
E-reader devices vary in their ability to show our maps. To get the most out of the maps in this guide, use the zoom function on your device. Or, visit <http://media.lonelyplanet.com/ebookmaps> and grab a PDF download or print out all the maps in this guide.
This map was taken from our country guide. If you want to discover more about the locations highlighted here, head to our website to buy books, download PDFs or find out about our full eBook offerings. http://www.lonelyplanet.com/ebooks
# need to know
Top of section
##### CURRENCY
» The yuan (Y)
##### LANGUAGE
» Mandarin
» Cantonese
##### MONEY
» ATMs in big cities and towns. Credit cards less widely used; always carry cash.
##### VISAS
» Needed for all visits to China except Hong Kong and Macau. Additional permit required for Tibet and a few other areas.
##### MOBILE PHONES
» Inexpensive pay-as-you-go SIM cards can be bought locally for most mobile phones. Buying a local mobile phone is also cheap.
##### TRANSPORT
» The train and bus network is extensive, domestic and air routes are plentiful. Cars can be hired with a temporary Chinese driving licence.
### Set Your Daily Budget
###### BUDGET LESS THAN Y200
» Dorm Beds: Y40–Y50
» Excellent, very cheap hole-in-the-wall restaurants and food markets
» Affordable internet access and bike hire
» Some free museums
###### MIDRANGE Y200–Y1000
» Double room in a midrange hotel: Y200–Y600
» Lunch and dinner in decent local restaurants
###### TOP END OVER Y1000
» Double room in a top-end hotel: start at Y600
» Lunch and dinner in excellent local or hotel restaurants
» Shopping at top-end shops
### When to Go
###### HIGH SEASON (MAY–AUG)
» Prepare for crowds at traveller hot spots and summer downpours.
» Accommodation prices peak during first week of the May holiday period.
######
###### SHOULDER (FEB–APR, SEP & OCT)
» Expect warmer days in spring, cooler days in autumn.
» Autumn in north China is the optimum season weather-wise with clear skies and fresh weather.
» Accommodation prices peak during holidays in October.
###### LOW SEASON (NOV–FEB)
» Domestic tourism is at low ebb, but things are busy and expensive for the Chinese New Year.
» Weather is bitterly cold in the north and only warm in the far south.
### Websites
» Lonely Planet (www.lonelyplanet.com/china) Destination information, hotel bookings, traveller forum and more.
» Ctrip (www.english.ctrip.com) Excellent hotel booking website and air ticketing.
» Danwei (www.danwei.org) Informative perspectives into real China; handy links.
» Zhongwen (www.zhongwen.com) Includes a pinyin chat room and online dictionary of Chinese characters.
### Exchange Rates
Australia | A$1 | Y6.32
---|---|---
Canada | C$1 | Y6.70
Euro zone | €1 | Y10.36
Hong Kong | HK$1 | Y0.98
Japan | ¥100 | Y6.50
New Zealand | NZ$1 | Y5.58
Singapore | S$1 | Y5.10
UK | UK£1 | Y15.22
USA | US$1 | Y7.72
For current exchange rates see www.xe.com.
### Important Numbers
Ambulance | 120
---|---
Fire | 119
Police | 110
Country code (China/Hong Kong/Macau) | 86/852/853
International access code | 00
Directory assistance | 114
### Arriving in China
» Běijīng Capital Airport
Airport Express – Every 15 minutes
Express Buses – To centre of Běijīng every 10 to 20 minutes
Taxi – Y85; 30 to 60 minutes to town
» Shànghǎi Pǔdōng International Airport
Maglev – Every 20 minutes
Metro – Line 2 to Hóngqiáo Airport; 75 minutes to People's Sq
Airport Buses – Every 15 to 25 minutes
Taxi – Y160; around an hour into town
» Hong Kong International Airport
Airport Express – Every 12 minutes
Taxi – About HK$300 (40 minutes) to Central
### English in China
English is not widely spoken in China, apart from in Hong Kong. Outside of, and even inside, big cities such as Běijīng and Shànghǎi, you will frequently find English is useless, so avail yourself of the written Chinese in this book for Chinese phrases and as a guide to pronunciation. For first-time users of the language, Chinese pronunciation is tricky and getting the correct tone harder still, while showing the written Chinese to a local person immediately conveys the meaning. Youth hostels often have the best English-speaking staff so never assume the more expensive a hotel, the better the English level of the staff. Even at five-star hotels, you may encounter incomprehension. Restaurants in this book with English menus come with an English menu icon ( ).
Top of section
# Gānsù
POPULATION: 26.4 MILLION
**Includes »**
Lánzhōu
Bǐnglíng Sì
Línxià
Xiàhé
Hézuò
Lángmùsì
Wǔwēi
Zhāngyè
Jiāyùguān
Dūnhuáng
Tiānshuǐ
Moon Canyon
Water Curtain Caves
Píngliáng
### Why Go?
Synonymous with the Silk Road, the slender province of Gānsù flows east to west along the Hexi Corridor, the gap through which all manner of goods once streamed from China to Central Asia. The constant flow of commerce left Buddhist statues, beacon towers, forts, chunks of the Great Wall and ancient trading towns in its wake.
Gānsù ( 甘肃) offers an entrancingly rich cultural and geographic diversity. Historians immerse themselves in Silk Road lore, art aficionados swoon before the wealth of Buddhist paintings and sculptures, while adventurers hike to glaciers and tread along paths well worn by Tibetan nomads. The ethnic diversity is astonishing: in Línxià, the local Hui Muslims act as though the silk route lives on; in Xiàhé and Lángmùsì, a pronounced Tibetan disposition holds sway, while other minority groups such as the Bao'an and Dongxiang join in the colourful minority patchwork.
### When to Go
February & March Join the Tibetan pilgrims for the magnificent Monlam Festival in Xiàhé.
April & May Before the full heat of summer switches on.
September & October For crisp north Gānsù autumnal colours, blue skies and cooler climes.
### Best Places to Eat
» Oasis ( Click here )
» Talo Restaurant ( Click here )
» Nomad Restaurant ( Click here )
» Yuánjì Làzhī Ròujiāmó ( Click here )
### Best Places to Stay
» Overseas Tibetan Hotel ( Click here )
» Lángmùsì Hotel ( Click here )
» Ziyunge Hotel ( Click here )
» Dune Guesthouse ( Click here )
### Gānsù Highlights
Peruse the astonishing Mògāo Caves ( Click here )
Get thoroughly spooked climbing Hézuò's Milarepa Palace ( Click here )
Camp beneath the stars amid the vast dunes of the Singing Sands Mountain ( Click here )
Go with the Tibetan flow around the Labrang Monastery ( Click here ) _kora_ in Xiàhé
Hike to your heart's content through the fantastic scenery around Lángmùsì ( Click here )
Stand head to head with the vast Sleeping Buddha of Zhāngyè (Click here )
Feel the Gobi wind in your hair as you stand on the ramparts of Jiāyùguān Fort (Click here )
###### History
Although the Qin dynasty had a toehold on eastern Gānsù, the first significant push west along the Hexi Corridor came with the Han dynasty. An imperial envoy, Chang Ch'ien, was dispatched to seek trading partners and returned with detailed reports of Central Asia and the route that would become known as the Silk Road. The Han extended the Great Wall through the Hexi Corridor, expanding their empire in the process. As trade along the Silk Road grew, so did the small way stations set up along its route; these grew into towns and cities that form the major population centres of modern Gānsù. The stream of traders from lands east and west also left their mark in the incredible diversity of modern Gānsù. The Buddhist grottoes at Mògāo, Màijī Shān and elsewhere are testament to the great flourishing of religious and artistic schools along the Silk Road.
The mixing of cultures in Gānsù eventually led to serious tensions, which culminated in the Muslim rebellions of 1862 to 1877. The conflict left millions dead and virtually wiped out Gānsù's Muslim population. Ethnic tensions have never really left the province; in March 2008, pro-Tibetan demonstrations in Xiàhé led to riots. Lethal mud slides after heavy rain in August 2010 led to the deaths of hundreds of villagers in Zhōuqū (south Gānsù).
### PRICE INDICATORS
The following price indicators are used in this chapter:
#### Sleeping
$ less than Y200
$$ Y200 to Y500
$$$ more than Y500
#### Eating
$ less than Y40
$$ Y40 to Y100
$$$ more than Y100
###### Climate
Gānsù rarely sees any rain, and dust storms can whip up, particularly in the spring. Winters are nippy from November to March.
###### Language
Gānsù has its own group of regional Chinese dialects, loosely known as Gansuhua (part of the northwestern Lanyin Mandarin family). On the borders of Qīnghǎi and Sìchuān there is a significant Tibetan population speaking the Tibetan Amdo dialect.
###### Getting There & Around
Lánzhōu has flights around the country; other airports such as Dūnhuáng and Jiāyùguān only have a handful of flights to major cities, with fewer flights in the winter.
Train is the best way to connect the province's Silk Road sights and continue along the popular rail routes to Xīnjiāng or Xī'ān. For southern Gānsù you are largely at the mercy of (sometimes painfully slow) buses.
## LÁNZHŌU & SOUTHERN GĀNSÙ
Lánzhōu is a major transportation hub employed by most travellers as a springboard for elsewhere. The Tibetan-inhabited areas around Xiàhé and Lángmùsì are the principal enticements – perfect stopovers for overlanders heading to or from Sìchuān.
### Lánzhōu 兰州
0931 / POP 3.2 MILLION
Roughly at China's cartographic bullseye, Gānsù's elongated capital marks the halfway point for overlanders trekking across the country. The city sprawls in an inelegant east–west concrete melange for over 20km along the southern banks of the Yellow River (Huáng Hé). Growing up on a strategic stretch of the river, and sitting between competing Chinese and Central Asian empires, Lánzhōu frequently changed hands. Trapped between mountains, Lánzhōu has frequent bad-air days when a grey sun sets anaemically over a hazy city.
Lánzhōu
Top Sights
White Cloud Temple A2
White Pagoda Temple A1
Sights
1 Beach A1
2 Water Wheels A1
Sleeping
3 Grand Soluxe Hotel Gānsù B2
4 Huálián Bīnguǎn D4
5 Jǐnjiāng Inn D3
6 JJ Sun Hotel D3
7 Zǐjīnghuā Jiǔdiàn D4
Eating
8 Héjiāhé D4
9 Hézhèng Lù Night Market EntranceD3
10 Jiànjūn Niúròumiàn C2
11 Néngrénjù D3
Shopping
12 Foreign Languages Bookshop B2
Information
13 Gānsù Airport Booking OfficeD2
14 Lǎobǎixìng PharmacyD3
Transport
15Bus 111 to South Bus StationB2
16 China Eastern AirlinesD2
17 East Bus Station D3
18Main Long-Distance Bus StationD4
19 Tiānshuǐ Bus StationD4
#### Sights
Gānsù Provincial Museum MUSEUM
( 甘肃省博物馆 ; Gānsù Shěng Bówùguǎn; Xijin Xilu; audio guide for Silk Road exhibition Y10; 9am-5pm Tue-Sun) This sparkling museum has an intriguing collection of Silk Road artefacts, including inscribed Han-dynasty wooden tablets used to relay messages along the Silk Road and a graceful Eastern Han (25 BC–AD 220) bronze horse galloping upon the back of a swallow. The latter, known as the 'Flying Horse of Wuwei' , was unearthed at Léitái and is much reproduced across northwestern China. Unearthed 120km northeast of Lánzhōu, a 2nd-century-BC silver plate depicting Bacchus, the Greco-Roman god of wine, may set your mind pondering. Among other items on view are Persian coins , some lovely Bodhisattva statues from Tiāntīshān and a collection of dinosaur skeletons upstairs, where you will also find a cafe. Bus 1 goes here.
White Cloud Temple TAOIST TEMPLE
Offline map ( 白云观 ; Báiyún Guàn; Binhe Zhonglu; 7am-5.30pm) This largely rebuilt Qing-dynasty Taoist temple is an oasis of reverential calm at the heart of the city. About 20 black-clad bearded monks inhabit the place – several of them are qualified to read fortunes; other soothsayers in eccentric attire and antique glasses muster outside the temple.
White Pagoda Hill PARK
( 白塔山 ; Báitǎ Shān; admission Y6; 6.30am-8.30pm summer) This park is on the northern bank of the Yellow River. At its zenith is White Pagoda Temple ( 白塔寺 ; Báitǎ Sì ) , originally built during the Yuan dynasty (1206–1368), from where there are good views across the city. A cable car (incl park ticket up/down/return Y25/15/30) spans the river; the terminal is just to the west of Zhōngshān Bridge. Bus 34 or 137 comes here from in front of the train station on Tianshui Nanlu.
Water wheels WATER WHEELS
Offline map ( 水车园 ; Shuǐchē yuán; admission Y4) A short stroll from White Cloud Temple are these two huge copies of irrigation devices that once lined the Yellow River.
Beach BEACH
Offline map East of the water wheels, this beach ( 河滩 ; Hétān) area is bursting on weekends with volleyball games, kites, speedboats and coracle raft trips (Y30 to Y40) across the chocolate-coloured river.
#### Sleeping
The most practical area to base yourself is in the east, home of the train station; always fish for discounts. Most budget hostels near the train station won't accept foreigners.
JJ Sun Hotel HOTEL $$$
Offline map ( 锦江阳光酒店 ; Jǐnjiāng Yángguāng Jiǔdiàn; 880 5511; www.jjsunhotel.com; 589 Donggang Xilu; 东岗西路 589 号 ; tw/s Y800/900, discounts of 30%; ) This good four-star choice has well-groomed, spacious and affordable rooms that are larger than those at the Grand Soluxe and come with very clean bathrooms. Pleasant wood-panelled restaurant on 2nd floor.
Zǐjīnghuā Jiǔdiàn HOTEL $$
Offline map ( 紫荆花酒店 ; Bauhinia Hotel; 863 8918; 36 Tianshui Nanlu; 天水南路 36 号 ; tw & d Y388-400, tr Y380, discounts of up to 70%; ) Once you get beyond the depressing ground-floor bar and dawdling lifts, rooms are good and discounts fab. Aim for a south-facing corner room, which nets you extra space and good mountain views at this colossal tower hotel near the train station.
Grand Soluxe Hotel Gānsù HOTEL $$$
Offline map ( 甘肃阳光大酒店 ; Gānsù Yángguāng Dàjiǔdiàn; 460 8888; www.sunshineplaza.com.cn; 428 Qingyang Lu; 庆阳路 428 号 ; d Y1060-1480, discounts of 40%; ) The gilded lobby is brash, but overall this is a reasonably luxurious 'five-star' option overseen by pleasant staff. Business kings are small with shower (no bath), but well turned out and good value with discounts; elite kings are larger.
Friendship Hotel HOTEL $
( 友谊宾馆 ; Yǒuyì Bīnguǎn; 268 9169; 16 Xijin Xilu; 西津西路 16 号 ; old wing tw Y60, with bathroom Y108-280, new wing tw Y380; ) The old-fashioned cheapo rooms with wood floorboards but no shower feel like a boarding school – or an asylum – but are decent and good value. The Y108 rooms are vast but crummy. For better rooms, head to the Jiābīn Lóu (Guest Hall), where much more pleasant doubles await. Although there's a tennis court and green grounds to the rear, the architecture is best described as 'Great Wall of Kitsch'.
Huálián Bīnguǎn HOTEL $
Offline map ( 华联宾馆 ; 499 2000; 7-9 Tianshui Nanlu; 天水南路 7-9 号 ; d Y189, tr Y319, discounts of 40-50%; ) This 360-room monster has comfortable, slightly scruffy rooms and a big lobby with a travel agency. The staff are friendly and speak English, but you'll have to put up with some traffic noise and slow lifts; discounts are attractive. It's right opposite the train station, with a handy internet cafe located next door. Trips to Bǐnglíng Sì arranged (Y198).
Jǐnjiāng Inn HOTEL $
Offline map ( 锦江之星 ; Jǐnjiāng Zhīxīng; 861 7333; 182 Tianshui Lu; 天水路 182 号 ; tw & d Y189; ) Neat and tidy express business-style hotel around 1km north of the train station with unfussy, compact and well-maintained rooms and snappy service. No discounts, but great value.
#### Eating & Drinking
Lánzhōu enjoys nationwide fame for its _niúròumiàn_ ( 牛肉面 ), beef noodle soup that's spicy enough to make you snort. Two handy phrases are _'jiā ròu'_ ( 加肉 ; add beef) and _'bùyào làjiāo'_ ( 不要辣椒 ; without chillies).
Hézhèng Lù night market MARKET $
Offline map ( 和政路夜市场入口; Hézhèng Lù Yèshìchǎng Rùkǒu) This bustling market, extending from Tianshui Lu to Pingliang Lu, is terrific for savouring the flavours of the northwest. The mix of Hui, Han and Uighur stalls offers everything from goat's head soup to steamed snails, _ròujiābǐng_ ( 肉夹饼 ; mutton served inside a 'pocket' of flat bread), lamb dishes seasoned with cumin, _dàpánjī_ (large plate of spicy chicken and potatoes), Sìchuān hole-in-the-wall outfits, dumplings, spare-rib noodles and more.
Néngrénjù HOTPOT $$
Offline map ( 能仁聚 ; 216 Tianshui Lu; hotpot for 2 Y50; 11am-10pm; ) Tasty Běijīng-style traditional lamb hotpot ( 涮羊肉 ; _shùan yángròu_ ) spot where you swiftly scald wafer-thin strips of lamb to bleach out the colour before dunking in sesame sauce; great for group dining with beers but also good solo; ensure you check your bill carefully, though.
Jiànjūn Niúròumiàn NOODLES $
Offline map ( 建军牛肉面 ; 234 Jingning Lu; meals Y7; 6am-5pm) This popular restaurant makes an early start but shuts early. Grab a ticket from the desk at front and exchange it with kitchen staff, who will ladle you out a huge, filling and sweltering bowl of delicious beef noodles ( 牛肉面 ; _niúròumiàn_ ), eye-rollingly spiced up with chilli and coriander.
Héjiāhé CHINESE FAST FOOD $
Offline map ( 和家和 ; Tianshui Nanlu; meals Y20; 6am-11pm) Convenient, bright and unfussy fast-food restaurant with a helpful photo menu and range of quickly delivered dishes, including _hóngshāoròu fàn_ ( 红烧肉饭 ; braised pork and rice; Y15) and _nǎichá_ ( 奶茶 ; bubble tea; Y4.50).
#### Shopping
Foreign Languages Bookshop BOOKS
Offline map ( 外文书店 ; Wàiwén Shūdiàn; 35 Zhangye Lu; 8.30am-6.30pm) In the centre of town.
#### Information
Bank of China ( 中国银行 ; Zhōngguó Yínháng; Tianshui Lu; 8.30am-noon & 2.30-6pm Mon-Fri) Has an indoor ATM.
China International Travel Service (CITS; 中国国际旅行社 ; Zhōngguó Guójì Lǚxíngshè; 232 3048; www.citsgs.com; Xijin Xilu) Small office next to Gansu Provincial Museum.
China Post ( 中国邮政 ; Zhōngguó Yóuzhèng; cnr Minzhu Lu & Pingliang Lu; 8am-7pm)
Hóngchén Internet Cafe ( 宏晨网吧 ; Hóngchén Wǎngbā; per hr Y2.5; 24hr) On the 2nd floor, next to Huálián Bīnguǎn.
Internet cafe ( 网吧 ; wǎngbā; 2nd fl, 449 Donggang Xilu; per hr Y2; 24hr)
Internet cafe ( 网吧 ; wǎngbā; per hr Y2; 24hr) Next to No 710 Donggang Xilu, in between Kodak Express outlet and Bank of China.
Lǎobǎixìng Pharmacy Offline map ( 老百姓大药房 ; Lǎobǎixìng Dàyàofáng; Tianshui Lu; 24hr) Evening service, knock on door.
Public Security Bureau (PSB; 公安局 ; Gōng'ānjú; 482 Wudu Lu; 8.30-11.30am & 2.30-5.30pm Mon-Fri) The foreign-affairs branch is located on the ground floor, next to a giant Orwellian tower. Visa extensions are generally granted on the same day; one photo required. At the time of writing the office was being refurbished and a temporary office was at 52 Huangheyan Nanbinhe Lu.
Western Travel Service ( 西部旅行社 ; Xībù Lǚxíngshè; 885 0529; 486 Donggang Xilu) Located on the 2nd floor of the west wing of Lánzhōu Fàndiàn. Has English-speaking staff and offers competitively priced tours and ticket bookings.
#### Getting There & Away
###### Air
Among other cities, Lánzhōu has flights to Běijīng (Y1340), Dūnhuáng (Y1260), Jiāyùguān (Y1080), Kūnmíng (Y1410), Shànghǎi (Y1750) and Xī'ān (Y600). Book tickets from:
China Eastern Airlines Offline map ( 东方航空公司 ; Zhōngguó Dōngháng Hángkōng; 882 1964; 586 Donggang Xilu; office 8.30am-7.30pm, phone line 24hr)
Gānsù Airport Booking Office Offline map ( 甘肃机场售票中心 ; Gānsù Jīchǎng Shòupiào Zhōngxīn; 888 9666; 520 Donggang Xilu; 8.30am-9pm) Can book all air tickets at discounted prices.
###### Bus
Lánzhōu has several bus stations, all with departures for Xīníng. The main long-distance bus station ( 长途车站 ; chángtú chēzhàn; Pingliang Lu) and the south bus station ( 汽车南站 ; qìchē nánzhàn; Langongping Lu) are the most useful.
The following services depart from the main long-distance bus station:
Píngliáng Y82, five to six hours, hourly (7.30am to 5pm)
Tiānshuǐ Y71.50, four hours, every 30 minutes (7am to 6pm)
Xīníng Y58, three hours, every 30 minutes (7.10am to 8.10pm)
Yínchuān Y120, six hours, every two hours (7.20am to 3.20pm)
The following services depart from the south bus station:
Hézuò Y32, four hours, every 30 minutes (7am to 4.30pm)
Lángmùsì Y73, eight hours, two daily (8.30am and 9.30am)
Línxià Y30, three hours, every 30 minutes (7am to 7pm)
Xiàhé Y45.50, six hours, three daily (7.30am, 8.30am and 2pm)
Zhāngyè Y100, 12 hours, one daily (6pm)
The west bus station ( 汽车西站 ; qìchē xīzhàn; Xijin Xilu) has departures to Liújiāxiá (Y10.50, two hours, every 20 minutes 7am to 6pm); for Bǐnglíng Sì, Click here . The east bus station ( 汽车东站 ; qìchē dōngzhàn; 841 8411; Pingliang Lu) has sleepers to Zhāngyè and Jiāyùguān, Tiānshuǐ (Y71.5) and Píngliáng (Y82 to Y98, regular, five to six hours).
Hidden off the main street, the Tiānshuǐ bus station Offline map ( 天水汽车站 ; Tiānshuǐ Qìchēzhàn; Tianshui Lu) has buses for eastern Gānsù, including Luòmén (Y50, four hours).
### GETTING TO GĀNNÁN
At the time of writing, the authorities were still twitchy about individual travellers taking buses southwest to Línxià, Hézuò, Xiàhé and Lángmùsì, so travellers buying tickets to these destinations at the south bus station were required to provide a photocopy of their passport information page and visa page. The ticket office could not provide these, so you had to supply them yourself; a shop left out of the bus station and across the road can photocopy your passport for you, but if you are taking an early bus get this done beforehand somewhere else as the shop may not be open. Be aware that this regulation may have changed by the time you read this.
###### Train
Lánzhōu is the major rail link for trains heading to and from western China. Departing from Lánzhōu, the T9205 (Y49, 7.29am) is a handy two-tier train that stops in Wǔwēi; it departs Wǔwēi at 10.19am to continue to Zhāngyè (Y41, two hours) and Jiāyùguān. There are also overnight trains to:
Dūnhuáng Y263, 12 hours
Jiāyùguān Y178, 10 hours
Turpan Y369, 22 hours
You can continue west to Ürümqi (Y390, 24 hours); east is to Xī'ān (hard sleeper Y175). In summer buy your onward tickets a couple of days in advance to guarantee a sleeper berth.
A soft seat in one of the double-decker express trains is by far the most civilised way to get to Xīníng (hard/soft seat Y33/50, 3½ hours). Trains depart at 10.50am and 7pm.
For details on trains to Lhasa.
#### Getting Around
The airport is 70km north of the city. Airport buses ( 896 8555) leave every hour from 8am to 7pm just west of the China Eastern Airlines office three hours before scheduled flight departures. The trip costs Y30 and takes 70 minutes. A taxi costs around Y120, or Y30 per seat. Lánzhōu badly needs a metro system.
Useful bus routes:
Buses 1, 6, 31 and 137 From the train station to the west bus station and the Friendship Hotel via Xiguan Shizi.
Bus 111 From Zhongshan Lu (at the Xiguan Shizi stop; 去汽车南站的 111 路公交车 ) to the south bus station.
Buses 7 and 10 From the train station up the length of Tianshui Nanlu before heading west and east, respectively.
Public buses cost Y1; taxis are Y7 for the first 3km. A taxi from the train station to the south bus station costs Y20.
### Bǐnglíng Sì 炳灵寺
Due to its relative inaccessibility, Bǐnglíng Sì (adult/student Y50/25) is one of the few Buddhist grottoes in China to survive the tumultuous 20th century unscathed. Over a period spanning 1600 years, sculptors dangling from ropes carved 183 niches and sculptures into the porous rock along the dramatic canyon walls. Today the cliffs are isolated by the waters of the Liújiāxiá Reservoir (Liújiāxiá Shuǐkù) on the Yellow River. All considered, come here for a nice day out rather than for the cave art alone, which doesn't compare to somewhere like Dūnhuáng.
As with other Silk Road grottoes, wealthy patrons, often traders along the route west, sponsored the development of Bǐnglíng Sì, which reached its height during the prosperous Tang dynasty. The star of the caves is the 27m-high seated statue of Maitreya , the future Buddha, but some of the smaller, sway-hipped Bodhisattvas and guardians, bearing an obvious Indian influence, are equally exquisite. Photos are allowed. Art buffs can climb the staircase to Tang-dynasty caves 169 and 172 for an extra fee of Y300.
If you've hired your own boat, and thus have more time at the site, you can take a jeep (Y40) or hike 2.5km further up the impressive canyon to a small Tibetan monastery .
Note that from November to March, water levels may be too low to visit the caves, so check before setting off.
Western Travel Service (Xībù Lǚxíngshè; 0931-885 0529; 486 Donggang Xilu) in Lánzhōu can organise a visit to the caves for two people for Y340 per person.
You can visit Bǐnglíng Sì as a day trip from Lánzhōu or en route to Línxià. Frequent buses from Lánzhōu's west bus station (Y12, two hours) run past the Liújiāxiá Reservoir, and will drop you 500m from the boat ticket office.
The going rates for a covered speedboat (seating up to eight people) are Y400 for the one-hour journey. The boat ticket office is good at hooking up independent travellers with small groups, which will make the price around Y65 to Y80 per person. For this you'll get about 1½ hours at the site, which is really a minimum. Private operators close to the dam will pester you with similar rates, and sometimes even cheaper speedboats (Y200). For those that have the time, the ferry (May to October) is just Y30 for a return trip, but it is a pretty dreary seven-hour return trip! Make sure you bring snacks, sunscreen, cold drinks and a couple of paperbacks.
If you're heading to Línxià after the caves, you can arrange for a speedboat to drop you off at Liánhuātái ( 莲花台 ) on the way back. From there, minibuses will taxi you on to Línxià (Y10, one hour).
### Línxià 临夏
0930 / POP 203,200
The bus from Lánzhōu descends after a while into a highly fertile valley before pulling into this slow-moving and lazy Silk Road town where residents carry on as though the camel caravans are just over the horizon. Han China runs out of steam and hits the buffers here: in this overt stronghold of Chinese Islam, the skyline is dominated by onion-domed mosques. Among the goods for sale you'll spot gourds, daggers, saddlery, carpets, textiles and oversized spectacles, as well as Muslim and Buddhist religious paraphernalia. Also noticeable are more Western songs on the radio and far fewer excruciating 'hulloos' from roadside quipsters. Línxià isn't quite a destination in itself, but many travellers break up the trip to or from Xiàhé here and it's a great place to get fed, watered, rested and recharged.
#### Sights
Wànshòu Temple TAOIST TEMPLE
( 万寿观 ; Wànshòu Guàn; admission Y10; 7am-8pm) If you have a bit of time to kill, this cedar-scented temple extends seven levels up the hillside at the northwest fringe of Línxià. Along the cliffs you can visit other surrounding temples overlooking the city. Take bus 6 to the west bus station and head for the nine-storey pagoda on the ridge located opposite.
#### Sleeping & Eating
Shuǐquán Bīnguǎn HOTEL $
( 水泉宾馆 ; 631 4968; 68 Jiefang Nanlu; 解放南路 68 号 ; s/d/tr with shared bathroom Y20/40/60, d with shower Y60-80; ) This cheapie in front of the Shuǐquán Mosque is handy for the bus station and has fine, clean and spacious rooms, but beds and pillows are hard. Light sleepers may get jolted by the early-morning call to prayer. Rooms on the street side get the most sunlight. Heading out of the south bus station, turn right and walk 200m.
Línxià Fàndiàn HOTEL $
( 临夏饭店 ; 623 0081; 9 Hongyuan Lu; 红园路 9 号 ; tw from Y180; ) The new block has the better, pricier rooms, while the cheaper ones are in the old block. It's not in the most exciting part of town, about 800m east of the west bus station.
Shuǐquán Cāntīng MUSLIM $
( 水泉餐厅 ; Jiefang Nanlu; meals Y25-50; 7.30am-9.30pm) Handily tucked away by the hotel of the same name, this is a good place for a plate of spicy _dàpánjī_ ( 大盘鸡 ; chicken with green and red peppers and potato in an oily chilli sauce; medium/large Y50/60); we recommend going for a medium plate unless you have a horse-like hunger or there are three of you. It can be a bit of a wait, but when it arrives the dish is a real feast.
Beidajie Yèshì NIGHT MARKET
At this market just west of Zhongxin Guangchang ( 中心广场 ; Centre Sq), you can sit down alfresco for lamb kebabs (Y0.70 each) and watch vendors fire up tasty _shā guō_ ( 砂锅 ; minihotpots; Y8) on sheets of flame from around 7pm.
Come evening, street vendors dole out _shā guō_ and hot snacks at other strategically placed main intersections.
#### Information
Bank of China ( 中国银行 ; Zhōngguó Yínháng; Jiefang Lu; 8.30am-noon & 2.30-6pm Mon-Fri) On left-hand side of Jiefang Lu around 100m north of Sāndàoqiáo Guǎngchǎng ( 三道桥广场 ); 24hr ATM.
Ránqíng Internet Bar ( 燃情岁月 ; Ránqíng Suìyuè; Jiefang Lu; per hr Y3.50; 24hr) On the 2nd floor behind the Héngshēng Hotel (Héngshēng Bīnguǎn) just before Zhongxin Guangchang.
#### Getting There & Away
Línxià has three long-distance bus stations: south _(nán zhàn),_ west _(xī zhàn)_ and east _(dōng zhàn)_ . You may dropped off at the west bus station but it is of little use otherwise. The east station is handy for Dōngxiāng and also has buses to Liújiāxiá (Y16, three hours, every 30 minutes 8am to 4pm). Bus 6 links the south and the west bus stations, or a taxi is Y4.
The following services depart from the south bus station :
Hézuò , Y20, two hours, every 30 minutes (6am to 5pm)
Lánzhōu , Y29.50, three hours, every 20 minutes (7.30am to 5.30pm)
Tiānshuǐ , Y80, 10 hours, one daily (6.20am)
Xiàhé , Y19, two hours, every 30 minutes (6.30am to 5pm)
Xīníng , Y56, eight hours, one daily (6am)
One interesting route is to the Mèngdá Nature Reserve in Qīnghǎi. The fastest way to the reserve is to catch transport to Dàhéjiā and charter a taxi (Y40) for the last 15km.
If you're on the slow road to Qīnghǎi, buses to Xúnhuà (Y30, 3½ hours, 8am to 3pm) leave every hour or two from a courtyard behind the Tiānhé Fàndiàn ( 天河饭店 ), reachable by walking 350m northeast from the south bus station to the first intersection, Sandaoqiao Guangchang ( 三道桥广场 ), then turning right and walking 350m to the hotel. From Xúnhuà you'll find onward transport to Xīníng or Tóngrén.
### Suǒnánbà (Dōngxiāng) 锁南坝 ( 东乡 )
0930 / POP 12,000
Spilling over a ridge high above Línxià and home to both Hui and Dongxiang minorities, this little market town's only street is a hive of activity, with locals trading wares and occasional shepherds shooing flocks about. The town is called Suǒnánbà, while the surrounding county is Dōngxiāng, but some people also call the town Dōngxiāng.
The Dongxiang people speak an Altaic language and are believed to be descendants of 13th-century immigrants from Central Asia, moved forcibly to China after Kublai Khan's Middle East conquest.
The local museum ( 东乡博物馆 ; Dōngxiāng Bówùguǎn; 712 3286; 8.30am-5pm) has an ethnographic room with traditional clothing, saddles and bronze items, much of it resembling items used by Mongols; you may have to ask staff to unlock the small exhibition halls. The museum is on the 3rd and 4th floors of the enormous pink-and-orange building opposite the bus station. Captions are in Chinese.
Frequent minibuses (Y5, 40 minutes, 6am to 8pm) head up on the pleasant journey past terraced fields from Línxià's east bus station. To continue to Lánzhōu (Y18, two hours), buses leave Suǒnánbà on the hour from the top of the hill (at the T-junction) between 8am and 4pm. The bus only turns up at the last minute, as the driver spends about 30 minutes trawling the main road looking for passengers.
### Dàhéjiā 大河家
0930 / POP 4500
With sweeping views over the Yellow River, towering red cliffs and (in summer) verdant green terraces, Dàhéjiā is a kaleidoscope of colour. The surrounding area is home to a significant population of Bao'an ( 保安族 ), Muslims who speak a Mongolic language. The Bao'an are famed for producing knives and share cultural traits with the Hui and Dongxiang. Their Mongol roots come out during summer festivals, when it is possible to see displays of wrestling and horse riding.
A 12km loop road from Dàhéjiā goes out to the peaceful Bao'an villages of Gānhétán ( 甘和谈 ), Méipó ( 媒婆 ) and Dàdūn ( 大敦 ). You can walk to the villages in about 40 minutes or hire a taxi (Y30).
Unless you have a special interest in minority culture in China, Dàhéjiā is a bit far for a side trip. However, the town is worth visiting if you're travelling on the road between Línxià and Xīníng. The Sānlián Bīnguǎn ( 三联宾馆 ; 139 9309 7599; dm Y20-30, tw with bathroom Y50-88) is a decent Hui-run hotel in town, near the Yellow River bridge.
Most buses between Línxià and Xīníng will stop here. From Línxià you can also catch an hourly minibus (Y18, two hours, 7am to 4.30pm) from the _dàxīqìchēzhàn_ ( 大西汽车站 ), which is different to the regular west bus station.
### Xiàhé 夏河
0941 / POP 70,000
The alluring monastic town of Xiàhé attracts an astonishing band of visitors, from backpack-laden students, insatiable wanderers, shaven-headed Buddhist nuns, Tibetan nomads in their most colourful finest, camera-toting tour groups and dusty, itinerant beggars. Most visitors are rural Tibetans, whose purpose is to pray, prostrate themselves and seek spiritual fulfilment at holy Labrang monastery (Lābǔléng Sì).
In a beautiful mountain valley at 2920m above sea level, Xiàhé has a certain rhythm about it and visitors quickly tap into its fluid motions. The rising sun sends pilgrims out to circle the 3km _kora_ (pilgrim path) that rings the monastery. Crimson-clad monks shuffle into the temples to chant morning prayers. It's easy to get swept up in the action, but some of the best moments come as you relax in a cosy teahouse, hands warmed by a hot bowl of yak tea.
The area was long part of the Tibetan region of Amdo. As a microcosm of southwestern Gānsù, the area's three principal ethnic groups are represented in Xiàhé. In rough terms, Xiàhé's population is 50% Tibetan, 40% Han and 10% Hui. Labrang Monastery marks the division between Xiàhé's mainly Han and Hui Chinese eastern quarter and the scruffy Tibetan village to the west.
Despite Xiàhé's ostensible tranquillity, these ethnic groups don't necessarily mix peacefully. The Tibetan community maintains a strong solidarity with their brethren on the plateau, and demonstrations and rioting here in the wake of the 2008 riots in Lhasa led to the region's being closed to individual travellers till early 2010.
#### Sights
Labrang Monastery TIBETAN MONASTERY
( 拉卜楞寺 ; Lābǔléng Sì; admission Y40) Even the most illustrious of China's other incense-wreathed temples pale in comparison with the vast magnitude of this astounding complex. The palpable spiritual energy that emanates from this sacred monastery is only matched by the potent veneration brought by its unending flow of Tibetan pilgrims. Even if Tibet is not on your itinerary, the monastery sufficiently conveys the esoteric mystique of its devout persuasions, leaving indelible impressions of a deeply sacred domain.
Xiàhé
Top Sights
Barkhang B1
Dewatsang Chapel B2
Gòngtáng Chörten B2
Hall of Hayagriva B2
Sights
1Monastery Ticket OfficeB1
2 Ngakpa Gompa A1
3 Nunnery A1
4 Thangka Display Terrace A2
Sleeping
5 Labrang Baoma Hotel C1
6 Labrang Red Rock International Hostel C2
7 Overseas Tibetan Hotel C2
8 Tara Guesthouse C2
Eating
Everest Café (see 7)
9 Nomad Restaurant C1
10 Snowy Mountain Café C2
11 Tsewong's Cafe C2
Drinking
12TeahousesC1
Information
13 Déshèngtáng PharmacyD1
14 OT Travels & ToursC2
Transport
15Bus StationD1
16Buses to DájiǔtānA2
The monastery is one of the six major Tibetan monasteries of the Gelugpa order (Yellow Hat sect of Tibetan Buddhism). The others are Ganden, Sera and Drepung Monasteries near Lhasa; Tashilhunpo Monastery in Shigatse; and Kumbum (Tǎ'ěr Sì; near Xīníng, Qīnghǎi.
Labrang monastery was founded in 1709 by Ngagong Tsunde (E'angzongzhe in Chinese), the first-generation Jamyang (a line of reincarnated Rinpoches or living Buddhas ranking third in importance after the Dalai and Panchen Lamas), from nearby Gānjiā. At its peak the monastery housed nearly 4000 monks, but their ranks greatly declined during the Cultural Revolution. Numbers are recovering, and are currently restricted to 1200 monks, drawn from Qīnghǎi, Gānsù, Sìchuān and Inner Mongolia.
With its endless squeaking prayer wheels, hawks circling overhead and the deep throb of Tibetan trumpets resonating from the surrounding hills, Labrang is a monastery in the entire sense of the word. In addition to the chapels, residences, golden-roofed temple halls and living quarters for the monks, Labrang is also home to six _tratsang_ (monastic colleges or institutes), exploring esoteric Buddhism, theology, medicine, astrology and law. Many of the chapel halls are illuminated in a yellow glow by yak butter lamps, their strong-smelling fuel scooped out from voluminous tubs.
The only way to visit the interior of these buildings is with a tour, which generally includes the Institute of Medicine , the Manjushri Temple , the Serkung (Golden Temple) and the main Prayer Hall (Grand Sutra Hall), plus a museum of relics and yak-butter sculptures. English tours (Y40) of the monastery leave the ticket office ( 售票处 ; Shòupiàochù) around 10.15am and 3.15pm; take the morning tour if you can as there's more to see. An alternative is to latch on to a Chinese tour. Even better is to show up at around 6am or 7am to be with the monks. At dusk the hillside resonates with the throaty sound of sutras being chanted behind the wooden doors.
The rest of the monastery can be explored by walking the _kora_ (see the boxed text, Click here ) and although many of the temple halls are padlocked shut, there are a couple of separate smaller chapels you can visit. Over three floors, the Barkhang Offline map (admission Y10; 9am-noon & 2-5pm) is the monastery's traditional printing press (with rows upon rows of over 20,000 wood blocks for printing) and is well worth a visit. Photos are allowed.
Its interior illuminated by a combination of yak-butter lamps and electric light bulbs by the thousand, the 31m-tall Gòngtáng Chörten Offline map ( 贡唐宝塔 ; Gòngtáng Bǎotǎ; admission Y10) is a spectacular stupa with lovely interior murals and fantastic views from the roof onto a landscape dotted with the port-red figures of monks. At the rear of the stupa is a Sleeping Buddha ( 卧佛 ; Wòfó) depicting Sakyamuni on the cusp of entering nirvana.
The Dewatsang Chapel Offline map ( 德哇仓文殊佛殿 ; Déwācāng Wénshū Fódiàn; admission Y10) , built in 1814, ranges over four floors and houses a vast 12m-statue of Manjushri (Wenshu) and thousands of Buddhas in cabinets around the walls. The Hall of Hayagriva Offline map ( 马头明王殿 ; Mǎtóu Míngwáng Diàn; Hall of Horsehead Buddha), destroyed during the Cultural Revolution, was reopened in 2007. Containing vivid and bright murals, the hall also encapsulates a startlingly fierce 12m-high effigy of Hayagriva – a wrathful manifestation of the usually calm Avalokiteshvara (Guanyin) – with six arms and three faces.
Access to the rest of the monastery area is free, and you can easily spend several hours just walking around and soaking up the atmosphere in the endless maze of mud-packed walls. The Tibetan greeting, in the local Amdo dialect, is ' _Cho day mo?_ ' (How do you do?) – a great icebreaker.
The best morning views of the monastery come from the Thangka Display Terrace , a popular picnic spot, or the forested hills south of the main town.
Nunnery BUDDHIST NUNNERY
Offline map This welcoming nunnery ( _ani gompa_ in Tibetan, __ 尼姑庵 , _nígū'ān_ in Chinese) __ is on the hill above the Tibetan part of town.
Ngakpa Gompa BUDDHIST MONASTERY
Offline map ( 红教寺 ; Hóngjiào Sì; admission Y5) Next door is the small Nyingmapa (Red Hat) school monastery, whose lay monks wear striking red and white robes and long, braided hair.
### WALK LIKE A TIBETAN
Following the 3km _kora_ (pilgrim path) encircling Labrang monastery is perhaps the best approach to grasping its layout, scale and significance. Lined with long rows of squeaking prayer wheels, white-washed _chörtens_ (Tibetan stupas) and chapels, the _kora_ passes Gòngtáng Chörten and Dewatsang Chapel. Tibetan pilgrims with beads in their hands and sunhats on their heads, old folk, mothers with babies and children, shabby nomads and more walk in meditative fashion clockwise along the path (called _zhuǎnjìngdào,_ 'scripture-turning way' in Chinese), rotating prayer wheels as they go. Look also for the tiny meditation cells on the northern hillside.
For a short hike, the more strenuous outer _kora_ path takes about an hour and climbs high above the monastery. From the nunnery in the west of town, make your way up the ridge behind and to the left, winding steeply uphill to a bunch of prayer flags and the ruins of a hermitage. The views of the monastery open up as you go along. At the end of the ridge there's a steep descent into town; alternatively, descend into the small valley to the side, passing a sky-burial site en route.
#### Tours
Lohsang at the OT Travels & Tours is excellent for information and tours of the surrounding area. Tsewong's Cafe is also a great resource for travellers, with a variety of tours and loads of info.
#### Festivals & Events
Festivals are central to the calendar for both the devotional monks and the nomads who stream into town from the grasslands in multicoloured splendour. Tibetans use a lunar calendar, so dates for individual festivals vary from year to year.
Monlam (Great Prayer) Festival BUDDHIST
This festival starts three days after the Tibetan New Year, which is usually in February or early March. On the morning of the 13th day of the festival, more than 100 monks carry a huge _thangka_ (sacred painting on cloth) of the Buddha, measuring more than 30m by 20m, and unfurl it on the hill facing the monastery. This is accompanied by spectacular processions and prayer assemblies.
On the 14th day there is an all-day session of Cham dances performed by 35 masked dancers, with Yama, the lord of death, playing the leading role. On the 15th day there is an evening display of butter lanterns and sculptures. On the 16th day the Maitreya statue is paraded around the monastery.
During the second month (usually starting in March or early April) there are several interesting festivals, with a procession of monastery relics on the seventh day.
#### Sleeping
Overseas Tibetan Hotel HOTEL $
Offline map ( 华侨饭店 ; Huáqiáo Fàndiàn; 712 2642; www.overseastibetanhotel.com; 77 Renmin Xijie; 人民西街 77 号 ; dm Y20, d Y160-200; ) Well-run and bustling place, owned by the energetic and bouncy Jesuit-educated Lohsang, a likeable Tibetan with faultless English who runs the _kora_ most mornings. Dorms are simple; pricier doubles are well laid out and attractive, coming with a bathroom. Also here are the Everest Cafe, internet access (Y5 per hour), bike hire and a travel agency.
Labrang Red Rock International Hostel HOSTEL $
Offline map ( 拉卜楞红石国际青年旅馆 ; Lābǔléng Hǒngshí Guójì Qíngnián Lǚguǎn; 712 3698; labrang hongshi@yahoo.cn; 253 Yagetang; 雅鸽搪 253 号 ; 8/4-bed dm Y30/35, d Y100; ) This Tibetan-themed, very quiet hostel has varnished pine-wood rooms, solar-powered hot showers, a restaurant and bar area and a beautiful display of _thangka_ . Doubles are clean and spacious. YHA card holders get a discount; internet is Y5 per hour. Walk past the Tara Guesthouse and turn left before the bridge.
Tara Guesthouse GUESTHOUSE $
Offline map ( 卓玛旅社 ; Zhuōmǎ Lǚshè; 712 1274; tsering tara@aol.com; 268 Yagetang; 雅鸽搪 268 号 ; dm Y10-30, s/tw Y30/50) This long-time budget place is run by monks from Sìchuān and has small, comfortable _kang_ rooms (shared shower room, no phone) arranged around a courtyard and frugal dorms. There's a terrace with great views over the monastery; hot water is solar powered. English is well spoken at the front desk.
Labrang Baoma Hotel HOTEL $$
Offline map ( 拉卜楞宝马宾馆 ; Lābǔléng Bǎomǎ Bīnguǎn; 712 1078; www.labranghotel.com; 77 Renmin Xijie; 人民西街 77 号 ; 4-bed dm Y40, s/d Y290/280, discounts of 45%; ) Pleasant and vibrantly colourful hotel with friendly staff, nice interior courtyard and comfortable ensuite doubles. Bike hire and laundry.
#### Eating & Drinking
For those of you who can't make it to Tibet, Xiàhé is an opportunity to develop an appetite for the flavours of the Land of Snows, whether it's _momo_ (boiled dumplings), _tsampa_ (a porridge of roasted barley flour), yak-milk yoghurt, or throat-warming glasses of the local firewater. For Chinese or Hui dishes, try the restaurants around the bus station; cake shops round out the picture.
Nomad Restaurant TIBETAN $
Offline map ( 牧民齐全饭庄 ; Mùmín Qíquán Fànzhuāng; dishes Y5-25) With its great service and commanding views of the monastery and _kora_ route, get into the swing of things with some hot yak milk (Y4), boiled yak meat (Y35), a bowl of _tsampa_ (Y8), a plate of _momo_ (Y10), vegetable hotpot (Y18) and a volatile shot of Nomad barley alcohol (Y6). It's on the 3rd floor, just before the monastery walls.
Snowy Mountain Cafe CAFE-RESTAURANT $
Offline map ( 雪山咖啡馆 ; Xuěshān Kāfēiguǎn; 139 9309 1241; www.snowymtncafe.com; dishes Y4-8) Popular upstairs foreign-owned spot for international dishes with a strong menu ranging from omelettes (cheese omelette Y12) to spag bolognese (Y25), winning pizzas (cheese Y32), Bistec a lo Pobre (steak with fried potatoes, onions and eggs; Y35) and beyond. It's also a good place for hoovering up travel information or organising plane and train tickets.
Tsewong's Cafe CAFE $
Offline map ( 泽旺小吃 ; CáixiàngZéwàng Kāfēiguǎn; 138 9397 9763; tsewongscafe@yahoo.com.cn; dishes Y20-50; 9am-late) Switched-on traveller cafe with much-loved pizzas (Y38 to Y48) and kebabs (more like a Turkish İskender kebab, with tomatoes, yoghurt and bread), _tsampa_ (Y10), a simple Chinese menu plus coffee, internet access and ticketing (Y50 per ticket).
Everest Cafe CAFE, RESTAURANT $
Offline map (77 Renmin Xijie; 人民西街 77 号 ; 7am-late) Popular spot for breakfast (Y20), lunch or a late-night beer; attached to the Overseas Tibetan Hotel.
#### Shopping
Xiàhé is excellent for Tibetan handicrafts, so why not don a cowboy hat or a Tibetan trilby, wrap yourself in a _chuba_ (Tibetan cloak), light up some juniper incense, wrap your head in a furry yellow monk's hat, jump into a pair of monk's boots, flap a prayer flag or shell out for brocaded silks, Tibetan cloth, Tibetan-style tents or a silver teapot? Stacks of handicraft shops line the upper part of the main road, before the monastery walls.
#### Information
It's not possible to change travellers cheques in Xiàhé.
China Post ( 中国邮政 ; Zhōngguó Yóuzhèng; 8am-6pm)
Déshèngtáng Pharmacy Offline map ( 德盛堂药店 ; Déshèngtáng Yàodiàn; 8.30am-8pm) Western, Chinese and Tibetan medicine; just west of post office.
Industrial & Commercial Bank of China (ICBC; 工商银行 ; Gōngshāng Yínháng) Has an ATM and changes US dollars.
Lèlè Wǎngbā ( 乐乐网吧 ; per hr Y3; 24hr) Internet access diagonally across from the bus station, in an off-street courtyard.
OT Travels & Tours Offline map ( 712 2642; othotel@public.lz.gs.cn) This reliable travel agency at the Overseas Tibetan Hotel can arrange cars and guides to nearby sights. Contact Losang.
Phoenix Internet Bar ( 凤凰网络 ; Fènghuáng Wǎngluò; per hr Y3; 8am-11pm) South of Tara Guesthouse.
Public Security Bureau (PSB; 公安局 ; Gōng'ānjú; 333 8010; 9am-noon & 3-6pm Mon-Fri) Does not handle visa extensions; you'll need to go to Hézuò, Línxià or Sōngpān.
Xùnjié Wǎngbā ( 迅捷网吧 ; per hr Y3; 24hr) Near the mosque.
#### Getting There & Away
There is no airport in Xiàhé, nor do trains run there, but it's regularly serviced by bus. Most travellers head on to either Lánzhōu or Sìchuān; the road less travelled takes you over the mountains to Tóngrén in Qīnghǎi.
The following bus services depart from Xiàhé.
Hézuò Y14, one hour, every 30 minutes (6.30am to 5.30pm)
Lángmùsì Y46.50, four hours, one daily (7.40am)
Lánzhōu Y49.50, 4½ hours, four daily (6.30am, 7.30am, 2.30pm and 8.30pm)
Línxià Y20, three hours, every 30 minutes (6am to 5.30pm)
Tóngrén Y25, five hours, one daily (6.30am)
Xīníng Y60, seven hours, one daily (6.10am)
If you can't get a direct ticket to/from Lánzhōu, take a bus to Línxià and change there. Allow time for the journey from Línxià, which can be a real test: the driver may dawdle for an hour for fares, insist on crawling by the side of the road to fill the final seat, stop at an abattoir so an animal carcass can be flung on board and then stop at checkpoints.
#### Getting Around
Most hotels and restaurants hire bikes for Y10 to Y15 per day. Taxis cost Y1 to Y2 per seat for a short trip around town, including to the bus station or monastery.
### Around Xiàhé
##### SĀNGKĒ GRASSLANDS 桑科草原
Expanses of open grassland where Tibetans graze yak herds around the village of Sāngkē ( 桑科 ) reward trips along the river 14km up the valley from Xiàhé. Development has turned the area into a small circus, complete with touristy horse rides and fake tourist yurts, but you can keep going to more distant and pristine grasslands in the direction of Amchog. You can cycle up to Sāngkē in about one hour. The twice-daily bus to Dájiǔtān ( 达久滩 ; Y10) from Xiàhé passes by Sāngkē, but timings mean you have to hitch back. A minivan costs about Y30 return.
##### GĀNJIĀ GRASSLANDS 甘加草原
For more adventure, the Gānjiā Grasslands (Gānjiā Cǎoyuán), 34km from Xiàhé, are far less developed and offer a great day trip from Xiàhé.
The bumpy road crosses the Naren-Ka pass before quickly descending into wide grasslands. Past Gānjiā Xiàn village, a side road climbs 12km to Trakkar Gompa ( 白石崖寺 ; Báishíyá Sì; admission Y15) , a monastery of 90 monks set against a backdrop of vertical rock formations. A 10-minute walk behind the monastery is the Nekhang ( 白石崖溶洞 ; Báishí Yá Róng dòng; admission Y20) , a cave complex where pilgrims lower themselves down ropes and ladders into two sacred underground chambers. A Dutch traveller fell to his death here in 2006, and to prevent the same fate we advise avoiding this place; your driver will probably suggest the same.
From Trakkar it's a short drive to the impressive, 2000-year-old, Han-dynasty village of Bājiǎo ( 八角 ; Karnang in Tibetan; admission Y10) , the remarkable 12-sided walls of which now shelter a small village. From here it's a short 5km diversion to the renovated Tseway Gompa ( 佐海寺 ; Zuǒhǎi Sì; admission Y10) , one of the few Bön monasteries in Gānsù. There are great views of Bājiǎo from the ridge behind the monastery.
It is also possible to hike over several days from the grasslands to 4636m-high Dálǐjiā Shān ( 达里加山 ; Dálǐjiā Mountain), but you will need to be well equipped for the camping trek; Xúnhuà-bound travellers from Línxià can get off the bus from Línxià at the Dálǐjiā mountain pass ( 达里加山口 ; Dálǐjiā Shānkǒu), from where you can trek up to the peak. Summer is the best season for such treks as you have more daylight hours, but note that the last Xúnhuà-bound bus will come through the pass at around 4pm, so you will need to hitch on to Xúnhuà if you miss it (or take camping gear). Alternatively, continue walking in the direction of Xúnhuà for around 15km to Dàowéi Tibetan Village ( 道帏藏族乡 ; Dàowéi Zàngzú Xiāng; also called Guru), where you may find a bed for the night, or take a minibus from Dàowéi to the larger Báizhuāng Village ( 白庄乡 ; Báizhuāng Xiāng), which has hotels. Dàowéi itself has a local monastery and is beautifully surrounded by climbable mountains.
OT Travels & Tours and Tsewong's Cafe, both in Xiàhé, can advise on all of these trips and arrange a car for four people and an English-speaking guide for around Y250 for the day; they can also arrange fun camping trips for overnighting on the grasslands.
### Hézuò 合作
0941 / POP 76,000
The booming regional capital of Gānnán ( 甘南 ) prefecture, Hézuò is a transit point for travellers plying the excellent overland route between Gānsù and Sìchuān provinces. The city is also the sight of the incredible Milarepa Palace, a bewitching Tibetan temple ranging spectacularly over nine floors.
#### Sights
Milarepa Palace TIBETAN TEMPLE
( 九层佛阁 ; Sekhar Gutok; Jiǔcéng Fógé; admission Y20; 7.30am-6pm) About 2km from the bus station along the main road towards Xiàhé is this towering temple, ringed by prayer wheels. The port-coloured building is highly unusual in the Tibetan world. It's really worth buying the entrance ticket to investigate the incredible interior (remove your shoes), where a sacred meteorite is also housed. The ground-floor hall is a powerful spectacle, a galaxy of Bodhisattvas, Buddhist statues and celestial figures gloomily illuminated by yak-butter lamps. Climb upstairs to a further staggering display of lamas and living Buddhas on the 2nd floor; more deities muster on the 4th floor. An unsettling array of fearsome, blue and turquoise tantric effigies awaits on the 6th floor. Make your way to the 8th floor for further effigies of Sakyamuni and Guanyin and views over the hills and town. The town's main monastery, Tso Gompa (admission Y20; 9am-6pm) , is next door. Bus 1 runs here from the centre of town.
#### Sleeping & Eating
For not-bad chicken burgers, try Màidíbǎo ( 麦迪堡 ) just north of the main square.
With Xiàhé just an hour to the north there is little reason to stay here, and cheap hotels are loath to take foreigners. If you get stuck, the Gānnán Fàndiàn ( 甘南饭店 ; 821 4733; Maqu Xilu; 玛曲西路 ; d Y150-240, tr Y300, discounts of 15%; ) has decent, clean and bright doubles with shower; it's located on the southwest corner of the main square.
#### Information
The post office is north of the square on Renmin Jie.
China Construction Bank ( 中国建设银行 ; Zhōngguó Jiànshè Yínháng) On the square south of the bus station; changes money.
Internet cafe ( 网吧 ; wǎngbā; Renmin Jie; per hr Y2.50; 24hr) North of the square on Renmin Jie.
Public Security Bureau (PSB; 公安局 ; Gōng'ānjú; 8.30am-noon & 2.30-5pm) Turn right out of the bus station onto Sāngqū Xīlù ( 桑曲西路 ); the PSB visa office is around 50m along on your left.
#### Getting There & Away
Hézuò is where buses from Zöigě (Ruò'ěrgài), in Sìchuān, and Xiàhé meet. Most buses to Lángmùsì go from the south bus station. The central main bus station has buses to:
Lángmùsì Y32.5, three hours, one daily (9am)
Lánzhōu Y32 to Y60, four hours, regular services (6.30am to 4.30pm)
Línxià Y20, 1½ hours, every 30 minutes
Xiàhé Y14, one hour, every 30 minutes
From the south bus station there are buses to:
Lángmùsì Y32.50, three hours, three daily (7am, 10.20am and 12.20pm)
Zöigě Y55, 3½ hours, one daily (7.30am)
A taxi between the two bus stations costs Y2 per person, or take bus 1 (Y1).
### Lángmùsì 郎木寺
0941 / POP 3000
Straddling the border between Sìchuān and Gānsù is Lángmùsì (Taktsang Lhamo in Tibetan), an alpine Amdo Tibetan village nestled among steep grassy meadows, evergreen forests of slender pine trees brushing the sky, crumbling stupas, piles of mani stones and snow-clad peaks. Lovely and moist compared to the lowlands, Lángmùsì is a delightful place, surrounded by countless red and white monastery buildings, flapping prayer flags and the mesmerising sound of monks chanting at twilight.
#### Sights
The White Dragon River ( 白龙江 ; Báilóng Jiāng) divides the town in two.
Kerti Gompa TIBETAN MONASTERY
( 格尔底寺 ; Géěrdǐ Sì; admission valid 3 days Y15) Rising up on the Sìchuān side of the river is this monastery – otherwise dubbed the Sìchuān Monastery – built in 1413, home to around 700 monks and composed of five temples and colleges. A short walk from the monastery stand small pavilions built over a brook whose waters power a round-the-clock revolving of prayer wheels housed inside (the _ne plus ultra_ of holiness)!
Serti Gompa TIBETAN MONASTERY
( 赛赤寺 ; Sàichì Sì; admission Y20) On the Gānsù side, higher up the hill, is this smaller monastery with its golden- and silver-roofed halls. The monastery dates from 1748 and is also simply referred to as Gānsù Monastery. Views are lovely from here. Like its cousin across the border in Sìchuān, the monastery is best visited in the morning (7am to 8am and 10.30am to 1pm) and late afternoon (6pm to 8pm).
#### Activities
Bountiful hiking opportunities radiate in almost every direction. Southwest of Kerti Gompa is Namo Gorge ( 纳摩大峡谷 ; Nàmó Dàxiágǔ), which makes for a superlative 90-minute (return) hike. The gorge contains several sacred grottoes, one dedicated to the Tibetan goddess Palden Lhamo, the other known as the Fairy Cave ( 仙女洞 ; Xiānnǚ Dòng), which gives the town its Tibetan name ( _lángmù_ meaning fairy). Cross rickety bridges flung over the gushing stream, trek past piles of mani stones and prayer flags and hike on into a splendid ravine. After about 30 minutes of clambering over rocks you reach a grassy plain surrounded by towering peaks.
Another popular trek is the hike along the White Dragon River to the river's source ( 白龙江源头 ; Báilóng Jiāng Yuántóu) where Chinese hikers go in search of _chóngcǎo_ ( 虫草 ), a coveted herb used in Chinese medicine.
A lovely walk heads out over the hills from Sertri Gompa to the small village of Jíkēhé Cūn ( 吉科合村 ); if you can ignore the mountainous backdrop, it's not unlike a jaunt across England's South Downs.
It's also possible to trek up Red Stone Mountain ( 红石崖 ; Hóngshí Yá) right next to the village.
Lángmùsì Tibetan Horse Trekking ( 667 1504; www.langmusi.net) , across from the Lángmùsì Bīnguǎn, runs guided horse treks from one to four days, overnighting at nomads' tents en route, with the option of climbing nearby Huágàishén Shān ( 华盖神山 ). Prices start from around Y180 per day.
Kelsang at the Lángmùsì Bīnguǎn can arrange guides (Y150 per day) for hikes up the gorge behind Kerti Gompa, and transport (Y100 to Y150) for a trip to some hot springs (admission Y5) outside town.
#### Festivals & Events
If you are in the area in late July, head out to Mǎqǔ ( 玛曲 ) to see the annual horse races . The dates change each year, so try contacting the Lángmùsì Bīnguǎn to find out when it is being held. Mǎqǔ is 67km west of Lángmùsì. Travellers cafes and hotels in Lángmùsì can arrange transport to the town.
#### Sleeping
Lángmùsì Hotel HOTEL $$$
( 667 1555; d Y666-699, tr Y700, discounts of up to 70%) With an over-the-top Tibetan-style lobby, this friendly four-storey place is the best in Lángmùsì, with very pleasant, clean and spacious standard doubles with bathrooms; the Tibetan-style deluxe rooms are virtually identical apart from carpets and ceiling pattern (but have showers). Excellent discounts. It's on the road south towards Kerti Gompa.
Lángmùsì Bīnguǎn HOTEL $
( 郎木寺宾馆 ; 667 1086; tibetanyakboy@yahoo.co.uk; dm Y30, tw with shower Y160-180, discounts of 30-50%) English-speaking staff here are very friendly and rooms with shower are fine, making this an OK place. If you prefer something more rustic, owner Kelsang can arrange for a homestay with a Tibetan family in a nearby village for Y70 per night.
Xiùfēng Bīnguǎn HOTEL $
( 秀峰宾馆 ; 667 1020; dm Y20, d Y100-120) Undergoing renovation and expansion at the time of writing, this pleasant place off the main street is run by a friendly Hui family and should have new doubles added by the time you read this.
Nomads Youth Hostel HOSTEL $
( 旅朋青年旅社 ; Lǚpéng Qīngnián Lǚshè; 667 1460; dm/d Y20/50) Popular with Chinese backpackers, this friendly place on the main street has scruffy and basic dorms, doubles with shared toilet, homely foyer and bar. Can arrange treks.
Sànà Bīnguǎn HOTEL $
( 萨娜宾馆 ; 667 1062; d Y60-160, tr per bed Y30) Another friendly place, accessed through the back of a shop on the main road.
#### Eating
Talo Restaurant RESTAURANT $
( 达老餐厅 ; Dálǎo Cāntīng; 825 5666) Decorated with yak skulls, prayer flags and _tangka,_ this friendly upstairs Tibetan restaurant has a great menu embracing pancakes (Y12), apple rings (Y20), a host of Tibetan dishes and other heart-warming food. Overlooking the main street, it's a great place for a beer. There's a smarter restaurant attached for more variety.
Several backpacker cafes offer similar menus, with big burgers, tasty pies and hot coffee; these include Lesha's Restaurant ( 667 1179) – on the main street – and Ali's Restaurant ( 667 1090) , just before the bridge on the way to Sertri Gompa. At the time of research, Lángmùsì Tibetan Horse Trekking was planning to open an internet-equipped restaurant-cafe across the road.
#### Information
There is nowhere to change money, so come with cash. At the time of writing there was no public internet access and the only internet cafe, on the other side of the road from the Lángmùsì Bīnguǎn, was shut; ask at Lángmùsì Tibetan Horse Trekking for the latest. The PSB ( 公安局 ; Gōngānjú) is just down from the Lángmùsì Hotel. You can burn photos onto CDs at Lángmùsì Tibetan Horse Trekking ( 9am-9pm) for Y10.
#### Getting There & Away
There's one daily bus to Zöigě (Ruò'ěrgài; Y22, one hour) at 7am and three daily buses to Hézuò (Y32.5, three hours), departing at 6.30am, 7am and noon. For Sōngpān you have to overnight in Zöigě or hire a car (Y800).
If you don't take a direct bus to Lángmùsì, you'll have to get off at the intersection 4km from the town, from where minivans ferry passengers into town for Y2.
## HEXI CORRIDOR
Bound by the Qílián Shān range to the south and the Mǎzōng (Horse's Mane) and Lóngshǒu (Dragon's Head) ranges to the north, the narrow strip of land that is Hexi Corridor ( 河西走廊 ; Héxī Zǒuláng), around which the province is formed, was once the sole western passage in and out of the Middle Kingdom.
### Wǔwēi 武威
0935 / POP 509,000
Wǔwēi stands at the strategic eastern end of the Hexi Corridor. It was from here, two millennia prior, that the emperors of China launched their expeditionary forces into the unknown west, eventually leading them to Jiāyùguān and beyond. Temples, tombs and traditional gates hint at Wǔwēi's Silk Road past, and the city is rapidly modernising around a glossy central square.
#### Sights
Léitái Sì TEMPLE
( 雷台寺 ; admission Y50; 8am-6pm) The pride and joy of the city, the bronze Flying Horse of Wǔwēi ( 飞马 ) was discovered here in 1969 and has since been adopted as the unofficial symbol of Gānsù. It was found in a secret tomb beneath this temple, built on top of steep earthen ramparts. While it's a thrill to explore a 2000-year-old tomb, there is precious little inside. The Flying Horse is now displayed in the Gānsù Provincial Museum ( Click here ). The site is located 1.2km north of Wénhuà Guǎngchǎng ( 文化广场 ; Culture Sq).
Confucius Temple CONFUCIAN TEMPLE
Offline map ( 文庙 ; Wénmiào; admission Y31; 7.30am-6pm) This Ming-era temple has quiet gardens and stele-filled pavilions. The most important stele features the extinct Xīxià language carved into one side and a Chinese translation on the other: a sort of Rosetta stone, the stele has allowed researchers to understand the once unintelligible Xīxià texts. The stele is now housed in a small museum ( 8.30am-6pm) across the street (shut for renovation at the time of writing); your ticket for the Confucius Temple allows you inside. To reach the temple, walk south from the main square to the reconstructed South Gate ( 南门 ), then turn left just before the gate and walk east for 650m to the temple.
Kumarajiva Pagoda BUDDHIST PAGODA
Located 400m north of Wénhuà Guǎngchǎng, this pagoda ( 罗什寺塔 ; Luóshísì Tǎ) is a brick structure originally dating to 488. Dedicated to the great translator of Buddhist sutras (whose tongue was buried beneath the pagoda), the pagoda was toppled during the great earthquake in 1927 and rebuilt. Pilgrims circumambulate the pagoda in clockwise fashion.
Ancient Bell Tower HISTORIC SITE
( 古钟楼 ; Gǔzhōng Lóu; admission Y10) This bell tower is pretty much all that survives of Dàyún Temple ( 大云寺古钟楼 ; Dàyúnsì Gǔzhōnglóu; admission Y5; 8am-6pm) , which was levelled by the great tremor of 1927. The flattened area around the temple looks like another earthquake has struck. From the square walk 250m north to the first intersection, then turn right (east) and walk 800m to the tower.
Hǎizàng Temple BUDDHIST TEMPLE
( 海藏寺 ; Hǎizàng Sì; admission Y10) A short trip on bus 5 (Y2) outside town, this temple is a fascinating active monastery. The Three Sages Hall (Sānshèng Diàn) contains a 'hermaphroditic Guanyin'; dating to the Ming dynasty, the venerably old Wúliàng Palace (Wúliàng Diàn) was once used to store sutras but now houses a reclining Buddha in a glass cabinet. An absorbing feature is the minute pavilion to the right of the Wuliang Palace containing a well whose 'magic waters' ( 神水 ; _shénshuǐ_ ) are connected by subterranean streams to a Holy Lake ( 圣湖 ; Shènghú) in the Potala Palace in Lhasa. Drinking the well's waters is said to cure myriad ailments.
#### Sleeping & Eating
Ziyunge Hotel HOTEL $$
( 紫云阁酒店 ; Zǐyúngé Jiǔdiàn; 225 3888; Mingqing Fanggu Wenhua Jie; 明清仿古文化街 ; s/d/tr Y198/280/218, discounts of 30%; ) Just east of South Gate, this great hotel has excellent, comfortable and spacious rooms with shower (and hairdryer) and new furnishings. You can often net a standard double for around Y120.
Yuánjì Làzhī Ròujiāmó SHǍNXĪ $
( 袁记腊汁肉夹馍 ; Mingqing Fanggu Wenhua Jie; 7.30am-9pm; meals Y12) Not far from the Ziyunge Hotel, this busy little restaurant serves some simply scrumptious _ròujiāmó_ (called the 'Chinese hamburger'; Y4) from Shǎnxī province and bowls of tasty hundun (Y3). Don't be put off by the plastic seats; the food is excellent.
#### Information
Bank of China ( 中国银行 ; Zhōngguó Yínháng) West end of the pedestrian shopping street ( 步行商业街 ; Bùxíng Shāngyè Jiē); can change money.
Internet cafe ( 网吧 ; Wǎngbā; per hr Y2; 24hr) West end of the pedestrian shopping street running west from Wénhuà Guǎngchǎng.
Public Security Bureau (PSB; 公安局 ; Gōng'ānjú) On Dong Dajie, east of Wénhuà Guǎngchǎng.
#### Getting There, Away & Around
###### Bus
From the west bus station ( 汽车西站 ), located 1.5km southwest of Cultural Sq, express buses run to:
Jiāyùguān Y86, seven hours, one daily (7.30pm)
Lánzhōu Y51, three hours, every 15 minutes (6am to 6pm)
Zhāngyè Y51, 3½ hours, hourly (7.50am to 5pm)
###### Train
Trains depart hourly to Zhāngyè (Y40). For Lánzhōu (Y45 to Y52) take the T296 express at 8.20am or the K592 at 8.20pm. Departing from Lánzhōu at 7.29am, the T9205 (Y49) is a handy two-tier train that stops in Wǔwēi; it departs Wǔwēi at 10.19am to continue to Zhāngyè (Y41, two hours) and Jiāyùguān.
The N857 and K591 are overnight trains to Dūnhuáng (Y118). The 7520 departs for Zhōngwèi (Y22) at 8.44am. A train ticket booking office ( 火车票代售点 ; Huǒchēpiào Dàishòudiǎn) is located at 26 Nanguan Xilu, west of the South Gate.
The station is located 3.5km south of Wénhuà Guǎngchǎng; the two are connected by buses 1 and 2 (Y1). Taxis start at Y3.
### Zhāngyè 张掖
0936 / POP 260,000
Colourful Zhāngyè, with its colossal Buddha, pagodas, traditional Chinese-style pedestrian streets and unique cliff temples at nearby Mǎtí Sì, makes for an absorbing Silk Road stopover. Marco Polo certainly enjoyed it – the great traveller stayed here for a year on his way to the court of Kublai Khan. Local authorities have honoured Polo's legacy by erecting a statue of the man; it stands near a quirky street lined with mock-Venetian architecture.
#### Sights
The sad remnants of Zhāngyè's earthen city walls can be seen on Beihuan Lu.
Great Buddha Temple BUDDHIST TEMPLE
( 大佛寺 ; Dàfó Sì; 821 9671; adult/student Y41/21; 8am-6pm) Originally dating to 1098 (Western Xia dynasty), this excellent temple contains an astonishing 35m-long sleeping Buddha – China's largest of this variety ( Click here ) – surrounded by mouldering clay arhats and Qing-dynasty murals. Take a good look at the main hall and the woodwork, including the doors – it's one of the few wooden structures from this era still standing in China. A colony of bats squeaks high up in its rafters along with flitting flocks of swallows. Until the 1960s, small children would clamber into the huge Buddha and play around inside his tummy. The stairs to the floor above are, sadly, inaccessible. Out the back is the impressive white earth stupa ( 土塔 ; _tǔ tǎ_ ) dating from the Ming dynasty, when this vast temple complex was called Hóngrén Temple ( 弘仁寺 ; Hóngrén Sì).
Wooden Pagoda BUDDHIST PAGODA
( 木塔 ; Mùtǎ; admission Y5; 7.30am-6.30pm) In the main square one block north of the Great Buddha Temple, this pagoda is a brick and wooden structure that was first built in AD 528. Note that this pagoda represents wood as the earth stupa represents earth in the Chinese theory of the five elements (wood, earth, water, fire and metal).
#### Sleeping & Eating
To eat, head 300m west of the drum tower and look for Mingqing Jie ( 明清街 ), an alley of faux-Qing architecture lined with dozens of clean, friendly restaurants.
Liángmào Bīnguǎn HOTEL $
( 粮贸宾馆 ; 825 2398; Dong Jie Shizi; 东街什字 ; dm Y18, s Y88, tw Y68-88, tr Y158, business d Y158; ) This seven-storey hotel has a wide range of clean, airy rooms strung out along curved corridors. It's 900m east of the drum tower.
Xīnyuán Bīnguǎn HOTEL $
( 馨园宾馆 ; 825 1766; Beishuiqiao Jie; 北水桥街 ; tw with shared shower Y90, s Y140, d Y120-140, discounts of 40%; ) This place has OK rooms and a good location in the western half of town near the Marco Polo statue, although the staff is rather slack.
#### Information
Several internet cafes can be found on Jīnmài Pedestrian St ( 金脉步行街 ; Jīnmài Bùxíng Jiē) just east of the drum tower.
Bank of China ( 中国银行 ; Zhōngguó Yínháng) At Dong Jie and 168 Xianfu Jie. Both branches have ATM and can change travellers cheques.
Shèngdá Internet Cafe ( 盛达网吧 ; Shèngdá Wǎngbā; Xijie; per hr Y2.50; 8am-midnight) East of junction between Mingqing Jie and Xijie.
#### Getting There & Around
###### Bus
The town has three bus stations, in the south, east and west. The west bus station (xī zhàn; 821 0597) has the most frequent departures:
Dūnhuáng Y108, 12 hours, two in the morning (7.50am and 11.30am), then two sleepers
Golmud 5.30pm
Jiāyùguān Y50.50, 3½ hours, hourly (9.30am to 5.10pm)
Lánzhōu Y98.50, eight hours, hourly (7am to 1.30pm, sleepers after that)
Wǔwēi Y51, 3½ hours, every 30 minutes (7.20am to 5pm)
Xīníng Y60.50, seven hours, two daily (7am and 6pm)
###### Train
Departing from Lánzhōu at 7.29am, the two-tier T9205 arrives in Zhāngyè at 12.29pm before proceeding to Jiāyùguān; another fast train departs for Jiāyùguān at 8pm. While arriving by train is no problem, departures are limited. The train ticket office (12 Oushi Jie; 欧式街 12 号 ; 8am-4pm) near the Marco Polo statue can book sleepers on the N857 to Dūnhuáng (hard sleeper Y160, 6¼ hours, 12.20am) and train N852 to Lánzhōu (hard sleeper Y94, 11 hours, 11.18pm). From Lánzhōu it's best to take the train as only night buses run.
A taxi to/from the train station is Y10, or take bus 1 (Y1). The station is 7km northeast of the city centre. Buses 4 and 13 run past the west bus station. Taxis start at Y4.
### Mǎtí Sì 马蹄寺
The temples at Mǎtí Sì (Horse Hoof Monastery; admission Y45) , built miraculously into the sandstone cliff (between the 5th and 14th centuries), are reached via twisting staircases, balconies, narrow passages and platforms that will leave your head spinning. Tibetan monks administer the place and locals will offer you horses for riding in the surrounding hills.
There are several good day hikes around here, including the five-hour loop through pine forest and talus fields to the Línsōng Waterfall ( 临松瀑布 ; Línsōng Pùbù) and back down past 'Sword Split Stone' ( 剑劈石 ; Jiànpīshí). For unrivalled panoramas, take the elevatorlike ascent of the ridge behind the white chörten at Sānshísāntiān Shíkū ( 三十三天石窟 ).
The Wòlóng Shānzhuāng ( 卧龙山庄 ; dm/tw Y20/100) at Mǎtí Sì is a good place to stay. If you're adequately prepared for camping, some overnight trips are also possible.
Buses leave every 30 minutes from Zhāngyè's south bus station for the crossroads village of Mǎtí Hé ( 马蹄河 , Y11, 1½ hours, 6.40am to 5.40pm), from where you can catch a minibus or taxi (Y20) for the final 7km or so. Direct buses to Mǎtí Sì depart at 3.40pm, and you might find a direct bus on weekend mornings. The last bus back from Mǎtí Hé leaves at 4.30pm.
### Jiāyùguān 嘉峪关
0937 / POP 170,000
You approach Jiāyùguān through the forbidding lunar landscape of north Gānsù. It's a fitting setting, as Jiāyùguān marks the symbolic end of the Great Wall, the western gateway of China proper and, for imperial Chinese, the beginning of the back of beyond. One of the defining points of the Silk Road, a Ming-dynasty fort was erected here in 1372 and Jiāyùguān came to be colloquially known as the 'mouth' of China, while the narrow Hexi Corridor, leading back towards the _nèidì_ (inner lands), was dubbed the 'throat'.
You'll need plenty of imagination to conjure up visions of the Silk Road, as modern Jiāyùguān is a city of straight roads and identikit blocks, almost as if airlifted into position from North Korea. But the Jiāyùguān Fort is an essential part of Silk Road lore and most certainly worth a visit.
Jiāyùguān
Sleeping
1 Jiāyùguān BīnguānA1
2 Jīnyè Bīnguǎn A3
3 Liángshijú Zhāodàisuǒ B3
4 Yíngbīn Hotel A3
Eating
5AìlǐA1
6 Fùqiáng Market EntranceA1
7 Jìngtiě Xiǎochīchéng B3
8 Liuyuan Restaurant A3
Information
9 People's No 1 HospitalB3
Transport
10Bicycle HireA1
11Bus StationA3
12 Jiāyùguān Airport Ticket Office A2
13 Train Booking Office B3
#### Sleeping
It's possible to spend the night at the fort at the Taihe Country Villa ( 639 6622) .
Yíngbīn Hotel HOTEL $
Offline map ( 迎宾宾馆 ; Yíngbīn Bīnguǎn; 620 1751; tw/tr without shower Y60/70, s/d/tw Y100/100/120) Bright inside with fine rooms (although the bathrooms look like they belong in an asylum), this place is good value and well located for restaurants and transport.
Jiāyùguān Bīnguǎn HOTEL $$$
Offline map ( 嘉峪关宾馆 ; 620 1588; 1 Xinhua Beilu; 新华北路 1 号 ; s Y668-780, d Y768, ste Y1880, discounts of 30-40%; ) Rooms are pleasant and reasonably modern with bathroom and computer; there are also a sauna, small gym, ticket agent and good service.
Liángshijú Zhāodàisuǒ GUESTHOUSE $
Offline map ( 粮食局招待所 ; 622 6293; 2nd fl, 24 Xinhua Zhonglu; s/tw without shower Y40/58, tw Y68) Just by the hospital, this clean and well-run guesthouse is central and good value.
Jīnyè Bīnguǎn HOTEL $
Offline map ( 金叶宾馆 ; 620 1333; 12 Lanxin Xilu; 兰新西路 12 号 ; d Y100-180, tr Y120, discounts of 40%; ) The ensuite rooms are good value at this clean and quiet hotel with a useful location by the bus station.
#### Eating
For cake, croissant and coffee, try branches of the bakery Aili.
Āmílái Niúyángròu Fěntāngguǎn LAMB NOODLES $
( 阿迷来牛羊肉粉汤馆 ; Shengli Nanlu; 胜利南路 ; 7am-2.30pm & 4-9pm) Excellent and filling bowls of _jiāgōng yángròu fěntāng_ ( 加工羊肉粉汤 ; lamb and vermicelli soup; Y14) – chuck in a _bǐng_ ( 饼 ; flat bread; Y0.50) and you've a meal. There's no English sign, but hunt out the red and green sign around 200m south of the intersection with Hekou Xilu.
Liuyuan Restaurant SÌCHUĀN $
Offline map ( 苑中苑酒店 ; Yuànzhōngyuàn Jiǔdiàn; Lanxin Xilu; dishes from Y15; ) Directly across from the bus station is this classy Sìchuān restaurant.
Fùqiáng Market MARKET $
Offline map For a fast, hot meal, try the food stalls at this market ( 富强市场 ; Fùqiáng Shìchǎng), north of the traffic circle.
Jìngtiě Xiǎochīchéng MARKET $
Offline map ( 镜铁小吃城 ; Jingtie Market; 10am-10pm) Also try this busy place, off Xinhua Zhonglu, where you can load up on lamb kebabs (Y10), lamb ribs (Y10), beer (Y3), _ròujiāmó_ , wonton soup, dumplings, roast duck and more.
#### Information
Bank of China ( 中国银行 ; Zhōngguó Yínháng; Xinhua Zhonglu; 9.30am-5.30pm Mon-Fri, 10am-4pm Sat & Sun) Has an ATM and can change money. It's south of Lanxin Xilu intersection.
China Post ( 中国邮政 ; Zhōngguó Yóuzhèng; cnr Xinhua Zhonglu & Xiongguan Donglu; 8.30am-7pm Mon-Fri, 10am-6pm Sat & Sun) At the traffic circle in the centre of town.
Jiāxiáng Internet Cafe ( 嘉祥网吧 ; Jiāxiáng Wǎngbā: Xiongguan Donglu; per hr Y4; 24hr) Pricey.
People's No 1 Hospital Offline map ( 第一人民医院 ; Dìyī Rénmín Yīyuàn; Xinhua Zhonglu)
Public Security Bureau (PSB; 公安局 ; Gōng'ānjú; 631 6927, ext 2039; 312 Guodao; 8.30am-noon & 2.30-6pm Mon-Fri) At the southern edge of town, diagonally opposite the stadium. Visa extensions available.
Xīnjùdiǎn Internet Cafe ( 新聚典网络 ; Xīnjùdiǎn Wǎngluò; per hr Y2; 24hr)
#### Getting There & Away
###### Air
Book air tickets at the Jiāyùguān Airport Ticket Office Offline map ( 嘉峪关机场售票处 ; Jiāyùguān Jīchǎng Shòupiàochù; Minhang Dasha, Xinhua Zhonglu; 8am-7.10pm) . Jiāyùguān's airport is 13km from town, offering flights to Běijīng (Y1880), Lánzhōu (Y1080), Shànghǎi (Y2190) and Xī'ān (Y1210).
###### Bus
Jiāyùguān's bus station ( 汽车站 ; Qìchēzhàn) is by a busy four-way junction on Lanxin Xilu, next to the main budget hotels. Doubling as a billiards hall, the station has buses to:
Dūnhuáng Y70, five hours, four daily (9am to 2.30pm)
Lánzhōu Y150.50, 12 hours, three daily (2.30pm, 4.30pm and 6.30pm), all sleepers
Wǔwēi Y96, seven hours, five daily (2.30pm to 8.30pm)
Zhāngyè Y44 to Y50.50, 3½ hours, every 30 minutes (7am to 3pm)
###### Train
Departing from Lánzhōu at 7.29am, the two-tier T9205 arrives in Jiāyùguān at 2.43pm. From Jiāyùguān there are daytime trains to:
Dūnhuáng Y28, four hours
Zhāngyè Y22, three hours
There are a couple of sleeper trains to:
Lánzhōu Y180, nine hours
Ürümqi Y220, 15 hours
Purchase tickets at the train booking office ( 火车站售票处 ; huǒchēzhàn shòupiàochù; 28 Xinhua Zhonglu; 8am-4.30pm Mon-Fri, to 4pm Sat & Sun) near the hospital, next to the China Construction Bank.
Jiāyùguān's Luhua train station is 5km south of the town centre. Bus 1 runs here from Xinhua Zhonglu (Y1). A taxi costs Y10.
#### Getting Around
Bikes are good for reaching some surrounding attractions. The gatekeeper at the Jiǔgāng Bīnguǎn ( 出租自行车 ; Chūzū Zìxíngchē) hires them for Y20 per day (Y400 deposit).
One airport bus (Y10) runs daily at 11am from the Jiāyùguān Airport Ticket Office to the airport; a taxi will cost around Y40.
Bus 2 (Y1) runs from the train station to the bus station.
### Around Jiāyùguān
A taxi to the Wei Jin Tombs, Jiāyùguān Fort and the Overhanging Great Wall should cost you no more than Y100 for a half-day; if you just go to the fort and Overhanging Great Wall, figure on Y50.
##### JIĀYÙGUĀN FORT 嘉峪关城楼
One of the classic images of western China, the Jiāyùguān Fort (Jiāyùguān Chénglóu; May-Oct/Nov-Apr Y100/80; 8.30am-7.30pm) guards the pass between the snowcapped Qílián Shān peaks and Hēi Shān (Black Mountains) of the Mǎzōng Shān range. The admission ticket also grants you access to the First Beacon Platform of the Great Wall and the Overhanging Great Wall.
Built in 1372, the fort was christened the 'Impregnable Defile Under Heaven'. Although the Chinese often controlled territory far beyond the Jiāyùguān area, this was the last major stronghold of imperial China – the end of the 'civilised world', beyond which lay only desert demons and the barbarian armies of Central Asia.
Towards the eastern end of the fort is the Gate of Enlightenment ( 光化楼 ; Guānghuá Lóu) and in the west is the Gate of Conciliation ( 柔远楼 ; Róuyuǎn Lóu), from where exiled poets, ministers, criminals and soldiers would have ridden off into oblivion. Each gate dates from 1506 and has 17m-high towers with upturned flying eaves and double gates that would have been used to trap invading armies. On the inside are horse lanes leading up to the top of the inner wall. On the west-facing side of the Gate of Enlightenment are the shadowy remains of slogans praising Chairman Mao, blasted by the desert winds. A further prolix quote from Mao stands out in yellow paint on the south wall of Wenchang Pavilion ( 文昌阁 ; Wénchāng Gé). Outside the fort, camel rides can be had for Y10.
Admission also includes an excellent Jiāyùguān Museum of the Great Wall ( 8.30am-7.30pm) , with photos, artefacts, maps and Silk Road exhibits.
Only 5km west of town, it's possible to cycle here in about half an hour. A one-way taxi trip to the fort costs about Y10.
##### OVERHANGING GREAT WALL 悬壁长城
Running north from Jiāyùguān, this section of wall (Xuánbì Chángchéng; adult/student Y21/11; 8.30am-dusk) is believed to have been first constructed in 1539, though this reconstruction dates from 1987. It's quite an energetic hike up to excellent views of the desert and the glittering snow-capped peaks in the distance. A smaller section of wall (admission Y25) is next door, but this one is included in the Jiāyùguān Fort ticket. Both sections of wall are 9km from the fort. A taxi is around Y50 return from town.
##### FIRST BEACON PLATFORM OF THE GREAT WALL 长城第一墩
Atop a 82m-high cliff overlooking the Taolai River, the remains of this beacon platform (Chángchéng Dìyī Dūn; admission Y21; 9am-5pm) are not much to look at (they resemble a shaped pile of dirt), but the views over the river in their dramatic gorge are impressive and you can walk alongside attached vestiges of the Great Wall. Descend to the subterranean viewing platform above the river or sweep across it on a pulley for Y31. Admission is included in the Jiāyùguān Fort ticket. A taxi from town is around Y35 return.
##### WEI JIN TOMBS 新城魏晋墓
These tombs (Xīnchéng Wèijìnmù; admission Y35; sunrise-sunset) date from approximately AD 220–420 (the Wei and Western Jin periods) and contain extraordinarily fresh brick wall paintings depicting scenes from everyday life, from making tea to picking mulberries for silk production. There are literally thousands of tombs in the desert 20km east of Jiāyùguān, but only one is currently open to visitors, that of a husband and wife. The small museum is also worth a look. You can preview some of the painted bricks at the Jiāyùguān Fort museum. A taxi will cost around Y50.
##### JULY 1ST GLACIER 七一冰川
About 90km southwest of Jiāyùguān, the July 1st Glacier (Qīyī Bīngchuān; admission Y51) sits high in the Qílián Shān range at 4300m. It is reached via the train to the iron-ore town of Jìngtiěshān ( 镜铁山 ; Y10), departing from Jiāyùguān's Luhua train station at 8am. It's a scenic three-hour train trip to Jìngtiěshān, where you can hire a taxi to the glacier (return Y120, 20km). Hikers can walk a 5km trail alongside the glacier. Icy winter weather grinds transport to a halt from November to March. In summer it's a great place to come to escape the heat of the desert below, but if you come in the spring or autumn it can be a cold and forbidding place – the glacier fills the rocky valley and there is little life up here. Global warming is having an effect on the glacier, which has retreated 50m in recent years.
You could theoretically do this in one day, but it's better to stay the night in Jìngtiěshān, where there is a cheap and basic hostel _(zhāodàisuǒ)_ . This will leave you with enough time the next morning to hire a taxi up to Tiān'é Hú (return Y50) and the Tibetan village of Qíqīng . Return trains depart around 1.46pm from Jìngtiěshān. A return taxi to the glacier from Jiāyùguān costs around Y400 (nine hours).
### Dūnhuáng 敦煌
0937 / POP 156,000
The fertile Dūnhuáng oasis has long been a refuge for weary Silk Road travellers. Most visitors only stayed long enough to swap a camel and have a feed; others settled down and built the forts, towers and magnificent cave temples that are now scattered over the surrounding area. These sites, along with some dwarfing sand dunes and desertscapes, make Dūnhuáng a magnificent place, despite its remoteness. The low-rise city itself is clean and well-endowed with budget hotels, travellers' cafes and souvenir shops. Look out for the vast Běidàqiáo wind farm on the approach to Dūnhuáng.
#### Sights
Dūnhuáng Museum MUSEUM
Offline map ( 敦煌博物馆 ; Dūnhuáng Bówùguǎn; 882 2981; Yangguan Donglu; 8am-6.30pm Apr-Oct) The Dūnhuáng Museum is largely unchanged since opening in 1984; there's little here you can't see at the Mògāo Caves or the Jade Gate Pass museum.
Dūnhuáng
Sights
1 Dūnhuáng Museum B1
Sleeping
2 Dūnhuáng Legend Hotel B1
3 Fēitiān Bīnguǎn B2
4 Gōngyì Měishù Zhāodàisuǒ A1
5 Grand Soluxe Hotel Dūnhuáng A1
Eating
6 Bǎilèjī B1
7 Charley Johng's Café B2
John's Information Cafe (see 3)
8 Làzhī Ròujiāmó A2
9 Night Market B1
10 Oasis B2
11 Shirley's Café A2
Zhèngzōng Lánzhōu Niúròumiàn (see 7)
Entertainment
12 Dūnhuáng Theatre B1
Information
Fēitiān Travel Service(see 3)
13 Train Booking Office A2
Transport
14 Air Ticket Office B1
15 CAACB1
16 Long-Distance Bus Station B2
17Minibus StandA2
18Minibuses to NánhúA1
#### Sleeping
Competition among Dūnhuáng's hotels is fierce, and you should get significant discounts (50% or more) outside of summer. Unless stated otherwise, the following are open year-round. At the time of writing, Charley Johng's Cafe was about to open its own hotel near the mosque; dorms were to be in the Y35 to Y40 price range, with doubles at around Y150. Ask at the cafe.
Dune Guesthouse GUESTHOUSE $
( 敦煌月泉山庄 ; Dūnhuáng Yuèquán Shānzhuāng; 388 2411; dm Y30, tents Y40 , d Y100, huts Y100-250) This excellent chilled-out backpacker retreat is right by Singing Sands Mountain (Click here ); it's run by the folks at Charley Johng's Cafe, so make enquiries there first. Cabins are out the back among the fruit trees. Tents and sleeping bags (Y20) are also for rent; sunhats and parasols are free. From the minibus 3 terminus walk north a short way, take the first turning left on the other side of the road past the vines and follow the signs.
Silk Road Dūnhuáng Hotel HOTEL $$
( 敦煌山庄 ; Dūnhuáng Shānzhuāng; 888 2088; www.dunhuangresort.com; Dunyue Lu; 敦月路 ; dm Y80, d Y350-1200, discounts of 20%; ) Around 2km from Singing Sands Mountain, this four-star resort-style outfit is tastefully designed with Central Asian rugs, a cool stone floor and Chinese antiques. Four-bed dorms are in the student building way round the back, and the cheaper doubles (with bathrooms) are in the 'Professional Quarters'; both come with views of the dunes. Pricier accommodation is in the main building; there are also courtyard villa suites. A taxi from town costs Y10, or take minibus 3 (Y1).
Dūnhuáng Legend Hotel HOTEL $$$
Offline map ( 敦煌飞天大酒店 ; Dūnhuáng Fēitiān Dàjiǔdiàn; 8885 3999; www.dhlegendhotel.com; 2 Mingshan Lu; 鸣山路 2 号 ; d Y698-888, discounts of 40%; ) Rooms at this four-star Chinese-oriented hotel are well furnished and good value with discount, but standard doubles only come with shower. No Western breakfasts.
Grand Soluxe Hotel Dūnhuáng HOTEL $$$
Offline map ( 敦煌阳光沙州大酒店 ; Dūnhuáng Yángguāng Shāzhōu Dàjiǔdiàn; 886 2888; 31 Yangguan Zhonglu; 阳关中路 31 号 ; tw & d Y860, ste Y1600, discounts of 40%; ) Opened in 2008, this pleasant hotel has comfortable and elegant rooms decorated with Chinese motifs and looking out over the river in a striking and modern building. Broadband included.
Fēitiān Bīnguǎn HOTEL $$
Offline map ( 飞天宾馆 ; 882 2337; 22 Mingshan Lu; 鸣山路 22 号 ; dm Y40, s/d/tr/ste Y320/320/388/788, discounts of 50%; ) This longstanding two-star hotel has a good location and decent rooms with dark wood furnishings. Hot water only from 7am to 10am and evenings. It's closed in winter.
Gōngyì Měishù Zhāodàisuǒ GUESTHOUSE $
Offline map ( 工艺美术招待所 ; 884 0919; 14 Yangguan Zhonglu; 阳关中路 14 号 ; d without shower Y40) On 3rd floor in courtyard opposite China Construction Bank off Yangguan Zhonglu. Friendly place with simple but cheap doubles.
#### Eating & Drinking
Several Western travellers' cafes can be found in town with dishes in the Y10 to Y20 mark. In addition to providing internet access and bike hire, these are good spots to exchange information with other travellers.
Oasis CAFE $
Offline map ( 150 0937 6021; Fanggu Shangye Yitiao Jie; 3pm-11pm Tue-Sun) Surely the best milk shakes (Y12; blueberry, peach, kiwifruit and more) in northwest China and some of the finest coffee too, including the endless coffee (Y18), perfect for an everlasting caffeine rush. There're good smoothies (Y10) as well at this relaxing, chilled-out spot run by an Oklahoman. Pristine loo too.
Night Market STREET MARKET $$
Offline map ( 夜市 ; Yèshì; till 2am) Lively spot off Yangguan Donglu with singing, music bands and roast lamb by the platter (Y40 per _jīn_ ). There are loads of Sìchuān, Korean noodles, claypot, barbecue and Lánzhōu noodles outfits here, so just take your pick. Look out for cooling cups of _xìngpíshuǐ_ ( 杏皮水 ; Y5, apricot juice).
Làzhī Ròujiāmó RÒUJIĀMÓ $
Offline map ( 腊汁肉夹馍 ; Mingshan Lu; 10am-10pm) The plastic flowers and tacky furniture won't win any awards, but this place does some very tasty _ròujiāmó_ ( 肉夹馍 ; Y5 to Y6) – the famous 'Chinese hamburger' from Shaanxi province.
Zhèngzōng Lánzhōu Niúròumiàn NOODLES $
Offline map ( 正宗兰州牛肉面 ; Mingshan Lu; meals Y15; 7am-10pm) One of several places you can hoover up a bowl of tasty and filling _hóngshāo niúròumiàn_ ( 红烧牛肉面 ; noodles with braised beef; Y12); it's a short walk north of the Fēitiān Bīnguǎn.
Zhāixīng Gé BAR
( 摘星阁 ; Silk Road Dunhuang Hotel; Dunyue Lu; 6.30am-2pm & 4.30pm-midnight) Tremendous spot for a rooftop sundowner gazing out over the golden sand dunes; although at Y30 for a small bottle of beer, it may be worth tanking up first at the far, far cheaper (but viewless) Silk Road Alehouse ( 丝路酒坊 ) bar outside.
Charley Johng's Cafe CAFE $
Offline map ( 查理约翰咖啡馆 ; Chálǐ Yuēhàn Kāfēitīng; 388 2411; dhzhzh@public.lz.gs.cn; 21 Mingshan Lu) Western snacks and dishes.
John's Information Cafe CAFE $
Offline map ( 约翰旅游信息咖啡厅 ; Yuēhàn Lǚyóu Xìnxī Kāfēitīng; 882 7000; johncafe@hotmail.com; Fēitiān Bīnguǎn, 22 Mingshan Lu) Al fresco seating, Western dishes, English-speaking staff.
Shirley's Cafe CAFE $
Offline map ( 谢里斯咖啡馆 ; Xièlǐsī Kāfēiguǎn) Simple cafe with Western dishes.
Bǎilèjī FAST FOOD $
Offline map ( 百乐基 ; Shazhou Beilu; 10am-11pm) Fast food.
#### Entertainment
_Dunhuang Goddess_ ( 敦煌神女 ; Dūnhuáng Shénnǚ; tickets Y180; 8.30pm) is an 80- minute acrobatic dramatisation of stories on the walls of the Mògāo Caves. It's held at the Dūnhuáng Theatre Offline map ( 敦煌大剧院 ; Dūnhuáng Dàjùyuàn); English subtitles are provided.
#### Information
Ask at any of the Western cafes in town for tourist info; they can also help with tours from camel rides to overnight camping excursions. Internet access at Shirley's Cafe is Y6 per hour.
Bank of China ( 中国银行 ; Zhōngguó Yínháng; Yangguan Zhonglu; 8am-noon & 3-6.30pm) Has an ATM and changes travellers cheques.
China Post ( 中国邮政 ; Zhōngguó Yóuzhèng; cnr Yangguan Zhonglu & Shazhou Beilu; 8am-7pm) Located in the China Telecom building on the main traffic circle.
Fēitiān Travel Service Offline map ( 飞天旅行社 ; Fēitiān Lǚxíngshè; 882 2726, ext 8619; Fēitiān Bīnguǎn, 22 Mingshan Lu) Can arrange buses to Mògāo, local tours and car hire.
Liányǒu Wǎngbā ( 连友网吧 ; cnr Mingshan Lu & Xinjiang Lu; per hr Y4; 8am-midnight) Internet access.
Public Security Bureau (PSB; 公安局 ; Gōng'ānjú; 886 2071; Yangguan Zhonglu; 8am-noon & 3-6.30pm Mon-Fri) Two days needed for visa extension.
#### Getting There & Away
###### Air
Apart from November to March, when there are only flights to/from Lánzhōu and Xī'ān, there are regular flights to/from Běijīng (Y1880), Lánzhōu (Y1150), Shànghǎi (Y2550), Ürümqi (Y710) and Xī'ān (Y1680).
Seats can be booked at the Civil Aviation Administration of China Offline map (CAAC; 民航售票处 ; Zhōngguó Mínháng; 882 2389; 12 Yangguan Donglu; 8am-noon & 2-8pm) or at the air ticket office Offline map ( 883 0008) in the lobby of the Yóuzhèng Bīnguǎn ( 邮政宾馆 ), west of China Post.
###### Bus
Arriving in Dūnhuáng you may be dropped off at a station just south of Yǒuhǎo Bīnguǎn. The bus to Ürümqi may stop in Turpan (Y150); otherwise, you'll need to take a bus to Hāmì (Y70, 8am and 2pm) from the east bus station on Sanwei Lu and change; buses to Liǔyuán ( 柳园 ; Y20, eight per day 8am to 6.30pm) also go from here. Dūnhuáng's main long-distance bus station ( 长途汽车站 ; Zhángtú Qìchēzhàn; 885 3746) has buses to:
Golmud Y90, nine hours, two daily (9am and 7.30pm)
Jiāyùguān Y60, five hours, two daily (8.30am and 9.30am), plus a sleeper for Y80 at 10.30am
Lánzhōu Y214, 17 hours, three daily (8am, 10.30am and 2pm), all sleepers
Urumqi Y185, 14 hours, one daily (6pm). Sleeper
Wǔwēi Y160, three daily (8am, 10.30am and 2pm), all sleepers
Zhāngyè Y120, three daily (8am, 10.30am and 2pm), all sleepers
###### Train
For Lánzhōu (Y268, 14 hours), take the K592 departing at 9.39am or the N858 departing at 9.25pm. For Ürümqi (Y249, 14 hours) take train T216 departing at 8.16pm. The same train also stops in Turpan (Y180, 12 hours). For Běijīng West, you'll have to take the bus to Liǔyuán first.
The station is 10km east of town. You can purchase tickets at the train booking office Offline map ( 铁路售票处 ; tiělù shòupiàochù; 595 9592; 31 Mingshan Lu; 8am-4pm summer, to 3.30pm winter) , south of Ningsai Lu, for a commission of Y5.
#### Getting Around
You can hire bikes from the travellers cafes for Y1 per hour. Getting to some of the outlying sights by bike is possible, but hard work at the height of summer.
To charter a ride for the sights around town, the minibus stand ( 小公共汽车站 ; Xiǎogōnggòng Qìchēzhàn) across from the Jiàrì Dàjiǔdiàn on Mingshan Lu is one place to start negotiations.
Dūnhuáng's airport is 13km east of town; taxis cost Y20. The train station is on the same road as the airport. Taxis start at Y5.
### Around Dūnhuáng
Most people visit the Mògāo Caves in the morning, followed by the Míngshā Shān sand dunes in the late afternoon.
##### MÒGĀO CAVES 莫高窟
The Mògāo Caves (Mògāo Kū) are, simply put, one of the greatest repositories of Buddhist art in the world. At its peak, the site housed 18 monasteries, over 1400 monks and nuns, and countless artists, translators and calligraphers. Wealthy traders and important officials were the primary donors responsible for creating new caves, as caravans made the long detour past Mògāo to pray or give thanks for a safe journey through the treacherous wastelands to the west. The traditional date ascribed to the founding of the first cave is AD 366.
The caves fell into disuse after the collapse of the Yuan dynasty and were largely forgotten until the early 20th century, when they were 'rediscovered' by a string of foreign explorers ( Click here ).
Entrance to the caves ( 886 9060; low/high season Y80/160; 8.30am-6pm May-Oct, 9am-5.30pm Nov-Apr, tickets sold till 1hr before closing) is strictly controlled – it's impossible to visit them on your own. The general admission ticket grants you a two-hour tour of 10 caves, including the infamous Library Cave (No 17; see the boxed text, Click here ) and a related exhibit containing rare fragments of manuscripts in classical Uighur and Manichean. Excellent English-speaking guides (Y20) are always available, and you can generally arrange tours in many other languages as well.
Of the 492 caves, 20 'open' caves are rotated fairly regularly, so recommendations are useless, but tours always include the two big Buddhas , 34.5m and 26m tall respectively. It's also possible to visit 12 of the more unusual caves for an additional fee; prices range from Y100 (No 217, early Tang) to Y500 (No 465, tantric art). Note that in some of the caves later frescoes may cover earlier wall paintings.
A torch (flashlight) is imperative – those used by the guides are weak, so bring your own if possible. Photography is strictly prohibited everywhere within the fenced-off caves area. Note that if it's raining, snowing or sand storming, the caves will be closed.
After the tour it's well worth visiting the Dūnhuáng Research Centre , where eight more caves, each representative of a different period, have been flawlessly reproduced, along with selected murals.
If you have a special interest in the site, check out the International Dūnhuáng Project (http://idp.bl.uk) , an online database of digitalised manuscripts from the Library Cave at Mògāo.
### SILK ROAD RAIDERS
In 1900, the self-appointed guardian of the Mògāo Caves, Wang Yuanlu, discovered a hidden library filled with tens of thousands of immaculately preserved manuscripts and paintings, dating as far back as AD 406.
It's hard to describe the exact magnitude of the discovery, but stuffed into the tiny room were texts in rare Central Asian languages, military reports, music scores, medical prescriptions, Confucian and Taoist classics, and Buddhist sutras copied by some of the greatest names in Chinese calligraphy – not to mention the oldest printed book in existence, the _Diamond Sutra_ (AD 868). In short, it was an incalculable amount of original source material regarding Chinese, Central Asian and Buddhist history.
Word of the discovery quickly spread and Wang Yuanlu, suddenly the most popular bloke in town, was courted by rival archaeologists Auriel Stein and Paul Pelliot, among others. Following much pressure to sell the cache, Wang Yuanlu finally relented and parted with an enormous horde of treasure. During his watch close to 20,000 of the cave's priceless manuscripts were whisked off to Europe for the paltry sum of UK£220.
Still today, Chinese intellectuals bitter at the sacking of the caves deride Stein, Pelliot and other 'foreign devils' for making off with a national treasure. Defenders of the explorers point out that had the items been left alone they may have been lost during the ensuing civil war or the Cultural Revolution.
###### Sights
Northern Wei, Western Wei & Northern Zhou Caves BUDDHIST CAVES
The earliest caves are distinctly Indian in style and iconography. All contain a central pillar, representing a stupa (symbolically containing the ashes of the Buddha), which the devout would circle in prayer. Paint was derived from malachite (green), cinnabar (red) and lapis lazuli (blue), expensive minerals imported from Central Asia.
The art of this period is characterised by its attempt to depict the spirituality of those who had transcended the material world through their asceticism. The Wei statues are slim, ethereal figures with finely chiselled features and comparatively large heads. The Northern Zhou figures have ghostly white eyes. Don't be fooled by the thick, black modernist strokes – it's the oxidisation of lead in the paint, not some forerunner of Picasso.
Sui Caves BUDDHIST CAVES
The Sui dynasty (AD 581–618) began when a general of Chinese or mixed Chinese- Tuoba origin usurped the throne of the Northern Zhou dynasty and reunited northern and southern China for the first time in 360 years.
The Sui dynasty was short-lived and very much a transition between the Wei and Tang periods. This can be seen in the Sui caves: the graceful Indian curves in the Buddha and Bodhisattva figures start to give way to the more rigid style of Chinese sculpture.
Tang Caves BUDDHIST CAVES
During the Tang dynasty (AD 618–907), China pushed its borders westward as far as Lake Balkash in today's Kazakhstan. Trade expanded and foreign merchants and people of diverse religions streamed into Cháng'ān, the Tang capital.
This was Mògāo's high point. Painting and sculpture techniques became much more refined, and some important aesthetic developments, notably the sex change (from male to female) of Guanyin and the flying apsaras _,_ took place. The beautiful murals depicting the Buddhist Western Paradise offer rare insights into the court life, music, dress and architecture of Tang China.
Some 230 caves were carved during the Tang dynasty, including two impressive grottoes containing enormous, seated Buddha figures. Originally open to the elements, the statue of Maitreya in cave 96 (believed to represent Empress Wu Zetian, who used Buddhism to consolidate her power) is a towering 34.5m tall, making it the world's third-largest Buddha. The Buddhas were carved from the top down using scaffolding, the anchor holes of which are still visible.
Post-Tang Caves BUDDHIST CAVES
Following the Tang dynasty, the economy around Dūnhuáng went into decline, and the luxury and vigour typical of Tang painting began to be replaced by simpler drawing techniques and flatter figures. The mysterious Western Xia kingdom, which controlled most of Gānsù from 983 to 1227, made a number of additions to the caves at Mògāo and began to introduce Tibetan influences.
###### Getting There & Away
The Mògāo Caves are 25km (30 minutes) southeast from Dūnhuáng. A green bus (one way Y8) starts waiting at around 8am and leaves at 8.30am from the intersection across from the Dūnhuáng Hotel; it returns at noon, which isn't really enough time at the caves. A return taxi costs from Y100 to Y150 for a day.
Some people ride out to the caves on a bicycle, but be warned that half the ride is through total desert – hot work in summer.
##### WESTERN THOUSAND BUDDHA CAVES 西千佛洞
These little-visited caves (Xī Qiānfó Dòng; admission Y40; 7am-5.30pm) , 35km west of Dūnhuáng, range from the Northern Wei to the Tang dynasties. There are 16 caves hidden in the cliff face of the Dǎng Hé gorge, of which six are open to the public. The art may not compare to Mògāo, but the lack of crowds is more restful – although some (eg cave 15) may require an additional fee. Afterwards, wander off on a walk through the desert canyon.
The caves are best reached by taxi (Y60 return) or minibus. Alternatively, catch a bus to Nánhú ( 南湖 ; 40 minutes) from the intersection of Heshui Lu and Yangguan Zhonglu in Dūnhuáng, and ask the driver to drop you off at the turn-off to the caves, from where it's a 10-minute walk across the desert.
##### SINGING SANDS MOUNTAIN & CRESCENT MOON LAKE 鸣沙山、月牙泉
Six kilometres south of Dūnhuáng at Singing Sands Mountain (Míngshā Shān; low/high season Y80/120; 6am-10pm) , the desert meets the oasis in most spectacular fashion. From here it's easy to see how Dūnhuáng gained its moniker 'Shāzhōu' (Town of Sand). The climb to the top of the dunes – the highest peak swells to 1715m – is sweaty work, but the view across the undulating desert sands and green poplar trees below is awesome. Hire a pair of bright orange shoe protectors ( 防沙靴 ; _fángshāxuē;_ Y10) or just shake your shoes out later.
At the base of the colossal dunes is a famous yet underwhelming pond, Crescent Moon Lake (Yuèyáquán). The dunes are a no-holds-barred tourist playpen, with camel rides (Y80 for a one-hour ride), dune buggies (Y150), 'dune surfing' (sand sliding; Y15 to Y20), paragliding (jumping off the dunes with a chute on your back; Y60), archery (Y1 per arrow) and even microlighting . But if your sole interest is in appreciating the dunes in peace, it's not hard to hike away from the action.
You can ride a bike to the dunes in around 20 minutes. Minibus 3 (Y1) shuttles between Dūnhuáng and the dunes from 7.30am to 10pm, departing from opposite the Yǒuhǎo Bīnguǎn. A taxi costs Y10 one way. Most people head out here at about 6pm when the weather starts to cool down.
Western cafes in town offer overnight camel trips to the dunes; Charley Johng's, for example, charges Y300 per person for an overnight stay in a tent and camel rides (with the ever-popular Mr Li); there are also five- to eight-day expeditions out to the Jade Gate Pass, Liuyuan and even as far as Lop Nor in the deserts of Xīnjiāng.
##### YǍDĀN NATIONAL PARK & JADE GATE PASS 雅丹国家地质公园、玉门关
The weird, eroded desert landscape of Yǎdān National Park (Yǎdān Guójiā Dìzhì Gōngyuán; incl tour Y60) is 180km northwest of Dūnhuáng, in the middle of the Gobi Desert's awesome nothingness. A former lake bed that eroded in spectacular fashion some 12,000 years ago, the strange rock formations provided the backdrop to the last scenes of Zhang Yimou's film _Hero_ . The desert landscape is dramatic, but you can only tour the site on a group minibus, so there's little scope to explore on your own.
To get to Yǎdān you have to pass by (and buy a ticket to) the Jade Gate Pass (Yùmén Guān; admission Y45) , 102km from Dūnhuáng. Both this and the South Pass ( 阳关 ; Yáng Guān), 78km west of Dūnhuáng, were originally military stations, part of the Han-dynasty series of beacon towers that extended to the garrison town of Loulan in Xīnjiāng. For caravans travelling westward, the Jade Gate marked the beginning of the northern route to Turpan, while the South Pass was the start of the southern route through Miran. The Jade Gate derived its name from the important traffic in Khotanese jade.
The entry fee includes a small museum (with scraps of real Silk Road silk); a nearby section of Han-dynasty Great Wall , built in 101 BC and impressive for its antiquity and refreshing lack of restoration; and the ruined city walls of Hécāng Chéng , 15km away on a side road.
The only way to get out here is to hire a car for a long day trip to take in Yǎdān, the Jade Gate and the Western Thousand Buddha Caves. Fēitiān Travel Service ( Click here ) organises air-conditioned cars for about Y450; you might get a minivan for around Y350.
## EASTERN GĀNSÙ
Most travellers speed through eastern Gānsù, catching mere glimpses from the train window as they shuttle between Lánzhōu and Xī'ān. This is a shame because the area contains some spectacular Silk Road remnants at Màijī Shān and the Water Curtain Caves, as well as a handsome regional hub in Tiānshuǐ. Moon Canyon, in the far southern part of the province, is the hidden gem of the region.
### Tiānshuǐ 天水
0938 / POP 450,000
Tiānshuǐ's splendid Buddhist caves at Màijī Shān entice a consistent flow of visitors to one of Gānsù's more attractive and laid-back cities. Industrial growth has sent the place on an outwards sprawl, but the old downtown of Tiānshuǐ (known as Qínchéng) has remained pleasantly low-rise and locals pass the time playing a lot of pool.
Tiānshuǐ is actually two separate towns 15km apart – the gritty railhead sprawl, known as Běidào ( 北道 ), and the central commercial area to the west, known as Qínchéng ( 秦城 ) – lashed together by a long freeway. Màijī Shān is 35km south of Běidào.
#### Sights
Tiānshuǐ's main draw is the grottoes at Màijī Shān, but if you have time to kill you could explore the other sights.
Fúxī Temple TEMPLE
( 伏羲庙 ; Fúxī Miào; off Jiefang Lu, Qincheng; admission Y30; 8am-6pm) Cracked during the Sìchuān earthquake of 2008, this Ming-dynasty temple was begun in 1483. The main hall is one of the most elaborate structures in Gānsù, with intricate wooden door panels and original paintings of the 64 hexagrams (varying combinations of the eight trigrams used in the I Ching) on the ceiling.
One of the mythic progenitors of the Chinese people, leaf-clad Fúxī was reputedly a local of Chenji (present-day Tiānshuǐ) who introduced the domestication of animals, hunting and the eight trigrams (used for divination) to early Chinese civilisation. A pleasant pedestrian area filled with itinerant musicians, wood carvers and souvenir stalls has been built at the front of the temple.
Yùquán Temple TAOIST TEMPLE
( 玉泉观 ; Yùquán Guàn; Renmin Xilu, Qincheng; adult/student Y20/10; 7.30am-6.30pm) Ascending in layers up the hillside above Qínchéng, this Taoist temple is a pleasant, green and rambling shrine. Of note are the ancient cypress trees, some more than 1000 years old.
#### Sleeping
Tiānshuǐ has plenty of accommodation, with discounts of up to 40% pretty standard. Cheap guesthouses _(zhāodàisuǒ)_ can be found on Yima Lu in Běidào. A good alternative is to spend the night by Màijī Shān, a far more rural experience.
##### QINCHENG
Tiānshuǐ Dàjiǔdiàn HOTEL $
( 天水大酒店 ; 828 9999; 1 Qincheng Dazhong Nanlu; 秦城大众南路 1 号 ; d without bathroom Y90, with bathroom Y146-190, tr Y97, discounts of 40%; ) The bargain but battle-scarred _pǔtōng_ (economy) rooms with shared bathroom are great for budget seekers, with hot showers down the hall. It's right at the commercial heart of town, next to KFC.
##### BEIDAO
Dōng'ān Fàndiàn HOTEL $
( 东安饭店 ; 261 3333; Yima Lu; 一马路 ; tw Y168, discounts of 40%; ) Very comfortable, with double-glazed windows, quality furnishings and good bathrooms with phone and hairdryer, this is a great three-star option 50m east of the train station. Excellent value.
Wànhuì Zhāodàisuǒ GUESTHOUSE $
( 万汇招待所 ; 492 7976; Yima Lu; 一马路 ; tw Y35-80) This serviceable Běidào guesthouse four shops west of the post office has frugal cheapies and better standard rooms. Reception's on the 3rd floor.
#### Eating
Tiānshuǐ is famed for its _miànpí_ ( 面皮 ) noodles, which can be found everywhere. In Qínchéng, good claypot, Sìchuān and noodle snack stalls stuff Xiaochi Jie ( 小吃街; Snack St), while fruit and walnut sellers cram Guangming Xiang, east and south of the Tiānshuǐ Dàjiǔdiàn.
Tasty _ròujiāmó_ and other fine snack food in Běidào fills Erma Lu, the pedestrian alley south of the train station. For chicken burgers, a branch of the fast-food chain Dico's can be found on Erma Lu.
Běidào Qīngzhēn Lǎozìhào Niúròu Miànguǎn NOODLES $
( 北道清真老字号牛肉面馆 ; Erma Lu, Beidao; meals Y8; 24hr) Get a ticket from the kiosk out front and collect your beef noodles ( _niúròumiàn;_ Y4) and flatbread ( _shāobǐng;_ Y0.50) from the kitchen window at this place with a 30-year history. The noodles are excellent, infused with dollops of scarlet-red chilli oil. For extra meat, ask for _jiāròu niúròumiàn_ ( 加肉牛肉面 ; Y7). There's no English sign, but it's obliquely opposite a branch of ICBC bank.
#### Information
Perhaps it's the bad air, but chemists ( 药房 ; _yàofáng_ ) are simply everywhere.
Bank of China ( 中国银行 ; Zhōngguó Yínháng) Běidào ( 8.30am-noon & 2.30-5.30pm) ; Qínchéng (Minzhu Donglu) The Běidào branch is opposite the train station and has Forex and ATM.
China Post ( 中国邮政 ; Zhōngguó Yóuzhèng; 8am-6pm) Qínchéng (Ziyou Lu) ; Běidào (Yima Lu)
Huáxīng Internet Cafe ( 华兴网吧 ; Huáxīng Wǎngbā; Yima Lu, Běidào; per hr Y2; 24hr)
Industrial & Commercial Bank of China ( 工商银行 ; Gōngshāng Yínháng; Lantian City Plaza; Qínchéng) Has 24-hour ATM.
Tianle Internet Cafe ( 天乐网吧 ; Tiānlè Wǎngbā; Xiaochi Jie; Qínchéng; per hr Y1.50; 24hr) Up steps west off Xiaochi Jie.
#### Getting There & Away
###### Bus
Buses from the long-distance bus station in Qínchéng run to:
Baoji Y48, two hours, regular services
Gāngǔ Y12, 90 minutes, every 20 minutes
Hanzhong Y88, seven to eight hours, one daily (6am)
Huīxiàn Y30, three hours, hourly
Lánzhōu Y55 to Y67, four hours, every 20 minutes
Línxià Y80, seven hours, one daily (6.30am)
Luòmén Y18, two hours, two daily (6.30am and 2.30pm)
Píngliáng Y70, five hours, four daily (6am, 7am, 8am and 9.30am)
Xī'ān Y100, 4½ hours, hourly
Yínchuān Y148, 12 hours, two daily (6am and 2.30pm)
Buses to Lánzhōu also depart throughout the day from the forecourt of the train station in Běidào. There are also two morning departures a day from here to Huīxiàn.
###### Train
Tiānshuǐ is on the Xī'ān–Lánzhōu railway line; there are dozens of daily trains in either direction. If you arrive early, you can visit Màijī Shān as a day trip, avoiding the need to stay overnight in Tiānshuǐ.
From Tiānshuǐ it's four to six hours to either Lánzhōu (hard seat Y62) or Xī'ān (Y61).
#### Getting Around
Taxis shuttle passengers between Qínchéng (from the Tiānshuǐ Dàjiǔdiàn and long-distance bus station) and the train station in Běidào for Y10. Alternatively, take the much slower bus 1 or 6 (Y3, 40 minutes) from Dazhong Lu.
### Around Tiānshuǐ
##### MÀIJĪ SHĀN 麦积山
Set among wild and lush green hills southeast of Tiānshuǐ, the riveting grottoes of Màijī Shān (Haystack Mountain) are some of China's most famous Buddhist rock carvings. The solitary, tree-capped rock sticks up from the verdant, rolling landscape like a vast Chinese haystack, hence the name.
###### Sights
Màijī Shān CAVES
(adult/student Y70/35; 8am-6pm) The cliff sides are riddled with niches and statues carved principally during the Northern Wei and Zhou dynasties (AD 386–581), with later additions. Vertigo-inducing catwalks and steep spiral stairways cling to the cliff face, affording close-ups of the art.
It's not certain just how the artists managed to clamber so high; one theory is that they created piles from blocks of wood reaching to the top of the mountain before moving down, gradually removing them as they descended. A number of the statues were slightly damaged by the Sìchuān earthquake of 2008 but have been repaired.
A considerable amount of pigment still clings to many of the statues – a lot of which are actually made of clay rather than hewn from rock – although you frequently have to climb up steps to peer at them through tight mesh grills. Also in many caves there is no natural illumination, so the figures of the Bodhisattvas sit hunched in the gloom or the frescoes are indiscernible. Much, though, is clearly visible and most of the more impressive sculptures decorate the upper walkways, especially at cave 4.
The entire undertaking is rounded off with a crescent of hawker stalls.
An English-speaking guide charges Y150 for the day. It's possible to view normally closed caves (eg Cave 133 and Cave 1) for an extra fee of Y500 per group.
Cave 13
Within the hard-to-miss Sui-dynasty trinity of Buddha and Bodhisattvas is the largest statue on the mountain: the cave's central effigy of Buddha tops out at 15.7m. When the statue was restored three decades ago, a handwritten copy of the _Sutra of Golden Light_ was discovered within the Buddha's fan.
Cave 4
This cave's marvellous seven niches are large grottoes originally dating from the Northern Wei, with later additions from the Sui, Tang and Song. Note the powerful guardian figures, typical of torsional, muscular and fierce Tang-dynasty examples. The radiant-looking Bodhisattvas are simply exquisite, while swallows flit out from the overhanging rock above.
Cave 3
Also called the 1000-Buddha Corridor, this cave features an impressive hall past twin rows of solemn-faced Buddhas (actually 297 carvings all told). Note the lower row is far more weathered and damaged.
Cave 155
The oldest statues can be found here.
Cave 148
The figures here are among those displaying the influence of the Gandhara style, which arrived in China from India along the Silk Road.
Cave 144
The statues here are almost completely weathered away.
Cave 54
A quantity of the graffiti defacing some statues is also reasonably old – the characters daubed here are full form.
Cave 59
The largely indistinct 1200-character testament on the wall of this cave dates from 1035, recording the monies collected for restoring the statues.
The admission ticket includes entry to a small botanic garden _(zhíwùyuán)_ . You only need around an hour or so for the grottoes and afterwards a hike up nearby Xiāngjí Shān ( 香积山 ) is lovely, with opportunities to break off into the woods which are full of birds and wildlife. At the base of the mountain is Ruiying Monastery ( 瑞应寺 ; Ruìyìng Sì; Y10) .
###### Sleeping
There are several places where you can spend the night, including the Arboretum Hotel within the botanic garden.
Zhōuyú Nóngjiālè FARMSTEAD $
( 周于农家乐 ; 139 1963 5896; beds Y20, d Y40) Tucked away in the woods, this place has simple but very cheap rooms in a farmstead environment; it also has heated _kàng_ beds for winter and can cook up meals. To find the farmstead, take the path up to Xiāngjí Shān for around 600m; it's on the right.
###### Getting There & Away
Minibus 34 (Y5, 40 minutes) leaves every seven minutes from in front of the Tiānshuǐ train station. It may drop you at the crossroads, 5km before the site, from where a taxi van will cost Y5 per seat to the ticket office. You can walk the last 2km to 3km from the ticket office to the caves or take the tour buggy ( _guāngguān chē;_ Y10). Horses can also be hired for Y20. A taxi from Tiānshuǐ costs around Y100 return. On the way back you may find the occasional minibus 34 waiting to fill up for the return trip (Y6).
### Moon Canyon 月亮峡
Tucked in a hidden corner of southeastern Gānsù is the pristine wilderness of Moon Canyon (Yuèliàng Xiá; admission Y20) , with its rushing rivers and towering rock walls, and the surrounding Three Beaches National Park ( 三滩自然保护区 ; Sāntān Zìrán Bǎohùqū).
At the entrance to the valley is Moon Canyon Retreat ( 月亮峡度假村 ; Yuèliàng Xiá Dùjiàcūn; 755 7888; www.threebeaches.com; dm/tents/cabins Y50/100/120, tw Y220; Apr-Oct) , with four spartan but low-impact lodges.
A new road leads 15km up to the village of Yánpíng ( 严坪 ), where there are half a dozen homestays ( 农家乐 ; nóngjiālè; dm Y10) , marked by tourism signs. Accommodation is basic but friendly, and local dishes are available. There is one shop in the village, so bring some snacks.
For those with camping equipment, it's a five-hour hike up to the Sāntān (Three Beaches); one possible three-day trek is to the purported old-growth forest ( 原始森林 ; _yuánshǐ sēnlín_ ) upstream. Jeeps ferry (mainly Chinese) tourists up to the first pool (Y250 return) but not beyond.
Moon Canyon is on the Chéngdū–Xī'ān rail line near the village of Jiālíng ( 嘉陵 ). There is only one stop per day in either direction (both at around 1pm) – the closest major rail links are Guǎngyuán (Sìchuān) and Bǎojī (Shaanxi). Frequent buses run between Tiānshuǐ and Huīxiàn ( 徽县 ; Y30, three hours), from where you can hire a minivan (Y60) for the final 26km. Alternatively, take a minibus from Huīxiàn on to Jiālíng and then hire a minivan (Y20) or walk the 6km from there.
### Gāngǔ 甘谷
0938
If you're Buddha-hopping across Gānsù, stop off at this village and make the one-hour hike up the hillside to an impressive carved image of Sakyamuni (complete with moustache). The path along the ridge is easy to follow and there are numerous little shrines along the way. The Buddha is easily visible from the road that runs past the town. Gāngǔ is 65km west of Tiānshuǐ and 30km east of Luòmén; local buses and trains between the two will stop here.
### Water Curtain Caves 水帘洞
0938
The Water Curtain Caves (Shuǐlián Dòng; admission Y25; 7am-7pm) are an embodiment of that classic image of China – Taoist and Buddhist temples sheltered by steep cliffs and the majestic image of a carved Buddha guarding the vacant canyons below. The caves are 17km north of Luòmén ( 洛门 ), a town on the main road between Lánzhōu and Tiānshuǐ.
The main sight is Lāshāo Sì ( 拉稍寺 ), an overhanging cliff sheltering an amazingly vibrant 31m-high painted figure of Sakyamuni seated cross-legged upon a throne of lotus petals, lions, deer and elephants. The bas-relief carving and accompanying mint-green and salmon coloured frescoes were completed in the Northern Wei dynasty (AD 386–534). The secondary sights here are the eponymous Taoist temple of Shuǐlián Dòng , a short walk uphill, and the faded remnants of the Thousand Buddha Cave ( 千佛洞 ; Qiānfó Dòng), a 10-minute walk up a side valley.
Minibuses in Luòmén will take you the 17km to the Water Curtain Caves for Y60 return; a motor tricycle is cheaper at around Y35. Half the road was washed out a few years back, so any vehicle you take needs to be sturdy enough for the rough journey (and getting here may well be impossible after heavy rain).
Luòmén is on the Lánzhōu–Xī'ān rail line, but only a couple of trains per day stop here. Two direct buses leave from Tiānshuǐ's long-distance bus station (in Qínchéng; two hours, Y18) at 6.30am and 2.30pm; otherwise change buses in Gāngǔ ( 甘谷 ). From Luòmén it's a 20-minute minibus ride (Y2) on to Wǔshān ( 武山 ) and then a short bus ride to Lǒngxī ( 陇西 ), from where there are frequent trains to/from Lánzhōu.
The only place to stay is the decent Luòmén Bīnguǎn ( 洛门宾馆 ; 322 7668; tw Y80) .
### Píngliáng 平凉
0933 / POP 106,800
A booming Chinese midsized town, Píngliáng is a logical base for visits to the nearby holy mountain of Kōngtóng Shān. The train station is in the northeastern part of town and the main bus station in the far western part. They are connected by Xi Dajie and Dong Dajie, home to the town's major hotels, restaurants and shops.
The Píngliáng Bīnguǎn ( 平凉宾馆 ; 825 3988; 86 Xi Dajie; 西大街 86 号 ; tw Y200-268) is a large midrange place in the town centre. Next door, the Qīnghuá Bīnguǎn ( 清华宾馆 ; 823 4241; 90 Xi Dajie; 西大街 90 号 ; dm Y25-35, d Y90) is a friendly budget option.
About 200m west of the Píngliáng Bīnguǎn is the Sìzhōng Alley market (Sìzhōng Xiàng shìchǎng), with numerous restaurants and stalls.
The following services depart from Píngliáng's main bus station, in the western part of town:
Gùyuán Y7 to Y18, 1½ hours, hourly (8.20am to 5pm)
Lánzhōu Y90, five hours, hourly (7am to 4.50pm)
Tiānshuǐ Y54, seven hours, two daily (6.40am and 8.50am).
Xī'ān Y70, six hours, five daily (7.40am to 3pm)
Yán'ān Y106, nine hours, one daily (6am)
For Tiānshuǐ there are more frequent departures from the east bus station _(qìchē dōngzhàn)_ .
Getting to Píngliáng is easiest by train. There are overnight trains to Lánzhōu (train N855; Y103, 11 hours), Xī'ān (train 2586; Y66, seven hours) and Yínchuān (train K361; Y122, 8½ hours).
### Around Píngliáng
##### KŌNGTÓNG SHĀN 崆峒山
On the border of Níngxià in the Liùpán Shān ( 六盘山 ) range, Kōngtóng Shān (winter/ summer Y60/120; 8am-6.30pm) is one of the 12 principal peaks in the Taoist universe. It was first mentioned by the philosopher Zhuangzi (399–295 BC), and illustrious visitors have included none other than the Yellow Emperor. Numerous paths lead over the hilltop past dozens of picturesque temples to the summit at over 2100m.
The main entrance is on the north side of the mountain. You can make a nice loop trip by descending via the steps on the mountain's south side and taking a taxi from the base. If you'd rather not walk, a cable car (suǒdào; return Y30) spans the reservoir on the south side to the top of the cliffs.
There is accommodation and food on the mountain at the Kōngtóng Shānzhuāng ( 崆峒山庄 ; dm Y40-60, tw Y240; closed Nov-Apr) .
Kōngtóng Shān is 11km west of Píngliáng. You might find a minibus (Y5) situated on the opposite side of the park across from the main bus station, or you can hire a minivan for Y20/40 one way/ return. Both will drop you close to the ticket office, where you need to pay for a separate vehicle to take you the 3.5km up to the mountain (per person/car Y10/50).
### **Understand China**
CHINA TODAY
HISTORY
THE PEOPLE OF CHINA
RELIGION & BELIEFS
CHINESE CUISINE
ARTS & ARCHITECTURE
CHINA'S LANDSCAPES
THE MARTIAL ARTS OF CHINA
#
Top of section
# China Today
» Population: 1.34 billion
» GDP (PPP): $8.75 trillion
» GDP per capita: $6600
» Labour force: 813 million
» Unemployment: 4.3%
» Highest point: Mount Everest (8848m)
» Annual alcohol consumption (per person): 5.2L
### China Superpower?
For decades, the world has been awestruck by China's potential. Gazing into the statistics of growth, it's all too easy to fall in with those who perceive China as an emergent superpower. The picture is even easier to see with a West crippled by austerity measures. Books such as _When China Rules the World_ by Martin Jacques triumphantly declare the establishment of a new world order.
China's apparent ability to shrug off the financial crisis (despite a downturn in exports) through a massive stimulus package revealed a robust resilience to ride out the worst. Despite a slowing in the rate of economic growth, the Chinese economy continues to expand at a rate of around 10% and the growing middle-classes are upbeat. China has it sewn up, say the pundits.
From a Western perspective, there is understandable agreement. China can be both ultramodern (space missions, the Pudong skyline, Maglev trains) and very powerful (a vast standing army, a gigantic economy), despite only three decades of growth. Naysayers discern a coming crash, initiated perhaps by the pricking of a property market bubble, Japan 1990s-style, and a subsequent cascade downwards, but just as many pundits are optimistic, insisting that the only way is up.
China's more balanced perspective is that it is a developing nation, and a vast difference in magnitude separates it from being a superpower. It is wise to remember that China's per capita GDP puts it roughly on a level with Namibia. China possesses colossal latent power by virtue of its size and huge population, but these dimensions have also hampered equal growth across the nation. Inequality in China is among the most extreme in the world, something perhaps unforgivable for a communist government. The urban middle class is growing rapidly, but most of China remains rural and poor.
China dazzles in its big cities, but often lacks even the most basic equipment and systems. The Dàlián oil spill in July 2010 came in the same week that China overtook the US as the world's largest energy consumer – making the nation a superpower at least in oil dependency terms. But the ensuing clean-up operation saw a ragtag navy of fishing boats tackling the spill, as workers used their bare hands, straw mats, pots and stockings full of human hair to battle the oil. What the world saw was the vast and poorly equipped mobilisation of one of China's greatest resources – its people – to tackle the spill. It worked, but it wasn't modern.
China is a growing power but has yet to commission its first aircraft carrier and is unable to project conventional military power far beyond its borders. The nation is also tentative about assuming a leadership role either in the Far East or on the world stage, partly because the US remains powerful in the Pacific region and also because China remains focused on, if not obsessed with, domestic concerns (and Taiwan).
### Harmony
The Chinese leadership under Hu Jintao has taken pains to stress 'harmony' throughout society, as part of China's formula of a 'peaceful rise'. Mocked by many Chinese, the vapid notion of 'harmony' is being sold across the nation at a time when China is undergoing a phenomenal period of social stress. Some analysts suggest that ostensible harmony is easier to achieve in authoritarian states like China, because the press is muffled, free speech disallowed and dissent quashed. The 11-year sentencing of Liu Xiaobo for his democratic agenda in Charter 08 is only harmonious in the sense he has been silenced, perhaps explaining why Běijīng reacted with such venom to his Nobel Peace Prize in 2010.
The laws of social entropy apply in China as elsewhere, however, and tensions inevitably ripple across the surface of society, or suddenly explode with eye-blinking ferocity. A series of bizarre kindergarten massacres in 2010 shocked the nation. Many Chinese called for greater understanding of those afflicted by mental health problems, a malady that carries great stigma in Chinese society. Others pointed to agonising dysfunction at the heart of modern Chinese society.
Ethnic relations are also prickly. The underlying tensions that ignited deadly riots in Tibet in 2008 and Xīnjiāng in 2009 are perhaps yet to be fully addressed, although Běijīng believes a combination of investment and blaming separatists and outsiders is the solution.
As a poke in the eye to those who saw China's growing middle class as a democratising influence, evidence suggests Běijīng is becoming less tolerant of dissent. Lawyers, human rights advocates and democracy activists who attempt to organise resistance to Běijīng's authority routinely face charges of endangering national security.
Meanwhile, morale is low in the ranks of Western businessmen in China as they bridle under regulations designed to protect local businesses.
A certain fragility exists in China's increasing sense of confidence and growing self-assurance. Some of this transmutes into a worrying nationalism, which is particularly appealing to young Chinese who perhaps lack other ideologies they can believe in.
### Top Books
When a Billion Chinese Jump (Jonathan Watts) China's environmental travails under the microscope, and it's not pretty.
The Rape of Nanking (Iris Chang) Puts into perspective China's deep-rooted ambivalence towards its island neighbour, Japan.
Diary of a Madman and Other Stories (Lu Xun) Astonishing tales from the father of modern Chinese fiction.
### Top Films
Still Life (Jia Zhangke; 2005) Bleak and hauntingly beautiful portrayal of a family devastated by the construction of the Three Gorges Dam.
Raise the Red Lantern (Zhang Yimou; 1991) The exquisitely fashioned tragedy from the sumptuous palette of the Fifth Generation.
### Dos & Don'ts
» Never, ever fight to settle the bill if your Chinese host is determined to pay.
» Take off your shoes when visiting a Chinese person's home, or offer to.
» Never give a clock as a gift as it has morbid overtones.
### Myths
» The Chinese are hard-working – for sure, but don't expect service with a smile at the train station ticket office.
» The Chinese are communists – some are, more aren't.
» You can see the Great Wall from space – motorways would be more visible as they're far wider.
#
Top of section
# History
The epic sweep of China's history paints a perhaps deceiving impression of long epochs of peace occasionally convulsed by break-up, internecine division or external attack. Yet China has, for much of its history, been in conflict either internally or with outsiders. Although China's size and shape has also continuously changed – from tiny beginnings by the Yellow River (Huáng Hé) to the subcontinent of today – an uninterrupted thread of history runs from its earliest roots to the full flowering of Chinese civilisation. Powerful links connect the Chinese of today with their ancestors 5000 or 6000 years ago, creating the longest-lasting civilisation on earth.
Ban Zhao was the most famous woman scholar in early China. Dating from the late 1st century AD, her work _Lessons for Women_ advocated chastity and modesty as favoured female qualities.
## FROM ORACLE BONES TO CONFUCIUS
The earliest 'Chinese' dynasty, the Shang, was long considered apocryphal. However, archaeological evidence – cattle bones and turtle shells in Hénán covered in mysterious scratches, recognised by a scholar as an early form of Chinese writing – proved that a society known as the Shang developed in central China from around 1766 BC. The area it controlled was tiny – perhaps 200km across – but Chinese historians have argued that the Shang was the first Chinese dynasty. By using Chinese writing on 'oracle bones', the dynasty marked its connection with the Chinese civilisation of the present day.
Sometime between 1050 and 1045 BC, a neighbouring group known as the Zhou conquered Shang territory. The Zhou was one of many states competing for power in the next few hundred years, but developments during this period created some of the key sources of Chinese culture that would last till the present day. A constant theme of the first millennium BC was conflict, particularly the periods known as the 'Spring and Autumn' (722–481 BC) and 'Warring States' (475–221 BC).
So far, some 7000 soldiers in the famous Terracotta Army have been found near Xī'ān. The great tomb of the first emperor still remains unexcavated, although it is thought to have been looted soon after it was built.
The Chinese world in the 5th century BC was both warlike and intellectually fertile, rather like ancient Greece during the same period. From this disorder emerged the thinking of Confucius (551–479 BC), whose system of thought and ethics underpinned Chinese culture for 2500 years. A wandering teacher, Confucius gave lessons in personal behaviour and statecraft, advocating an ordered and ethical society obedient towards hierarchies. Confucius' desire for an ordered and ethical world seems a far cry from the warfare of the time he lived in.
### CONFUCIUS TEMPLES 文庙
Despite the rechampioning of the Shāndōng sage as a lynchpin of CCP (Chinese Communist Party) efforts to create a 'harmonious' society, Confucian temples _(wénmiào)_ remain passive and inanimate places (unless it's Kǒngzi's birthday). This, however, is part of their appeal: they are peaceful, unhurried and often silent.
» Confucius Temple, Qūfù: the mother of all patriarchal temples, in Qūfù, Confucius' birthplace
» Confucius Temple, Běijīng: China's second largest Confucius temple and a haven of peace in Běijīng
» Confucius Temple, Jiànshuǐ: locals insist it's China's biggest
» Confucius Temple, Píngyáo: housing Píngyáo's oldest building in one of China's most magnificent old towns
» Confucius Temple, Tài Shān: not such an amazing temple, but its location atop one of China's most famous mountains is peerless
## EARLY EMPIRES
The Warring States period ended decisively in 221 BC. The Qin kingdom conquered other states in the central Chinese region and Qin Shi Huang declared himself emperor. The first in a line of rulers that would last until 1912, later histories portrayed Qin Shi Huang as particularly cruel and tyrannical, but the distinction is dubious as the ensuing Han dynasty (206 BC–AD 220) adopted many of the short-lived Qin's practices of government.
Qin Shi Huang oversaw vast public works projects, including walls built by some 300,000 men, connecting defences into what would become the Great Wall. He unified the currency, measurements and written language, providing the basis for a cohesive state.
Establishing a trend that would echo through Chinese history, a peasant, Liu Bang, rose up and conquered China, founding the Han dynasty. The dynasty is so important that the name Hàn ( 汉 ; 漢 ) still refers to ethnic Chinese. Critical to the centralisation of power, Emperor Wu (140–87 BC) institutionalised Confucian norms in government. Promoting merit as well as order, he was the first leader to experiment with examinations for entry into the bureaucracy, but his dynasty was plagued by economic troubles, as estate owners controlled more and more land. Indeed, the issue of land ownership would be a constant problem throughout Chinese history, to today. Endemic economic problems and the inability to exercise control over a growing empire led to the collapse and downfall of the Han. Social problems included an uprising by Taoists (known as the Yellow Turbans). Upheaval would become a constant refrain in later Chinese dynasties.
Parts of the Grand Canal still function as a waterway and other sections are being enlisted as elements of the south–north water diversion project ( Click here ).
The Han demonstrated clearly that China is fundamentally a Eurasian power in its relations with neighbouring peoples. To the north, the Xiongnu (a name given to various nomadic tribes of Central Asia) posed the greatest threat to China. Diplomatic links were also formed with Central Asian tribes, and the great Chinese explorer Zhang Qian provided the authorities with information on the possibilities of trade and alliances in northern India. During the same period, Chinese influence percolated into areas that would later become known as Vietnam and Korea.
### RUINS
Many of China's historical artefacts may be in a state of perpetual ruin, but some vestiges get top-billing:
» Ruins of the Church of St Paul: China's most sublime architectural wreck
» Jiànkòu Great Wall: no other section of the Great Wall does the tumble-down look in such dramatic fashion
» Great Fountain Ruins: sublime tangle of Jesuit-designed stonework
» Xanadu: a vivid imagination is required to conjure up impressions of Kublai Khan's pleasure palace
» Ming City Wall Ruins Park: Běijīng's last section of Ming city wall
Evidence from Han tombs suggests that a popular item of cuisine was a thick vegetable and meat stew, and that flavour enhancers such as soy sauce and honey were also used.
## DISUNITY RESTORED
Between the early 3rd and late 6th centuries AD, north China witnessed a succession of rival kingdoms vying for power while a potent division formed between north and south. Riven by warfare, the north was controlled by non-Chinese rule, most successfully by the Northern Wei dynasty (386–534), founded by the Tuoba, a northern people who embraced Buddhism and left behind some of China's finest Buddhist art, including the famous caves outside Dūnhuáng. A succession of rival regimes followed until nobleman Yang Jian (d 604) reunified China under the fleeting Sui dynasty (581–618). His son Sui Yangdi contributed greatly to the unification of south and north through construction of the Grand Canal, which was later extended and remained the empire's most important communication route between south and north until the late 19th century. After instigating three unsuccessful incursions onto Kor- ean soil, resulting in disastrous military setbacks, Sui Yangdi faced revolt on the streets and was assassinated in 618 by one of his high officials.
### HISTORY BOOKS
» _The City of Heavenly Tranquillity: Beijing in the History of China_ (Jasper Becker; 2009): Becker's authoritative and heartbreaking rendering of Běijīng's transformation from magnificent Ming capital to communist-capitalist hybrid
» _The Penguin History of Modern China: The Fall and Rise of a Great Power 1850–2008_ (Jonathan Fenby): highly readable account of the paroxysms of modern Chinese history
» _China, A History_ (John Key; 2008): an accessible and well-written journey through Middle Kingdom history
## THE TANG: CHINA LOOKS WEST
The Tang rule (618–907) was an outward-looking time, when China embraced the culture of its neighbours – marriage to Central Asian people or wearing Indian-influenced clothes was part of the era's cosmopolitan élan – and distant nations that reached China via the Silk Road. The Chinese nostalgically regard the Tang as their cultural zenith. The output of the Tang poets is still regarded as China's finest, as is Tang sculpture, while its legal code became a standard for the whole East Asian region.
The Tang saw the first major rise to power of eunuchs. Often from ethnic minority groups, they were brought to the capital and given positions within the imperial palace. In many dynasties they had real influence.
The Tang was founded by the Sui general Li Yuan, his achievements consolidated by his son Taizong (626–49). Cháng'ān (modern Xī'ān) became the world's most dazzling capital, with its own cosmopolitan foreign quarter, a population of a million, a market where merchants from as far away as Persia mingled with locals and an astonishing city wall that eventually enveloped 83 sq km. The city exemplified the Tang devotion to Buddhism, with some 91 temples recorded in the city in 722, but a tolerance of and even absorption with foreign cultures allowed alien faiths a foothold, including Nestorian Christianity, Manichaeism, Islam, Judaism and Zoroastrianism.
Taizong was succeeded by a unique figure: Chinese history's sole reigning woman emperor, Wu Zetian (625–705). Under her leadership the empire reached its greatest extent, spreading well north of the Great Wall and far west into inner Asia. Her strong promotion of Buddhism, however, alienated her from the Confucian officials and in 705 she was forced to abdicate in favour of Xuanzong, who would preside over the greatest disaster in the Tang's history: the rebellion of An Lushan.
Xuanzong appointed minorities from the frontiers as generals, in the belief that they were so far removed from the political system and society that ideas of rebellion or coups would not enter their minds. Nevertheless, it was An Lushan, a general of Sogdian-Turkic parentage, who took advantage of his command in north China to make a bid for imperial power. The fighting lasted from 755 to 763, and although An Lushan was defeated, the Tang's control over China was destroyed forever. It had ceded huge amounts of military and tax-collecting power to provincial leaders to enable them to defeat the rebels, and in doing so dissipated its own power. This was a permanent change in the relationship between the government and the provinces; previous to 755, the government had an idea of who owned what land throughout the empire, but after that date the central government's control was permanently weakened. Even today, the dilemma has not been fully resolved.
The features of the largest Buddhist statue in the Ancestor Worshipping Cave at the Lóngmén Caves outside Luòyáng are supposedly based on Tang female emperor Wu Zetian, a famous champion of Buddhism.
In its last century, the Tang withdrew from its former openness, turning more strongly to Confucianism, while Buddhism was outlawed by Emperor Wuzong from 842 to 845. The ban was later modified, but Buddhism never regained its previous power and prestige. The Tang decline was marked by imperial frailty, growing insurgencies, upheaval and chaos.
### HISTORY MUSEUMS
» Hong Kong Museum of History: one of the former British territory's best museums: a colourful narrative supported by imaginative displays
» Shànghǎi History Museum: excellent chronicle of Shànghǎi's colourful journey from 'Little Sūzhōu' to 'Whore of the Orient' and beyond
» Macau Museum: the ex-Portuguese territory's fascinating history brought vividly to life
» Shaanxi History Museum: eye-opening chronicle of ancient Chang'an
## OPEN MARKETS, BOUND FEET
Further disunity – the fragmentary-sounding Five Dynasties or Ten Kingdoms period – followed the fall of the Tang until the Northern Song dynasty (960–1127) was established. The Song dynasty existed in a state of constant conflict with its northern neighbours. The Northern Song was a rather small empire coexisting with the non-Chinese Liao dynasty (which controlled a belt of Chinese territory south of the Great Wall that now marked China's northern border) and less happily with the Western Xia, another non-Chinese power that pressed hard on the northwestern provinces. In 1126 the Song lost its capital, Kāifēng, to a third non-Chinese people, the Jurchen (previously an ally against the Liao). The Song was driven to its southern capital of Hángzhōu for the period of the Southern Song (1127–1279), yet the period was culturally rich and economically prosperous.
The full institution of a system of examinations for entry into the Chinese bureaucracy was brought to fruition during the Song. At a time when brute force decided who was in control in much of medieval Eur- ope, young Chinese men sat tests on the Confucian classics, obtaining office if successful (most were not). The system was heavily biased towards the rich, but was remarkable in its rationalisation of authority, and lasted for centuries. The classical texts set for the examinations became central to the transmission of a sense of elite Chinese culture, even though in later centuries the system's rigidity failed to adapt to social and intellectual change.
China's economy prospered during the Song rule, as cash crops and handicraft products became far more central to the economy, and a genu- inely China-wide market emerged, which would become even stronger during the Ming and Qing dynasties. The sciences and arts also flourished under the Song, with intellectual and technical advances across many disciplines. Kāifēng emerged as an eminent centre of politics, commerce and culture.
Little if anything remains of the synagogue in the Song capital of Kāifēng, but the city once harboured the country's largest population of Chinese Jews, some of whom survive to this day.
The cultural quirk of foot binding appears to have emerged during the Song. It is still unknown how the custom of binding up a girl's feet in cloths so that they would never grow larger than the size of a fist began, yet for much of the next few centuries, it became a Chinese social norm.
### A BEASTLY AFFAIR
In February 2009, China was in uproar about the sale of two bronze animal heads by the auction house Christie's. The saga was the latest twist and turn in a story stretching back to 1860, when the Old Summer Palace in Běijīng was torched by Anglo-French troops at the end of the Second Opium War and the animal heads were pilfered.
The 12 heads belonged to a dozen statues with human bodies and animal heads (representing the 12 animals of the Chinese zodiac) that jetted water from their mouths in 12 two-hour sequences, part of an elaborate structure called the Hǎiyàntáng.
Four of the original 12 animal heads have been repatriated (by being bought at auction or donated) and can be seen at the Poly Art Museum. Of the eight still abroad, the rat and rabbit heads became the focus of a powerful Chinese sense of injustice in 2009 when they appeared at Christie's.
A convincing moral argument exists that the animal heads should be returned to China; however, others pointed to the lack of conclusive evidence that the animal heads had been stolen by French or British troops; the possibility also existed, others argued, that they had been plundered by Chinese for sale abroad to international clients.
The animal heads are perhaps a peculiar choice of national ire for the Chinese, considering they are evidently Western in fashion, designed by the Jesuit minds which also fashioned the Western palace buildings at the Old Summer Palace. It has also been suggested that the Empress Dowager disliked the heads so much that she had them removed; if that story is true, where were they stored? Although the Old Summer Palace was certainly torched by the French and the British, there are also indications that some Chinese also joined in the looting, eager to get back at Manchu rule.
What is evident is that the ruins, and the animal heads, have become eternal symbols of China's humiliation at the hands of the foreign powers, and icons that increasingly resonate as the country assumes a more central role in international affairs.
## MONGOLS TO MING
The fall of the Song reinforced notions of China's Eurasian location and growing external threats. Genghis Khan (1167–1227) was beginning his rise to power, turning his sights on China; he took Běijīng in 1215, destroying and rebuilding it; his successors seized Hángzhōu, the Southern Song capital, in 1276. The court fled and, in 1279, Southern Song resistance finally expired. Kublai Khan, grandson of Genghis, now reigned over all of China as emperor of the Yuan dynasty. Under Kublai, the entire population was divided into categories of Han, Mongol and foreigner, with the top administrative posts reserved for Mongols, even though the examination system was revived in 1315. The latter decision unexpectedly strengthened the role of local landed elites: since elite Chinese could not advance in the bureaucracy, they decided to spend more time tending their large estates instead. Another innovation was the use of paper money, although overprinting created a problem with inflation.
The Mongols ultimately proved less able at governance than warfare, their empire succumbing to rebellion within a century and eventual vanquishment. Ruling as Ming emperor Hongwu, Zhu Yuanzhang established his capital in Nánjīng, but by the early 15th century the court had begun to move back to Běijīng, where a hugely ambitious reconstruction project was inaugurated by Emperor Yongle (r 1403–24), building the Forbidden City and devising the layout of the city we see today.
Although the Ming tried to impose a traditional social structure in which people stuck to hereditary occupations, the era was in fact one of great commercial growth and social change. Women became subject to stricter social norms (for instance, widow remarriage was frowned upon) but female literacy also grew. Publishing, via woodblock technology, burgeoned and the novel appeared.
Emperor Yongle, having usurped power from his nephew, was keen to establish his own legitimacy. In 1405 he launched the first of seven great maritime expeditions. Led by the eunuch general Zheng He (1371–1433), the fleet consisted of more than 60 large vessels and 255 smaller ones, carrying nearly 28,000 men. The fourth and fifth expeditions departed in 1413 and 1417, and travelled as far as the present Middle East. The great achievement of these voyages was to bring tribute missions to the capital, including two embassies from Egypt. Yet ultimately, they were a dead end, motivated by Yongle's vanity to outdo his father, not for the purpose of conquest nor the establishment of a settled trade network. The emperors after Yongle had little interest in continuing the voyages, and China dropped anchor on its global maritime explorations.
Mass publishing, using woodblock printing, took off during the Ming dynasty. Among the bestsellers of the era were swashbuckling novels such as _The Water Margin_ and _The Romance of the Three Kingdoms_ .
The Great Wall was re-engineered and clad in brick while ships also arrived from Europe, presaging an overseas threat that would develop from entirely different directions. Traders were quickly followed by missionaries, and the Jesuits, led by the formidable Matteo Ricci, made their way inland and established a presence at court. Ricci learned fluent Chinese and spent years agonising over how Christian tenets could be made attractive in a Confucian society with very different norms. The Portuguese presence linked China directly to trade with the New World, which had opened up in the 16th century. New crops, such as potatoes, maize, cotton and tobacco, were introduced, further stimulating the commercial economy. Merchants often lived opulent lives, building fine private gardens (as in Sūzhōu) and buying delicate flowers and fruits.
The Ming was eventually undermined by internal power struggles. Natural disasters, including drought and famine, combined with a menace from the north. The Manchu, a nomadic warlike people, saw the turmoil within China and invaded.
### OLD TOWNS & VILLAGES 古镇
For strong shades of historic China, make a beeline for the following old towns _(gǔzhèn)_ :
» Píngyáo: the best preserved of China's ancient walled towns
» Fènghuáng: exquisite riverside setting, pagodas, temples, covered bridges and ancient city wall
» Hóngcūn: gorgeous Huīzhōu village embedded in the lovely south Ānhuī countryside
» Tiánluókēng Tǔlóu Cluster: overnight in a photogenic Hakka roundhouse
» Shāxī: flee modern China along Yúnnán's ancient Tea-Horse Rd
In the 18th century, the Chinese used an early form of vaccination against smallpox that required not an injection, but instead the blowing of serum up the patient's nose.
## THE QING: THE PATH TO DYNASTIC DISSOLUTION
After conquering just a small part of China and assuming control in the disarray, the Manchu named their new dynasty the Qing (1644–1911). Once ensconced in the (now torched) Forbidden City, the Manchu realised they needed to adapt their nomadic way of life to suit the agricultural civilisation of China. Threats from inner Asia were neutralised by incorporating the Qing homeland of Manchuria into the empire, as well as that of the Mongols, whom they had subordinated. Like the Mongols before them, the conquering Manchu found themselves in charge of a civilisation whose government they had defeated, but whose cultural power far exceeded their own. The result was quite contradictory: on the one hand, Qing rulers took great pains to win the allegiance of high officials and cultural figures by displaying a familiarity and respect for traditional Chinese culture; on the other hand, the Manchu rulers were at great pains to remain distinct. They enforced strict rules of social separation between the Han and Manchu, and tried to maintain – not always very successfully – a culture that reminded the Manchu of their nomadic warrior past. The Qing flourished most greatly under three emperors who ruled for a total of 135 years: Kangxi, Yongzheng and Qianlong.
To show that he was familiar with classical Chinese culture, emperor Kangxi sponsored a great encyclopaedia of Chinese culture, which is still read by scholars today.
Much of the map of China that we know today derives from the Qing period. Territorial expansion and expeditions to regions of Central Asia spread Chinese power and culture further than ever. The expansion of the 18th century was fuelled by economic and social changes. The discovery of the New World by Europeans in the 15th century led to a new global market in American food crops, such as chillies and sweet potatoes, allowing food crops to be grown in more barren regions, where wheat and rice had not flourished. In the 18th century, the Chinese population doubled from around 150 million to 300 million people.
Historians now take very seriously the idea that in the 18th century China was among the most advanced economies in the world. The impact of imperialism would help commence China's slide down the table, but the seeds of decay had been sown long before the Opium Wars of the 1840s. Put simply, as China's size expanded, its state remained too small. China's dynasty failed to expand the size of government to cope with the new realities of a larger China.
### FOREIGN CONCESSIONS & COLONIES
China's coastline is dotted with a string of foreign concession towns that ooze charm and a sensation of 19th- and early-20th-century grandeur.
» Shànghǎi, French Concession: Shànghǎi's most stylish concession goes to the French
» Gǔlàng Yǔ, Xiàmén: thoroughly charming colonial remains on a beautiful island setting
» Qīngdǎo: wander the German district for cobbled streets and Teutonic architecture
» Hong Kong: Heung Gong – 'Fragrant Harbour': outstanding ex-colonial cachet on the Guǎngdōng coast
» Macau: an unforgettable cocktail of Cantonese and Portuguese flavour
» Shāmiàn Island: gentrified and leafy lozenge of Guǎngzhōu sand, decor- ated with a handsome crop of buildings and streets
## WAR & REFORM
For the Manchu, the single most devastating incident was not the Opium Wars, but the far more destructive anti-Qing Taiping War of 1856–64, an insurgency motivated partly by a foreign credo (Christianity). Established by Hakka leader Hong Xiuquan, the Heavenly Kingdom of Great Peace (Taiping Tianguo) banned opium and intermingling between the sexes, made moves to redistribute property and was fiercely anti-Manchu. The Qing eventually reconquered the Taiping capital at Nánjīng, but upwards of 20 million Chinese died in the uprising.
The events that finally brought the dynasty down, however, came in quick succession. Foreign imperialist incursions continued and Western powers nibbled away at China's coastline; Shànghǎi, Qīngdǎo, Tiānjīn, Gǔlàng Yǔ, Shàntóu, Yāntái, Wēihǎi, Níngbō and Běihǎi would all either fall under semicolonial rule or enclose foreign concessions. Hong Kong was a British colony and Macau was administered by the Portuguese. Attempts at self-strengthening – involving attempts to produce armaments and Western-style military technology – were dealt a brutal blow by the Sino-Japanese War of 1894–95. Fought over control of Korea, it ended with the humiliating destruction of the new Qing navy. Not only was Chinese influence in Korea lost, but Taiwan was ceded to Japan.
Life stories in China went through unimaginable transformations in the early 20th century. Henrietta Harrison's _The Man Awakened from Dreams_ (2005) and Robert Bickers' _Empire Made Me_ (2003) grippingly describe these changes for a rural scholar and a Shànghǎi policeman.
Japan itself was a powerful Asian example of reform. In 1868 Japan's rulers, unnerved by ever-greater foreign encroachment, had overthrown the centuries-old system of the Shōgun, who acted as regent for the emperor. An all-out program of modernisation, including a new army, constitution, educational system and railway network was undertaken, all of which gave Chinese reformers a lot to ponder.
One of the boldest proposals for reform, which drew heavily on the Japanese model, was the program put forward in 1898 by reformers including the political thinker Kang Youwei (1858–1927). However, in September 1898 the reforms were abruptly halted, as the Dowager Empress Cixi, fearful of a coup, placed the emperor under house arrest and executed several of the leading advocates of change. Two years later, Cixi made a decision that helped to seal the Qing's fate. In 1900 north China was convulsed by attacks from a group of peasant rebels whose martial arts techniques led them to be labelled the Boxers, and who wanted to expel the foreigners and kill any Chinese Christian converts. In a major misjudgement, the dynasty declared in June that it supported the Boxers. Eventually, a multinational foreign army forced its way into China and defeated the uprising which had besieged the foreign Legation Quarter in Běijīng. The imperial powers then demanded huge financial compensation from the Qing. In 1902 the dynasty reacted by implementing the Xinzheng (New Governance) reforms. This set of reforms, now half-forgotten in contemporary China, looks remarkably progressive, even set against the standards of the present day.
The Cantonese revolutionary Sun Yatsen (1866–1925) remains one of the few modern historical figures respected in both China and Taiwan. Sun and his Revolutionary League made multiple attempts to undermine Qing rule in the late 19th century, raising sponsorship and support from a wide-ranging combination of the Chinese diaspora, the newly emergent middle class, and traditional secret societies. In practice, his own attempts to end Qing rule were unsuccessful, but his reputation as a patriotic figure dedicated to a modern republic gained him high prestige among many of the emerging middle-class elites in China, though much less among the key military leaders.
The end of the Qing dynasty arrived swiftly. Throughout China's southwest, popular feeling against the dynasty had been fuelled by reports that railway rights in the region were being sold to foreigners. A local uprising in the city of Wǔhàn in October 1911 was discovered early, leading the rebels to take over command in the city and hastily declare independence from the Qing dynasty. Within a space of days, then weeks, most of China's provinces did likewise. Provincial assemblies across China declared themselves in favour of a republic, with Sun Yatsen (who was not even in China at the time) as their candidate for president.
Běijīng's Foreign Legation quarter east of Tiān'ānmén Sq still contains the old embassy buildings, churches, post offices and banks of the foreign powers of the late 19th and early 20th centuries.
## THE REPUBLIC: INSTABILITY & IDEAS
The Republic of China lasted less than 40 years on the mainland and continues to be regarded as a dark chapter in modern Chinese history, when the country was under threat from what many described as 'imperialism from without and warlordism from within'. Yet there was also breathing room for new ideas and culture. In terms of freedom of speech and cultural production, the republic was a much richer time than any subsequent era in Chinese history. Yet the period was certainly marked by repeated disasters, rather like the almost contempor- aneous Weimar Republic in Germany.
Sun Yatsen returned to China and only briefly served as president, before having to make way for militarist leader Yuan Shikai. In 1912 China held its first general election, and it was Sun's newly established Kuomintang (Nationalist; Guómíndǎng, literally 'Party of the National People') party that emerged as the largest grouping. Parliamentary democracy did not last long, as the Kuomintang itself was outlawed by Yuan, and Sun had to flee into exile in Japan. However, after Yuan's death in 1916, the country split into rival regions ruled by militarist warlord-leaders. Supposedly 'national' governments in Běijīng often controlled only parts of northern or eastern China and had no real claim to control over the rest of the country. Also, in reality, the foreign powers still had control over much of China's domestic and international situation. Britain, France, the US and the other Western powers showed little desire to lose those rights, such as extraterritoriality and tariff control.
The city of Shànghǎi became the focal point for the contradictions of Chinese modernity. By the early 20th century, Shànghǎi was a wonder not just of China, but of the world, with skyscrapers, art deco apartment blocks, neon lights, women (and men) in outrageous new fashions, and a vibrant, commercially minded, take-no-prisoners atmosphere. The racism that accompanied imperialism was visible every day, as Europeans kept themselves separate from the Chinese. Yet the glamour of modernity was undeniable too, as workers flocked from rural areas to make a living in the city, and Chinese intellectuals sought out French fashion, British architecture and American movies. In the prewar period, Shànghǎi had more millionaires than anywhere else in China, yet its inequalities and squalor also inspired the first congress of the Chinese Communist Party (CCP).
The militarist government that held power in Běijīng in 1917 provided 96,000 Chinese who served on the Western Front in Europe, not as soldiers but digging trenches and doing hard manual labour. This involvement in WWI led to one of the most important events in China's modern history: the student demonstrations of 4 May 1919.
Double-dealing by the Western Allies and Chinese politicians who had made secret deals with Japan led to an unwelcome discovery for the Chinese diplomats at the Paris Peace Conference in 1919. Germany had been defeated, but its Chinese territories – such as Qīngdǎo – were not to be returned to China but would instead go to Japan. Five days later, on 4 May 1919, some 3000 students gathered in central Běijīng, in front of the Gate of Heavenly Peace, and then marched to the house of a Chinese government minister closely associated with Japan. Once there, they broke in and destroyed the house. This event, over in a few hours, became a legend.
The student demonstration came to symbolise a much wider shift in Chinese society and politics. The May Fourth Movement, as it became known, was associated closely with the New Culture, underpinned by the exciting ideas of 'Mr Science' and 'Mr Democracy'. In literature, a May Fourth generation of authors wrote works attacking the Confucianism that they felt had brought China to its current crisis, and explored new issues of sexuality and self-development. The CCP, later mastermind of the world's largest peasant revolution, was founded in the intellectual turmoil of the movement, many of its founding figures associated with Peking University, such as Chen Duxiu (dean of humanities), Li Dazhao (head librarian) and the young Mao Zedong, a mere library assistant.
Chiang's New Life Movement and the Chinese Communist Party ideology were attempts to mobilise society through renewal of the individual. But only the communists advocated class war.
## THE NORTHERN EXPEDITION
After years of vainly seeking international support for his cause, Sun Yatsen found allies in the newly formed Soviet Russia. The Soviets ordered the fledgling CCP to ally itself with the much larger 'bourgeois' party, the Kuomintang. Their alliance was attractive to Sun: the Soviets would provide political training, military assistance and finance. From their base in Guǎngzhōu, the Kuomintang and CCP trained together from 1923, in preparation for their mission to reunite China.
Sun died of cancer in 1925. The succession battle in the party coincided with a surge in antiforeign feeling that accompanied the May Thirtieth Incident. Under Soviet advice, the Kuomintang and CCP prepared for their 'Northern Expedition', the big 1926 push north that was supposed to finally unite China. In 1926–27, the Soviet-trained National Revolutionary Army made its way slowly north, fighting, bribing or persuading its opponents into accepting Kuomintang control. The most powerful military figure turned out to be an officer from Zhèjiāng named Chiang Kaishek (1887–1975). Trained in Moscow, Chiang moved steadily forward and finally captured the great prize, Shànghǎi, in March 1927. However, a horrific surprise was in store for his communist allies. The Soviet advisers had not impressed Chiang and he was convinced their intention was to take power in alliance with the Kuomintang as a prelude to seizing control themselves. Instead, Chiang struck first. Using local thugs and soldiers, Chiang organised a lightning strike by rounding up CCP activists and union leaders in Shànghǎi and killing thousands of them.
## KUOMINTANG RULE
Chiang Kaishek's Kuomintang government officially came to power in 1928 through a combination of military force and popular support. Marked by corruption, it suppressed political dissent with great ruthlessness. Yet Chiang's government also kick-started a major industrialisation effort, greatly augmented China's transport infrastructure and successfully renegotiated what many Chinese called 'unequal treaties' with Western powers. In its first two years, the Kuomintang doubled the length of highways in China and increased the number of students studying engineering. The government never really controlled more than a few (very important) provinces in the east, however, and China remained significantly disunited. Regional militarists continued to control much of western China; the Japanese invaded and occupied Manchuria in 1931; and the communists re-established themselves in the northwest.
In 1934 Chiang Kaishek launched his own ideological counter- argument to communism: the New Life Movement. This was supposed to be a complete spiritual renewal of the nation, through a modernised version of traditional Confucian values, such as propriety, righteousness and loyalty. The New Life Movement demanded that the renewed citizens of the nation must wear frugal but clean clothes, consume products made in China rather than seek luxurious foreign goods, and behave in a hygienic manner. Yet Chiang's ideology never had much success. Against a background of massive agricultural and fiscal crisis, prescriptions about what to wear and how to behave lacked popular appeal.
The new policies did relatively little to change the everyday life for the population in the countryside, where more than 80% of China's people lived. Some rural reforms were undertaken, including the establishment of rural cooperatives, but their effects were small. The Nationalist Party also found itself unable to collect taxes in an honest and transparent way.
Exact mortality figures have never been worked out, but the minimum number of deaths in China during WWII appears to be around 15 million, with some 80 million Chinese becoming refugees.
## THE LONG MARCH
The communists had not stood still and after Chiang's treachery, most of what remained of the CCP fled to the countryside. A major centre of activity was the base area in impoverished Jiāngxī province, where the party began to try out systems of government that would eventually bring them to power. However, by 1934, Chiang's previously ineffective 'Extermination Campaigns' were making the CCP's position in Jiāngxī untenable. The CCP commenced its Long March, travelling over 6400km. Four thousand of the original 80,000 communists who set out eventually arrived, exhausted, in Shaanxi (Shǎnxī) province in the northwest, far out of the reach of the Kuomintang. It seemed possible that within a matter of months, however, Chiang would attack again and wipe them out.
The approach of war saved the CCP. There was growing public discontent at Chiang Kaishek's seeming unwillingness to fight the Japanese. In fact, this perception was unfair. The Kuomintang had undertaken retraining of key regiments in the army under German advice, and also started to plan for a wartime economy from 1931, spurred on by the Japanese invasion of Manchuria. However, events came to a head in December 1936, when the militarist leader of Manchuria (General Zhang Xueliang) and the CCP kidnapped Chiang. As a condition of his release, Chiang agreed to an openly declared United Front: the Kuomintang and communists would put aside their differences and join forces against Japan.
Mao Zedong is one of the most intriguing figures of 20th-century history. Philip Short's _Mao: A Life_ (1999) is the most detailed and thoughtful recent account of his life in English.
## WAR & THE KUOMINTANG
China's status as a major participant in WWII is often overlooked or forgotten in the West. The Japanese invasion of China, which began in 1937, was merciless, with the notorious Nanjing Massacre (also known as the Rape of Nánjīng; just one of a series of war crimes committed by the Japanese Army during its conquest of eastern China. The government had to operate in exile from the far southwestern hinterland of China, as its area of greatest strength and prosperity, China's eastern seaboard, was lost to Japanese occupation.
In China itself, it is now acknowledged that both the Kuomintang and the communists had important roles to play in defeating Japan. Chiang, not Mao, was the internationally acknowledged leader of China during this period, and despite his government's multitude flaws, he maintained resistance to the end. However, his government was also increasingly trapped, having retreated to Sìchuān province and a temporary capital at Chóngqìng. Safe from land attack by Japan, the city still found itself under siege, subjected to some of the heaviest bombing in the war. From 1940, supply routes were cut off as the road to Burma was closed by Britain, under pressure from Japan, and Vichy France closed connections to Vietnam. Although the US and Britain brought China on board as an ally against Japan after Pearl Harbor on 7 December 1941, the Allied 'Europe First' strategy meant that China was always treated as a secondary theatre of war. Chiang Kaishek's corruption and leadership qualities were heavily criticised, and while these accusations were not groundless, without Chinese Kuomintang armies (which kept one million Japanese troops bogged down in China for eight years), the Allies' war in the Pacific would have been far harder. The communists had an important role as guerrilla fighters, but did far less fighting in battle than the Kuomintang.
The Soviets withdrew all assistance from the PRC in 1960, leaving the great bridge across the Yangzi River at Nánjīng half-built. It became a point of pride for Chinese engineers to finish the job without foreign help.
The real winners from WWII, however, were the communists. They undertook important guerrilla campaigns against the Japanese across northern and eastern China, but the really key changes were taking place in the bleak, dusty hill country centred on the small town of Yán'ān, capital of the CCP's largest base area. The 'Yán'ān way' that developed in those years solidified many CCP policies: land reform involving redistribution of land to the peasants, lower taxes, a self-sufficient economy, ideological education and, underpinning it all, the CCP's military force, the Red Army. By the end of the war with Japan, the communist areas had expanded massively, with some 900,000 troops in the Red Army, and party membership at a new high of 1.2 million.
Above all, the war with Japan had helped the communists come back from the brink of the disaster they had faced at the end of the Long March. The Kuomintang and communists plunged into civil war in 1946 and after three long years the CCP won. On 1 October 1949 in Běijīng, Mao declared the establishment of the People's Republic of China. The cult of Mao's personality, which began with the sinisterly named Rectification movements during the war, would culminate in the disastrous Cultural Revolution of the 1960s.
Ding Ling's novel _The Sun Shines on the Sanggan River_ (1948) gives a graphic account of the violence, as well as the joy, that greeted land reform (ie redistribution) in China in the early 1950s.
## MAO'S CHINA
Mao's China desired, above all, to exercise ideological control over its population. It called itself 'New China', with the idea that the whole citizenry, down to the remotest peasants, should find a role in the new politics and society. The success of Mao's military and political tactics also meant that the country was, for the first time since the 19th century, united under a strong central government.
Most Westerners – and Western influences – were swiftly removed from the country. The US refused to recognise the new state at all. However, China had decided, in Mao's phrase, to 'lean to one side' and ally itself with the Soviet Union in the still-emerging Cold War. The 1950s marked the high point of Soviet influence on Chinese politics and culture. However, the decade also saw rising tension between the Chinese and the Soviets, fuelled in part by Khrushchev's condemnation of Stalin (which Mao took, in part, as a criticism of his own cult of personality). Sino-Soviet differences came to a head in 1960 with the withdrawal of Soviet technical assistance from China, and relations remained frosty until the 1980s.
Mao's experiences had convinced him that only violent change could shake up the relationship between landlords and their tenants, or capitalists and their employees, in a China that was still highly traditional. The first year of the regime saw some 40% of the land redistributed to poor peasants. At the same time, some one million or so people condemned as 'landlords' were persecuted and killed. The joy of liberation was real for many Chinese; but campaigns of terror were also real and the early 1950s were no golden age.
As relations with the Soviets broke down in the mid-1950s, the CCP leaders' thoughts turned to economic self-sufficiency. Mao, supported by Politburo colleagues, proposed the policy known as the Great Leap Forward (Dàyuèjìn), a highly ambitious plan to harness the power of socialist economics to boost production of steel, coal and electricity. Agriculture was to reach an ever-higher level of collectivisation. Family structures were broken up as communal dining halls were established: people were urged to eat their fill, as the new agricultural methods would ensure plenty for all, year after year.
During the Cultural Revolution, some 2.2 billion Chairman Mao badges were cast. Read _Mao's Last Revolution_ (2006) by Roderick MacFarquhar and Michael Schoenhals for the history; see Zhang Yimou's film _To Live_ (1994) to understand the emotions.
However, the Great Leap Forward was a monumental failure. Its lack of economic realism caused a massive famine and at least 20 million deaths. Yet the return to a semimarket economy in 1962, after the Leap had comprehensively ended, did not dampen Mao's enthusiasm for revolutionary renewal. This led to the last and most fanatical of the campaigns that marked Mao's China: the Cultural Revolution of 1966–76.
### SLOGANEERING
In communist China, political slogans were always one of the first instruments to hand in the propaganda department's ample tool chest. Typically painted in vermillion letters on walls, banners or posters, communist slogans were punchy, formulaic, systematic and unsophisticated. Their language was forthright and simple, appealing directly to the masses. The emphasis on rote learning in Chinese education gave slogans added authority and easy memorability while their appearance everywhere reinforced the ever-presence and watchfulness of the communist state. During the Cultural Revolution they became increasingly violent and intimidating. Slogans from this period survive fitfully around China, including in the following places, although many have either been scrubbed out or buried beneath cement or plaster.
» Nánjiēcūn: literally everywhere
» Chuāndǐxià: on external house walls in the village
» 798 Art District, Běijīng: throughout the district
» Huā'è Lóu: Hakka roundhouse in eastern Guǎngdōng
» Jiāyùguān Fort: in yellow letters and ghostly shadows on buildings and walls
## CULTURAL REVOLUTION
Mao had become increasingly concerned that post-Leap China was slipping into 'economism' – a complacent satisfaction with rising standards of living that would blunt people's revolutionary fervour. Mao was particularly concerned that the young generation might grow up with a dimmed spirit of revolution. For these reasons, Mao decided that a massive campaign of ideological renewal, in which he would attack his own party, must be launched.
Still the dominant figure in the CCP, Mao used his prestige to undermine his own colleagues. In summer 1966, prominent posters in large, handwritten characters appeared at prominent sites, including Peking University, demanding that figures such as Liu Shaoqi (president of the PRC) and Deng Xiaoping (senior Politburo member) must be condemned as 'takers of the capitalist road'. Top leaders suddenly disappeared from sight, only to be replaced by unknowns, such as Mao's wife Jiang Qing and her associates, later dubbed the 'Gang of Four'. Meanwhile, an all-pervasive cult of Mao's personality took over. One million youths at a time, known as Red Guards, would flock to hear Mao in Tiān'ānmén Sq. Posters and pictures of Mao were everywhere. The Red Guards were not ashamed to admit that their tactics were violent. Immense violence permeated throughout society: teachers, intellectuals and landlords were killed in their thousands.
While Mao initiated and supported the Cultural Revolution, it was also genuinely popular among many young people (who had less to lose). However, police authority effectively disappeared, creative activity came to a virtual standstill and academic research was grounded.
The Cultural Revolution could not last. Worried by the increasing violence, the army forced the Red Guards off the streets in 1969. The early 1970s saw a remarkable rapprochement between the US and China: the former was desperate to extricate itself from the quagmire of the Vietnam war; the latter terrified of an attack from the now-hostile USSR. Secretive diplomatic manoeuvres led, eventually, to the official visit of US President Richard Nixon to China in 1972, which began the reopening of China to the West. Slowly, the Cultural Revolution began to cool down, but its brutal legacy survives today. Those guilty of murder and violence re-entered society with little or no judgment while today's CCP discourages analysis and debate of the 'decade of chaos'.
## REFORM
Mao died in 1976, to be succeeded by the little-known Hua Guofeng (1921–2008). Within two years, Hua had been outmanoeuvred by the greatest survivor of 20th-century Chinese politics, Deng Xiaoping. Deng had been purged twice during the Cultural Revolution, but after Mao's death he was able to reach supreme leadership in the CCP with a radical program. In particular, Deng recognised that the Cultural Revolution had been highly damaging economically to China. Deng enlisted a policy slogan originally invented by Mao's pragmatic prime minister, Zhou Enlai – the 'Four Modernisations'. The party's task would be to set China on the right path in four areas: agriculture, industry, science and technology, and national defence.
To make this policy work, many of the assumptions of the Mao era were abandoned. The first, highly symbolic move of the 'reform era' (as the post-1978 period is known) was the breaking down of the collective farms. Farmers were able to sell a proportion of their crops on the free market, and urban and rural areas were also encouraged to establish small local enterprises. 'To get rich is glorious,' Deng declared, adding, 'it doesn't matter if some areas get rich first.' As part of this encouragement of entrepreneurship, Deng designated four areas on China's coast as Special Economic Zones (SEZs), which would be particularly attractive to foreign investors.
Politics was kept on a much shorter rein than the economy, however. Deng was relaxed about a certain amount of ideological impurity, but some other members of the leadership were concerned by the materialism in reform-era China. They supported campaigns of 'antispiritual pollution', in which influences from the capitalist world were condemned. Yet inevitably the overall movement seemed to be towards a freer, market-oriented society.
One product of the new freedom of the 1980s was a revived Chinese film industry. _Red Sorghum,_ the first film directed by Zhang Yimou, was a searingly erotic film of a type that had not been seen since 1949.
The new freedoms that the urban middle classes enjoyed created the appetite for more. After student protests demanding further opening up of the party in 1985–86, the prime minister (and relative liberal) Hu Yaobang was forced to resign in 1987 and take responsibility for allowing social forces to get out of control. He was replaced as general secretary by Zhao Ziyang, who was more conservative politically, although an economic reformer. In April 1989 Hu Yaobang died, and students around China used the occasion of his death to organise protests against the continuing role of the CCP in public life. At Peking University, the breeding ground of the May Fourth demonstrations of 1919, students declared the need for 'science and democracy', the modernising watchwords of 80 years earlier, to be revived.
In spring 1989 Tiān'ānmén Sq was the scene of an unprecedented demonstration. At its height, nearly a million Chinese workers and students, in a rare cross-class alliance, filled the space in front of the Gate of Heavenly Peace, with the CCP profoundly embarrassed to have the world's media record such events. By June 1989 the numbers in the square had dwindled to only thousands, but those who remained showed no signs of moving. Martial law was imposed and on the night of 3 June, tanks and armoured personnel carriers were sent in. The death toll has never been officially confirmed, but it seems likely to have been in the high hundreds or even more. Hundreds of people associated with the movement were arrested, imprisoned or forced to flee to the West.
For some three years, China's politics were almost frozen, but in 1992 Deng, the man who had sent in the tanks, made his last grand public gesture. That year, he undertook what Chinese political insiders called his 'southern tour', or _nánxún._ By visiting Shēnzhèn, Deng indicated that the economic policies of reform were not going to be abandoned. The massive growth rates that the Chinese economy has posted ever since have justified his decision. Deng also made another significant choice: grooming Jiang Zemin – the mayor of Shànghǎi, who had peacefully dissolved demonstrations in Shànghǎi in a way that the authorities in Běijīng had not – as his successor by appointing him as general secretary of the party in 1989.
Chinese communist politics are often hard to understand. A lively guide written by a former diplomat is Kerry Brown's _Struggling Giant: China in the 21st Century_ (2007).
## 21ST-CENTURY CHINA
Since 2002, President Hu Jintao and Prime Minister Wen Jiabao have made more efforts to deal with the inequality and poverty in the countryside, but this remains a major concern, along with reform of the CCP itself.
China has placed scientific development at the centre of its quest for growth, sending students abroad in their tens of thousands to study science and technology, and develop a core of scientific knowledge within China itself.
As a permanent member of the UN Security Council and in its quest for economic and diplomatic influence in Africa and South America, China has a powerful international role. It is, however, hesitant to assume a more influential position in international affairs. China's preference for remaining neutral but friendly and business-like may also be tested: crises such as the ever-volatile North Korean situation, Iran's nuclear ambitions and the scramble for mineral resources in Africa and energy resources around the globe mean that China is having to make hard choices about which nations it wishes to favour.
Nationalism has become a popular rallying cry at home. This does not necessarily mean xenophobia or antiforeign sentiment, although anti-Japanese feelings are easily roused. It is clear, however, that China's own people consider that the country's moment has arrived, and that they must oppose attempts – whether by the West or Japan – to prevent it taking centre stage in the region. Its long history has, for now, begun to bring China back to the prominence it once enjoyed.
TIMELINE
c 4000 BC
Archaeological evidence for the first settlements along the Yellow River (Huáng Hé). Even today, the river remains a central cultural reference point for the Chinese.
c 1700 BC
Craftsmen of the Shang dynasty master the production of bronzeware, in one of the first examples of multiple production in history. The bronzes were ritual vessels.
c 600 BC
Laotzu (Laozi), founder of Taoism, is supposedly born. The folk religion of Taoism coexisted with later introductions such as Buddhism, a reflection of Chinese religion's syncretic, rather than exclusive, nature.
551 BC
The birth of Confucius. Collected in _The Analects,_ his ideas of an ethical, ordered society that operated through hierarchy and self-development would dominate Chinese culture until the early 20th century.
214 BC
Emperor Qin indentures thousands of labourers to link existing city walls into one Great Wall, made of tamped earth. The stone-clad bastion dates from the Ming dynasty.
c 100 BC
The Silk Road between China and the Middle East means that Chinese goods become known in places as far off as Rome.
c 100 BC
Buddhism first arrives in China from India. This religious system ends up thoroughly assimilated into Chinese culture and is now more powerful in China than in its country of origin.
AD 755–763
An Lushan rebels against the Tang court. Although his rebellion is put down, the court cedes immense military and fiscal power to provincial leaders, a recurring problem through Chinese history.
874
The Huang Chao rebellion breaks out, which will help reduce the Tang empire to chaos and lead to the fall of the capital in 907.
c 1000
The major premodern inventions – paper, printing, gunpowder, compass – are commonly used in China. The economy begins to commercialise and create a countrywide market system.
1215
Genghis Khan conquers Běijīng as part of his creation of a massive Eurasian empire under Mongol rule. The Mongols overstretch themselves, however, and neglect good governance.
1286
The Grand Canal is extended to Běijīng. Over time, the canal becomes a major artery for the transport of grain, salt and other important commodities between north and south China.
1298–99
Marco Polo writes his famous account of his travels to China. Inconsistencies in his story have led some scholars to doubt whether he ever went to China at all.
1368
Zhu Yuanzhang founds the Ming dynasty and tries to impose a rigid Confucian social order on the entire population. However, China is now too commercialised for the policy to work.
1406
Ming Emperor Yongle begins construction of the 800 buildings of the Forbidden City. This complex, along with much of the Great Wall, shows the style and size of late-imperial architecture.
1557
The Portuguese establish a permanent trade base in Macau, the first of the European outposts that will eventually lead to imperialist dominance of China from the mid-19th century.
c 1600
The period of China's dominance as the world's greatest economy begins to end. By 1800 European economies are industrialising and clearly dominant.
1644
Běijīng falls to peasant rebel Li Zicheng and the last Ming emperor Chongzhen hangs himself in Jǐngshān Park; the Qing dynasty is established.
1689
The Treaty of Nerchinsk is signed, delineating the border between China and Russia: this is the first modern border agreement in Chinese history, as well as the longest lasting.
1793
British diplomat Lord Macartney visits Běijīng with British industrial products, but is told by the Qianlong emperor that China has no need of his products.
1823
The British are swapping roughly 7000 chests of opium annually – with about 140 pounds of opium per chest, enough to supply one million addicts – compared to 1000 chests in 1773.
1839
The Qing official Lin Zexu demands that British traders at Guǎngzhōu hand over 20,000 chests of opium, leading the British to provoke the First Opium War in retaliation.
1842
The Treaty of Nánjīng concludes the first Opium War. China is forced to hand over Hong Kong island to the British and open up five Chinese ports to foreign trade.
1856
Hong Xiuquan claims to be Jesus' younger brother and starts the Taiping uprising. With the simultaneous Nian and Muslim uprisings, the Taiping greatly undermines the authority of the Qing dynasty.
1882
Shànghǎi is electrified by the British-founded Shanghai Electric Company. Shànghǎi's first electricity-producing plant generates 654kw and the Bund is illuminated by electric light the following year.
1898
Emperor Guangxu permits major reforms, including new rights for women, but is thwarted by the Dowager Empress Cixi, who has many reformers arrested and executed.
1898
The New Territories adjoining Kowloon in Hong Kong are leased to the British for 99 years, eventually returning, along with the rest of Hong Kong, in 1997.
1900
The Hanlin Academy in Běijīng – centre of Chinese learning and literature – is accidentally torched by Chinese troops during the Boxer Rebellion, destroying its priceless collection of books.
1904–05
The Russo-Japanese War is fought entirely on Chinese territory. The victory of Japan is the first triumph by an Asian power over a European one.
1905
Major reforms in the late Qing, including the abolition of the 1000-year-long tradition of examinations in the Confucian classics to enter the Chinese bureaucracy.
1908
Two-year-old Puyi ascends the throne as China's last emperor. Local elites and new classes such as businessmen no longer support the dynasty, leading to its ultimate downfall.
1911
Revolution spreads across China as local governments withdraw support for the dynasty, and instead support a republic under the presidency of Sun Yatsen (fundraising in the US at the time).
1912
Yuan Shikai, leader of China's most powerful regional army, goes to the Qing court to announce that the game is up: on 12 February the last emperor, six-year-old Puyi, abdicates.
1915
Japan makes the '21 demands', which would give it massive political, economic and trading rights in parts of China. Europe's attention is distracted by WWI.
1916
Yuan Shikai tries to declare himself emperor. He is forced to withdraw and remain president, but dies of uremia later that year. China splits into areas ruled by rival militarists.
1925
The shooting of striking factory workers on 30 May in Shànghǎi by foreign-controlled police inflames Nationalist passions, giving hope to the Kuomintang party, now regrouping in Guǎngzhōu.
1926
The Northern Expedition: Kuomintang and communists unite under Soviet advice to unite China by force, then establish a Kuomintang government.
1927
The Kuomintang leader Chiang Kaishek turns on the communists in Shànghǎi and Guǎngzhōu, having thousands killed and forcing the communists to turn to a rural-based strategy.
1930s
Cosmopolitan Shànghǎi is the world's fifth-largest city (and the largest city in the Far East), supporting a polyglot population of four million people.
1930
Chiang's Kuomintang government achieves 'tariff autonomy': for the first time in nearly 90 years, China regains the power to tax imports freely, an essential part of fiscal stability.
1931
Japan invades Manchuria (northeast China), provoking an international crisis and forcing Chiang to consider anti-Japanese, as well as anticommunist, strategies.
1932
War breaks out in the streets of Shànghǎi in February–March, a sign that conflict between the two great powers of East Asia, China and Japan, may be coming soon.
1935
Mao Zedong begins his rise to paramount power at the conference at Zūnyì, held in the middle of the Long March to the northwest, on the run from the Kuomintang.
1937
The Japanese and Chinese clash at Wanping, near Běijīng, on 7 July, sparking the conflict that the Chinese call the 'War of Resistance', which only ends in 1945.
1938
Former prime minister Wang Jingwei announces he has gone over to Japan. He later inaugurates a 'restored' Kuomintang government with Japan holding the whip hand over government.
1939
On 3–4 May Japanese carpet bombing devastates the temporary Chinese capital of Chóngqìng. From 1938 to 1943, Chóngqìng is one of the world's most heavily bombed cities.
1941
In the base area at Yán'ān (Shaanxi), the 'Rectification' program begins, remoulding the Communist Party into an ideology shaped principally by Mao Zedong.
1941
The Japanese attack the US at Pearl Harbor. China becomes a formal ally of the US, USSR and Britain in WWII, but is treated as a secondary partner at best.
1943
Chiang Kaishek negotiates an agreement with the Allies that, when Japan is defeated, Western imperial privileges in China will end forever, marking the twilight of Western imperialist power in China.
1946
Communists and the Kuomintang fail to form a coalition government, plunging China back into civil war. Communist organisation, morale and ideology all prove key to the communist victory.
1949
Mao Zedong stands on top of the Gate of Heavenly Peace in Běijīng on 1 October, and announces the formation of the PRC, saying 'The Chinese people have stood up'.
1950
China joins the Korean War, helping Mao to consolidate his regime with mass campaigns that inspire (or terrify) the population.
1957
A brief period of liberalisation under the 'Hundred Flowers Movement'. However, criticisms of the regime lead Mao to crack down and imprison or exile thousands of dissidents.
1958
The Taiwan Straits Crisis. Mao's government fires missiles near islands under the control of Taiwan in an attempt to prevent rapprochement between the US and USSR in the Cold War.
1962
The Great Leap Forward causes mass starvation. Politburo members Liu Shaoqi and Deng Xiaoping reintroduce limited market reforms, which will lead to their condemnation during the Cultural Revolution.
1966
The Cultural Revolution breaks out, and Red Guards demonstrate in cities across China. The movement is marked by a fetish for violence as a catalyst for transforming society.
1972
US President Richard Nixon visits China, marking a major rapprochement during the Cold War, and the start of full diplomatic relations between the two countries.
1973
Deng Xiaoping returns to power as deputy premier. The modernising faction in the party fights with the Gang of Four, who support the continuing Cultural Revolution.
1976
Mao Zedong dies, aged 83. The Gang of Four are arrested by his successor and put on trial, where they are blamed for all the disasters of the Cultural Revolution.
1980
The one-child policy is enforced. The state adopts it as a means of reducing the population, but at the same time imposes unprecedented control over the personal liberty of women.
1987
_The Last Emperor,_ filmed in the Forbidden City, collects an Oscar for Best Picture, and marks a new openness in China towards the outside world.
1988
The daring series _River Elegy (Héshāng)_ is broadcast on national TV. It is a devastating indictment of dictatorship and Mao's rule in particular, and is banned in China after 1989.
1989
Hundreds of civilians are killed by Chinese troops in the streets around Tiān'ānmén Sq. No official reassessment has been made, but rumours persist of deep internal conflict within the party.
1997
Hong Kong is returned to the People's Republic of China. Widespread fears that China will interfere directly in its government prove wrong, but politics becomes more sensitive to Běijīng.
2001
China joins the World Trade Organization, giving it a seat at the top table that decides global norms on economics and finance.
2004
The world's first commercially operating Maglev train begins scorching a trail across Shànghǎi's Pǔdōng District.
2006
The Three Gorges Dam is completed. Significant parts of the landscape of western China are lost beneath the waters, but energy is also provided for the expanding Chinese economy.
2008
Běijīng hosts the 2008 Summer Olympic Games and Paralympics. The Games go smoothly and are widely considered to be a great success in burnishing China's image overseas.
2008
Violent riots in Lhasa, Tibet, again put the uneasy region centre stage. Protests spread to other Tibetan areas in Gānsù, Sìchuān and Qīnghǎi provinces.
2009
July riots in Ürümqi leave hundreds dead as interethnic violence flares between Uighurs and Han Chinese. Běijīng floods the region with soldiers and implements a 10-month internet blackout.
2010
A huge 7.1-magnitude earthquake in the Qīnghǎi region of the far west flattens the remote town of Yùshù in April, killing thousands.
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# The People of China
Despite being the world's most populous nation – the stamping ground of roughly one-fifth of humanity – China is often regarded as being largely homogenous, at least from a remote Western perspective. This is probably because Han Chinese – the majority ethnic type in this energetic and bustling nation – constitute over nine-tenths of the population. But rather like Chinese cuisine, and of course the nation's mystifying linguistic Babel, you only have to get your travelling shoes on and you encounter a vibrant and expectation-defying patchwork and mixed salad of ethnicities.
### Ethnic Makeup
Han Chinese – the predominant clan in China and the nation's 56th recognised ethnic group – make up the lion's share of China's people, 92% of the total figure. Because Han civilisation is the dominant culture of the land, when we think of China – from its writing system to its visual arts, calligraphy, literature and politics – we associate it with Han culture.
The Han Chinese are distributed throughout China but predomin- antly concentrate along the Yellow River, Yangzi River and Pearl River basins. A glance at the map of China, however, reveals that these core heartland regions of Han China are fragments of contemporary China's massive expanse. The colossal regions of Tibet, Qīnghǎi, Xīnjiāng, Inner Mongolia and the three provinces of the northeast (Manchuria) are all historically non-Han regions, areas of which remain essentially non-Han today.
### CHINA DEMOGRAPHICS
» Population: 1.34 billion
» Birth rate: 12.17 births per 1000 people
» Percentage of people over 65 years of age: 8.6%
» Urbanisation rate: 2.7%
» Sex ratio (under age of 15): 1.17 (boys to girls)
» Life expectancy: 74.5 years
Many of these regions are peopled by some of the remaining 8% of the population: China's 55 other ethnic minorities, known collectively as _shǎoshù mínzú_ ( 少数民族 ; minority nationals). The largest minority groups in China include the Zhuang ( 壮族 ), Manchu ( 满族 ; Man zu), Miao ( 苗族 ), Uighur ( 维吾尔族 ; Weiwu'er zu), Yi ( 彝族 ), Tujia ( 土家族 ), Tibetan ( 藏族 ; Zang zu), Hui ( 回族 ), Mongolian ( 蒙古族 ; Menggu zu), Buyi ( 布依族 ), Dong ( 侗族 ), Yao ( 瑶族 ), Korean ( 朝鲜族 ; Chaoxian zu), Bai ( 白族 ), Hani ( 哈尼族 ), Li ( 黎族 ), Kazak ( 哈萨克族 ; Hasake zu) and Dai ( 傣族 ). Population sizes differ dramatically, from the sizeable Zhuang in Guǎngxī to small numbers of Menba ( 门巴族 ) in Tibet. Ethnic labelling can be quite fluid: the roundhouse-building Hakka ( 客家 ; Kejia) were once regarded as a separate minority, but are today considered to be Han Chinese.
The Naxi created a written language over 1000 years ago using an extraordinary system of pictographs – the only hieroglyphic language still in use today.
China's minorities tend to cluster along border regions, in the northwest, the west, the southwest, the north and northeast of China, but are also distributed throughout the country. Some people are found in just one area (such as the Hani in Yúnnán); others, such as the Muslim Hui, are found across China.
Wedged into the southwest corner of China between Tibet, Myanmar (Burma), Vietnam and Laos, fecund Yúnnán province alone is home to over 20 ethnic groups, making it one of the most ethnically diverse provinces in the country. See that chapter for an introduction to the minority peoples of the region.
### ETHNIC RELATIONS
As with most fractious features of Chinese society, Běijīng goes to superhuman lengths to present China's ethnic relations as 'harmonious'. Newspapers, TV reports, museum exhibitions and ethnic performances tirelessly depict tribes of joyful minor- ities. It is part of the deintellectualisation of sensitive issues which bashes the square peg of China's ethnic relations into a seemingly round hole.
The chemistry between China's ethnic minorities and the Han majority (who wield the political and often the business power) is certainly more complex than 'harmonious'. Like an occasionally unhappy marriage, composure can be maintained on the outside, with an effort of will. When ethnic relations swiftly unravel – with occasionally shocking violence – Běijīng prefers to publicly blame 'outside forces' instead of addressing domestic causes. One of the responses to the Tibet disturbances of 2008 and the vicious Ürümqi riots of 2009 was to flood the areas with troops. Troops tend to stay in place, so they become part of the long-term stick-rather-than-carrot solution. Ürümqi also found itself without internet access for 10 months, a sign of Běijīng's distrust of access to electronic information.
### The Chinese Character
As a race, the Han Chinese are quite reserved. Shaped by Confucian principles, the Chinese of today's China are thoughtful and discreet, but also very pragmatic. Conservative and somewhat introverted, they favour dark clothing over bright or loud colours.
Chinese people (apart from the Shanghainese, some Chinese may insist) are very generous. Don't be surprised if a Chinese person you have just met on a train invites you for a meal in the dining carriage. They will probably insist on paying, in which case do not attempt to thwart their efforts. The Chinese also simply adore children and are particularly warm to them.
The Chinese are also an exceptionally proud people. They are proud of their civilisation and history, their written language and their inventions and achievements. This pride rarely comes across as arrogance or self-assurance, however, and is frequently tinged with a lack of confidence. The Chinese may, for example, be very proud of the railway to Tibet or of China's newfound world status, but there is little self-satisfaction in the nation's opaque political culture or manifest corruption.
The modern Chinese character has been shaped by recent political realities, and while Chinese people have always been reserved and circumspect, in today's China they may appear even more prudent. While Chinese people are often very honest and frank about certain things (asking your age and how much you earn or expressing a dislike for Japan), they can be painfully tight-lipped on other subjects (such as the relevance of free speech in the context of China). All of this makes the Chinese appear rather complicated, despite their reputation for being straightforward.
For an academic look at internal colonisation and Han perspectives on minority regions, read _Frontier People: Han Settlers in Minority Areas of China_ by Mette Halskov Hansen _._
### Women in China
Chairman Mao once said that women hold up half the sky. Women in today's China officially share complete equality with men; in reality, however, as with other nations that profess sexual equality, the reality is often far different. Chinese women do not enjoy strong political representation; the Chinese Communist Party is a largely patriarchal (and aged) organisation. Iconic political leaders from the early days of the Chinese Communist Party were all men and the influential echelons of the party remain a largely male domain.
High-profile, successful Chinese women are very much in the public eye, but the relative lack of career opportunities for females in other fields also indicates a continuing bias against women in employment. Women in today's China enjoy more freedom than ever before and a revolution in their status has taken place since 1949, but sexual discrimination in the workplace survives.
### WHO'S IN THE MIDDLE?
China's middle class ( _zhōng chǎn_ ) is a controversial subject: for starters, no one agrees on how it should be defined. China's State Information Centre takes a numbers approach, identifying the middle class as those whose annual income is between US$7300 and US$73,000 (Y50,000 and Y500,000). International banks and market research groups tend to raise the bar slightly higher, identifying the minimum cut-off at US$10,000 (Y68,382) and looking at factors such as whether or not households own a car, apartment, eat out regularly and so on.
Other economists, however, are less enthusiastic. Dragonomics, which publishes the _China Economic Quarterly,_ believes that middle class is a misleading term; many Chinese described as such are in fact considerably poorer than their counterparts in developed countries. Their study argues that the country consists of 'consuming China' – 110 million people living in the Běijīng, Shànghǎi and Guǎngzhōu metropolitan areas – and 'surviving China' – everyone else. But however you define it, everyone does agree that the middle class – or the consumers – are on the rise. According to the state, over half of China's urban population will have an annual income of over $7300 by 2025.
In traditional China, an ideal woman's behaviour was governed by the 'three obediences and four virtues' of Confucian ( Click here ) thought. The three obediences were: submission to the father before marriage, husband after marriage and sons in the case of widows. The four virtues were propriety in behaviour, demeanour, speech and employment.
The Communist Party after 1949 tried to outlaw old customs and put women on equal footing with men. They abolished arranged marriages and encouraged women to get an education and join the workforce. Pictures from this time show sturdy, ruddy-cheeked women with short cropped hair and overalls, a far cry from the corpulent palace ladies of the Tang or the pale, willowy beauties featured in later traditional paintings. In their quest for equality, the Communist Party successfully desexualised women in the 1950s and '60s, manufacturing a further form of imprisonment that contemporary Chinese women regard with disdain.
Women's improved social status today has meant that more women are putting off marriage until their late 20s or early 30s, choosing instead to focus on education and career opportunities. This has been enhanced by the rapid rise in house prices, further encouraging women to leave marriage (and having children) till a later age. Equipped with a good education and a high salary, they have high expectations of their future husbands (some of whom may be wary of courting girls with doctorates, in case they are outshone). Premarital sex and cohabitation before marriage are increasingly common in larger cities and lack the stigma they had several years ago.
Again, there is a strong rural–urban divide and all is not well down on the farm. Urban women are far more optimistic and freer, while women from rural areas, where traditional beliefs are at their strongest, fight an uphill battle against discrimination. Rural China is heavily weighted against girls, where a marked preference for baby boys over baby girls exists. This has resulted in an imbalance between China's population of men to women, a consequence of female foeticide, selective abortions and even infanticide. China's women are more likely to commit suicide than men (bucking the global trend), while rural Chinese women are up to five times as likely to kill themselves. When one considers the fact that most of the Chinese population lives in rural areas, the problem comes into frightening perspective.
The law can also be vicious, with handcuffed prostitutes shamefully paraded in public. Very few women smoke in public and do so in private, revealing a taboo in this area.
Chinese suspicions of most '-isms' and avoidance of collective action not proscribed by the authorities perhaps contribute to the scarcity of a feminist movement in China.
### CHINA'S ONE-CHILD POLICY
The 'one-child policy' (actually a misnomer) was railroaded into effect in 1979 in a bid to keep China's population to one billion by the year 2000; the latest government estimate claims the population will peak at 1.5 billion in 2033. The policy was originally harshly implemented but rural revolt led to a softer stance; nonetheless, it has generated much bad feeling between local officials and the rural population. All non-Han minorities are exempt from the one-child policy.
Rural families are now allowed to have two children if the first child is a girl, but some have upwards of three or four kids. Additional children often result in fines and families having to shoulder the cost of education themselves, without government assistance. Official stated policy opposes forced abortion or sterilisation, but allegations of coercion continue as local officials strive to meet population targets. The government is taking steps to punish officials who force women to undergo inhumane sterilisation procedures. Families who do abide by the one-child policy will often go to great lengths to make sure their child is male. In parts of China, this is creating a serious imbalance of the sexes – in 2007, 111 boys were born for every 100 girls. That could mean that by 2020, over 30 million men may be unable to find spouses.
### Lifestyle
The people of China today enjoy a far more diverse set of lifestyles than at any other time in their history. Beyond ethnic differences, the big divide is between the city and the countryside. The culture of the big city – with its bars, white-collar jobs, desirable schools, dynamism and cosmopolitan flair – stands in marked contrast to rural China, where little may have changed in the past three decades. Many of China's cities – take Tiānjīn, for example – are clearly international in aspiration, but the countryside remains deeply poor, especially in the southwest. China calls itself a 'developing country', which it is, but tremendous imbalances divide fully developed areas from regions that have seen little development.
Further polarisations include the generation gap. A vivid absence of sympathy exists between youngsters and their parent's, and in particu- lar their grandparent's, generation. This misunderstanding can, in a Western context, be explained by youthful rebellion and nonconform- ity. Chinese youths, however, are generally more conformist than their Western counterparts; what is more evident is the juxtapos- ition of two completely opposing political cultures and generations, one that was communist and the other which is staunchly materialist and ideology-free.
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# Religion & Beliefs
Despite the pragmatic nature of the Chinese people, ideas have always possessed a particular volatility and potency in China. Communism itself is – or was – a forceful ideology that briefly assumed immense authority over the minds of China's citizens. The Taiping Rebellion of the 19th century fused Christianity with revolutionary principles of social organisation, almost sweeping away the Qing dynasty in the process and leaving 20 million dead in its horrifying 20-year spasm. The momentary incandescence of the Boxer Rebellion drew upon a volatile cocktail of martial arts practices and superstition, fused with xenophobia. The chaos of the Cultural Revolution is perhaps further suggestion of what can happen when ideas are allowed the full supremacy they seek.
The Chinese Communist Party (CCP) today remains fearful of ideas and beliefs that compromise its primacy. Proselytising is not permitted, religious organisation is regulated and organisations such as Falun Gong can be banned. Nonetheless, worship and religious practice is generally permitted and China's spiritual world provides a vivid and colourful backdrop to contemporary Chinese life.
### Religion Today
An estimated 400 million Chinese adhere to a particular faith in today's China. Although the CCP made strident efforts after 1949 to supplant religious worship with a nationwide fervour for the secular philosophy of communism, it long ago gave up attempting to force its will. Middle aged and elderly Chinese once zealously believed in Mao Zedong's ideology, but the central tenets of that era – Marxist-Leninist collectivism and progress towards a communist society – were abandoned in favour of once heretical economic reform.
With Chinese society showing signs of stress, however, religion is enjoying an upswing as the people return to religion for spiritual solace at a time of great change and dislocation. The hopeless, poor and destitute may turn to religion as they feel abandoned by communism and the safety nets it once offered. Yet the educated and prosperous are similarly turning to religion for a sense of guidance and direction.
Religious belief in China is generally marked by great tolerance. Although faiths are quite distinct, some crossover and convergence exists between Buddhism, Taoism and Confucianism, and you may discover shrines where all three faiths have a presence. Guanyin, the Buddhist Goddess of Mercy, has an equivalent in Tianhou, the Taoist goddess and protector of fisher folk, and the two goddesses appear interchangeable. You may encounter other symbioses too: elements of Taoism and Buddhism can be discerned in the thinking of some Chinese Christians.
### Buddhism
Although not an indigenous faith, Buddhism (Fó Jiào) is the religion most deeply associated with China, Tibet and Chinatowns abroad. Buddhism's peak has long waned but the faith still exercises a powerful influence over the spiritual persona of China. Many Chinese may not be regular temple goers but they possess an interest in Buddhism; they may merely be 'cultural Buddhists', with a fondness for Buddhist civilisation.
China's oldest surviving Buddhist temple is the White Horse Temple in Luòyáng; other Buddhist temples may well have existed but have since vanished.
Chinese towns with any history should have several Buddhist temples, but the number is well down on pre-1949 figures. The small town of Zhèngdìng, for example, has four Buddhist temples, but at one time had eight. Běijīng once had hundreds of Buddhist temples, compared to the 20 or so you can find today.
Some of China's greatest surviving artistic achievements are Buddhist in inspiration. The largest and most ancient repository of Chinese, Central Asian and Tibetan Buddhist artwork can be found at the Mogao Caves in Gānsù, while the carved Buddhist caves at both Lóngmén and Yúngāng are spectacular pieces of religious and creative heritage.
#### Origins
Founded in ancient India around the 5th century BC, Buddhism teaches that all of life is suffering, and that the cause of this anguish is desire, itself rooted in sensation and attachment. Suffering can only be overcome by following the eightfold path, a set of guidelines for moral behaviour, meditation and wisdom. Those who have freed themselves from suffering and the wheel of rebirth are said to have attained nirvana or enlightenment. The term Buddha generally refers to the historical founder of Buddhism, Siddhartha Gautama, but is also sometimes used to denote those who have achieved enlightenment.
Siddhartha Gautama left no writings; the sutras that make up the Buddhist canon were compiled many years after his death.
During the Cultural Revolution, many Christian churches around China served as warehouses or factories, and were gradually rehabilitated in the 1980s.
#### Buddhism in China
Like other faiths such as Christianity, Nestorianism, Islam and Judaism, Buddhism originally reached China via the Silk Road. The earliest recorded Buddhist temple in China proper dates back to the 1st century AD, but it was not until the 4th century when a period of warlordism coupled with nomadic invasions plunged the country into disarray, that Buddhism gained mass appeal. Buddhism's sudden growth during this period is often attributed to its sophisticated ideas concerning the afterlife (such as karma and reincarnation), a dimension unaddressed by either Confucianism or Taoism. At a time when existence was especially precarious, spiritual transcendence was understandably popular.
Beyond Tibet, China has four sacred Buddhist mountains, each one the home of a specific Bodhisattva. The two most famous mountains are Wǔtái Shān and Éméi Shān, respectively ruled over by Wenshu and Puxiang.
As Buddhism converged with Taoist philosophy (through terminology used in translation) and popular religion (through practice), it went on to develop into something distinct from the original Indian tradition. The most famous example is the esoteric Chan school (Zen in Japanese), which originated sometime in the 5th or 6th century, and focused on attaining enlightenment through meditation. Chan was novel not only in its unorthodox teaching methods, but also because it made enlightenment possible for laypeople outside the monastic system. It rose to prominence during the Tang and Song dynasties, after which the centre of practice moved to Japan. Other major Buddhist sects in China include Tiantai (based on the teachings of the Lotus Sutra) and Pure Land, a faith-based teaching that requires simple devotion, such as reciting the Amitabha Buddha's name, in order to gain rebirth in paradise. Today, Pure Land Buddhism is the most common.
#### Buddhist Schools
Regardless of its various forms, most Buddhism in China belongs to the Mahayana school, which holds that since all existence is one, the fate of the individual is linked to the fate of others. Thus, Bodhisattvas – those who have already achieved enlightenment but have chosen to remain on earth – continue to work for the liberation of all other sentient beings. The most popular Bodhisattva in China is Guanyin, the Goddess of Mercy.
Ethnic Tibetans and Mongols within the PRC practise a unique form of Mahayana Buddhism known as Tibetan or Tantric Buddhism (Lǎma Jiào). Tibetan Buddhism, sometimes called Vajrayana or 'thunderbolt vehicle', has been practised since the early 7th century AD and is influenced by Tibet's pre-Buddhist Bon religion, which relied on priests or shamans to placate spirits, gods and demons. Generally speaking, it is much more mystical than other forms of Buddhism, relying heavily on mudras (ritual postures), mantras (sacred speech), yantras (sacred art) and secret initiation rites. Priests called lamas are believed to be reincarnations of highly evolved beings; the Dalai Lama is the supreme patriarch of Tibetan Buddhism.
### GUANYIN 观音
The boundlessly compassionate countenance of Guanyin, the Buddhist Goddess of Mercy, can be encountered in temples across China. The goddess (more strictly a Bodhisattva or a Buddha-to-be) goes under a variety of aliases: Guanshiyin (literally 'Observing the Cries of the World') is her formal name, but she is also called Guanzizai, Guanyin Dashi and Guanyin Pusa, or, in Sanskrit, Avalokiteshvara. Known as Kannon in Japan and Guanyam in Cantonese, Guanyin shoulders the grief of the world and dispenses mercy and compassion. Christians will note a semblance to the Virgin Mary in the aura surrounding the goddess, which at least partially explains why Christianity has found a slot in the Chinese consciousness.
In Tibetan Buddhism, her earthly presence manifests itself in the Dalai Lama, and her home is the Potala Palace in Lhasa. In China, her abode is the island of Pǔtuóshān in Zhèjiāng province, the first two syllables of which derive from the name of her palace in Lhasa.
In temples throughout China, Guanyin is often found at the very rear of the main hall, facing north (most of the other divinities, apart from Weituo, face south). She typically has her own little shrine and stands on the head of a big fish, holding a lotus in her hand. On other occasions, she has her own hall, often towards the rear of the temple.
The goddess (who in earlier dynasties appears to be male rather than female) is often surrounded by little effigies of the _luóhàn_ (or _arhat_ ; those freed from the cycle of rebirth), who scamper about; the Guānyīn Pavilion outside Dàlǐ is a good example of this. Guanyin also appears in a variety of forms, often with just two arms, but sometimes also in a multi-armed form (as at the Pǔníng Temple in Chéngdé;. The 11-faced Guanyin, the fierce horse-head Guanyin, the Songzi Guanyin (literally 'Offering Son Guanyin') and the Dripping Water Guanyin are just some of her myriad manifestations. She was also a favourite subject for _déhuà_ (white-glazed porcelain) figures, which are typically very elegant.
### Taoism
A home-grown philosophy-cum-religion, Taoism is also perhaps the hardest of all China's faiths to grasp. Controversial, paradoxical, and – like the Tao itself – impossible to pin down, it is a natural counterpoint to rigid Confucianist order and responsibility.
The Chinese verb for 'to know' is _zhīdào_ ( 知道 ), literally 'know the _dao_ ' or 'to know the way', indicating a possible Taoist etymology.
Taoism predates Buddhism in China and much of its religious culture connects to a distant animism and shamanism, despite the purity of its philosophical school. In its earliest and simplest form, Taoism draws from _The Classic of the Way and its Power_ (Taote Jing; Dàodé Jìng), penned by the sagacious Laotzu (Laozi; c 580–500 BC) who left his writings with the gatekeeper of a pass as he headed west on the back of an ox. Some Chinese believe his wanderings took him to a distant land in the west where he became Buddha.
_The Classic of the Way and its Power_ is a work of astonishing insight and sublime beauty. Devoid of a god-like being or deity, Laotzu's writings instead endeavour to address the unknowable and indescribable principle of the universe which he calls Dao ( _dào;_ 道 ), or 'the Way'. This way is the way or method by which the universe operates, so it can be understood to be a universal or cosmic principle.
The opening lines of _The Classic of the Way and its Power_ confess, however, that the treatise may fail in its task: 道可道非常道 , 名可名非常名 ; 'The way that can be spoken of is not the real way, the name that can be named is not the true name'. Despite this disclaimer, the 5000-character book, completed in terse classical Chinese, somehow communicates the nebulous power and authority of 'the Way'. The book remains the seminal text of Taoism, and Taoist purists see little need to look beyond its revelations.
One of Taoism's most beguiling precepts, _wúwéi_ (inaction) cham pions the allowing of things to naturally occur without interference. The principle is enthusiastically pursued by students of Taiji Quan, Wuji Quan and other soft martial arts (Click here ) who seek to equal nothingness in their bid to lead an opponent to defeat himself.
### Confucianism
The very core of Chinese society for the past two millennia, Confucianism (Rújiā Sīxiǎng) is a humanist philosophy that strives for social harmony and the common good. In China, its influence can be seen in everything from the emphasis on education and respect for elders to the patriarchal role of the government.
The Qin emperor Qinshi Huangdi ordered an infamous burning of Confucian writings and buried Confucians scholars alive.
Confucianism is based upon the teachings of Confucius (Kǒngzǐ;), a 6th-century-BC philosopher who lived during a period of constant warfare and social upheaval. While Confucianism changed considerably throughout the centuries, some of the principal ideas remained the same – namely an emphasis on five basic hierarchical relationships: father-son, ruler-subject, husband-wife, elder-younger, and friend-friend. Confucius believed that if each individual carried out his or her proper role in society (ie, a son served his father respectfully while a father provided for his son, a subject served his ruler respectfully while a ruler provided for his subject, and so on) social order would be achieved. Confucius' disciples later gathered his ideas in the form of short aphorisms and conversations, forming the work known as _The Analects_ (Lúnyǔ).
Early Confucian philosophy was further developed by Mencius (Mèngzǐ) and Xunzi, both of whom provided a theoretical and practical foundation for many of Confucius' moral concepts. In the 2nd century BC, Confucianism became the official ideology of the Han dynasty, thereby gaining mainstream acceptance for the first time. This was of major importance and resulted in the formation of an educated elite that served both the government as bureaucrats and the common people as exemplars of moral action. During the rule of the Tang dynasty an official examination system was created, which, in theory, made the imperial government a true meritocracy. However, this also contributed to an ossification of Confucianism, as the ideology grew increasingly mired in the weight of its own tradition, focusing exclusively on a core set of texts.
Nonetheless, influential figures sporadically reinterpreted the philosophy – in particular Zhu Xi (1130–1200) who brought in elements of Buddhism and Taoism to create Neo Confucianism (Lǐxué or Dàoxué) – and it remained a dominant social force up until the 1911 Revolution toppled the imperial bureaucracy. In the 20th century, intellectuals decried Confucian thought as an obstacle to modernisation and Mao further levelled the sage in his denunciation of 'the Four Olds'. But feudal faults notwithstanding, Confucius' call for social harmony has again resurfaced in government propaganda.
### Christianity
The explosion of interest in Christianity in China over recent years is unprecedented except for the wholesale conversions that accompanied the tumultuous rebellion of the pseudo-Christian Taiping in the 19th century. That Chinese Christians made up a considerable proportion of the volunteers helping with relief efforts after the huge Sìchuān earthquake of May 2008 indicates the increasing penetration of the religion into modern Chinese society.
Believing he was the son of God and brother of Jesus Christ, Hakka rebel Hong Xiuquan led the bloody and tumultuous pseudo-Christian Taiping Rebellion against the Qing dynasty from 1856 to 1864.
Christianity first arrived in China with the Nestorians, a sect from ancient Persia that spilt with the Byzantine Church in 431 AD, who arrived in China via the Silk Road in the 7th century. A celebrated tablet in Xī'ān records their arrival. Much later, in the 16th century, the Jesuits arrived and were popular figures at the imperial court, although they made few converts.
Large numbers of Catholic and Protestant missionaries established themselves in the 19th century, but left after the establishment of the PRC in 1949. Christianity is perhaps uniquely placed to expand in China today due to its industrious work ethic, associations with first-world nations, its emphasis on human rights and charitable work. Some estimates point to as many as 100 million Christians in China. However, the exact population is hard to calculate as many groups – outside the four official Christian organisations – lead a strict underground existence (in what are called 'house churches') out of fear of a political clampdown.
In 2003, former Běijīng bureau chief of Time magazine David Aikman wrote _Jesus in Beijing: How Christianity is Transforming China and Changing the Global Balance of Power_ , in which he predicts almost one third of Chinese turning to Christianity within 30 years.
### Islam
Islam (Yīsīlán Jiào) in China dates to the 7th century, when it was first brought to China by Arab and Persian traders along the Silk Road. Later, during the Mongol Yuan dynasty, maritime trade increased, bringing new waves of merchants to China's coastal regions, particularly the port cities of Guǎngzhōu and Quánzhōu. The descendants of these groups – now scattered across the country – gradually integrated into Han culture, and are today distinguished primarily by their religion. In Chinese, they are referred to as the Hui.
Other Muslim groups include the Uighurs, Kazaks, Kyrgyz, Tajiks and Uzbeks, who live principally in the border areas of the northwest. It is estimated that 1.5% to 3% of Chinese today are Muslim.
Kāifēng in Hénán province is home to the largest community of Jews in China. The religious beliefs and customs of Judaism (Yóutài Jiào) have died out, yet the descendants of the original Jews still consider themselves Jewish.
### Communism
Ironically (or perhaps intentionally), Mao Zedong, while struggling to uproot feudal superstition and religious belief, sprung to godlike status in China through his personality cult. In the China of today, Mao retains a semi-deified aura.
Communism sits awkwardly with the economic trajectory of China over the past 30 years. Once a philosophy forged in the white-hot crucible of civil war, revolution and the patriotic fervour to create a nation free from foreign interference, communism had largely run its credible course by the 1960s. By the death of Mao Zedong in 1976, the political philosophy had repeatedly brought the nation to catastrophe, with the Hundred Flowers Movement, the Great Leap Forward and the disastrous violence of the Cultural Revolution.
The Chinese for 'comrade' is _tóngzhì_ ( 同志 ), a term still used by elderly Chinese. Younger Chinese use it rarely, as it also means 'homosexual' or 'gay'.
Communism remains the official guiding principle of the CCP. However, young communist aspirants are far less likely to be ideologues than pragmatists seeking to advance within the party structure. In real terms, many argue that communism has become an adjunct to the survival of the CCP.
### NATIONALISM
In today's China, '-isms' ( 主义 ; _zhǔyì_ or 'doctrines') are often frowned upon. Any _zhǔyì_ may suggest a personal focus that the CCP would prefer people channel into hard work instead. 'Intellectualism' is suspect as it may clash with political taboos. 'Idealism' is non-pragmatic and potentially destructive, as Maoism showed.
Many argue that China's one-party state has reduced thinking across the spectrum via propaganda and censorship, dumbing-down and an educational system that emphasises patriotic education. This has, however, helped spawn another '-ism': nationalism.
Nationalism is not restricted to Chinese youth but it is this generation – with no experience of the Cultural Revolution's terrifying excesses – which most closely identifies with its message. The _fènqīng_ (angry youth) has been swept along with China's rise; while they are no lovers of the CCP, they yearn for a stronger China that can stand up to 'foreign interference' and dictate its own terms.
The CCP actively encourages strong patriotism, but is nervous about its transformation into nationalism and its potential for disturbance. Much nationalism in the PRC has little to do with the CCP but everything to do with China; while the CCP has struggled at length to identify itself with China's civilisation and core values, it has been only partially successful. With China's tendency to get quickly swept along by passions, nationalism is an often unseen but quite potent force in today's China.
Communism in China owes something to Confucianism. Confucius' philosophy largely concerns itself with the affairs of man and human society and the relationship between rulers and the ruled, rather than the supernatural world. Establishing a rigid framework for human conduct, the culture of Confucianism has been requisitioned by communists seeking to establish authority over society.
With the collapse of the Soviet Union in 1989, Běijīng became aware of the dangers of popular power and sought to maintain the coherence and strength of the state. This has meant that the CCP still seeks to impose itself firmly on the consciousness of Chinese people through patriotic education, propaganda, censorship, nationalism and the building of a strong nation.
Communism also has considerable nostalgia value for elderly Chinese who bemoan the loss of values in modern-day China and pine for the days when they felt more secure and society was more egalitarian. Chairman Mao's portrait still hangs in abundance across China, from drum towers in Guǎngxī province to restaurants in Běijīng, testament to a generation of Chinese who still revere the communist leader.
### Animism
Around 3% of China's population is animist, a primordial religious belief akin to shamanism. Animists see the world as a living being, with rocks, trees, mountains and people all containing spirits that need to live in harmony. If this harmony is disrupted, restoration of this balance is attempted by a shaman who is empowered to mediate between the human and spirit world. Animism is most widely believed by minority groups and exists in a multitude of forms, some of which have been influenced by Buddhism and other religions.
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Top of section
# Chinese Cuisine
While weighing up the immensity of China, it's also worth recalling that this is a land simply obsessed with food. Food plays a central and prominent role in both Chinese society and the national psyche. Work, play, romance, business and the family all revolve around food. Meals are occasions to clinch deals, strike up new friendships, rekindle old ones and fall in love. When people meet, a common Chinese greeting is ' _Nǐ chīfàn le ma_ ?' – 'Have you eaten yet?'. All you need to fully explore this tasty domain is a pair of chopsticks, an explorative palate and a passion for the unusual and unexpected.
## REAL CHINESE FOOD
Your very first impressions of China were quite possibly via your taste buds. Chinatowns the world over teem with the aromas of Chinese cuisine, ferried overseas by China's versatile and hard-working cooks. Chinese food is a wholesome point of contact – and a very tasty one at that – between an immigrant Chinese population and local people. Chinatowns across the globe swarm with diners on Sundays looking to 'yum cha' and heartily feast on dim sum.
But what you see – and taste – abroad is usually just a wafer-thin slice of a very hefty and wholesome pie. Chinese cuisine in the West is culled from the cookbook of an emigrant community that largely emerged from China's southern seaboard. In a similar vein, the sing-song melodies of Cantonese was for decades the most-heard dialect in the world's Chinatowns, even though the dialect is hardly representative of the Chinese language. So although you may be hard pressed to avoid dim sum __ and _cha siu_ in your local Chinatown, finding more 'obscure' specialties from Yúnnán, the Northeast or Xīnjiāng can be a tough task. If you do happen upon dishes from other parts of China, they may all be curiously Cantonese in flavour. Local Chinatown 'Szechuan' cooking is even further from the authentic eye-watering western cuisine of Sìchuān than its curious spelling. The Peking duck at your local restaurant is at best a distant and second-rate cousin of the authentic article crisply fired up over fruit tree wood in the ovens of Běijīng _kǎoyādiàn_ (roast duck restaurants). Běijīng chefs wouldn't go near them with a barge pole.
To get an idea of the size of its diverse menu, remember that China is not that much smaller than Europe. Just as Europe is a patchwork of different nation states, languages, cultural traditions and climates, China is similarly a smorgasbord of dialects, languages, ethnic minorities and often extreme geographic and climatic differences. Your average Tibetan nomad has never eaten dim sum __ and probably never will. Inner Mongolian herdsmen are not famed for their love of hairy crabs from Shànghǎi. The sheer size of the land, the strength of local culture and differences in geography and altitude means there can be little in common between the cuisines of Xīnjiāng and Tibet, even though they are adjacent to each other. Eating your way around China is one of the best ways to journey the land, so pack a sense of culinary adventure along with your travelling boots!
### TRAVEL YOUR TASTE BUDS
China is such a gourmand's paradise you won't know when to stop. In the north, fill up on a tasty dish of wontons _(húndún)_ , stuffed with juicy leeks and minced pork or Mongolian hotpot _(ménggǔ huǒguǒ)_ , a hearty brew of mutton, onions and cabbage.
China's arid northwest locals can pop a bowl of noodles topped with sliced donkey meat ( _lǔròu huáng miàn)_ under your nose or sizzling lamb kebobs _(kǎo yángròu)_ in your fingers. Stop by Xīān for warming bowls of mutton broth and shredded flat bread _(yángròu pàomó)._ A bowl of Lánzhōu hand-pulled noodles _(lǎ miàn)_ is a meal in itself.
In case you're pining for something sweet and savoury, head to Shànghǎi for delicious honey-smoked carp _(mìzhǐ xǔnyú)_ or a tongue-tingling plate of hot and sour squid _(suǎnlà yóuyú)._ Cleanse your palate with a glass of heady Shàoxīng yellow wine _(Shàoxǐng huángjiǔ)_ or the more delicate flavours of Dragonwell tea _(lóngjǐng chá)_ . It may not exactly give you wings, but a dish of Huángshān braised pigeon _(Huángshǎn zhāngā)_ will definitely give you the stamina to clamber up the misty inclines of Huángshān.
Some like it hot, and little comes hotter than the fiery flavours of Sìchuān. Begin with mouth-numbing mapo tofu _(mápó dòufu),_ followed by the celebrated spicy chicken with peanuts _(gǒngbào jǐdǐng)._ If the smoke still isn't coming out of your ears, fish smothered in chilli _(shuǐzhǔ yú)_ should have you breathing fire. Alternatively, test your mettle with a volcanic Chóngqìng hotpot.
In the south, relax with morning dim sum in Guǎngzhōu or a bowl of Cantonese snake soup ( _shé gēng_ ) in one of the city's boisterous night markets. While in Macau, taste the Macanese dish _porco à alentejana,_ a mouthwatering casserole of pork and clams.
And wherever you go in China you'll be pursued by the toe-curling smell of stinky tofu ( _chòu dòufu_ ) — trust us, it tastes better than it smells.
## REGIONAL COOKING
China's immense geographical, topographical and climatic disparities combined with millennia of local cooking traditions have forged China's various schools of cuisine. While many regions proudly lay claim to their own distinctive style of cooking and considerable shades exist in between, China is traditionally carved up into four principal schools: northern, eastern, western and southern.
Did you know that chilli peppers arrived in China from Peru and Mexico during the rule of the Ming dynasty?
The development of China's varied regional cuisines has been influenced by the climate, abundance of certain crops and animals, the type of terrain, proximity to the sea and last, but not least, the influence of neighbouring nations and the import of ingredients and aromas. Naturally sea fish and seafood is prevalent in coastal regions of China, while in Inner Mongolia and Xīnjiāng there is a dependence on meat such as beef and lamb.
Of their various cooking schools, the Chinese traditionally say ' 南甜北咸东辣西酸 ' or 'Sweet in the south, salty in the north, hot in the east and sour in the west'. It's a massive generalisation, but as with most generalisations, there's more than a grain of truth.
Flash-frying in hot peanut or vegetable oil is a typical sight in street-side restaurants, markets or the kitchens of even the best establishments. The technique evolved due to the historical scarcity of fuel, so meat and vegetables could be cut into small chunks and fried exceedingly quickly at a high temperature.
### Northern School
In the dry north Chinese wheat belt there's an accent on millet, sorghum, maize, barley and wheat rather than rice (which requires an abundance of water). With a more down-to-earth spectrum of flavours rather than the finer and sweeter aromas of southern cooking, northern cooking is rich and wholesome. Filling breads – such as _mántou_ ( 馒头 ) or _bǐng_ ( 饼 ; flat breads) – are steamed, baked or fried while noodles may form the basis of any northern meal, although the ubiquitous availability of rice means it can always be found. Northern cuisine is frequently quite salty, and appetising dumplings ( 铰子 ; _jiǎozi_ ) are widely eaten.
Northern cooking has a reputation in other parts of China for being rather pedestrian and unsophisticated, but it is filling and appetising and particularly well suited to the harsh and hardy winter climate.
Note, however, that Shāndōng cuisine – _lǔcài_ ( 鲁菜 ) – is also one of the eight great Chinese cooking traditions, so the northern school is far from peripheral. Furthermore, with Běijīng the principal capital through the Yuan, Ming and Qing dynasties, Imperial cooking is also a chief characteristic of the northern school. Peking Duck is Běijīng's signature dish, served with typical northern ingredients – pancakes, spring onions and fermented bean paste. You can find it all over China, but it's only true to form in the capital, roasted in ovens fired up with fruit tree wood.
The influence of Manchurian cooking and the cold climate of the three northeastern provinces – Liǎoníng, Jíli'n and Hēilóngjiāng – have left a legacy of rich and hearty stews, dense breads and dumplings. The cooking of the nomadic Mongolians has also left a pronounced mark on northern meat cooking, especially in the Mongolian hotpot and the Mongolian barbecue. Milk from nomadic herds of cattle, goats and horses has also made its way into northern cuisine, as yoghurts for example.
Meat roasting is also more common in the north than in other parts of China. Meats in northern China are braised until falling off the bone, or are slathered with spices and barbecued until smoky. Pungent garlic, chives and spring onions are used with abandon, and are also used raw.
Hallmark northern dishes:
### PINYIN | ### SCRIPT | ### ENGLISH
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_Běijīng kǎoyā_ | 北京烤鸭 | Peking duck
_jiāo zhá yángròu_ | 焦炸羊肉 | deep-fried mutton
_qīng xiāng shāo jī_ | 清香烧鸡 | chicken wrapped in lotus leaf
_shuàn yángròu_ | 涮羊肉 | lamb hotpot
_mántou_ | 馒头 | steamed buns
_jiǎozi_ | 饺子 | dumplings
_ròu bāozi_ | 肉包子 | steamed meat buns
_sān měi dòufu_ | 三美豆腐 | sliced bean curd with Chinese cabbage
_sì xǐ wánzi_ | 四喜丸子 | steamed and fried pork, shrimp and bamboo shoot balls
_yuán bào lǐ jí_ | 芫爆里脊 | stir-fried pork tenderloin with coriander
_zào liū sān bái_ | 糟溜三白 | stir-fried chicken, fish and bamboo shoots
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### Southern School
The southern Chinese – particularly the Cantonese – spearheaded successive waves of immigration overseas, leaving an aromatic constellation of Chinatowns around the world as outposts of the Chinese culinary empire. Consequently, this is the school of cooking most Westerners are very familiar with, even though, being modified to suit local tastes, it is quite different from the southern cooking of China. Cantonese cooking ( 粤菜 ; _yuècài_ ) is also further from the Western palate than many richer-tasting northern Chinese dishes.
Legend credits Marco Polo with bringing pasta to Italy from China in 1295.
The regional joshing continues: non-southern Chinese accuse southern cooking of lacking flavour. Indeed, Cantonese restaurants can be thin on the ground in China outside Cantonese-speaking areas. Cantonese restaurants, when you do find them, are frequently vast aircraft-hanger size dim sum restaurants or hotel restaurants, rather than hole-in-the-wall diners (although these can be found).
Southern cooking may lack the richness and saltiness of northern cooking, but instead more subtle aromas are tempted to the surface. The Cantonese astutely believe that good cooking does not require much flavouring, for it is the _xiān_ (natural freshness) of the ingredients that mark a truly high-grade dish. Hence the near obsessive attention paid to the freshness of ingredients in southern cuisine.
The hallmark dish is dim sum __ ( 点心 ; Mandarin: _diǎnxīn_ ), the signature dining experience of every Chinatown the world over and a standard Sunday institution. Yum cha (literally 'drink tea') – another name for dim sum dining – in Guǎngzhōu and Hong Kong can actually be enjoyed any day of the week. Dishes – often in steamers – are wheeled around on trolleys so you can see what you want to order.
Rice is the primary staple of southern cooking. Sparkling paddy fields glitter across southern China; the humid climate, plentiful rainfall and well-irrigated land means that rice has been farmed in the south since the Chinese first populated the region during the Han dynasty (206 BC–AD 220).
Southern-school dishes:
### PINYIN | ### SCRIPT | ### ENGLISH
---|---|---
_bái zhuó xiā_ | 白灼虾 | blanched prawns with shredded scallions
_dōngjiāng yánjú jī_ | 东江盐焗鸡 | salt-baked chicken
_gālí jī_ | 咖喱鸡 | curried chicken
_háoyóu niúròu_ | 蚝油牛肉 | beef with oyster sauce
_kǎo rǔzhū_ | 烤乳猪 | crispy suckling pig
_mì zhī chāshāo_ | 密汁叉烧 | roast pork with honey
_shé ròu_ | 蛇肉 | snake
_tángcù lǐjī/ gǔlǎo ròu_ | 糖醋里脊 / 咕老肉 | sweet and sour pork fillets
_tángcù páigǔ_ | 糖醋排骨 | sweet and sour spare ribs
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### HITTING THE HOT SPOT
The Sìchuān hotpot sets foreheads streaming and tummies aquiver all over China from sultry Hǎinán Island to the frigid borderlands of Hēilóngjiāng. It is a fierce and smouldering concoction, bursting with fire and boiling with volcanic flavour.
The Mongolian hotpot is a very different and more subtle creature indeed. Mutton or lamb is the principal meat in a Mongolian hotpot, with scalded strips of meat rescued from the boiling soup and doused in thick sauces, especially sesame sauce ( 芝麻酱 ; _zhīmajiàng_ ). Vegetables – cabbage, mushrooms and potatoes – are also cast into the boiling froth and eaten when soft. The hotpot dates to when Mongolian soldiers would use their helmets as a pot, heating them up over a fire with broth, meat, vege- tables and condiments.
### Western School
The cuisine of landlocked Western China, a region heavily populated by ethnic minorities, enters an entirely different spectrum of flavours and sensations. The trademark ingredient of the western school is the fiercely hot red chilli, a potent firecracker of a herb. Aniseed, coriander, garlic and peppercorns are also thrown in to give dishes that extra pungency.
The standout cuisine of the western school is fiery Sìchuān ( 川菜 ; _chuāncài_ ), renowned for its eye-watering peppery aromas. One of the herbs that differentiates Sìchuān cooking from other spicy cuisines is the use of 'flower pepper' _(huājiāo)_ , a numbing peppercorn-like herb that floods the mouth with an anaesthetising fragrance. Meat, particularly in Húnán, is marinated, pickled or otherwise processed before cooking, which is generally by stir or explode-frying.
Sìchuān restaurants are everywhere in China, swarming around train stations, squeezed away down food streets or squished into street markets with wobbly stools and rickety tables parked out front. Across the land, legions of _xiǎochī_ (hole-in-the-wall diners) are Sìchuān restaurants dishing up spicy standbys. A Sìchuān dish you can find cooked up by chefs across China is the delicious sour cabbage fish soup ( 酸菜鱼 ; _suāncàiyú_ ; wholesome fish chunks in a spicy broth). The Chóngqìng hotpot is a force to be reckoned with but must be approached with a stiff upper lip (and copious amounts of liquid refreshment). Húnán food ( 湘菜 ; _xiāngcài_ ) is similarly extremely spicy but without the numbing sensations of Sìchuān cooking. Communist firebrand Mao Zedong was a Húnán native who liked his dishes off-the-scale, like his politics.
For the lowdown on Muslim Uighur cuisine from China's northwest, see the boxed text.
Other western-school dishes:
### PINYIN | ### SCRIPT | ### ENGLISH
---|---|---
_gōngbào jīdīng_ | 宫爆鸡丁 | spicy chicken with peanuts
_shuǐ zhǔ niúròu_ | 水煮牛肉 | spicy fried and boiled beef
_shuǐzhǔyú_ | 水煮鱼 | fried and boiled fish, garlic sprouts and celery
_dāndanmiàn_ | 担担面 | spicy noodles
_huíguō ròu_ | 回锅肉 | boiled and stir-fried pork with salty and hot sauce
_Chóngqìng huǒguō_ | 重庆火锅 | Chóngqìng hotpot
_suāncàiyú_ | 酸菜鱼 | sour cabbage fish soup
_yú xiāng ròusī_ | 鱼香肉丝 | fish-flavour pork strips
_bàngbàng jī_ | 棒棒鸡 | shredded chicken in a hot pepper and sesame sauce
_gānshāo yán lǐ_ | 干烧岩鲤 | stewed carp with ham and hot and sweet sauce
_málà dòufu_ | 麻辣豆腐 | spicy tofu
_zhàcài ròusī_ | 榨菜肉丝 | stir-fried pork or beef tenderloin with tuber mustard
_zhāngchá yā_ | 樟茶鸭 | camphor tea duck
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### Eastern School
The eastern school of Chinese cuisine derives from a fecund and fertile region of China, cut by waterways and canals, dotted with lakes, fringed by a long coastline and nourished by a subtropical climate. Jiāngsū province itself – one of the core regions of the eastern school – is famed as the Land of Fish and Rice, a tribute to its abundance of food and produce. The region was also historically prosperous and in today's export-oriented economy, today's eastern provinces are among China's wealthiest. This combination of riches and bountiful food created a culture of epicurism and gastronomic appreciation.
The Song dynasty saw the blossoming of the restaurant industry here; in Hángzhōu, the southern Song dynasty capital, restaurants and teahouses accounted for two-thirds of the city's business during a splendidly rich cultural era. At this time, one of Hángzhōu's most famous dishes – _dōngpō ròu_ (named after the celebrated poet and governor of Hángzhōu, Su Dongpo) – achieved fame.
At [www.chinavista.com/
culture/cuisine/recipes.html](http://www.chinavista.com/culture/cuisine/recipes.html) there's a great collection of Chinese recipes divided by province.
Generally more oily and sweeter than other Chinese schools, the eastern school revels in fish and seafood, reflecting of its geographical proximity to major rivers and the sea. Fish is usually _qīngzhēng_ ( 清蒸 ; steamed) but can be stir-fried, pan-fried or grilled. Hairy crabs _(dàzháxiè)_ are a Shànghǎi speciality between October and December. Eaten with soy, ginger and vinegar and downed with warm Shàoxīng wine, the best crabs come from Yangcheng Lake. The crab is believed to increase the body's _yīn_ (coldness), so _yang_ (warmth) is added by imbibing lukewarm rice wine with it. It is also usual to eat male and female crabs together.
As with Cantonese food, freshness is a key ingredient in the cuisine and sauces and seasonings are only employed to augment essential flavours. Stir-frying and steaming are also used, the latter with Shànghǎi's famous _xiǎolóngbāo_ , steamer buns filled with nuggets of pork or crab swimming in a scalding meat broth. Learning how to devour these carefully without the meat juice squirting everywhere and scalding the roof of your mouth (or blinding your neighbour) requires some – quite enjoyable – practice.
China's best soy sauce is also produced in the eastern provinces, and the technique of braising meat using soy sauce, sugar and spices was perfected here. Meat cooked in this manner takes on a dark mauve hue auspiciously described as 'red', a colour associated with good fortune. ' _Nóngyóu chìjiàng_ means 'rich oil and red sauces', a defining characteristic of the cuisine', says Jereme Leung of Shànghǎi's Whampoa Club. 'Soy sauce from the region is the hardest thing to substitute when trying to produce this characteristic abroad.'
Famous dishes from the eastern school:
### PINYIN | ### SCRIPT | ### ENGLISH
---|---|---
_jiāng cōng chǎo xiè_ | 姜葱炒蟹 | stir-fried crab with ginger and scallions
_xiǎolóngbāo_ | 小笼包 | steamer buns
_mìzhī xūnyú_ | 蜜汁熏鱼 | honey-smoked carp
_níng shì shànyú_ | 宁式鳝鱼 | stir-fried eel with onion
_qiézhī yúkuài_ | 茄汁鱼块 | fish fillet in tomato sauce
_qīng zhēng guìyú_ | 清蒸鳜鱼 | steamed Mandarin fish
_sōngzǐ guìyú_ | 松子鳜鱼 | Mandarin fish with pine nuts
_suānlà yóuyú_ | 酸辣鱿鱼 | hot and sour squid
_yóubào xiārén_ | 油爆虾仁 | fried shrimp
_zhá hēi lǐyú_ | 炸黑鲤鱼 | fried black carp
_zhá yúwán_ | 炸鱼丸 | fish balls
|
|
## DINING: THE INS & OUTS
### Chinese Restaurants
Restaurants in China serve scrumptious food, but finding eateries with any sense of warmth or charm can be a real task outside the big cities. With their huge round tables and thousand-candle-power electric lights, large banqueting-style restaurants are impersonal, with little sense of intimacy or romance. Waiting staff can be both intrusive and snobbish and are rarely trained to give you breathing space. Don't be surprised if your waitress stands nearby, staring at you as you experiment with your rudimentary chopstick techniques. At the lower end of the scale are the cheap Chinese restaurants, where diners leave chicken bones on the tabletop, loudly slurp their noodles, chain-smoke and shout into mobiles. At each extreme, the food is the focal point of the meal and that is what diners are there for. Many restaurants charge for the pre-packed moist tissues which may be handed to you; you are not charged if you refuse them. Always check your bill carefully as foreigners may be overcharged in some restaurants.
### Dining Times
The Chinese eat early. Lunch usually commences from around 11.30am, either self-cooked or a takeaway at home, or in a street-side restaurant. Rushed urban diners may just grab a sandwich, a fast-food burger or a lunchbox ( 合饭 ; _héfàn_ ). Dinner usually kicks off from around 6pm. Reflecting these dining times, some restaurants open at around 11am to close for an afternoon break at about 2.30pm before opening again at around 5pm and closing in the late evening. Chinese diners don't hang around at the end of dinner parties or banquets: they may suddenly rise en masse and depart with little warning, leaving you wondering what happened.
_Chinese Cuisine_ by Susana Foo features enlightening Chinese recipes adapted for Western ingredients.
### Menus
In Běijīng, Shànghǎi and other large cities, you may be proudly presented with an English menu ( 英文菜谱 ; Yīngwén Càipǔ). In lesser towns and out in the sticks, don't expect anything other than a Chinese- language menu and a hovering waitress with zero English. The best is undoubtedly the ever-handy photo menu, even though what's pictured on the menu may be a very distant relative of what appears on your table. If you like the look of what other diners are eating, just point over with your chopsticks ( 我要那个 ; _wǒ yào nèi gè;_ 'I want that' – a very handy phrase). Alternatively, pop into the kitchen and point out the meats and vegetables you would like to eat.
The ever-elusive English language menu, if you locate one, may also be misfiring. In the run up to the Běijīng Olympic Games in 2008, the authorities attempted to standardise English translations of Chinese menus throughout the city. The plan was to rid English menus citywide of such lost-in-translation bloopers as 'government abused chicken' _(gōngbào jīdīng),_ 'grilled enema', 'potato wire' and other surreal dishes. Quite how successful this campaign was is open to question.
### TIPPING
Tipping is never done at cheap restaurants in mainland China. Smart, international restaurants will encourage tipping but it is not obligatory and it's uncertain whether waiting staff receive their tips at the end of the night. Hotel restaurants automatically add a 15% service charge and some high-end restaurants may do the same.
### Desserts & Sweets
The Chinese do not generally eat dessert, but fruit – typically watermelon _(xīguā)_ or oranges _(chéng)_ – often concludes a meal. Ice cream can be ordered in some places, but in general sweet desserts _(tiánpǐn)_ are consumed as snacks and are seldom available in restaurants.
### Table Manners
Chinese meal times are generally relaxed affairs with no strict rules of etiquette. Meals can commence in Confucian vein before spiralling into total Taoist mayhem, fuelled by incessant toasts with _báijiǔ_ (a white spirit) or beer and furious smoking by the men.
_Zòngzi_ (dumplings made of glutinous rice wrapped in bamboo or reed leaves) are eaten during the Dragon Boat festival.
Meals typically unfold with one person ordering on behalf of a group. When a group dines, a selection of dishes is ordered for everyone to share rather than individual diners ordering a dish just for themselves. As they arrive, dishes are placed communally in the centre of the table or on a lazy Susan which may be revolved by the host so that the principal guest gets first choice of whatever dish arrives. Soup may arrive midway through the meal or at the end. Rice often arrives at the end of the meal; if you would like it earlier, just ask.
It is good form to fill your neighbours' tea cups or beer glasses when they are empty. Show your appreciation to the pourer by gently tapping your middle finger on the table. To serve yourself tea or any other drink without serving others first is bad form. When your teapot needs a refill, signal this to the waiter by taking the lid off the pot.
It's best to wait until someone announces a toast before drinking your beer; if you want to get a quick shot in, propose a toast to the host. The Chinese do in fact toast each other much more than in the West, often each time they drink. A toast is conducted by raising your glass in both hands in the direction of the toastee and crying out _gānbēi_ , literally 'dry the glass', which is the cue to drain your glass in one hit. This can be quite a challenge if your drink is 65% _báijiǔ_ , and your glass is rapidly refilled to the meniscus after you drain it, in preparation for the next toast.
Smokers can light up during the meal, unless you are in the no-smoking area of a restaurant. Depending on the restaurant, smokers may smoke through the entire meal. If you are a smoker, ensure you hand around your cigarettes to others as that is standard procedure (cigarettes are generally cheap in China).
Last but not least, never insist to the last on paying for the bill if someone is tenaciously determined on paying – usually the person who invited you to dinner. By all means offer, but then raise your hands in mock surrender when resistance is met; to pay for a meal when another person is determined to pay is to make them lose face.
Chinese toothpick etiquette is similar to that found in other Asian nations: one hand excavates with the toothpick, while the other hand shields the mouth.
### CHOPSTICKS
Sooner or later you may need to start twiddling those fiddly chopsticks ( 筷子 ; _kuàizi_ ), and it's worth coming to China primed, if not totally prepared. Much Chinese food is cooked in small bite-size chunks, arriving on the table in communal dishes. Being already sliced up, there is little need for a knife, so chopsticks are perfectly suited to Chinese cuisine.
In smarter restaurants you will receive a pair of white plastic imitation ivory chopsticks that will come wrapped in its own paper sheath. You may also have a chopstick rest. Cheaper restaurants still equip diners with throwaway bamboo chopsticks which are incredibly wasteful. China gets through 45 billion pairs annually: a lot of bamboo. Don't worry about not mastering chopsticks; even Chinese diners have occasional problems with slippery button mushrooms, recalcitrant peanuts or evasive broccoli. You can practise at home with a pair of pencils! Some restaurants also use metal chopsticks, but these are quite rare. Some travellers invest in a pair of their own chopsticks, which is a good idea if you are concerned about the wastefulness of using bamboo chopsticks or have concerns regarding hygiene.
Whatever type you use, don't point them at people and don't stick them upright in bowls of rice; it's a portent of death.
### Street Food
Snacking your way around China is a fine way to sample the different flavours of the land while on the move. Most towns have a street market or a night market ( 夜市 ; _yèshì_ ) for good-value snacks and meals so you can either take away or park yourself on a wobbly stool and grab a beer. Street markets such as Kāifēng's boisterous night market abound with choices you may not find in restaurants. Vocal vendors will be forcing their tasty creations on you but you can also see what people are buying, so all you have to do is join the queue and point.
### Eating with Kids
As with travelling with children in China, dining out with kids can be a challenge. Budget eateries won't have kids' menus; nor will they have booster seats. Smarter restaurants may supply these but it can be touch and go. Children will be shrieking to go instantly to McDonalds or KFC. In large cities you will be able to find more restaurants switched on to the needs of families, especially Western restaurants that may have a play area, kids menu, activities, booster seats and other paraphernalia.
### Breakfast
Breakfast in China is generally light, simple and over-and-done-with quickly. The meal may merely consist of a bowl of rice porridge ( 粥 ; _zhōu_ ) or its watery cousin, rice gruel ( 稀饭 ; _xīfàn_ ). Pickles, boiled eggs, steamed buns, fried peanuts and deep-fried dough sticks ( 油条 ; _yóutiáo_ ) are also popular, washed down with warm soybean milk. Breakfast at your Chinese hotel may consist of some or all of these. Coffee is rarely drunk at breakfast time, unless the family is modern, urban and middle class, but it's easy to find cafes, especially in large towns. Sliced bread ( 面包 ; _miànbāo_ ) was once rare but is increasingly common, as is butter ( 黄油 ; _huángyóu_ ).
### Vegetarianism
If you'd rather chew on a legume than a leg of lamb, it can be hard going trying to find truly vegetarian dishes. China's history of famine and poverty means the consumption of meat has always been a sign of status, and is symbolic of health and wealth. Eating meat is also considered to enhance male virility, so vegetarian men raise eyebrows. Partly as a result of this, there is virtually no vegetarian movement in China, although Chinese may forgo meat for Buddhist reasons. For the same reasons, they may avoid meat on certain days of the month but remain carnivorous at other times. As a Westerner, trying to explain your secular and ethical reasons for not eating meat may inspire bemusement.
When trying to pursue a vegetarian diet in China, you will find that vegetables are often fried in animal-based oils, while vegetable soups may be made with chicken or beef stock, so simply choosing vegetable items on the menu is ineffective. In Běijīng and Shànghǎi you will, however, find a generous crop of vegetarian restaurants to choose from alongside outfits such as Element Fresh which have a decent range of healthy vegetarian options.
Out of the large cities, you may be hard pressed to find a vegetarian restaurant. Your best bet may be to head to a sizeable active Buddhist temple or monastery, where you could well find a Buddhist vegetarian restaurant that is open to the public. Buddhist vegetarian food typically consists of 'mock meat' dishes created from tofu, wheat gluten, potato and other vegetables. Some of the dishes are almost works of art, with vegetarian ingredients sculpted to look like spare ribs or fried chicken. Sometimes the chefs go to great lengths to create 'bones' from carrots and lotus roots. Some of the more famous vegetarian dishes include vegetarian 'ham', braised vegetarian 'shrimp' and sweet and sour 'fish'.
If you want to say 'I am a vegetarian' in Chinese, the phrase to use is 我吃素 _(wǒ chī sù)_ .
### Tea
An old Chinese saying identifies tea as one of the seven basic necessities of life, along with fuel, oil, rice, salt, soy sauce and vinegar. The Chinese were the first to cultivate tea, and the art of brewing and drinking tea has been popular since Tang times (AD 618–907).
Interestingly, tea was once used as a form of currency in China.
China has three main types of tea: green tea ( _lǚ chá_ ), black tea ( _hóng chá_ ) and _wūlóng_ (a semifermented tea, halfway between black and green tea). In addition, there are other variations, including jasmine _(cháshuǐ)_ and chrysanthemum _(júhuā chá)_ . Some famous regional teas of China are Fújiàn's _tiě guānyīn_ , _pú'ěr_ from Yúnnán and Zhèjiāng's _lóngjǐng_ tea. Eight-treasure tea _(bābǎo chá)_ consists of rock sugar, dates, nuts and tea combined in a cup; it makes a delicious treat. Tea is to the Chinese what fine wine is to the French, a beloved beverage savoured for its fine aroma, distinctive flavour and pleasing aftertaste.
### CHINA'S COOKING OIL SCANDAL
In 2010, diners in China were appalled to discover that one in 10 meals cooked in Chinese restaurants was prepared with cooking oil dredged up from sewers and drains. Oil is lavishly employed in Chinese cooking and generates considerable waste.
This waste oil ( 地沟油 ; _dìgōuyóu_ ) is harvested by night soil collectors who scoop out the solidified oil from drains near restaurants and sell it on for around Y300 a barrel. The oil is then processed, sold to restaurant owners and it re-enters the food chain. It is a stomach-churningly lucrative industry. Quoting a professor from Wuhan Polytechnic University, _The China Youth Daily_ revealed that up to three million tons of waste oil is recycled annually in China, or around 10% of all cooking oil consumed. The processed waste oil retails for around half the price of ordinary cooking oil but is sometimes mixed in with ordinary cooking oil prior to being sold. Once used again, there is nothing to stop the waste oil from being harvested afresh for further recycling. At present no regulations preventing the recycling of waste oil exist in China, so the industry is set to grow further.
### Alcoholic Drinks
If tea is the most popular drink in China, then beer ( 啤酒 ; _píjiǔ_ ) is surely second. Many towns and cities have their own brewery and label, although a remarkable feat of socialist standardisation ensures a striking similarity in flavour and strength. You can drink bathtubs of the stuff and still navigate a straight line. If you want your beer cold, ask for _liáng de_ ( 凉的 ) and if you want it truly arctic, call for _bīngzhèn de_ ( 冰镇的 ).
The best-known beer is Tsingtao, made with Laoshan mineral water, which lends it a sparkling quality. It's originally a German beer since the town of Qīngdǎo (formerly spelled 'Tsingtao') was once a German concession and the Chinese inherited the brewery, which dates to 1903, along with Bavarian beer-making ways. Experts claim that draught _(zhāpí)_ Tsingtao is superior to the bottled variety, although the very best can be bought by the bag on the streets of Qīngdǎo.
Several foreign beers are also brewed in China. If you crave variety, many of the bars listed in this book should have a selection of foreign imported beers; prices will be high, however.
Also look out for black beer from Xīnjiāng and dark beers from other local breweries (eg Reeb beer in Shànghǎi) which offer more bite. Rather more alternative beers include Inner Mongolian milk beer and pineapple beer from Běijīng.
China has cultivated vines and produced wine for an estimated 4000 years. The word 'wine' gets rather loosely translated – many Chinese 'wines' are in fact spirits that will have you wincing. Milder rice wine is intended mainly for cooking rather than drinking but is often drunk warm. Chinese wine-producing techniques differ from those of the West: Western producers try to prevent oxidation in their wines, but oxidation produces a flavour that Chinese tipplers find desirable and go to great lengths to achieve. Chinese diners are also keen on wines with different herbs and other materials soaked in them, which they drink for their health and for restorative or aphrodisiac qualities.
Wine with dead bees, pickled snakes or lizards is desirable for its alleged tonic properties – in general, the more poisonous the creature, the more potent the tonic effects. Maotai, a favourite of Chinese drinkers, is a spirit called _báijiǔ_ made from sorghum (a type of millet) and used for toasts at banquets. The cheap alternative is Erguotou, distilled in Běijīng but available all over China; look out for the Red Star (Hongxing) brand to avoid being hit by moonshine that will bring on a thundering hangover. _Báijiǔ_ ranges across the alcohol spectrum from milder forms to around 65% proof. In its fiercer forms, the drink is highly volatile, liable to remove the roof of your mouth and turn your legs to rubber.
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Top of section
# Arts & Architecture
China is custodian of one of the world's richest cultural and artistic legacies. Until the 20th century, China's arts were deeply conservative and resistant to change; in the last hundred years revolutions in technique and content have fashioned a dramatic transformation. Despite this evolution, China's arts – whatever the period – remain united by a common aesthetic that taps into the very soul and essence of the nation.
## AESTHETICS
In reflection of the Chinese character, Chinese aesthetics have trad- itionally been marked by restraint and understatement, a preference for oblique references over direct explanation, vagueness in place of specificity and an avoidance of the obvious and a fondness for the subtle. Traditional Chinese aesthetics sought to cultivate a more reserved art- istic impulse and these principles compellingly find their way into virtually every Chinese art form, from painting to sculpture, ceramics, calligraphy, film, poetry and literature.
## CALLIGRAPHY
Although calligraphy ( 书法 ; _shūfǎ_ ) has a place among most languages that employ alphabets, the art of calligraphy in China is taken to unusual heights of intricacy and beauty. Although Chinese calligraphy is beautiful in its own right, the complex infatuation Chinese people have for their written language helps elucidate their great respect for the art of calligraphy.
The most abstract calligraphic form is grass hand script _(cǎoshū),_ which even Chinese people have difficulty reading.
To understand how perfectly suited written Chinese is for calligraphy, it is vital to grasp how written Chinese works. A word in English represents a sound alone; a written character in Chinese combines both sound and a picture. Indeed, the sound element of a Chinese character – when present – is often auxiliary to the presentation of a visual image, even if abstract.
Furthermore, although some Chinese characters were simplified in the 1950s as part of a literacy drive, most characters have remained unchanged for thousands of years. This longevity stems from the pictorial nature of Chinese characters. As characters are essentially images, they inadequately reflect changes in spoken Chinese over time. A phonetic written language such as English alters over the centuries to reflect changes in the sound of the language. Being pictographic, Chinese cannot easily do this, so while the spoken language has transformed over the centuries, the written language remained more static. Indeed, one only has to look at the diversity of Chinese dialects – which all use the same written characters – to grasp that Chinese characters must essentially be pictorial.
The character 永, which means 'eternal', contains the five fundamental brushstrokes necessary to master calligraphy.
As Chinese calligraphers are engaged therefore in representing pictures, it is simpler to fathom why calligraphy in China is considered so vital among the arts. This also explains why Chinese calligraphy is the trickiest of China's arts to comprehend for Western visitors, unless they have a sound understanding of written Chinese. The beauty of a Chinese character may be partially appreciated by a Western audience, but for a full understanding it is also essential to understand the meaning of the character in context.
There are five main calligraphic scripts – seal script, clerical script, semicursive script, cursive script and standard script – each of which reflects the style of writing of a specific era. Seal script, the oldest and most complex, was the official writing system during the Qin dynasty and has been employed ever since in the carving of the seals and name 'chops' that are used to stamp documents. Expert calligraphers have a preference for using full-form characters _(fántǐzì)_ rather than their simplified variants _(jiǎntǐzì)_ .
## PAINTING
### Traditional Painting
Unlike Chinese calligraphy, no 'insider' knowledge is required to fully admire traditional Chinese painting. Despite its symbolism, obscure references and the occasional abstruse hand of Chinese philosophy, Chinese painting is largely accessible. For this reason, traditional Chinese paintings – especially landscapes – have long been treasured in the West for their beauty.
As described in Xie He's 6th-century-AD treatise, the _Six Principles of Painting_ , the chief aim of Chinese painting is to capture the innate essence or spirit _(qì)_ of a subject and endow it with vitality. The brush line, varying in thickness and tone, was the second principle (referred to as the 'bone method') and is the defining technique of Chinese painting. Traditionally, it was imagined that brushwork quality could reveal the artist's moral character. As a general rule, painters were less concerned with achieving outward resemblance (that was the third principle) than with conveying intrinsic qualities.
Early painters dwelled on the human figure and moral teachings, while also conjuring up scenes from everyday life. By the time of the Tang dynasty, a new genre, known as landscape painting, had begun to flower. Reaching full bloom during the Song and Yuan dynasties, landscape painting meditated on the environment around man. Towering mountains, ethereal mists, open spaces, trees and rivers, and light and dark were all exquisitely presented in ink washes on silk. Landscape paintings attempted to capture the metaphysical and the absolute, drawing the viewer into a particular realm where the philosophies of Taoism and Buddhism found expression. Man is typically a small and almost insignificant subtext to the performance. The dream-like painting sought to draw the viewer in rather than impose itself on him or her.
On a technical level, the success of landscapes depended on the artists' skill in capturing light and atmosphere. Blank, open spaces devoid of colour create light-filled voids, contrasting with the darkness of mountain folds, filling the painting with _qì_ and vaporous vitality. Specific emotions are not aroused but instead nebulous sensations permeate. Painting and classical poetry often went hand in hand, best exemplified by the work of Tang-dynasty poet/artist Wang Wei (699–759).
### Modern Art
After 1949, classical Chinese techniques had been abandoned and foreign artistic techniques imported wholesale. Washes on silk were replaced with oil on canvas and China's traditional obsession with the mysterious and ineffable made way for attention to detail and realism.
By 1970, Chinese artists had aspired to master the skills of socialist-realism, a vibrant communist-endorsed style that drew from European neo-classical art, the lifelike canvases of Jacques Louis David and the output of Soviet Union painters. Saturated with political symbolism and propaganda, the blunt artistic style was produced on an industrial scale.
The entire trajectory of Chinese painting – which had evolved in glacial increments over the centuries – had been redirected virtually overnight. Vaporous landscapes, in which people played an incidental role, had been replaced with hard-edged panoramas dominated by communists. Traditional Taoist and Buddhist philosophy was overturned; man was now a master of nature, which would bend to his will. Dreamy vistas were out; smoke stacks, red tractors and muscled peasants were in.
Human activity in these paintings was directed towards the glory of the communist revolution and the individual artistic temperament was subscripted to the service of the state. The communist vision conceived of man as the governor of his destiny; art was just another foot soldier in the quest. Dumbed-down, Chinese art became art for the masses.
Consultant designer of the Bird's Nest, Chinese artist Ai Weiwei later distanced himself from the stadium, saying it was a 'pretend smile' of bad taste; the artist has become a thorn in the side of the Chinese authorities.
It was only with the death of Mao Zedong in September 1976 that the shadow of the Cultural Revolution – when Chinese aesthetics were conditioned by the threat of violence – began its retreat. The individual artistic temperament was once again allowed freedom to explore inner persuasions. Painters such as Luo Zhongli employed the realist techniques gleaned from China's art academies to depict the harsh real- ities etched in the faces of contemporary peasants. Others escaped the suffocating confines of socialist realism to navigate new horizons. A voracious appetite for Western art introduced fresh concepts and ideas. The ambiguity of exact meaning in the fine arts also offered a degree of protection from state censors.
For in-depth articles and reviews of contemporary Chinese arts and artists, click on www.newchineseart.com, run by the Shànghǎi-based gallery Art Scene China.
One group of artists, the Stars, found retrospective inspiration in Picasso and German Expressionism. The ephemeral group had a lasting impact on the development of Chinese art in the 1980s and 1990s, paving the way for the New Wave movement that emerged in 1985. New Wave artists were greatly influenced by Western art, especially the iconoclastic Marcel Duchamp. In true nihilist style, the New Wave artist Huang Yongping destroyed his works at exhibitions, in an effort to escape from the notion of 'art'. Political realities became instant subject matter as performance artists wrapped themselves in plastic or tape to symbolise the repressive realities of modern-day China.
The Tiān'ānmén Square protests in 1989 fostered a long-lasting cynicism that permeated artworks with loss, loneliness and social isolation. An exodus of artists to the West commenced. A long-lasting liaison with pop art generated ironic commentary on the increasingly consumerist nature of Chinese society and the bankruptcy of political ideology. Cynical realists Fang Lijun and Yue Minjun fashioned grotesque portraits that conveyed hollowness and mock joviality, tinged with despair.
Much Chinese art since 1990 has dwelled obsessively on contemporary socio-economic realities, with consumer culture, materialism, urbanisation and social change a repetitive and tiring focus. More universal themes have become apparent, however, as the art scene has matured. Meanwhile, many artists who left China in the 1990s have returned, setting up private studios and galleries. Government censorship remains, but artists are branching out into other areas and moving away from overtly political content and China-specific concerns.
In 2007, Zhang Xiaogang's paintings, the most famous of which are monochromatic Cultural Revolution–era family-style portraits, earned nearly US$57 million in auctions, the second-highest amount among living artists anywhere. In 2008 Christie's in Hong Kong sold Zeng Fanzhi's painting _Mask Series 1996 No. 6_ (featuring masked members of China's communist youth organisation, the Young Pioneers) for US$9.7 million, which is the highest price yet paid for a contemporary Chinese artwork.
Major art festivals in China include Běijīng's 798 International Art Festival (May), China International Gallery Exposition (October) and Běijīng Biennale (October 2011); the Shànghǎi Biennale (September to November 2012); Guǎngzhōu Triennial (September to November 2011); and Hong Kong's one-day Clockenflap festival (no set dates).
## CERAMICS
China's very first vessels – dating back over 8000 years – were simple handcrafted earthenware pottery, primarily used for religious purposes. The invention of the pottery wheel during the late Neolithic period, however, led to a dramatic technological and artistic leap.
In 2010, a Qing dynasty Chinese vase sold for £53.1 million after being discovered in the attic of a house in northwest London and put up for auction.
Over the centuries, Chinese potters perfected their craft, introducing many new exciting styles and techniques. The spellbinding artwork of the Terracotta Warriors in Xī'ān reveals a highly developed level of technical skill achieved by Qin-dynasty craftsmen. Periods of artistic development, under the cosmopolitan Tang dynasty, for example, prompted further stylistic advances. The Tang dynasty 'three-colour ware' is a much admired type of ceramic from this period, noted for its vivid yellow, green and white glaze. Demand for lovely blue-green celadons grew in countries as distant as Egypt and Persia.
The Yuan dynasty saw the first development of China's standout 'blue-and-white' _(qīnghuā)_ porcelain. Cobalt blue paint, from Persia, was applied as an underglaze directly to white porcelain with a brush, the vessel was covered with another transparent glaze, and fired. This technique was perfected during the Ming and such ceramics became hugely popular all over the world, eventually acquiring the name 'China- ware', whether produced in China or not.
Although many different kilns were established over China, the most famous was at Jǐngdézhèn in Jiāngxī province, where royal porcelain was fired up.
During the Qing dynasty, porcelain techniques were further refined and developed, showing superb craftsmanship and ingenuity. British and European consumers dominated the export market, displaying an insatiable appetite for Chinese vases and bowls decorated with flowers and landscapes. The Qing is also known for its stunning monochromatic ware, especially the ox-blood vases and highly meticulous imperial yellow bowls, and enamel decorated porcelain. The Qing is also notable for its elaborate and highly decorative wares.
Jǐngdézhèn remains an excellent place to visit ceramic workshops and purchase various types of ceramic wares, from Mao statues to trad- itional glazed urns. The Shànghǎi Museum has a premier collection of porcelain, while several independent retailers in Běijīng and Shànghǎi also sell more modish and creative pieces.
## SCULPTURE
The earliest sculpture in China dates to the Zhou and Shang dynasties, when small clay and wooden figures were commonly placed in tombs to protect the dead and guide them on their way to heaven.
With the arrival of Buddhism, sculpture turned towards spiritual figures and themes, with sculptors frequently enrolled in huge carving projects for the worship of Sakyamuni. Influences also arrived along the Silk Road from abroad, bringing styles from as far afield as Greece and Persia, via India. The magnificent Buddhist caves at Yúngāng in Shānxī province date back to the 5th century and betray Indian influence.
Chisellers also began work on the Lóngmén Caves in Hénán province at the end of the 5th century. The earliest effigies are similar in style to those at Yúngāng, revealing Indian influence and more other-worldliness in their facial expressions. Later cave sculptures at Lóngmén were completed during the Tang dynasty and reveal a more Chinese style.
The most superlative examples are at the Mògāo Caves at Dūnhuáng in Gānsù province, where well-preserved Indian and Central Asian style sculptures, particularly of the Tang dynasty, carry overtly Chinese characteristics – many statues feature long, fluid bodies and have warmer, more refined facial features.
The Shànghǎi Museum has a splendid collection of Buddhist sculpture, as does Capital Museum and the Poly Art Museum, both in Běijīng.
Beyond China's grottoes, other mesmerising Chinese sculpture hides away in temples across China. The colossal statue of Guanyin in Pǔníng Temple in Chéngdé is a staggering sight, carved from five different types of wood and towering over 22m in height. Shuānglín Temple outside Píngyáo in Shānxī province is famed for its painted statues from the Song and Yuan dynasties.
### BATTLE OF THE BUDDHAS
Hands down China's largest Buddha gazes out over the confluence of the waters of the Dàdù River and the Mín River at Lèshān in Sìchuān. When the even bigger Buddha at Bamyan in Afghanistan was demolished by the Taliban, the Lèshān Buddha enjoyed instantaneous promotion to the top spot as the world's largest. The Buddha in the Great Buddha Temple at Zhāngyè in Gānsù province may not take it lying down, though: he is China's largest 'housed reclining Buddha'. Chinese children once climbed inside him to scamper about within his cavernous tummy.
Lounging around in second place is the reclining Buddha in the Mògāo Caves, China's second largest. The vast reclining Buddha at Lèshān is a whopping 170m long and the world's largest 'alfresco' __ reclining Buddha. Bristling with limbs, the Thousand Arm Guanyin statue in the Pǔníng Temple's Mahayana Hall in Chéngdé also stands up to be counted: she's the largest wooden statue in China (and possibly the world). Not to be outdone, Hong Kong fights for its niche with the Tian Tan Buddha Statue, the world's 'largest outdoor seated bronze Buddha statue'.
## LITERATURE
### Classical Poetry
From the Han dynasty through the Song dynasty, Chinese poetry was the primary means of literary expression for the educated elite and is still considered China's most sophisticated literary genre.
The traditional Chinese character for poetry 詩 _(shī)_ consists of 'words' 言 (the meaning element) placed next to a 'temple' 寺 (the sound element).
Even more so than classical Chinese, classical poetry employs a vastly pared down syntax (articles, prepositions, plurals and sometimes even the subject are implicit) to maximise brevity and to ensure each line has an equal number of characters (and therefore syllables). The use of rhyme, parallel couplets, word play, harmony, literary allusion and assonance were all of central importance. Classical poems aim to conjure up a 'painting' through which the poet could evoke his or her emotion. The written character is also an important part of this representation, as each character is a picture in itself, so images are partially conjured up by their effective employment.
For a translation of Tang dynasty verse, try to find a copy of Vikram Seth's _Three Chinese Poets_ .
China's earliest collection of poems is the _Book of Songs_ (Shījìng; also called the Classic of Poetry), apocryphally collated by Confucius and dating to the sixth century BC. One of the five classics, the _Book of Songs_ contains over 300 delightful poems infused with pastoral themes and folk rhythms.
_The Song of Chu_ (Chǔcí), contains poems by Qu Yuan (c 340–278 BC), China's greatest early poet and author of _Li Sao_ (The Lament). Another of China's most famous poets was Tao Yuanming (365–427), much loved for the unfussiness of his landscape verse.
Classical poetry matured into a golden age during the Tang dynasty (618–907), when trade with the outside world burgeoned and China prospered. It was also a time of stunning artistic invention and creativity, reflected in the poetry of the day. Li Bai (Li Po; the Taoist), Du Fu (Tu Fu; the Confucian), Wang Wei (the Buddhist) and Bai Juyi (the Populist – he purportedly rewrote all poems his servants were unable to understand) were all Tang poets. Other great poets of this era include Meng Haoran, Liu Zongyuan and Li Shangying. Li Bai in particular is much-loved by the Chinese for his Taoist eccentricities and devotion to nature and wine, while Du Fu is admired for his more restrained and occasionally maudlin eloquence. At the start of the Tang dynasty a type of strict eight-line verse called _lǜshī_ appeared, which brought structure and symmetry to classical poetry.
During the Song dynasty a more romantic lyric poetry called _cí_ emerged – originally lyrics intended to be set to music. Su Shi (Su Dongpo), Li Qingzhao and Ou Yangxiu are some of the most famous poets from this era.
With the rapid decline of classical literature in the early 20th century, Chinese verse came under the revolutionising influence of Western poetic devices and techniques, an acquisition that permanently changed its complexion.
### Classical Novels
Until the early 20th century, classical literature ( 古文 ; _gǔwén_ ) had been the principal form of writing in China for thousands of years. A breed of purely literary writing, classical Chinese employed a stripped-down form of written Chinese that did not reflect the way people actually spoke or thought. Its grammar differed from the syntax of spoken Chinese and it employed numerous obscure Chinese characters. Classical Chinese maintained divisions between educated and uneducated Chinese, putting literature beyond the reach of the common person and fashioning a cliquey lingua franca __ for Confucian officials and scholars.
The _I Ching_ (Yìjīng; Book of Changes) is the oldest Chinese text and is used for divination. It is comprised of 64 hexagrams, composed of broken and continuous lines, that represent a balance of opposites (yin and yang), the inevitability of change and the evolution of events.
Classical novels evolved from the popular folktales and dramas that entertained the lower classes. During the Ming dynasty they were penned in a semi-vernacular (or 'vulgar') language, and are often irreverently funny and full of action-packed fights.
The best-known novel outside China is _Journey to the West_ (Xīyóu Jì) – more commonly known as _Monkey_ . Written in the 16th century, it follows the misadventures of a cowardly Buddhist monk (Tripitaka; a stand-in for the real-life pilgrim Xuan Zang) and his companions – a rebellious monkey, lecherous pig-man and exiled monster-immortal – on a pilgrimage to India. In 2007 a Chinese director collaborated with the creators of the virtual band Gorillaz to transform the story into a circus opera that has played to considerable international acclaim.
_The_ _Water Margin/Outlaws of the Marsh/All Men Are Brothers_ (Shuǐhǔ Zhuàn) is, on the surface, an excellent tale of honourable bandits and corrupt officials along the lines of Robin Hood. On a deeper level, though, it is a reminder to Confucian officials of their right to rebel when faced with a morally suspect government (at least one emperor officially banned it).
### Modern Literature
Classical Chinese maintained its authority over literary minds till the early 20th century, until it came under the influence of the West.
Torch-bearing author Lu Xun wrote his short story _Diary of a Madman_ in 1918. It was revolutionary stuff. The opening paragraph of Lu's seminal and shocking fable is conceived in classical (archaic) language. The stultified introduction – peppered with archaic characters and the excruciatingly pared-down grammar of classical Chinese – presents itself as one solid block of text, without new paragraphs or indentation. The passage concludes abruptly and the reader is confronted with colloquial and vernacular Chinese _(báihuà)_ : 今天晚上 , 很好的月光 ( _jīntiān wǎnshàng, hěnhǎo de yuèguāng_ ; 'Tonight there is good moonlight.').
The story continues in modern Chinese to its conclusion. For Lu Xun to write his short story in the spoken vernacular was explosive, as Chinese people were finally able to read language as it was spoken. Magnifying the power of the story was its subject matter: the diary's narrator is convinced those around him are cannibals (a metaphor for the self-consuming nature of traditional, Confucian society). _Diary of a Madman_ is a haunting and unsettling work, raising doubts as to the real madness of its narrator and concluding with lines that offer a glimmer of salvation. From this moment on, mainstream Chinese literature would be written as it was thought and spoken: Chinese writing had been instantaneously modernised.
_The Book and the Sword_ by Jin Yong/Louis Cha (2004) is China's most celebrated martial-arts novelist's first book. The martial-arts genre _(wǔxiá xiǎoshuō)_ is a direct descendant of the classical novel.
Other notable contemporaries of Lu Xun include Ba Jin ( _Family_ ; 1931), Mao Dun ( _Midnight_ ; 1933), Lao She ( _Rickshaw Boy/Camel Xiangzi_ ; 1936) and the modernist playwright Cao Yu ( _Thunderstorm_ ). Lu Xun and Ba Jin translated a great deal of foreign literature into Chinese.
Few contemporary voices have been translated into English, but there's enough material to keep a serious reader busy. The provocative Mo Yan ( _Life and Death Are Wearing Me Out_ ; 2008), Yu Hua ( _To Live_ ; 1992) and Su Tong ( _Rice_ ; 1995) have written momentous historical novels set in the 20th century; all are excellent, though not for the faint of heart. Zhu Wen mocks the get-rich movement in his brilliantly funny short stories, published in English as _I Love Dollars and Other Stories of China_ (2007). It's a vivid and comic portrayal of the absurdities of everyday China.
_Wolf Totem_ (2009) by Jiang Rong is an astonishing look at life on the grasslands of Inner Mongolia during the Cultural Revolution and the impact of modern culture on an ancient way of life.
'Hooligan author' Wang Shuo ( _Please Don't Call Me Human_ ; 2000) remains China's best-selling author with his political satires and convincing depictions of urban slackers. Chun Sue ( _Beijing Doll_ ; 2004) and Mian Mian ( _Candy_ ; 2003) examine the dark urban underbellies of Běijīng and Shànghǎi, respectively. Alai ( _Red Poppies_ ; 2002), an ethnic Tibetan, made waves by writing in Chinese about early-20th-century Tibetan Sìchuān – whatever your politics, it's both insightful and a page-turner. Émigré Ma Jian ( _Red Dust_ ; 2004) writes more politically critical work; his debut was a Kerouacian tale of wandering China as a spiritual pollutant in the 1980s. China's most renowned dissident writer, Gao Xingjian, won the Nobel Prize for Literature in 2000 for his novel _Soul Mountain_ , an account of his travels along the Yangzi after being misdiagnosed with lung cancer. All of his work has been banned in the PRC since 1989.
In _The Vagrants_ (2009), author Yi Yunli fashions a wonderfully written, bleak and disturbing portrait of dissent and oppression in a Chinese town in 1979.
Controversial blogger Han Han catapulted himself into the literary spotlight with his novel _Triple Door_ , a searing critique of China's educational system.
### NON-NATIVE TONGUES
Beyond translations of famous Chinese works, an accessible corpus of literature exists from Chinese émigrés conceiving works in English and French.
» _Wild Swans_ (Jung Chang; 1992) Prize-winning autobiographical saga about three generations of Chinese women struggling to survive the tumultuous events of 20th-century China. Chang is also the co-author of the controversial best-selling biography _Mao: The Unknown Story_ (2005).
» _Balzac and the Little Seamstress_ (Dai Sijie; 2000) Two teenagers find a secret cache of Western novels during the Cultural Revolution, helping them – and the local tailor's daughter – to escape from the tediousness of rural re-education. Originally written in French.
» _A Concise Chinese-English Dictionary for Lovers_ (Guo Xiaolu; 2007) Written deliberately in Chinglish, Guo humorously recounts the experiences of a Chinese girl sent to London to study.
» _Ocean of Words_ (1996) _, Waiting_ (1999), _The Bridegroom_ (2000) _, The Crazed_ (2002) _, War Trash_ , _A Free Life_ (2007) __ The most prolific of the diaspora writers, Ha Jin has won both the National Book Award (USA) and the PEN/Faulkner Award (among others).
» _A Thousand Years of Good Prayers_ (Yiyun Li; 2006) Prize-winning short stories depicting the lives of everyday Chinese caught up in the changes of the past two decades.
» _Red Azalea_ (1994), _Becoming Madame Mao_ (2000), _Wild Ginger_ (2002), _Empress Orchid_ (2004), _The Last Empress_ (2007) __ Anchee Min spins fiction out of the life stories of some of China's most ambitious (and least-loved) women.
» _Death of a Red Heroine_ (2000), _A Loyal Character Dancer_ (2002), _When Red is Black_ (2004), _A Case of Two Cities_ (2006), _Red Mandarin Dress_ (2007), _The Mao Case_ (2009) Qiu Xiaolong's insightful Inspector Chen novels feature a literary-minded cop and a vivid street-level portrayal of changing Shànghǎi.
» _The Girl Who Played Go_ (Shan Sa; 2001) A local girl in Japanese-occupied Manchuria and an undercover Japanese soldier match wits in an epic game of go _(wéiqí)_ and in the process fall fatally in love. Originally written in French.
» _The People's Republic of Desire_ (Annie Wang; 2006) A candid exploration of sexuality in modern Běijīng.
» _On the Smell of an Oily Rag_ (Yu Ouyang; 2008) Clever cross-cultural observances from a Chinese émigré living in Australia.
## FILM
The moving image in the Middle Kingdom dates to 1896, when Spaniard Galen Bocca unveiled a film projector and blew the socks off wide-eyed crowds in a Shànghǎi teahouse. Shànghǎi's cosmopolitan verve and exotic looks would make it the capital of China's film industry, but China's very first movie – _Conquering Jun Mountain_ (an excerpt from a piece of Beijing Opera) – was actually filmed in Běijīng in 1905.
A worker in a foot-massage parlour is raped by her boss, setting in motion a series of devastating consequences for both of them in Li Yu's _Lost in Beijing_ (2007).
Shànghǎi opened its first cinema in 1908. In those days, cinema owners would cannily run the film for a few minutes, stop it and collect money from the audience before allowing the film to continue. The golden age of Shànghǎi film-making came in the 1930s when the city had over 140 film companies. Its apogee arrived in 1937 with the release of _Street Angel_ , a powerful drama about two sisters who flee the Japan- ese in northeast China and end up as prostitutes in Shànghǎi; and _Crossroads_ , a clever comedy about four unemployed graduates. Japanese control of China eventually brought the industry to a standstill and sent many film-makers packing.
China's film industry was stymied after the Communist Revolution, which sent film-makers scurrying to Hong Kong and Taiwan, where they played key roles in building up the local film industries that flourished there. Cinematic production in China was co-opted to glorify communism and generate patriotic propaganda. The days of the Cultural Revolution (1966–76) were particularly dark. Between 1966 and 1972, just eight movies were made on the mainland, as the film industry was effectively shut down.
The 2010 remake of _The Karate Kid_ , starring Jackie Chan, is set in Běijīng and authentically conveys the city despite having nothing to do with karate.
It wasn't until two years after the death of Mao Zedong that the Běijīng Film Academy, China's premier film school, reopened in September 1978. Its first intake of students included Zhang Yimou, Chen Kaige and Tian Zhuangzhuang – masterminds of the celebrated 'Fifth Generation'. The cinematic output of the Fifth Generation signalled an escape from the dour, colourless and proletarian Mao era, and a second glittering golden age of Chinese film-making arrived in the 1980s and 1990s with their lush and lavish tragedies. A bleak but beautifully shot tale of a Chinese Communist Party cadre who travels to a remote village in Shaanxi province to collect folk songs, Chen Kaige's _Yellow Earth_ aroused little interest in China but proved a sensation when released in the West in 1985.
Wong Kar Wai's outstanding _Chungking Express_ (1994) __ and _In the Mood for Love_ (2000) are examples of Hong Kong movie-making at its very best.
It was followed by Zhang's _Red Sorghum_ , which introduced Gong Li and Jiang Wen to the world. Gong became the poster girl of Chinese cinema in the 1990s and the first international movie star to emerge from the mainland. Jiang, the Marlon Brando of Chinese film, has proved both a durable leading man and an innovative, controversial director of award-winning films such as _In the Heat of the Sun_ and _Devils on the Doorstep_ .
Rich, seminal works such as _Farewell My Concubine_ (1993; Chen Kaige) and _Raise the Red Lantern_ (1991; Zhang Yimou) were garlanded with praise, receiving standing ovations and winning major film awards. Their directors were the darlings of Cannes; Western cinema-goers were entranced. Many Chinese cinema-goers also admired their artistry, but some saw Fifth Generation output as pandering to the Western market.
In 1993, Tian Zhuangzhuang made the brilliant _The Blue Kite_ . A heartbreaking account of the life of one Běijīng family during the Cultural Revolution, it so enraged the censors that Tian was banned from making films for years.
Each generation charts its own course and the ensuing Sixth Generation – graduating from the Běijīng Film Academy post–Tiān'ānmén Square protests – was no different. Sixth Generation film directors eschewed the luxurious beauty of their forebears, and sought to capture the angst and grit of modern urban Chinese life. Their independent, low-budget works put an entirely different and more cynical spin on mainland Chinese film-making, but their darker subject matter and harsh film style (frequently in black and white) left many Western viewers cold.
Independent film-making found an influential precedent with Zhang Yuan's 1990 debut _Mama_ . Zhang is also acclaimed for his candid and gritty documentary-style _Beijing Bastards_ (1993). _The Days_ , directed by Wang Xiaoshui, follows a couple drifting apart in the wake of the Tiān'ānmén Square protests. Wang also directed the excellent _Beijing Bicycle_ (2001), inspired by De Sica's _Bicycle Thieves_ .
Jia Zhangke has emerged as the most acclaimed of China's new film-makers. His meditative and compassionate look at the social impact of the construction of the Three Gorges Dam on local people, _Still Life_ (2006), scooped the Golden Lion at the 2006 Venice Film Festival.
In a protectionist move, Běijīng caps the number of foreign films that can be shown annually in cinemas to around 20. Yet the film industry in China still has to outmanoeuvre taboos. Directors still walk on eggshells and even oblique criticism of the authorities remains hazardous. Many Chinese directors seek sanctuary in the highly popular historical and martial-arts epics starring Andy Lau, Jet Li and Samo Hong, but these may have increasingly limited appeal abroad, while contemporary Chinese TV dramas are often wooden and clunky, hobbled by creative hesitancy.
## ARCHITECTURE
### Traditional Architecture
Four principal styles governed traditional Chinese architecture: imperial, religious, residential and recreational. The imperial style was naturally the most grandiose, overseeing the design of buildings employed by successive dynastic rulers; the religious style was employed for the construction of temples, monasteries and pagodas, while the residential and recreational style took care of the design of houses and private gardens.
Building boom: China consumes roughly 50% of the world's concrete and 36% of its steel.
Whatever the style, Chinese buildings traditionally followed a similar basic ground plan, consisting of a symmetrical layout oriented around a central axis – ideally running north–south, to conform with basic feng shui _(fēngshuǐ)_ dictates and to maximise sunshine – with an enclosed courtyard _(yuàn)_ flanked by buildings on all sides.
In China, tower blocks are only built to last for 25 to 30 years. In 2009, a newly-built Shànghǎi tower block collapsed, killing one worker and raising further concerns about quality control.
In many aspects, imperial palaces are glorified courtyard homes (south-facing, a sequence of courtyards, side halls and perhaps a garden at the rear) completed on a different scale. Apart from the size, the main dissimilarity would be guard towers on the walls and possibly a moat, imperial yellow roof tiles, ornate dragon carvings (signifying the emperor), the repetitive use of the number nine and the presence of temples.
Many residential quarters of the well-to-do, and temples or halls within imperial palaces were protected by a spirit wall _(yǐngbì)_ at their entrance, designed to thwart bad spirits, but also to put a stop to prying eyes. Despite the loss of countless spirit walls, China remains dotted with them, often obsolete as the buildings they once shielded have vanished. Dàtóng's Nine Dragon Screen is a spectacular example.
Behind the entrance in palaces and wealthier residential buildings stood a public hall; behind this was the private living quarters, erected around another courtyard with a garden; most buildings were constructed as one-storey edifices. A sense of harmony prevailed over the entire design, ordered by symmetry and a certain reserve, which also meant that no one particular structure took precedence. Compounds were enlarged simply by adding more courtyards.
### Religious Architecture
Chinese Buddhist, Taoist and Confucian temples tend to follow a strict, schematic pattern. All temples are laid out on a north–south axis in a series of halls, with the main door of each hall facing south.
Chinese temples are very different from Christian churches, with a sequence of halls and buildings interspersed with breezy open-air courtyards. The roofless courtyards allow the weather to permeate within the temple and also permits the _qì_ ( 气 ) to circulate, dispersing stale air and allowing incense to be burned.
#### Buddhist Temples
Once you have cracked the logic of Buddhist temples, you can discover how most temples conform to a predictable pattern.
The first hall and access portal to the temple is generally the Hall of Heavenly Kings, where a sedentary, central statue of the tubby Bodhisattva Maitreya is flanked by the ferocious Four Heavenly Kings. Behind you'll find the first courtyard, where the Drum Tower and Bell Tower may rise to the east and west and smoking braziers may also be positioned.
The main hall is often the Great Treasure Hall sheltering glittering statues of the past, present and future Buddhas, seated in a row. This is the main focal point for worshippers at the temple. On the east and west interior wall of the hall are often 18 _luóhàn_ (arhat) in two lines, either as statues or paintings. In some temples, they gather in a throng of 500, housed in a separate hall. A statue of Guanyin (the Goddess of Mercy) frequently stands at the rear of the main hall, facing north, atop a fish's head or a rocky outcrop. The goddess may also be venerated in her own hall and occasionally presents herself with a huge fan of arms, in her 'Thousand Arm' incarnation. The awesome effigy of Guanyin in the Mahayana Hall at Pǔníng Temple in Chéngdé is the supreme example.
The rear hall may be where the sutras (Buddhist scriptures) were once stored, in which case it will be called the Sutra Storing Building. A pagoda may rise above the main halls or may be the only surviving fragment of an otherwise destroyed temple. Conceived to house the remains of Buddha and later other Buddhist relics, pagodas were also used for storing sutras, religious artefacts and documents.
#### Taoist Temples
Taoist shrines are more nether-worldly than Buddhist shrines, although the basic layout echoes Buddhist temples. Decorated with a distinct set of motifs, including the _bāguà_ (eight trigrams) formations, reflected in eight-sided pavilions and halls and the Taiji yin/yang _(yīn/yáng)_ diagram. Effigies of Laotzu, the Jade Emperor and other characters popularly associated with Taoist myth, such as the Eight Immortals and the God of Wealth, are customary.
Taoist temple entrances are often guarded by Taoist door gods, similar to Buddhist temples; the main hall is usually called the Hall of the Three Clear Ones, devoted to a triumvirate of Taoist deities.
Taoist monks (and nuns) are easily distinguished from their shaven-headed Buddhist confrères by their long hair, twisted into topknots, straight trousers and squarish jackets.
#### Confucian Temples
Confucian temples bristle with steles celebrating local scholars, some supported on the backs of _bìxì_ (mythical tortoise-looking dragons). A statue of Kongzi (Confucius) usually resides in the main hall, overseeing rows of musical instruments and flanked by disciples. A mythical animal, the _qílín_ (a statue exists at the Summer Palace in Běijīng), is commonly seen. The _qílín_ was a hybrid animal that appeared on earth only in times of harmony. The largest Confucian temple in China is at Qūfù in Shāndōng, Confucius' birthplace.
### Modern Architecture
China is one of today's most exciting nations for breaking the architectural mould, ripping up the rule book, risk taking and a healthy but chancy dose of leaping-before-looking. Architecturally in today's China, anything goes. You only have to look at the Pǔdōng skyline to witness a melange of competing modern designs, some dramatic, inspiring and novel, others cheesy and rash. The skyline represents a nation brimming over with confidence and newfound zeal, but overhung with awkwardness.
If modern architecture in China is regarded as anything post-1949, then China has ridden a roller-coaster ride of styles and fashions. In Běijīng, stand between the Great Hall of the People (1959) and the National Centre for the Performing Arts (2008) and weigh up how far China has travelled in the past 50 years. Interestingly, neither building possesses evident Chinese motifs; both are united by foreign styling, Soviet design for the former and French imagination for the latter. The same applies to the complex form of Běijīng's CCTV Building, where a continuous loop through horizontal and vertical planes required some audacious engineering.
While much of the country's interior still lacks the financial muscle necessary to consider anything beyond simple functionality, the coastal areas are widely regarded as an architect's dreamland – no design is too outrageous to be built, zoning laws have been scrapped and the labour force is large and inexpensive. Planning permission can be simple to arrange – often all it requires is sufficient _guānxī_ (connections).
In Tàiyuán, the World Trade Hotel is a rather tasteless downsized reproduction of New York's former towers.
Many of the top names in international architecture – IM Pei, Rem Koolhaas, Norman Foster, Kengo Kuma, Jean-Marie Charpentier, Herzog & de Meuron – have all designed at least one building in China in the past decade. Other impressive examples of modern architecture include the National Stadium (aka the 'Bird's Nest'), the National Aquatics Center (aka the 'Water Cube') and Běijīng South train station, all in Běijīng; the art deco–esque Jīnmào Tower, the towering Shànghǎi World Financial Center, Tomorrow Square and South Railway Station in Shànghǎi; and the new Sūzhōu Museum in Sūzhōu, a stunning fusion of geometric lines and classical Chinese garden design. The Bank of China Tower remains an iconic piece of architecture, as is the HSBC Building, both in Hong Kong's Central district.
### ART DECO IN SHÀNGHǍI
Fans of art deco must visit Shànghǎi. The reign of art deco is one of the city's architectural high-water marks and the city boasts more art deco buildings than any other city, from the drawing boards of the French firm Leonard, Veysseyre and Kruze and others. Largely emptied of foreigners in 1949, Shànghǎi largely kept its historic villas and buildings intact, including its fabulous art deco monuments. The Peace Hotel, Bank of China building, Cathay Theatre, Green House, Paramount Ballroom, Broadway Mansions, Liza Building, Savoy Apartments, Picardie Apartments and Majestic Theatre are all art deco gems. For a comprehensive low-down on the style, hunt down a copy of _Shanghai Art Deco_ by Deke Erh and Tess Johnston.
## GARDENS
Originally designed as either imperial parks or as private compounds attached to a residence, Chinese gardens are entirely different in concept from European garden design. Like an ink painting, Chinese garden design was rooted in the Chinese notion of the natural world and humankind's place within it. While European gardens emphasised col- our, flowers, grass and either a geometrical precision or a semi-wild abandonment to nature, Chinese gardens instead aimed to recreate the constituent parts of nature, from mountains and hills to lakes, ponds and vegetation. Colours are largely subdued while the size of the garden is typically small and enclosed.
A vibrant focus is devoted to the arrangements of rocks and rockeries, the placing of ponds and the use of foliage, small trees and shrubs. Pavilions, walkways, corridors and bridges bring in human features, however these are never dominant or overbearing and instead complement the picture. Man is an element of the garden but his presence is as an observer and participant rather than as a central focus or force.
The landscapes of a traditional Chinese painting are always central to a successful garden. Windows may find themselves strategically placed to frame a particular view, and in private compounds, plants were often selectively grown against a backdrop of whitewashed walls, which recalled the empty space of a painting. Mountains _(shān)_ and water _(shuǐ)_ are essential components of traditional paintings and find themselves replicated in garden design through rockeries and fish-filled ponds. The play of light is similarly a vital ingredient, playing off water surfaces, reflecting from white walls and casting shadows.
Another important feature of gardens is symbolism. Plants were chosen as much for their symbolic meaning as their beauty (the pine for longevity, the peony for nobility), and the giant eroded rocks suggest mountains as well as the changing, indefinable nature of the Tao. Likewise, the names of gardens and halls are often literary allusions to ideals expressed in classical poetry.
Yet there is also a sense of artificiality in Chinese gardens. The hand of Confucian man is always recognisable, no matter how successfully the garden reproduces a Chinese landscape. This strong artificiality is very recognisable in modern Chinese parks, which derive from traditional garden design. Concrete paths, walkways, hard-edged borders, artificial ponds and regularly planted trees are typical of modern Chinese parks. Park goers in today's parks in China are guided in definite directions by paths, rather than being encouraged to wander at random. Nature is recreated, but from the artificial viewpoint of man rather than through encouraging the original landscape to reveal itself.
Gardens were particularly prevalent in southeastern China south of the Yangzi River, notably in Hángzhōu, Yángzhōu and Sūzhōu.
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# China's Landscapes
## THE LAND
The world's third-largest country – roughly the same size as the USA – China covers a colossal 9.5-million sq km, only surpassed in area by Russia and Canada. Straddling natural environments as diverse as subarctic tundra in the north and tropical rainforests in the south, the land embraces the world's highest mountain range and one of its hottest deserts in the west to the steamy, typhoon-lashed coastline of the South China Sea. Fragmenting this epic landscape is a colossal web of waterways, including one of the world's mightiest rivers – the Yangzi ( 长江 ; Cháng Jiāng).
### Mountains
China's terrain is in large parts mountainous and hilly, commencing in dramatically precipitous fashion in the vast and sparsely populated Tibetan west and levelling out gradually towards the fertile, well-watered, populous and wealthy provinces of eastern China.
This mountainous disposition sculpts so many of China's natural scenic wonders, from the glittering Dragon's Backbone Rice Terraces of Guǎngxī to the exhilaration of Mt Everest, the stunning beauty of Jiǔzhàigōu National Park in Sìchuān, the ethereal peaks of misty Huángshān in Ānhuī, the vertiginous inclines of Huà Shān in Shaanxi (Shǎnxī), the divine karst geology of Yángshuò in Guǎngxī and the volcanic drama of Heaven Lake in Jílín.
Averaging 4500m above sea level, the Tibet–Qīnghǎi region's highest peaks thrust up in the Himalayan mountain range along its southern rim, where mountains average about 6000m above sea level, with 40 peaks rising dizzyingly to 7000m or more. Also known as the planet's 'third pole', this is where the world's highest peak, Mt Everest – called Zhūmùlǎngmǎfēng by the Chinese – thrusts up jaggedly from the Tibet– Nepal border. Low temperatures, high winds and intense solar radiation are regional characteristics.
Frozen reservoirs of water, China's glaciers – 15% of the world's ice mass – have depleted by around 20% since the mid-1960s and at current rates are set to vanish by 2100.
This vast high-altitude region (Tibet alone constitutes one-eighth of China's landmass) is home to an astonishing 37,000 glaciers, the third-largest mass of ice on the planet after the Arctic and Antarctic. This colossal body of frozen water ensures that the Tibet–Qīnghǎi region is the source of many of China's largest rivers, including the Yellow (Huáng Hé), Mekong (Láncāng Jiāng), Salween (Nù Jiāng) Rivers and, of course, the mighty Yangzi, all of whose headwaters are fed by snowmelt from here. Global warming, however, is eating into this glacial mass: by some estimates, 40% of the region's glaciers will have disappeared by 2050, resulting in flooding in the short term and growing aridity in the long term.
Tibet is also an immense storehouse of mineral wealth, helping to clarify its Chinese name ( 西藏 ; Xīzàng; 'Western Treasure House'). Deep within the mountains of Tibet lie enormous deposits of gold, copper, uranium, lithium, lead and other valuable minerals and ores.
This mountainous disposition finds repeated refrain throughout China, albeit on a less dramatic scale, as the land continually wrinkles into spectacular mountain ranges. China's hills and mountains may form a dramatic and sublime backdrop, but they generate huge agricultural complications. Many farmers cultivate small plots of land assiduously eked out in patchworks of land squashed between hillsides, mountain cliffs and ravines, in the demanding effort to feed 20% of the world's population with just 10% of its arable land. Only 15% of China's land can be cultivated; up hillside gradients, the inclines are valiantly levelled off, wherever possible, into bands of productive terraced fields.
### MOUNTAINS, MYTH & MAGIC
Steeped in legend and superstition and infused with spirits and deities, China's mountains have long been cherished by devout bands of Taoists and Buddhists who erected temples and founded monastic communities on their slopes. Mt Kailash and many other peaks in Tibet are powerfully associated with Buddhist divinities and Bodhisattvas, drawing legions of pilgrims and worshippers to complete a _kora_ (pilgrim path) around their slopes. Outside Tibet, each of China's five sacred Buddhist mountains has its ruling Bodhisattva, whose presence permeates their shrines, gullies and peaks. In Pǔtuóshān it is the merciful Guanyin (see the boxed text, Click here ) who is worshipped; in Wǔtái Shān, erudite Wenshu (Manjushri) is the presiding deity. Huà Shān, Sōng Shān, Wǔdāng Shān and other Taoist peaks are famed for the recluses who retreated to their crags and caves to cultivate 'internal power' and devise mind-boggling martial-arts skills ( Click here ).
### Deserts
Official state estimates predict one-seventh of China's population may need to be resettled due to growing desertification in the north of China.
China contains head-spinningly vast – and growing – desert regions that occupy almost a fifth of the country's landmass, largely in its mighty northwest. These are inhospitably sandy and rocky expanses where summers are torturously hot and winters bone-numbingly cold. North towards Kazakhstan and Kyrgyzstan from the plateaus of Tibet and Qīnghǎi lies Xīnjiāng's Tarim Basin, the largest inland basin in the world. This is the location of the mercilessly thirsty Taklamakan Desert – China's largest desert and the world's second largest mass of sand after the Sahara Desert. China's biggest shifting salt lake, Lop Nur (the site of China's nuclear bomb tests) is also here.
The harsh environment shares many topographical features in common with the neighbouring nations of Afghanistan, Kyrgyzstan and Kazakhstan and is almost the exact opposite of China's lush and well-watered southern provinces. But despite the scorching aridity of China's northwestern desert regions, their mountains (the mighty Tiān Shān, Altai, Pamir and Kunlun ranges) contain vast supplies of water, largely in the form of snow and ice.
China has earmarked a staggering US$140 billion for an ambitious program of wind farms; ranging from Xīnjiāng province to Jiāngsū province in the east, the huge wind farms are due for completion in 2020.
Northeast of the Tarim Basin is Ürümqi, the world's furthest city from the sea. The Tarim Basin is bordered to the north by the lofty Tiān Shān range – home to the glittering mountain lake of Tiān Chí – and to the west by the mighty Pamirs, which border Pakistan. Also in Xīnjiāng is China's hot spot, the Turpan Basin, known as the 'Oasis of Fire' and entering the record books as China's lowest-lying region and the world's second-deepest depression after the Dead Sea in Israel. China's most famous desert is of course the Gobi, although most of it lies outside the country's borders.
The Silk Road into China steered its epic course through this entire region, ferrying caravans of camels laden with merchandise, languages, philosophies, customs and peoples from the far-flung lands of the Middle East. Today the region is rich in fossil fuels, containing one-third of China's known gas and oil reserves as well as vast and unexploited coal deposits.
East of Xīnjiāng extend the epic grasslands and steppes of Inner Mongolia in a huge and elongated belt of land that stretches to the region once called Manchuria.
### Rivers & Plains
The other major region comprises roughly 45% of the country and contains 95% of the population. This densely populated part of China descends like a staircase from west to east, from the inhospitable high plateaus of Tibet and Qīnghǎi to the fertile but largely featureless plains and basins of the great rivers that drain the high ranges. As a general rule of thumb, as you head east towards the seaboard, provinces become wealthier.
These plains are the most important agricultural areas of the country and the most heavily populated. It's hard to imagine, but the plains have largely been laid down by siltation by the Yangzi and other great rivers over many millennia. The process continues: the Yangzi alone deposits millions of tonnes of silt annually and land at the river mouth is growing at a rate of 100m a year. Hardly any significant stands of natural vegetation remain in this area, although several mountain ranges are still forested and provide oases for wildlife and native plants.
The Yellow River, about 5460km long and the second-longest river in China, is often touted as the birthplace of Chinese civilisation. China's longest river, the Yangzi, is one of the longest rivers in the world. Its watershed of almost 2 million sq km – 20% of China's land mass – supports 400 million people. Dropping from its source high on the Tibetan plateau, it runs for 6300km to the sea, of which the last few hundred kilometres is across virtually flat alluvial plains. The Yangzi has been an important thoroughfare for humans for centuries, used throughout China's history for trade and transport; it even has its own unique wildlife, but all this has been threatened by the controversial Three Gorges Dam Project. The dam will generate power and is supposed to thwart the Yangzi's propensity to flood – floodwaters periodically inundate millions of hectares and destroy hundreds of thousands of lives.
## WILDLIFE
China's vast size, diverse topography and climatic disparities support an astonishing range of habitats for a wide-ranging diversity of animal life. Scattered from steamy tropical rainforests in the deep southwest to subarctic wilderness in the far north, from the precipitous mountains of Tibet to the low-lying deserts of the northwest and the huge Yangzi River, China's wild animals comprise nearly 400 species of mammal (including some of the world's rarest and most charismatic species), more than 1300 bird species, 424 reptile species and over 300 species of amphibian. The Tibetan plateau alone is the habitat of over 500 species of birds, while half of the animal species in the northern hemisphere can be found in China.
It is unlikely you will see many of these creatures in their natural habitat unless you are a specialist, or have a lot of time, patience, persistence, determination and luck. If you go looking for large animals in the wild on the off chance, your chances of glimpsing one are virtually nil. But there are plenty of pristine reserves within relatively easy reach of travellers' destinations such as Chéngdū in and Xī'ān. More and more visitors are including visits to protected areas as part of their itinerary for a look at China's elusive wildlife residents – outside of China's rather pitiful zoos.
### Mammals
China's towering mountain ranges form natural refuges for wildlife, many of which are now protected in parks and reserves that have escaped the depredations of loggers and dam-builders. The barren high plains of the Tibetan plateau are home to several large animals, such as the _chiru_ (Tibetan antelope), Tibetan wild ass, wild sheep and goats, and wolves. In theory, many of these animals are protected but in practice poaching and hunting still threaten their survival.
Eleven Siberian tigers starved to death at the Shenyang Forest wild-animal zoo in China's northeast in 2010, underscoring concerns about the treatment of tigers in China.
The beautiful and retiring snow leopard, which normally inhabits the highest parts of the most remote mountain ranges, sports a luxuriant coat of fur against the cold. It preys on mammals as large as mountain goats, but is unfortunately persecuted for allegedly killing livestock.
The Himalayan foothills of western Sìchuān support the greatest diversity of mammals in China. Aside from giant pandas, other mammals found in this region include the panda's small cousin, the raccoon-like red panda, as well as Asiatic black bears and leopards. Among the grazers are golden takin, a large goatlike antelope with a yellowish coat and a reputation for being cantankerous, argali sheep and various deer species, including the diminutive mouse deer.
Changqing Nature Reserve in Shaanxi province is well worth a visit for its relatively unspoilt montane forest and the chance to see giant pandas in the wild. Find out more at www.cqpanda.com.
The sparsely populated northeastern provinces abutting Siberia are inhabited by reindeer, moose, musk deer, bears, sables and Manchurian tigers. Overall, China is unusually well endowed with big and small cats. The world's largest tiger, the Manchurian Tiger _(Dōngběihǔ)_ – also known as the Siberian Tiger – only numbers a few hundred in the wild, its remote habitat being one of its principal saviours. Three species of leopard can be found, including the beautiful clouded leopard of tropical rainforests, plus several species of small cat, such as the Asiatic golden cat and a rare endemic species, the Chinese mountain cat.
Rainforests are famous for their diversity of wildlife, and the tropical south of Yúnnán province, particularly the area around Xīshuāngbǎnnà, is one of the richest in China. These forests support Indochinese tigers and herds of Asiatic elephants.
The wild mammals you are most likely to see are several species of monkey. The large and precocious Père David's macaque is common at Éméi Shān in Sìchuān, where bands often intimidate people into handing over their picnics; macaques can also be seen on Hǎinán's Monkey Island. Several other monkey species are rare and endangered, including the beautiful golden monkey of the southwestern mountains and the snub-nosed monkey of the Yúnnán rainforests. But by far the most endangered is the Hǎinán gibbon, numbering just a few dozen individuals on Hǎinán island thanks to massive forest clearance.
The giant panda is western Sìchuān's most famous denizen, but the animal's solitary nature makes it extremely hard to observe in the wild, and even today, after decades of intensive research and total protection in dedicated reserves, sightings are rare. A census revised the world population of this amazing and appealing animal upwards after an estimated 39 pandas were located in Wánglǎng Nature Reserve in Sìchuān. Another positive development has been the 'bamboo tunnel', an area of reforestation designed to act as a corridor for the pandas to move between two fragmented patches of forest.
### Birds
At www.cnbirds.com, China Birding is an excellent resource for overwintering sites, migration routes, the geographical distribution of your feathered friends in China as well as lots of excellent photos.
Most of the wildlife you'll see will be birds, and with more than 1300 species recorded, including about 100 endemic or near-endemic species, China offers some great bird-watching opportunities. Spring is usually the best time to see them, when deciduous foliage buds, migrants return from their wintering grounds and nesting gets into full swing. BirdLife International (www.birdlife.org/regional/asia), the worldwide bird conservation organisation, recognises 12 Endemic Bird Areas (EBAs) in China, nine of which are wholly within the country and three are shared with neighbouring countries.
Although the range of birds is huge, China is a centre of endemicity for several species and these are usually the ones that visiting birders will seek out. Most famous are the pheasant family, of which China boasts 62 species, including many endemic or near-endemic species.
Other families well represented in China include the laughing thrushes, with 36 species; parrotbills, which are almost confined to China and its near neighbours; and many members of the jay family. The crested ibis is a pinkish bird that feeds on invertebrates in the rice paddies, and was once found from central China to Japan.
Among China's more famous large birds are cranes, and nine of the world's 14 species have been recorded here. In Jiāngxī province, on the lower Yangzi, a vast series of shallow lakes and lagoons was formed by stranded overflow from Yangzi flooding. The largest of these is Póyáng Lake, although it is only a few metres deep and drains during winter. Vast numbers of waterfowl and other birds inhabit these swamps year-round, including ducks, geese, herons and egrets. Although it is difficult to get to, birders are increasingly drawn to the area in winter, when many of the lakes dry up and attract flocks of up to five crane species, including the endangered, pure white Siberian crane.
Parts of China are now established on the itineraries of global ecotour companies. Check websites such as www.eurobirding.com for bird-watchers' trip reports and more information on bird-watching in China. Recommended destinations include Zhālóng Nature Reserve, one of several vast wetlands in Hēilóngjiāng province. Visit in summer to see breeding storks, cranes and flocks of wildfowl before they fly south for the winter. Běidàihé, on the coast of the China Sea, is well known for migratory birds on passage. Other breeding grounds and wetlands include Qīnghǎi Hú in Qīnghǎi, Cǎohǎi Lake in Guìzhōu, Jiǔzhàigōu in Sìchuān and Mai Po Marsh in Hong Kong. For the latter, the Hong Kong Bird Watching Society (www.hkbws.org.hk) organises regular outings and publishes a newsletter in English.
Most bird-watchers and bird tours head straight for Sìchuān, which offers superb birding in sites such as Wòlóng. Here, several spectacular pheasants, including golden, blood and kalij pheasants, live on the steep forested hillsides surrounding the main road. As the road climbs towards Beilanshan Pass, higher-altitude species such as eared pheasants and the spectacular Chinese monal may be seen. Alpine meadows host smaller birds, and the rocky scree slopes at the pass hold partridges, the beautiful grandala and the mighty lammergeier (bearded vulture), with a 2m wingspan.
### Reptiles & Amphibians
The Chinese alligator – known as the 'muddy dragon' – is one of the smallest of the world's crocodilians, measuring only 2m in length, and is harmless to humans. Owing to habitat clearance and intense pressure to turn its wetlands to agriculture along the lower Yangzi, fewer than 130 of these crocs still exist in the wild. A captive breeding program has been successful, but as yet there are few options for releasing this rare reptile back into the wild.
The cold, rushing rivers of the southwestern mountains are home to the world's largest amphibian, the giant salamander. This enormous amphibian can reach 1m in length and feeds on small aquatic animals. Unfortunately, it is now critically endangered in the wild and, like so many other animals, hunted for food. More than 300 other species of frog and salamander occur in China's waterways and wetlands, and preying on them is a variety of snakes, including cobras and vipers. One of China's more unusual national parks is Snake Island, near Dàlián in Liáoníng province. This 800-hectare dot in the China Sea is uninhabited by people, but supports an estimated 130,000 Pallas' pit vipers, an extraordinary concentration of snakes that prey on migrating birds that land on the island every spring and autumn in huge numbers. By eating several birds each season, the snakes can subsist on lizards and invertebrates for the rest of the year until migration time comes round again.
### THE YANGZI DOLPHIN
The Yangzi floodway was big enough to favour the evolution of distinct large river creatures, including the Yangzi dolphin _(baiji)_ and Chinese alligator, both now desperately endangered. The Yangzi dolphin, one of just a few freshwater dolphin species in the world (others occur in the Ganges and Amazon River systems) and by far the rarest, migrated to the Yangzi River from the Pacific Ocean over 20 million years ago and adapted itself to its freshwater habitat. The dolphin largely lost the use of its eyes in the gloomy Yangzi waters and instead steered a course through the river using a form of sonar.
From being quite commonplace – around 6000 dolphins still lived in the Yangzi River during the 1950s – numbers fell drastically during the three decades of explosive economic growth from the 1970s, and the last confirmed sighting was in 2002. The creature is a victim – one of many – of human activity in the region, succumbing to drowning in fishing nets and lethal injuries from ships' propellers.
### Plants
Bamboo comprises 99% of the giant panda's diet, and it spends up to 16 hours a day feeding, during which time it may eat up to 20kg of bamboo shoots, stems and leaves.
China is home to more than 32,000 species of seed plant and 2500 species of forest tree, plus an extraordinary plant diversity that includes some famous 'living fossils' – a diversity so great that Jílín province in the semifrigid north and Hǎinán province in the tropical south share few plant species. Many reserves still remain where intact vegetation ecosystems can be seen firsthand, but few parts of the country have escaped human impact. Deforestation continues apace in many regions and vast areas are under cultivation with monocultures such as rice.
Apart from rice, the plant probably most often associated with China and Chinese culture is bamboo, of which China boasts some 300 species. Bamboos grow in many parts of China, but bamboo forests were once so extensive that they enabled the evolution of the giant panda, which eats virtually nothing else, and a suite of small mammals, birds and insects that live in bamboo thickets. Most of these useful species are found in the subtropical areas south of the Yangzi, and the best surviving thickets are in southwestern provinces such as Sìchuān.
Many plants commonly cultivated in Western gardens today origin- ated in China, among them the ginkgo tree, a famous 'living fossil' whose unmistakable imprint has been found in rocks 270 million years old. The unique and increasingly rare dove tree or paper tree, whose greatly enlarged white bracts look like a flock of doves, grows only in the deciduous forests of the southwest.
Deciduous forests cover mid-altitudes in the mountains, and are characterised by oaks, hemlocks and aspens, with a leafy understorey that springs to life after the winter snows have melted. Among the more famous blooms of the understorey are rhododendrons and azaleas, and many species of each grow naturally in China's mountain ranges. Best viewed in spring, some species flower right through summer; one of the best places to see them is at Sìchuān's Wòlóng Nature Reserve. Both rhododendrons and azaleas grow in distinct bands at various heights on the mountainsides, which are recognisable as you drive through the reserve to the high mountain passes. At the very highest elevations, the alpine meadows grazed by yaks are often dotted with showy and colourful blooms.
Deforestation has levelled huge tracts of China's once vast and beautiful primeval forests. At the end of the 19th century, 70% of China's northeast was still forest. Unsustainable clear-cutting in the 20th century – especially during the rapacious Great Leap Forward – was not banned there until the mid-1980s, by which time only 5% of old-growth woodland remained. Logging controls were more strictly enforced after the great floods of 1998, when deforestation was identified as contributing to the floodwaters. Since then a vigorous replanting campaign was launched to once again cover huge tracts of China with trees, but these cannot restore the rich biodiversity that once existed.
### Endangered Species
Almost every large mammal you can think of in China has crept onto the endangered species list, as well as many of the so-called 'lower' animals and plants. The snow leopard, Indochinese tiger, chiru antelope, crested ibis, Asiatic elephant, red-crowned crane and black-crowned crane are all endangered.
Deforestation, pollution, hunting and trapping for fur, body parts and sport are all culprits. The Convention on International Trade in Threatened and Endangered Species (CITES) records legal trade in live reptiles and parrots, and astonishingly high numbers of reptile and wild cat skins. The number of such products collected or sold unofficially is anyone's guess.
### EATEN TO EXTINCTION
China's taste for exotic animals is helping drive many to extinction. In 2007 a deserted ship containing 5000 rare creatures was discovered floating off south China. The cargo included 44 leatherback turtles, over 2500 monitor lizards, 31 pangolins and a large consignment of bear paws. It is assumed the cargo was heading for the restaurants of south China. In 2010 another ship containing hundreds of dead pangolins was found. As a result of voracious demand for exotic meat in China, species such as the pangolin have vanished from China and neighbouring countries, so traffickers have turned to Malaysia and other Southeast Asian nations, where populations are also rapidly dwindling.
Snakes feature prominently on China's menus – more than 10,000 tonnes of serpents are dished up every year to diners – and in traditional Chinese medicine, as snake parts are believed to restore health and boost sexual prowess. The venom of dangerous species such as vipers is particularly sought for medicine. The situation is so dire that no fewer than 43 of China's 200 snake species are said to be endangered. Nature, however, has a way of fighting back and the depletion of snake numbers leads pretty quickly to an increase in rodent numbers, with resulting crop destruction.
Despite the threats, a number of rare animal species cling to survival in the wild. Notable among them are the Chinese alligator in Ānhuī, the giant salamander in the fast-running waters of the Yangzi and Yellow Rivers, the Yangzi River dolphin in the lower and middle reaches of the river (although there have been no sightings since 2002), and the pink dolphin of the Hong Kong islands of Sha Chau and Lung Kwu Chau. The giant panda is confined to the fauna-rich valleys and ranges of Sìchuān, but your best chances for sighting one is in Chéngdū's Giant Panda Breeding Research Base. You may be lucky enough to chance upon a golden monkey in the mountains of Sìchuān, Yúnnán and Guìzhōu.
Intensive monoculture farmland cultivation, the reclaiming of wetlands, river damming, industrial and rural waste, and desertification are reducing unprotected forest areas and making the survival of many of these species increasingly precarious. Although there are laws against killing or capturing rare wildlife, their struggle for survival is further complicated as many remain on the most-wanted lists for traditional Chinese medicine and dinner delicacies. In Tibet, the _chiru_ antelope has long been hunted for a fleece that provides a lucrative type of wool. Despite conservation efforts, poaching still continues in an area that is hard to effectively monitor due to its size and a lack of human resources.
The World Health Organization estimates that air pollution causes more than 650,000 fatal illnesses per year in China, while more than 95,000 die annually from consuming polluted drinking water.
## THE ENVIRONMENT
China may be vast, but with two-thirds of the land either mountain, desert or uncultivable, the remaining third is overwhelmed by the people of the world's most populous nation. For social and political reasons, China is only now experiencing its – and the world's – most rapid period of urbanisation in history, so the city often impinges in inescapable fashion.
Deforestation and overgrazing have accelerated the desertification of vast areas of China, particularly in the western provinces. Deserts now cover almost one-fifth of the country and China's dustbowl is the world's largest, swallowing up 200 sq km of arable land every month.
### TOP BOOKS ON CHINA'S ENVIRONMENT
» _When a Billion Chinese Jump_ (2010) Jonathan Watts' sober and engaging study of China's environmental concerns.
» _The River Runs Black: The Environmental Challenge to China's Future_ (2004) Elizabeth Economy's frightening look at the unhappy marriage between breakneck economic production and environmental degradation.
» _The China Price: The True Cost of Chinese Competitive Advantage_ (2008) Alexandra Harney's telling glimpse behind the figures of China's economic rise.
» _China's Water Crisis_ (2004) Ma Jun rolls up his sleeves to examine the sources of China's water woes.
» _Mao's War Against Nature_ (2001) Judith Shapiro looks at the ideological confrontation between communism and the environment.
In 2010 China overtook the USA as the world's largest energy consumer; in the same year the nation replaced Japan as the world's second-largest economy and is tipped to overtake the USA by 2030 (some say by 2020).
For decades China neglected the environment as it was costly to protect; environmental concerns were parked on the back-burner to be dealt with once the national economy had developed. China embarked on a course of development first, clean up later. The costs of such procrastination may, however, return to haunt Běijīng. The World Bank calculates the annual cost of pollution alone in China at almost 6% of the national GDP; when all forms of environmental damage are incorporated, the figure leaps as high as 12%, meaning China's environmental costs may outweigh economic growth. This alone should be enough to focus minds.
### A Greener China?
Běijīng has pledged US$6.8 billion to plant a 'green wall' of millions of trees along 5700km to halt the encroaching desert sands.
The debacle of the 2009 climate summit in Copenhagen painted China as an obstinate deal-breaker. China is paradoxically painfully aware of its accelerated desertification, growing water shortages, shrinking glaciers, increasingly acidic rain and progressively polluted environment, but remains unclear whether or how to fully champion the development of greener and cleaner energy sources.
One of the aims of the Three Gorges Dam is to help prevent flooding on the Yangzi River. The river has caused hundreds of catastrophic floods, including the disastrous inundation of 1931, in which an estimated 145,000 died.
Evidence of ambitious and bold thinking is easy to find: in 2010 China announced it would pour billions into developing electric and hybrid vehicles; Běijīng is committing itself to overtaking Europe in investment in renewable energy by 2020; the construction of wind farms (in blustery Gānsù, for example) continues apace; and China leads the world in production of solar cells.
Its authoritarian system of governance allows China to railroad through daring initiatives. However, this same government is also fond of reaching for the familiar tools in its workshop, relying heavily on technological 'solutions' and huge engineering programs to combat environmental problems. For example, China is attempting to engineer itself out of its water crisis by diverting some of the waters of the Yangzi River to thirsty north China, when devising more manageable solutions to water use may be more advisable for a sustainable future.
### SOUTH–NORTH WATER DIVERSION PROJECT
Water is the lifeblood of economic and agricultural growth, but as China only possesses around 7% of the world's water resources (with almost 20% of its population), the liquid is an increasingly precious resource.
In a region of low rainfall, north China is facing a grim water crisis. Farmers are draining aquifers that have taken thousands of years to accumulate, while Chinese industry is using three to 10 times more water per unit of production than developed nations. Meanwhile, water usage in large cities such as Běijīng and Tiānjīn continues to climb as migrants move in from rural areas. By some estimates, the aquifers of north China may only have another 30 years of life left.
The Chinese Communist Party (CCP) remains hypnotised by monumental engin- eering projects as solutions. To combat the water crisis, the CCP embarked on the construction of the US$62 billion South–North Water Diversion Project, a vast network of rivers, canals and lakes lashing north and south. The logic is to divert surplus water from the Yangzi River to the dwindling and long overexploited Yellow River.
The project has been snared by complications. There are concerns that pollution in the Yangzi River waters will become progressively concentrated as water is extracted, while Yangzi cities such as Nánjīng and Wǔhàn are increasingly anxious they will be left with less water. Alarm has also arisen at the pollution in channels – including the Grand Canal, which linked Hángzhōu with north China – earmarked to take the diverted waters. There are worries that these polluted reaches are almost untreatable, making elements of the project unviable.
Critics also argue that the project, which will involve the mass relocation of hundreds of thousands of people, will not address the fundamental issue of China's water woes – the absence of policies for the sustainable use of water as a precious resource.
Some greener initiatives, such as the Three Gorges Dam, sport green credentials in some areas (no greenhouse gases, renewable energy source, small carbon footprint) but are environmentally unsound in others (water-polluting, seismic effects, local climate change). Other initiatives may also be little more than hype, as China learns to twiddle the 'soft power' knobs in a public relations exercise with an increasingly attentive outside world. The world's first ecologically sustainable city at Dōngtān on Chongming Island at the mouth of the Yangzi River was projected to house 25,000 people by the time of the 2010 World Expo. There was considerable international press attention when the idea was launched, but the city has yet to be built.
In reflection of its water woes, China has developed the world's most intensive cloud-seeding program.
One of China's main quandaries is coal. China's coal-fired growth comes at a time when the effort to tackle global warming has become a chief global priority. Coal is cheap, easy to extract and remains China's number one energy source, generating almost 70% of power requirements. Huge untapped reserves in the northwest await exploitation, vast coalfields in Inner Mongolia are now being mined and the economics of coal mining in China make it a cheap and reliable fuel source. Nonetheless, coal is an unrenewable resource and experts predict China's reserves will be depleted within a century. But with energy requirements booming in step with economic growth, it is unlikely China will shake off its increasing addiction to the fuel that has created some of the most polluted cities on the planet.
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# The Martial Arts of China
Unlike Western fighting arts – Savate, kickboxing, boxing, wrestling etc _–_ Chinese martial arts are deeply impregnated with religious and philosophical values. And, some might add, a morsel or two of magic. Many eminent exponents of _gōngfū_ ( 功夫 ) were devout monks or religious recluses who drew inspiration from Buddhism and Taoism and sought a mystical communion with the natural world around them. Their arts were not leisurely pursuits but were closely entangled with the meaning and purpose of their lives.
Often misinterpreted, _gōngfū_ teaches an approach to life that stresses patience, endurance, magnanimity and humility. For those who truly take to the Chinese martial arts, it's a rewarding journey with a unique destination. When two people discover they share an interest in martial arts, it's the cue for an endless exchange of techniques and anecdotes. It's a club mentality for members only.
Several Chinese styles of _gōngfū_ include drunken sets, where the student mimics the supple movements of an inebriate.
## STYLES & SCHOOLS
China lays claim to a bewildering range of martial-arts styles. There's the flamboyant and showy, inspired by the movements of animals or insects (such as Praying Mantis Boxing), but there are also schools more empirically built upon the science of human movement (eg Wing Chun). Some pugilists stress a mentalist approach (eg Xingyi Quan) although others put their money on physical power (White Eyebrow Boxing). On the more obscure fringes are the esoteric arts, abounding with metaphysical feats, arcane practices and closely guarded techniques.
Many fighting styles were once secretively handed down for generations within families and it is only relatively recently that outsiders have been accepted as students. Some schools, especially the more obscure of styles, have died out partly because of their exclusivity.
Some styles have found themselves divided into competing factions, each laying claim to the original teachings and techniques. Such styles may find themselves in a state of schism, where the original principles have become either distorted or lost. Other styles though became part of the mainstream and flourished; Wing Chun in particular has been elevated into a globally recognised art, largely due to its associations with Bruce Lee (even though he ultimately developed his own style).
Unlike with Taekwondo or Karate-do, there is frequently no international regulatory body that oversees the syllabus, tournaments or grading requirements for China's individual martial arts. Consequently students of China's myriad martial arts may be rather unsure of where they stand or what level they have attained. With no standard syllabus, it is often down to the individual teacher to decide what to teach his or her student, and how quickly. A teacher of Five Ancestors Boxing (Wǔzúquán) may communicate the art in whatever increments he deems appropriate, but may only disclose the top-drawer skills that are crucial for success to his most trusted disciples.
A Malaysian Five Ancestors master once broke the leg of a Thai boxer, with his finger!
### Hard School
Although there is considerable blurring between the two camps, Chinese martial arts are often distinguished between hard and soft schools. Typically aligned with Buddhism, the hard or 'external' ( 外家 ; _wàijiā_ ) school tends to be more vigorous, athletic and focussed on the development of power. Many of these styles are related to Shàolín Boxing _(shàolín quánfǎ)_ and the Shàolín Temple in Hénán province.
Shàolín Boxing is forever associated with Bodhidharma, an ascetic Indian Buddhist monk who visited the Shàolín Temple and added a ser- ies of breathing and physical exercises to the Shàolín monk's sedentary meditations. The Shàolín monk's legendary endeavours and fearsome physical skills became known throughout China and beyond. Famous external schools include White Eyebrow Boxing, Long Boxing and Tiger Boxing.
### Soft School
Usually inspired by Taoism, the soft or 'internal' Chinese school ( 内家 ; nèijiā) develops pliancy and softness as a weapon against hard force. Taichi (Taiji Quan) is the best known soft school, famed for its slow and lithe movements and an emphasis on cultivating _qì_ (energy). Attacks are met with yielding movements that smother the attacking force and lead the aggressor off balance. Adept taichi students are able to cause considerable damage to an attacker, although the road to mastery is a long and difficult one, involving a re-education of physical movement and suppression of one's instinct to tense up when threatened. Other soft schools include the circular moves of Bāguà Zhǎng and the linear boxing patterns of Xingyi Quan, based on five basic punches – each linked to one of the five elements of Chinese philosophy – and the movements of 12 animals.
### Forms
Most students of Chinese martial arts – hard or soft – learn forms ( 套路 ; _tàolu_ ), a series of movements linked together into a pattern, which embody the principal punches and kicks of the style. In essence, forms are unwritten compendiums of the style, to ensure passage from one generation to the next. The number and complexity of forms varies from style to style: taichi may only have one form, although it may be very lengthy (the long form of the Yang style takes around 20 minutes to perform). Five Ancestors Boxing has dozens of forms, while Wing Chun only has three empty-hand forms.
### Qìgōng
Closely linked to both the hard and especially the soft martial-arts schools is the practice of _qìgōng_ , a technique for cultivating and circulating _qì_ around the body. _Qì_ can be developed for use in fighting to protect the body (eg iron-shirt _qìgōng_ ), as a source of power or for curative and health-giving purposes.
## MARTIAL ARTS CASE STUDY: BĀGUÀ ZHǍNG
One of the more esoteric and obscure of the soft Taoist martial arts, Bāguà Zhǎng ( 八卦掌; Eight Trigram Boxing, also known as Pa-kua) is also one of the most intriguing. The Bāguà Zhǎng student wheels around in a circle, rapidly changing direction and speed, occasionally thrusting out a palm strike.
Bāguà Zhǎng draws its inspiration from the trigrams (an arrangement of three broken and unbroken lines) of the classic _Book of Changes_ (Yìjīng or I Ching), the ancient oracle used for divination. The trigrams are typically arranged in circular form and it is this pattern that is traced out by the Bāguà Zhǎng exponent. Training commences by just walking the circle so the student gradually becomes infused with its patterns and rhythms.
A hallmark of the style is the exclusive use of the palm, not the fist, as the principal weapon. This may seem curious and perhaps even ineffectual, but in fact the palm can transmit a lot of power – consider a thrusting palm strike to the chin, for example. The palm is also better protected than the fist as it is cushioned by muscle. The fist also has to transfer its power through a multitude of bones that need to be correctly aligned to avoid damage while the palm sits at the end of the wrist. Consider hitting a brick wall as hard as you can with your palm (and then imagine doing it with your fist!). In fact, Bāguà Zhǎng fighters were feared among Chinese boxers for their ferocity and unorthodox moves.
Praying Mantis master Fan Yook Tung once killed two stampeding bulls with an iron-palm technique.
The student must become proficient in the subterfuge, evasion, speed and unpredictability that are hallmarks of Bāguà Zhǎng. Force is generally not met with force, but deflected by the circular movements manifested in students through their meditations upon the circle. Circular forms – arcing, twisting, twining and spinning – are the mainstay of all movements, radiating from the waist.
Despite being dated by historians to the 19th century, Bāguà Zhǎng is quite probably a very ancient art. Beneath the Taoist overlay, the movements and patterns of the art suggest a possibly animistic origin, which gives the art its timeless rhythms.
## MARTIAL ARTS CASE STUDY: WING CHUN
Conceived by a Buddhist nun called Ng Mui from the Shàolín Temple who taught her skills to a young girl called Wing Chun ( 詠春 ), Wing Chun (Yǒng Chūn) is a fast and dynamic system of fighting that promises quick results for novices. This was the style that taught Bruce Lee how to move and, although he ultimately moved away from it to develop his own style, Wing Chun had an enormous influence on the Hong Kong fighter and actor.
Wing Chun emphasises speed rather than strength. Evasion, rapid strikes and low kicks are the hallmarks of the style. Forms are simple and direct, dispensing with the pretty flourishes that clutter other styles.
The art can perhaps best be described as scientific. There are none of the animal forms that make other styles so exciting and mysterious. Instead, Wing Chun is built around its centre line theory, which draws an imaginary line down the human body and centres all attacks and blocks along that line. The line runs through the sensitive regions: eyes, nose, mouth, throat, heart, solar plexus and groin and any blow on these points is debilitating and dangerous.
The three empty hand forms – which look bizarre to non-initiates – train arm and leg movements that both attack and defend this line. None of the blocks stray beyond the width of the shoulders, as this is the limit of possible attacks, and punches follow the same theory. Punches are delivered with great speed in a straight line, along the shortest distance between puncher and punched. All of this gives Wing Chun its distinctive simplicity.
A two-person training routine called _chi sau_ (sticky hands) teaches the student how to be soft and relaxed in response to attacks, as pliancy generates more speed. Weapons in the Wing Chun arsenal include the lethal twin Wing Chun butterfly knives and an extremely long pole, which requires considerable strength to handle with skill.
## COURSES & BOOKS
Martial-arts courses can be found in abundance across China, from Běijīng, Hong Kong, Shànghǎi, Wǔdāng Shān in Húběi, Yángshuò in Guǎngxī and the Shàolín Temple in Hénán. See under Courses in these sections for more.
Try to track down a copy of John F Gilbey's _The Way of a Warrior_ , a tongue-in-cheek, well-written and riveting account of the Oriental fighting arts.
## SEND US YOUR FEEDBACK
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## OUR READERS
Many thanks to the travellers who used the last edition and wrote to us with helpful hints, useful advice and interesting anecdotes:
A Avais Akhtar, Nancy Aki, Amdoboy, Sebastian Arabito, Ben Archer, Gregory Aroney B Kevin Bao, Malcolm Battle, Sebastien Beauchamps, Andrea Biggi, Bastiaan Bijl, Diego Bonifacino, Robert Brandl, Michael Breede, Sander Breedeveld, Melissa Bromwich, Robert Brooks, Sarah Bullen, Wolf Burian, Brian Burk C Steve Cannings, Sabina Carlsson, Ans & Bas Castelein-de Groot, Javier Castro Guinea, Nate Cavalieri, Anita Chakraborty, Kaung Chiau Lew, Yangs Chuyuan, Sue Colley, Samantha Cook, Madeline Corrigan D Peter Dahler, David Daily, Liam D'Arcy-Brown, Melanie Davison, Fabien De Vel, Maria De Lange, Susannah Deane, Joseph Distler, Jeff Ditter, Chris Dronen E Phillip Ekkels, Jeff Emmett, Brian Engel, Caroline English, Helen Ennis F Carina Fabisak, Zhang Fan, Richard Forsyth, Clive Foss, Bonnie Fox, Caroline Frances-King, Kathleen Freed, Tizian Fritz G Dave G, Klaus Gabriel, Barbara Gallagher, Pierre Gallant, Bernd Gammerl, Adrian Gaunt, Will George, Jonas Gerson, Yotam Gingold, Aaron Glick, Matthew Gollings, Yuri Gorelik, Dianna Graham, Chretien Gregoire, Patrick Gross, Martin Grznar, Heiko Günther, Rani Gustafson H Michael Haas, Lance Hall, Tim Harford-Cross, Linda Harries, Pierre Heisbourg, Barbara Heusi, Steven Heywood, Stephen Hoare-Vance, Laura Hornikx, Luke Howie, Spencer Humiston, Scott Humm, Andrew Humphrey, Dagmar Hussel I Jon Ingleson, Jeannie Ivanov J Bradwell Jackson, Ralpha Jacobson, Guillaume Jacques, Andrea James, Aleksandra Järvinen, Cai Jinming, Job Jobsen, Robert John, Eva Johnson, Steve Jomphe, Peter Jost, Joyce K Kyra Kane, Carol Kempe, Matthew Kennedy, David Kerkhoff, Niels Kibshede, Amanda King, Janis Kirpitis, Suzanne Klein, Tim Klink, Kelly Knowles, Miriam Kochman, Nina Kubik-Cheng L David Lamb, Winona Landis, Bregje Laumans, Ines Laura, Paul Lavender, Allison Leathart, Winston Lee, Julian Lees, Rhonda Lerner, Oliver Lewis, Dr Yngve Lööf, Amanda Love, Jerome Luepkes, Steven Lum M Rodney Mantle, Katharina Markgraf, Mizio Matteucci, Virginia Medinilla, Michiel Mertens, Tomer Metz, Michelle, Robert Molesworth, Ulrike Morrenth, Jens Müller, Ami Muranetz N Kester Newill, Dennis Nicoll O Lucie Ohankova, Justin O'Hearn, Russell Osborne, Kristel Ouwehand P Riccardo Paccapelo, Marcus Pailing, Col Palmer, Eva Papadopoulou, Terence Parker, Gavin Parnaby, John Pascoe, Daniel Paulsen, Woo Peiyi, Jonathan & Noa Perry, Bianca Peters, Emma Petrini, Claire Phillips, John Pinger, Igor Polakovic, Jan Polatschek, Jiri Preclik, Anthony Pugh, Wayne Purcell R Rahmat Rahardja Ong, David Ramirez, Stefan Ratschan, Ron Read, Anthony Reindl, Toby Robertson, Ian Roger, Martin Röjdmark, Frank Roosen S Radim Sarapatka, Maddy Savitt, Jeannette Schönau, Heiko Schultz, Henry Scott, Serena, Amit Shachaf, Bella Shah, Rolf Siebert, Siham, Ruth Simister, Stephen Smart, Susan Snoeks, Brechtje Spreeuwers, Kurt Stecker, Prasan Stianrapopangs, Chantal Stieber, Lorenz Stoehr, Meaghan Stolk, Dan Straw T Craig Tafel, Noreen Tai, Shohei Takashiro, Caroline Theyse, Marianne Tihon, Annika Tiko, Franciska Tillema, Tom, Martina Tomassini, Yves Traynard, Dana Trytten, Ben Tuff U Nathalie Unterbrink V Adrienne Van Gelder, Filip Van Den Heuvel, Jolanda Van Dongen, Jos Van Der Horst, René Van Gurp, Tessa Van Gelderen, Cecilia Vázquez Ramírez, Jimena Velasco, Danny Verheij, Ruben Versmessen, Andrea Votavova, Otto Vroege W Robert W Rae, Andreas Wachaja, Felix Wagner, Clive Walker, Cheryl Wallace, Eimhin Walsh, Peter Williams, Steve Wilson, Daniel Wong Y Curtis Yallop, John Young, Wen Yu Ho Z Gottfried Zantke, Gail Zohar, Norbert Zussy
## AUTHOR THANKS
#### Damian Harper
Thanks to Emily Wolman and the staff at Lonely Planet; also thanks to my co-authors. Gratitude as always to Daisy, Timothy Jiafu and Emma Jiale. On the road thanks to everyone who helped out and offered encouragement, especially Mr Sun (sorry, didn't get your first name!), Xie Jianguo and Jamie Chen.
#### Piera Chen
A warm thank you to William Lee, Frank Lei, Fred Yeung, Venessa Cheah, Yvonne Ieong, Freddie Hai, Jacqueline Chu and Olivia Aires for enriching my research. Thanks also to my parents and my brother, whose memories of Macau and Hong Kong inspired me in rather unexpected ways, and to Susanna Eusantos for taking care of my daughter. As always, much love and gratitude to Sze Pang-cheung, my husband.
#### Chung Wah Chow
Heartfelt thanks to Leo Liu, Yang Liyan, Emmanuelle Maillard, Kara Jenkinson, Ronald van der Weerd and Einat Keinan in Guǎngxī; Wanny Liang, Christy Cai, Tom Bird, Trey and Hera Menefee, David Abrahamson, Chiu Yi Ting and Angelo Chiu in Guǎngdōng. Thanks also to Leona Wong and Brian Glucroft for keeping me company; and to Daniel McCrohan for keeping the chapter in good shape. Special thanks to Antoine Godde and Sarah Chan for your invaluable help and support.
#### Min Dai
Thanks as ever to Damian for his invaluable help. Thanks also to Margaux, Li Jianjun, Liu Meina, Sansan, Jiafu and Jiale for their support; much gratitude also to the residents of Píngyáo for such a great trip. A debt of thanks to the friendly Wǔtáishān monk who lent me his umbrella and the ever-so-friendly inhabitants of Nánjiēcūn for doing things differently.
#### David Eimer
Special gratitude goes to Li Xinying for her help and patience. Thanks to Chris Taylor in Kūnmíng for the Daliv tips and the old school Lonely Planet stories, as well as to the Bird Bar crew for proving that the grass is always greener in Yúnnán. As ever, thanks to the many people who provided insights along the way, whether knowingly or unwittingly.
#### Robert Kelly
A warm thanks to Damian Harper, and Emily Wolman at Lonely Planet. To all the gang in Hǎinán who have gone from contacts to friends, my best to you all. As always, deepest thanks to Huei-ming, Kate and Sean for holding down the fort while I was away. And a final dedication to my beloved sister Dawn, who passed away during this project, but who loved my work and was always thrilled to receive phone calls 'from the strangest places'.
#### Michael Kohn
So many people along the way made my research easier. Thanks to the crew at Fubar, especially Hiroshi Kuwae, Manus McMathuna and Elizabeth Arnold. Travel partners along the way included Vijay, Vivian and Sayaka, cyclists Adam and Cat (congrats on the nuptials), and Yakov (the pious one). Help also arrived from Xiao Sheng (Ürümqi), Moon (Kashgar) YK and Liman Tan (Hotan) and Zorigoo (Hohhot). In Lonely Planet–land, thanks to coordinating author Damian Harper for encouragement. Behind the scenes, thanks to editors Emily Wolman and Liz Heynes. As ever, thanks to Baigal and little Molly, who make coming home the best part of the trip.
#### Shawn Low
Thanks to Emily for entrusting me with this gig and to Damian for guidance. Thanks to Di Schallmeiner for coordinating and all the Lonely Planet crew for their hard work on this kick-ass book. On the road, thanks goes to Húyùe, Dāndān, Huáhóng, Choi Lee, Joshua Maddox and his crew. Howie and Christine: big thumbs up too for the hospitality. And of course, my dearest Wency, for her patience, support, assistance and excellent Mandarin.
#### Bradley Mayhew
Thanks to Bill of Tibetan Connections and to Tenzin, Xiaojin and Lumbum in Lhasa. Cheers to Andre and Alyson for a fine trip out to Western Tibet and to Tibet co-author Mike Kohn who supplied much of the research for this chapter. Thanks to Tashi at Yabshi Phunkang, to Lobsang for help as always, to Nyima and Tashi at Dropenling and to Liz Heynes and Emily Wolman for helping with style issues.
#### Daniel McCrohan
Thanks to Wangden Tsering (Xīníng), Steve Wilson, Wang Li, Daniel Lotinga (all Chóngqìng), Peter Goff (Chéngdù), Amanda and Josh Henck (Jiǔzhàigōu) and Angela Lankford (Tǎgōng). Extra big thanks to Gong Ying (Chóngqìng) and Kieran Fitzgerald (Jiǔzhàigōu). And gigantic thanks to Jamin York (Yùshù), Tom Herbert and Isabel Brough (both Chéngdù). Love, as always, to all my family in the UK and to my newfound family in Belgium/Holland/Greece. Extra special love to Taotao, Dudu and Yoyo.
#### Christopher Pitts
As always, thanks to everyone who offered valuable insight or provided company along the way. In Shànghǎi, much gratitude is owed to Gerald Neumann. Thanks to fellow authors Damian Harper and Daniel McCrohan, as well as all who work behind the scenes. Particular thanks as well to Anne-Marie and Patrick for helping out with the kids, and my mum and dad, who, in hindsight, did an exemplary job raising us. Finally, love to Perrine, Elliot and Céleste – what would I do without you?
## ACKNOWLEDGMENTS
Climate map data adapted from Peel MC, Finlayson BL & McMahon TA (2007) 'Updated World Map of the Köppen-Geiger Climate Classification', _Hydrology and Earth System Sciences,_ 11, 163344.
Cover photograph: Monks circumambulating Gongtang Pagoda in Labrang Monastery (Labuleng Si), Xiahe, Gansu, Krzysztof Dydynski / Lonely Planet Images: www.lonelyplanetimages.com.
## THIS BOOK
This 12th edition of Lonely Planet's _China_ was researched and written by a team of stellar authors, led by Damian Harper, who also coordinated and contributed to the 11th edition. The guidebook was commissioned in Lonely Planet's Oakland office and produced by the following:
Commissioning Editor Emily K Wolman
Coordinating Editors Dianne Schallmeiner, Branislava Vladisavljevic
Coordinating Cartographers David Kemp, Peter Shields
Coordinating Layout Designer Yvonne Bischofberger
Managing Editors Sasha Baskett, Liz Heynes, Annelies Mertens
Managing Cartographers David Connolly, Hunor Csutoros, Alison Lyall
Managing Layout Designers Jane Hart, Indra Kilfoyle, Celia Wood
Assisting Editors Susie Ashworth, Janet Austin, Sarah Bailey, Carolyn Boicos, Andrea Dobbin, Trent Holden, Kim Hutchins, Alan Murphy, Alison Ridgway, Helen Yeates
Assisting Cartographers Anita Banh, Enes Bašić, András Bogdanovits, Ildikó Bogdanovits, Valeska Cañas, Diana Duggan, Corey Hutchison, Anthony Phelan, Andy Rojas, Andrew Smith, Brendan Streager
Assisting Layout Designers Mazzy Prinsep, Jessica Rose, Jacqui Saunders, Kerrianne Southway
Cover Research Naomi Parker
Internal Image Research Aude Vauconsant
Thanks to Mark Adams, Imogen Bannister, Xiao Bianr, Rebecca Chau, Stefanie Di Trocchio, Janine Eberle, Michael Essex, Joshua Geoghegan, Mark Germanchis, Michelle Glynn, Lauren Hunt, Laura Jane, David Kemp, Nic Lehman, Tim Lu, John Mazzocchi, Daniel Moore, Wayne Murphy, Adrian Persoglia, Piers Pickard, Averil Robertson, Lachlan Ross, Michael Ruff, Julie Sheridan, Laura Stansfeld, John Taufa, Sam Trafford, Juan Winata, Nick Wood
#### Ebook thanks to
Ross Butler, John Carney, Hunor Csutoros, Samantha Curcio, Mark Germanchis, Liz Heynes, Matt Langley, Chris Lee Ack, Nic Lehman, Corine Liang, Ross Macaw, Douglas McClurg, Piers Pickard, Lachlan Ross
# OUR STORY
A beat-up old car, a few dollars in the pocket and a sense of adventure. In 1972 that's all Tony and Maureen Wheeler needed for the trip of a lifetime - across Europe and Asia overland to Australia. It took several months, and at the end - broke but inspired - they sat at their kitchen table writing and stapling together their first travel guide, _Across Asia on the Cheap_. Within a week they'd sold 1500 copies. Lonely Planet was born.
Today, Lonely Planet has offices in Melbourne, London and Oakland, with more than 600 staff and writers. We share Tony's belief that 'a great guidebook should do three things: inform, educate and amuse'.
# Our Writers
### Damian Harper
Coordinating author, Běijīng, Journey to the Great Wall, Tiānjīn & Héběi, Cruising the Yangzi, Gānsù After graduating with a degree in Chinese (modern and classical) from London's School of Oriental and African Studies, Damian moved to pre-handover Hong Kong. He then embarked on an epic nine-province journey for the 6th edition of Lonely Planet's _China_ . Since then he has worked on five further editions and has worked in Shànghǎi and Běijīng (developing a Mandarin accent somewhere between the two), contributing to multiple editions of the Lonely Planet _Beijing_ and _Shanghai_ city guides.
### Piera Chen
Hong Kong, Macau Piera has been travelling to Macau since she was six. Over the years, while working in Hong Kong, it was poetry readings, _fado_ (Portuguese music) concerts, and a masterfully executed _pato de cabidela_ (duck stewed in its own blood) that kept luring her back. For this book, she spoke to insiders of the casino industry, and for both the Hong Kong and Macau chapters, she scoured the streets for indie music dives, art spaces, and other unpolished gems. Piera also co-authored the 14th Lonely Planet _Hong Kong & Macau _ city guide.
### Chung Wah Chow
Guǎngdōng, Guǎngxī Chung Wah is a Hong Kong native who has travelled extensively in the mainland. The sheer diversity of China's languages has always fascinated her. Cantonese, Hakka, Tai, Uighur, Teochew and Hokkien – she loves them all. With an advanced degree in translation studies, a penchant for travel and discovering new sounds and words, Chung Wah merged her talents by becoming a travel writer. She contributed to the previous Lonely Planet edition of _China_ and co-authored Lonely Planet's _Hong Kong & Macau _ city guide.
### Min Dai
Zhèjiāng, Shānxī, Hénán, Húběi Min Dai grew up in the old town of balmy Qīngdǎo on the Shāndōng coast before studying for four years at Běijīng Normal University. She moved to London in the mid-1990s but her seaside roots see her holidaying occasionally in Brighton, Hastings, Margate and even Bournemouth. Min Dai has also lived in Shànghǎi, Běijīng, Hong Kong and Singapore and returns to China frequently to visit family and friends and to journey across her homeland. Married with two children, Min Dai has worked on two editions of Lonely Planet's _China_ .
### David Eimer
Shaanxi (Shǎnxī), Húnán, Guìzhōu, Yúnnán David first came to China in 1988. Since then, he has travelled across the country, from the far west to the Russian and Korean borders in the northeast, through the south and southwest and along the eastern coast. After stints as a journalist in LA and London, he succumbed to his fascination with China in 2005 and moved to Běijīng. As well as contributing to newspapers and magazines, David worked on the last edition of _China_ for Lonely Planet, has co-authored the _Beijing_ and _Shanghai_ city guides and wrote the most recent _Beijing_ _Encounter_ .
### Robert Kelly
Liáoníng, Jílín, Hēilóngjiāng, Hǎinán Ever since he learned that his dad's airline job meant he could fly for peanuts, Robert has been travelling. He first landed in China in the mid-80s, and has popped around Asia ever since, eventually settling down in Taiwan 15 years ago. For this book, Robert researched the very southern point and the very northern tip of China. If there was ever a perfect lesson in the need to avoid summaries and stereotypes when talking about China, this was it. This is Robert's sixth title for Lonely Planet.
### Michael Kohn
Xīnjiāng, Níngxià, Inner Mongolia Michael grew up in Northern California and made his first trip to China in 1994. He jumped ship in Hong Kong, went to Tibet and later hiked along the Great Wall. Michael has returned to China a dozen times. This is his second tour of duty on Lonely Planet's _China_ guide. He has also updated Lonely Planet guides to Tibet, Central Asia and Mongolia and has written two books of his own. Michael is currently based in Ulaanbaatar. His work can be read online at www.michaelkohn.us.
### Shawn Low
Shāndōng, Jiāngsū, Fújiàn, Ānhuī Shawn left his Singapore home for Melbourne and made his way into Lonely Planet as a book editor. Since then, he's done a stint as a commissioning editor, authored guides to Singapore and Southeast Asia, and is now Lonely Planet's Asia-Pacific Travel Editor. His fascination with China began after he was dispatched to Yúnnán to host an episode of National Geographic & Lonely Planet's _Roads Less Travelled_ . Returning to China as an author felt like an obvious thing to do – so he did.
### Bradley Mayhew
Tibet A mountain junkie, Bradley has been visiting the Tibetan plateau for 20 years, since studying Chinese at Oxford University. Bradley has coordinated the last four editions of the _Tibet_ guide and is also the co-author of Lonely Planet's _Bhutan_ , _Nepal_ , _Trekking in the Nepal Himalaya_ and _Central Asia_ , as well as the _Odyssey Guide to Uzbekistan_ . He has lectured on Central Asia to the Royal Geographical Society and was the subject of a Arte/SWR documentary retracing the route of Marco Polo. See what he's up to at www.bradleymayhew.blogspot.com.
### Daniel McCrohan
Sìchuān, Chóngqìng, Qīnghǎi Daniel trained as journalist in the UK and worked for several years on newspapers before turning to travel writing. An Asia fanatic, he travelled extensively throughout the continent for more than 15 years before settling down in China in 2005. He now lives with his wife and their children in a courtyard home in one of Běijīng's _hútòng_ (alleyways). Daniel has worked on Lonely Planet guides to China, India, Shànghǎi and Tibet. He also worked as a presenter for the Lonely Planet TV series _Best in China_ . Find him on www.danielmccrohan.com.
### Christopher Pitts
Shànghǎi, Jiāngxī A Philadelphia native, Chris started off his university years studying classical Chinese poetry before a week in 1990s Shànghǎi (en route to school in Kūnmíng) abruptly changed his focus to the idiosyncracies of modern China. After spending several years in Asia memorising Chinese characters, he abruptly traded it all in and moved to Paris, where he currently lives with his family, Perrine, Elliot and Céleste. He works as a freelance writer, editor and translator for various publishers. Visit his website at www.christopherpitts.net.
Published by Lonely Planet Publications Pty Ltd
ABN 36 005 607 983
12th edition – June 2011
ISBN 978 1 74321 269 1
© Lonely Planet 2011 Photographs © as indicated 2011
All rights reserved. No part of this publication may be sold or hired without the written permission of the publisher. Lonely Planet and the Lonely Planet logo are trademarks of Lonely Planet and are registered in the US Patent and Trademark Office and in other countries. Lonely Planet does not allow its name or logo to be appropriated by commercial establishments, such as retailers, restaurants or hotels. Please let us know of any misuses: lonelyplanet.com/ip.
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La Haute-Asie ou Haute Asie est un ensemble géographique que l'on situe généralement entre l'Asie centrale, la Sibérie et l'Himalaya.
Délimitation
Le terme peut avoir différentes acceptions, liées à la manière de définir l'Asie centrale. Depuis l'indépendance des ex-républiques soviétiques en 1991, l'expression Asie centrale tend à désigner uniquement l'espace de ces dernières. La Haute Asie comprend donc le Tibet, le Xinjiang et la Mongolie ainsi que la Mongolie intérieure. On y ajoute parfois la Sibérie centrale du Sud, entre le sud du lac Baïkal et l'Altaï.
Description
En 1892-1894, la Haute-Asie est explorée par le géographe et explorateur Jules-Léon Dutreuil de Rhins, qui trouve la mort dans cette expédition, tué par des Tibétains. Son assistant Fernand Grenard survit et publie en 1897-1898 les observations de la mission.
Fernand Grenard rédige la synthèse sur la Haute-Asie publiée dans le tome VIII de la Géographie universelle en 1930. Il y décrit le Tibet, la région qu'on appelait alors le Turkestan chinois et la Mongolie.
Notes et références
Voir aussi
Articles connexes
Asie centrale
Sibérie
Bibliographie
.
Région en Asie
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One of the most powerful games ever! The outstanding graphics take you through six screens of a daring attempt to rescue a young woman captured by a ruthless stree gang.
"Spike" and "Hammer" are the heroes that must save the kidnapped woman. One player can fight alone or two players can fight as a team. If play stops before the rescue is complete, the game can be continued from that point by adding additional coins. The graph at the bottom of the screen indicates power.
H: 71.5", W: 24.5", D: 30"
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At its decennial, a look back at how MCS came to be
Johanna Alonso
UMBC's media and communications studies department, which is currently celebrating its ten year anniversary, "was born in a log cabin in American Studies," according to founding chair Jason Loviglio; he started it as a side-project while working as an assistant professor of American Studies. But ten years later, the once under-resourced department is thriving, boasting 300 majors and eight full-time faculty members. A recent panel featured MCS alumni working in everything from broadcast journalism to public relations to nonprofits.
It is hard to define the major concisely. The department's website describes the curriculum as "[focusing] on communication skills, a critical understanding of the media, and the use of relevant new technologies," while Loviglio himself defines it as "a humanities-based liberal arts discipline that is interested in the historical and the theoretical and critical and practical aspects of human communication." In addition to the liberal arts basis around which the department is centered, the curriculum features everything from image editing to podcasting to public relations, depending on individual student's interests.
One MCS student, junior Andrew Grabowski, was drawn to the major because he felt it would help him cultivate his interests in culture and entertainment. "I just always felt very in touch with things on the internet, different social media," he explains. "I've always found it interesting to analyze trends of what's happening." Though he did not have a clear-cut career path in mind, he knew that studying MCS would provide him with a great breadth of options.
Junior Sam Saper views the major in a similar way – though he is unsure of exactly how he plans to use it, he "[thinks] it helps to have this skill set that can be used in a number of different ways. And then the guidelines associated with that, putting those two together, I can figure something out."
Conversely, freshman MCS and English double major Anjali DasSarma came to UMBC already knowing she wanted to become a journalist, and she chose majors she felt would best help her reach this goal. Of her experience in the department thus far, DasSarma says, "in these few core classes that I've taken, it's really a background on the history of communications and I'm a firm believer that you have to learn the history of things before you can move forward."
Although history is featured prominently in the MCS curriculum, the field is anything but antiquated. On the contrary, it is constantly shifting alongside the media landscape. Effective navigation of these changes is important for the department. For example, MCS faculty members meet every summer to discuss how to teach the most relevant and up-to-date software in MCS 101, a class that features a lab portion in which students study programs like Adobe InDesign and Photoshop.
But perhaps the most prominent change that has come to the department in its ten years is a revamped curriculum set to be implemented this summer. "The current curriculum," requires students to take six core classes, as well as six electives, which could be drawn from departments ranging from theatre to gender and women's studies and beyond. "[It] is an artifact of a time when it was literally me and one other guy," Loviglio states. "We had to create a BA education, so we did it on the backs of lots of partnered departments."
The new curriculum will include more core classes, including a research methods class intended to help prepare students for their capstone projects. There will also be a wider selection of MCS electives offered. Notably absent from the new curriculum is the depth of field requirement, which required all MCS students to also be enrolled in a relevant minor or certificate program.
According to Loviglio, this is a change a decade in the making: a sign of the program coming into its own and moving away from relying on other departments. "We want to own more of the education, we want to own more of the curriculum," he explains. And above all? "We want students to be successful."
Quadmania is an annual tradition in the spring at UMBC that features a carn
Investigation into the student who spoiled Avengers: Endgame
This is a work of satire. It started out as a normal day of class, down in
Students plan to bring TEDx to UMBC's campus
For entrepreneurs, innovators and professionals, presenting a TED Talk is t
Eat Less Chicken: The implications of UMBC's decision to expand Chick-fil-A
If there's one thing consumers have learned, it's that there are very f
UMBC continues its Take Back the Night tradition
A white shirt with a red hand-print hung on a clothesline, displaying the w
UMBC to instate virtual parking, including supporting app
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 2,189
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\section{Introduction}
\label{sec:intro}
\vspace{-5pt}
\begin{figure}[t]
\begin{center}
\includegraphics[width=\linewidth]{fig/intro.pdf}
\end{center}
\vspace{-13pt}
\caption{Overall scheme of RGB-D panorama synthesis. Our method takes RGB-D input from cameras and depth sensors in arbitrary configurations and synthesizes an RGB-D panorama.}
\label{fig:intro}
\vspace{-18pt}
\end{figure}
Providing omnidirectional depth along with RGB information is important for numerous applications, \eg, VR/AR.
However, as the omnidirectional RGB-D data is not always available, synthesizing RGB-D panorama data from the limited information of the scene can be useful.
Even though prior works have tried to
synthesize RGB panorama images from perspective RGB images~\cite{hara2020spherical,sumantri2020360},
these methods show limited performance on synthesizing panoramas from small partial views and can not be directly extended for RGB-D panorama synthesis.
By contrast, \textit{jointly learning to synthesize depth data along with the RGB images} allows to synthesize RGB-D panorama with two distinct advantages: (1) RGB images and depth data share the semantic correspondence that can improve the quality of the output RGB-D panorama. (2) Synthesized depth panorama provides omnidirectional 3D information, which can be potentially applied to plentiful applications.
Therefore, it is promising to synthesize RGB-D panorama from the cameras and depth sensors, such that we can synthesizing realistic 3D indoor models.
In this paper, we consider a novel problem: \emph{RGB-D panorama synthesis from limited input information about a scene}. To maximize the usability, we consider the arbitrary configurations of cameras and depth sensors.
To this end, we design the arbitrary sensor configurations by randomly sampling the number of sensors, their intrinsic parameters, and extrinsic parameters, assuming that the sensors are calibrated such that we can align the depth data with the RGB image.
This enables to represent most of the possible combinations of cameras and depth sensors. Accordingly, we propose a novel bi-modal panorama synthesis (BIPS) framework to synthesize RGB-D indoor panoramas from the camera and depth sensors in arbitrary configurations via adversarial learning (See Fig.~\ref{fig:overall}). Especially, we focus on the indoor environments as the RGB-D panorama can provide the complete 3D model for many applications.
We thus design a generator that fuses the bi-modal (RGB and depth) features. Through the generator, multiple latent features from one branch can help the other by providing the relevant information of different modality.
For synthesizing the depth of \emph{indoor} scenes, we rely on the fact that the overall layout usually made of flat surfaces, while interior components have various structures.
Thus, we propose to separate the depth of a scene $I^{d}$ into two components: layout depth $I^{d,lay}$ and residual depth $I^{d,res}$. Here, $I^{d,lay}$ corresponds to the depth of planar surfaces, and $I^{d,res}$ corresponds to the depth of other objects, \eg, furniture.
With this relation, we propose a joint learning scheme called \textit{Residual Depth-aided Adversarial Learning (RDAL)}.
RDAL jointly trains RGB panorama, layout depth and residual depth to synthesize more realistic RGB-D panoramas and 3D indoor models (Sec.~\ref{generator}).
Previously, some metrics \cite{salimans2016improved, heusel2017gans} have been proposed to evaluate the outputs of generative models using latent feature distribution of a pre-trained classification network \cite{szegedy2016rethinking}. However, the input modality of utilizing off-the-shelf network is only limited to perspective RGB images.
Therefore, a new tailored evaluation metric for RGB-D panoramas is needed. For this reason, we propose a novel metric, called Fréchet Auto-Encoder Distance (FAED),
to evaluate the perceptual quality for RGB-D panorama synthesis (Sec.~\ref{subsec:FAED}).
FAED adopts an auto-encoder to reconstruct the inputs from latent features with unlabeled dataset.
Then, the latent feature distribution of the trained auto-encoder is used to calculate the Fréchet distance between the synthesized and real RGB-D data.
Extensive experimental results demonstrate that our RGB-D panorama synthesis method significantly outperforms
the extensions of the prior image inpainting \cite{marinescu2020bayesian, zhao2021large, suvorov2021resolution}, image outpainting \cite{boundless, sumantri2020360}, and image-guided depth synthesis methods \cite{Cheng_2020_TPAMI, park2020non, Li_2020_WACV, hu2020PENet} modified to synthesize RGB-D panorama from partial arbitrary RGB-D inputs.
Moreover, we show the validity of the proposed FAED for evaluating the quality of synthesized RGB-D panorama by showing how well it captures the disturbance level \cite{heusel2017gans}.
In summary, our main contributions are three-fold: (I) We introduce a new problem of generating RGB-D panoramas from partial and arbitrary RGB-D inputs.
(II) We propose a BIPS framework that allows to synthesize RGB-D panoramas via residual depth-aided adversarial learning.
(III) We introduce a novel evaluation metric, FAED, for RGB-D panorama synthesis and demonstrate its validity.
\section{Related Works}
\vspace{-5pt}
\label{sec:relatedworks}
\noindent \textbf{Image Inpainting}
Conventional approaches explore diffusion or patch matching~\cite{ballester2001filling, barnes2009patchmatch, bertalmio2000image, criminisi2003object, efros1999texture, bertalmio2003simultaneous, criminisi2004region}.
However, they require visible regions sufficiently enough to inpaint the missing regions,
thus limiting their ability to synthesize novel textures or structures. The learning-based methods often use generative adversarial networks (GANs) to synthesize texture or structures~\cite{zheng2019pluralistic, li2017generative, iizuka2017globally, yu2018generative}, optimized by the minimax loss~\cite{isola2017image}.
Some works explored different convolution layers, \eg, partial convolution~\cite{liu2018image} and gated convolution~\cite{yu2019free,navasardyan2020image}, to better handle invalid pixels in the input data to the convolution kernel.
Moreover, attention mechanism~\cite{vaswani2017attention, wan2021high} has also been applied to better capture the contextual information and handle missing contents~\cite{yu2018generative, xie2019image, liu2019coherent, wang2019musical, liao2021image}.
Recently, research has been made to synthesize high-resolution outputs~\cite{suin2021distillation, wang2021parallel, peng2021generating} or semantically diverse outputs~\cite{liu2021pd, zhao2020uctgan}.
Although endeavours have been made to tackle this large completion problem \cite{marinescu2020bayesian, zhao2021large, suvorov2021resolution}, they often fail to synthesize visually pleasing panoramas due to only using perspective RGB inputs.
\noindent\textbf{Image Outpainting}
Conventional methods extend an input image to a larger seamless one; however, they require manual guidance \cite{seamcarving, patchmatch, zhang2013framebreak} or image sets of the same scene category \cite{infiniteimages, photouncrop, biggerpicture}.
By contrast, learning-based methods synthesize large images with novel textures that do not exist in the input perspective image~\cite{sabini2018painting, unsup_holistic, deep_portrait, structureaware, 9191339, multimodalout, Mastan2021DeepCFLDC, spiral, Kim2021PaintingOA}.
Some approaches focus on driving scenes \cite{widecontext, sienet} or synthesize panorama-like landscapes with iterative extension or multiple perspective images \cite{yang2019very, boundless,hara2020spherical,sumantri2020360}.
Although performance has been greatly improved so far, the existing methods are still afflicted by the limited quality from the perspective images.
\begin{figure*}[t!]
\begin{center}
\hspace*{-0.0\linewidth}\includegraphics[width=.94\textwidth]{fig/overall_structure.pdf}
\end{center}
\vspace{-0.5cm}
\caption{Overall structure of our bi-modal indoor panorama synthesis (BIPS) framework. Our framework takes RGB-D input provided by arbitrary sensor configurations, integrates the bi-modal input data with BFF branch in generator network, and jointly trains to synthesize layout depth and residual depth. Then, perceptual quality of the synthesized RGB-D panorama is measured by our proposed FAED metric.}
\vspace{-14pt}
\label{fig:overall}
\end{figure*}
\noindent \textbf{Image-guided Depth Synthesis}
One line of research attempts to fuse the bi-modal information, \ie, the RGB image and sparse depth. Some methods, \eg~\cite{mal2018sparse}, fuse the sparse depth and RGB image via early fusion while others~ \cite{self_sparsetodense, jaritz2018sparse, tang2019learning, 2020, li2020multi, Huang_2020_TIP} utilize a late fusion scheme,
or jointly utilize both the early and late fusion~\cite{Gansbeke_2019_MVA, Lee_2020_Access, wang2020fisnets}. Another line of research focuses on utilizing affinity or geometric information of the scene via surface normal, occlusion boundaries, and the geometric convolutional layer~\cite{Lee_2019_ICRA, Qiu_2019_CVPR, Xu_2019_ICCV, Zhang_2018_CVPR, hu2020PENet,Cheng_2020_TPAMI,cspn++, park2020non}.
However, these works only generate dense depth maps that has the same FoV as the input perspective RGB images.
\noindent \textbf{Evaluation of Generative Models}
Image quality assessment can be classified into three groups: full-reference (FR), reduced-reference (RR), and no-reference (NR).
There exist many conventional FR metrics, \eg, PSNR, MSE, and SSIM, and deep learning (DL)-based FR metrics, \eg, LPIPS \cite{zhang2018unreasonable}. These metrics typically calculate either pixel-wise, or patch-wise similarity to the ground truth images.
By contrast, NR methods, \eg, BRISQUE~\cite{mittal2012no} and NIQE~\cite{mittal2012making} assess image quality without any reference image.
Among the DL-based NR metrics, Inception Score (IS) ~\cite{salimans2016improved} and Fréchet Inception Distance (FID)~\cite{heusel2017gans} are two popular approaches~\cite{borji2019pros}.
IS and FID scores are calculated based on pretrained classification models, \eg, Inception model~\cite{szegedy2016rethinking}, aiming to capture the high-level features.
Unfortunately, these metrics are less applicable for RGB-D panorama evaluation because (1) they are trained only with perspective RGB images, and (2) there are no labeled panorama images to train them.
Therefore, they are highly sensitive to the distortion of panoramic images, making them hard to capture perceptual quality properly on panoramic images.
Furthermore, naively using them on RGB-D information leads to imprecise measure of the semantic correspondence between the two different modalities. Therefore, \textit{we propose FAED, which aims to evaluate RGB-D panorama quality between the RGB and depth pairs.
FAED can be adaptively applied to generative models on multi-modal domain, that lacks labeled dataset}.
\vspace{-5pt}
\section{Proposed Methods}
\vspace{-2pt}
\vspace{-2pt}
\subsection{Problem Formulation}
\vspace{-3pt}
\label{subsubsec:simulation}
Previous works, \eg, \cite{sumantri2020360, hara2020spherical} generate an equirectangular projection (ERP) image ($ERP^{rgb}$) from input perspective image(s) ($I^{rgb}_{in}$).
Then, an RGB panorama $I^{rgb}_{out}$ can be created via a function $G$, mapping $I^{rgb}_{in}$ into a $ ERP^{rgb}$~\cite{he2017geometry}, which can be formulated as $I^{rgb}_{out} = ERP^{rgb}=G(I^{rgb}_{in})$.
However, as it is crucial to provide omnidirectional depth information \cite{rosin2019rgb, alaee2018user} in many applications, many studies tried to synthesize depth panoramas from input RGB panorama images and partial depth measurements~\cite{wang2020bifuse, hirose2021depth360}.
One solution to synthesize an RGB-D panorama would be to first synthesize RGB panorama from input perspective images, and then utilizing the depth synthesis methods to generate an omnidirectional depth map. However, such an approach is cumbersome and less effective, as shown in the experimental results (See Table~\ref{tab:ablation}).
We solve this novel yet challenging problem by jointly utilizing the input RGB image ($I^{rgb}_{in}$) and depth data ($I^{d}_{in}$). Our goal is to directly generate the RGB panorama ($ERP^{rgb}$) and depth panorama ($ERP^{d}$) simultaneously via a mapping function $G$, which can be described as $(I^{rgb}_{out},I^{d}_{out})=(ERP^{rgb},ERP^{d})= G(I^{rgb}_{in}, I^{d}_{in})$.
$G$ can be formulated by learning a \textit{single} network to synthesize $ERP^{rgb}$ and $ERP^{d}$ using
$I^{rgb}_{in}$ and $I^{d}_{in}$ obtained in arbitrary sensor configurations.
As the information in the left and right boundaries in ERP images should be connected, our designed G uses circular padding~\cite{schubert2019circular} before each convolutional operation.
Consequently, we configure the parameters of cameras and depth sensors, and randomly sample the parameters to provide the input to the $G$ during training.
These parameters can handle most of the possible sensor configurations.
Figure~\ref{fig:input_mask} shows the input masks, sampled from the sensor configurations. To handle the cases where only cameras or depth sensors are used, we choose whether to use cameras only, depth sensors only, or both, randomly.
\noindent \textbf{Parameters of RGB Cameras} We denote the parameters of RGB cameras, horizontal FoV as $\delta_{H}$, vertical FoV as $\delta_{V}$, pitch angle as $\psi$, and number of viewpoints as $n$. When $n>1$, we arrange the viewpoints in a circle having the sampled pitch angle from the equator and at the same intervals.
We do not consider roll and yaw, as they
do not affect the results (\ie, the output is equivariant to the horizontal shift of input) thanks to using circular padding.
Practically, we sample the parameters from $\delta_{H} \sim \mathcal{U}[60^{\circ}, 90^{\circ}]$, $\delta_{V} \sim \mathcal{U}[60^{\circ}, 90^{\circ}]$, $\psi \sim \mathcal{U}[-90^{\circ}, 90^{\circ}]$, and $n \sim \mathcal{U}\{1,2,3,4\}$, where $\mathcal{U}\left [ \cdot \right ]$ represents uniform distribution.
\noindent \textbf{Parameters of Depth Sensors} $I^{d}_{in}$ can be obtained from mechanical LiDARs or perspective depth sensors, thus we should generate arbitrary depth input masks for both. For the LiDARs, we denote the parameters as lower FoV $\delta_{L}$, upper FoV $\delta_{U}$, pitch angle $\psi$, yaw angle $\omega$, and the number of channels $\eta$. The yaw angle is needed here to consider the relative yaw motion to the camera arrangement.
For the perspective depth sensors providing dense depth, they have many similar parameters and viewpoints with those of the RGB-D cameras. Therefore, we use the same sampled parameters with the cameras (\ie, $(\delta_{H}, \delta_{V}, \psi, n)$).
In practice, we first sample the parameters from $\psi \sim \mathcal{U}[-90^{\circ}, 90^{\circ}]$, $\omega \sim \mathcal{U}[0,360^{\circ}]$, and $\eta \sim \mathcal{U}\{2, 4, 8, 16\}$. Then, we sample $\delta_{L}$ and $\delta_{U}$ from $\mathcal{U}\{\eta, 2\eta, 3\eta\}$.
Finally, our problem is formulated as:
\vspace{-5pt}
\begin{equation}
\begin{split}
(I^{rgb}_{out},I^{d}_{out})=(ERP^{rgb},ERP^{d})= \\ G(I^{rgb}_{in}(\delta_{H}, \delta_{V}, \psi, n), I^{d}_{in}(\delta_{L}, & \delta_{U}, \psi, \omega, \eta, \delta_{H}, \delta_{V}, n))
\end{split}
\end{equation}
\vspace{-5pt}
\begin{figure}[t]
\begin{center}
\hspace*{-0.0\linewidth}\includegraphics[width=.96\linewidth]{fig/input_mask.pdf}
\end{center}
\vspace{-0.6cm}
\caption{Sampled input masks. The upper row shows the visible regions of cameras and perspective dense depth sensors with parameters $(\delta_{H}, \delta_{V}, \psi, n)$, and the lower row shows the visible regions of mechanical LiDARs, with parameters $(\delta_{L}, \delta_{U}, \psi, \omega, \eta)$.}
\label{fig:input_mask}
\vspace{-14pt}
\end{figure}
\vspace{-15pt}
\subsection{RGB-D Panorama Synthesis Framework}
\label{subsec:network_architecture}
\vspace{-0.1cm}
\noindent\textbf{Overview} An overview of the proposed BIPS framework is depicted in Fig.~\ref{fig:overall}. BIPS consists of a generator $G$ (Sec.\ref{generator}) and a discriminator $D$ (Sec.~\ref{disc}). $G$ takes the perspective RGB image $I^{rgb}_{in}$ and depth $I^d_{in}$ as inputs.
We notice that the quality of the RGB-D panorama depends on both the overall (mostly rectangular) layout and how the furniture are arranged in the indoor scene. Inspired by \cite{zeng2020joint}, we separate the depth data $I^d_{gt}$ into \textit{layout depth} $I^{d,lay}_{gt}$, and \textit{residual depth (the interior components) $I^{d,res}_{gt}$} which is defined as ($I^d_{gt}$ - $I^{d,lay}_{gt}$ ). The generator $G$ outputs the RGB panorama image $I^{rgb}_{out}$, the layout depth $I^{d,lay}_{out}$ and residual depth $I^{d,res}_{out}$ simultaneously. As these are jointly trained with adversarial loss, we call this learning scheme as \textit{Residual Depth-aided Adversarial Learning (RDAL)}.
\vspace{-12pt}
\subsubsection{Generator}
\vspace{-5pt}
\label{generator}
\noindent \textbf{Input Branch}
$G_{in}$ consists of two encoding branches, $G_{in}^{rgb}$ and $G_{in}^{depth}$ which takes $I^{rgb}_{in}$ and $I^d_{in}$, respectively.
These branches independently process $G_{in}^{rgb}$ and $G_{in}^{depth}$ with six conv layers before fusing them.
As the inputs have a resolution of 512 $\times$1024, the filter size of the first conv layer is set as 7 and then reduced to 3 and 4 gradually.
\noindent \textbf{Bi-modal Feature Fusion (BFF) Branch }
BFF branch $G_{BFF}$ takes $G_{in}^{rgb} (I^{rgb}_{in})$ and $G_{in}^{depth} (I^{d}_{in})$ as inputs, as shown in Fig.~\ref{fig:generator}. Although $I^{rgb}_{in}$ and depth $I^d_{in}$ are in two different modalities, we assume that the cameras and depth sensors are well calibrated and synchronized.
Then, to utilize this highly correlated bi-modal information in its two branches, $G_{BFF}$ consists of two-stream encoder-decoder networks fusing the bi-modal features. These two encoder-decoder networks have an identical structure (see Fig.~\ref{fig:generator}).
Moreover, the bi-modal features are fused in between the layers of $G_{BFF}$. In particular, the features from both branches are concatenated and fed back to each other. Overall, the fusion is done after the features pass two `DownBlocks' and before passing two `UpBlocks'. In addition, multi-scale residual connections are used to vitalize transfer of information between the layers and branches. As multiple latent features from one branch help the other by sharing the information apart in both ways, $G_{BFF}$ can generate features by fully exploiting the information of the 3D scene.
\noindent \textbf{The Output Branch}
Realistic indoor space comes from precise layout structure
and high perceptual interior. Therefore, to enable RDAL to jointly train the layout and residual depth of the indoor scene, we design $G_{out}$ to have three decoding branches.
Each of them generates RGB panorama $I^{rgb}_{out}$, layout depth panorama $I^{d,lay}_{out}$, and residual depth panorama $I^{d,res}_{out}$ respectively, as shown in Fig.~\ref{fig:generator}.
Intuitively, $I^{d,lay}_{out}$ determines the layout structure and $I^{d,res}_{out}$ determines the interior objects.
Then, element-wise addition of $I^{d,lay}_{out}$ and $I^{d,res}_{out}$ gives the output total depth map panorama.
\begin{figure}[t]
\begin{center}
\hspace*{-0.0\linewidth}\includegraphics[width=\linewidth]{fig/Generator_concat.pdf}
\end{center}
\vspace{-0.4cm}
\caption{The proposed generator ($G$). It consists of two input branches, a BFF branch, and three output branches. A larger version of the image can be found in the suppl. material.}
\vspace{-0.5cm}
\label{fig:generator}
\end{figure}
\vspace{-12pt}
\subsubsection{Discriminator}
\label{disc}
\vspace{-5pt}
We use the multi-scale discriminator $D$ from \cite{wang2018high}, but modify it to have five input and output channels (three for $I^{rgb}$, one for $I^{d,lay}$, one for $I^{d,res}$). The detailed discriminator structure can be found in the suppl. material.
\vspace{-10pt}
\subsubsection{Loss Function}
\vspace{-5pt}
For training $G$, we use weighted sum of pixel-wise L1 loss and adversarial loss. The pixel-wise L1 loss between the GT and the output panorama, denoted as $L_{pixel}$, consists of three terms as the $G$ has three outputs (RGB, layout depth, residual depth panorama):
\begin{equation}
L^{total}_{pixel} = L^{rgb}_{pixel} + L^{d,lay}_{pixel} + L^{d,res}_{pixel}.
\end{equation}
For the adversarial loss $L_{adv}$, we used LSGAN loss~\cite{mao2017least}: $L_{adv} = \frac{1}{2}\mathop{\mathbb{E}}{ [ (D({I^{total}_{out}})-1)^2] }$,
where $I^{total}_{out}$ is concatenation of generator outputs $I^{rgb}_{out}$, $I^{d,lay}_{out}$ and $I^{d,res}_{out}$, and $D$ is a discriminator trained to output $one$ for GT and $zero$ for $I^{total}_{out}$ with MSE loss.
By decomposing the total depth loss into $L^{d,lay}$ and $L^{d,res}$, our RDAL scheme allows the generator $G$ to synthesize RGB-D panorama that generates highly plausible interior.
Finally, the total loss for generator is:
\begin{equation}
L_G=\lambda L^{total}_{pixel} + L_{GAN}\\[-5pt]
\end{equation}
where $\lambda$ is a weighting factor. The generator $G$ is trained by minimizing the total loss $L_G$.
Detailed loss terms can be found in the suppl. material.
\subsection{Fréchet Auto-Encoder Distance (FAED)}
\label{subsec:FAED}
\vspace{-0.15cm}
\subsubsection{Auto-Encoder Network}
\vspace{-0.1cm}
\label{subsubsec:A}
Similar to the high-level features in a CNN trained with large-scale semantic labels, latent features $f_{latent}$ in a trained auto-encoder also contain high-level information, as it is forced to reconstruct the input from the latent features. Therefore, we propose to train an auto-encoder, which can be done without any labels in the dataset, and use the latent features in the auto-encoder to extract perceptually meaningful information. In this way, performance evaluation can be performed for any data that lacks a labeled dataset.
The auto-encoder $A$ consists of an encoder and decoder: $A_{encoder}$ and $A_{decoder}$, as shown in Fig.~\ref{fig:autoencoder}.
The detailed structure of $A$ is given in the suppl. material.
\begin{figure}[t]
\begin{center}
\hspace*{-0.0\linewidth}\includegraphics[width=.91\linewidth]{fig/autoencoder_new2.pdf}
\end{center}
\vspace{-0.5cm}
\caption{The proposed FAED metric for RGB-D panorama quality evaluation. It measures the distance of the distributions of latent features extracted from the pre-trained auto-encoder network on RGB-D panorama.
}
\label{fig:autoencoder}
\vspace{-15pt}
\end{figure}
\vspace{-0.25cm}
\subsubsection{Calculation of FAED for RGB-D Panorama}
\vspace{-0.1cm}
We denote
$f_{latent}$ at $c$-th channel, $h$-th row, and $w$-th column as $f_{latent}(c,h,w)$.
Note that as we use ERP, the $h$ and $w$ has one-to-one relation to latitude and longitude.
\noindent\textbf{Longitudinal Invariance} To evaluate the performance of $G$, we extract $f_{latent}$ from generated samples using $A_{encoder}$. However, as we generate the upright ERP image, it is expected to have a distance metric that is invariant to the longitudinal shift. This is because an upright ERP panorama represents the same scene when it's cyclically shifted in the longitudinal direction. Therefore, to make the resulting distance metric invariant to the longitudinal shift, we take the mean for the longitudinal direction of $f_{latent}$ as:
\vspace{-4pt}
\begin{equation}
f_{latent}^\prime(c,h) = \frac{1}{W} \sum_{w} f_{latent}(c,h,w). \\[-4pt]
\end{equation}
\noindent\textbf{Latitudinal Equivariance}
As the ERP has varying sampling rates depending on the latitude $\phi$, we apply different weights on $f_{latent}^\prime$ based on the latitude.
Specifically, we multiply $cos(\phi)$ to feature at the latitude $\phi$, because in ERP, each pixel occupies $cos(\phi)$ area in the spherical surface, compared with the pixels in the equator. Formally, the resulting feature $f_{latent}^{\prime\prime}$ is expressed as:
\vspace{-4pt}
\begin{equation}
f_{latent}^{\prime\prime}(c,h) = \cos \phi \cdot f_{latent}^\prime(c,h).
\end{equation}
\begin{table*}[t!]
\caption{Quantitative results of RGB panorama synthesis on Structured3D dataset.
As \cite{sumantri2020360} uses 4 identical perspective RGB masks on horizontal central line, we report our results in same setting. In other cases, we follow designed arbitrary configuration of RGB sensor that uses 1\~4 number of inputs.
Zero number of depth input means that depth map is not used for RGB panorama synthesis.
For FAED calculation, GT depth is used along with synthesized RGB panorama. \textbf{Bold} numbers indicate the best results.
}
\label{tab:result_rgb}
\vspace{-8pt}
\footnotesize
\resizebox{\textwidth}{!}{%
\begin{tabular}{c|c|cc|ccc|c|c}
\hline
\multirow{2}{*}{Category} & \multirow{2}{*}{Method} & \multicolumn{2}{c||}{Input no. ($n$)} & \multicolumn{3}{c|}{RGB metric} & Layout metric & Proposed metric \\ \cline{3-9}
& & \multicolumn{1}{c|}{RGB} & \multicolumn{1}{c||}{Depth} & \multicolumn{1}{c|}{PSNR($\uparrow$)} & \multicolumn{1}{c|}{SSIM($\uparrow$)} & LPIPS($\downarrow$) & 2D Corner error($\downarrow$) & FAED($\downarrow$) \\ \Xhline{3\arrayrulewidth}
\multirow{3}{*}{Inpainting} & BRGM~\cite{marinescu2020bayesian} & \multicolumn{1}{c|}{\multirow{5}{*}{1/2/3/4}} & \multicolumn{1}{c||}{\multirow{5}{*}{0}} & \multicolumn{1}{c|}{14.00} & \multicolumn{1}{c|}{0.5310} & 0.6192 & 72.52 & 442.3 \\ \cline{2-2} \cline{5-9}
& CoModGAN~\cite{zhao2021large} & \multicolumn{1}{c|}{} & \multicolumn{1}{c||}{} & \multicolumn{1}{c|}{14.35} & \multicolumn{1}{c|}{0.5837} & 0.4768 & 62.45 & 208.2 \\ \cline{2-2} \cline{5-9}
& LaMa~\cite{suvorov2021resolution} & \multicolumn{1}{c|}{} & \multicolumn{1}{c||}{} & \multicolumn{1}{c|}{13.74} & \multicolumn{1}{c|}{0.5207} & 0.5658 & 51.12 & 379.2 \\ \cline{1-2} \cline{5-9}
Outpainting & Boundless~\cite{boundless} & \multicolumn{1}{c|}{} & \multicolumn{1}{c||}{} & \multicolumn{1}{c|}{13.74} & \multicolumn{1}{c|}{0.5663} & 0.6144 & 74.47 & 429.4 \\ \cline{1-2} \cline{5-9}
\multirow{1}{*}{} & Ours & \multicolumn{1}{c|}{} & \multicolumn{1}{c||}{} & \multicolumn{1}{c|}{\textbf{16.21}} & \multicolumn{1}{c|}{\textbf{0.6161}} &\textbf{ 0.4549 } & \textbf{39.63 } & \textbf{162.3} \\
\Xhline{3\arrayrulewidth}
Panorama syn. & Sumantri \etal \cite{sumantri2020360}& \multicolumn{1}{c|}{\multirow{2}{*}{4}} & \multicolumn{1}{c||}{\multirow{2}{*}{0}} & \multicolumn{1}{c|}{\textbf{18.49}} & \multicolumn{1}{c|}{\textbf{0.6680}} & 0.4190 & 50.76 & 443.4 \\ \cline{1-2} \cline{5-9}
& Ours & \multicolumn{1}{c|}{} & \multicolumn{1}{c||}{} & \multicolumn{1}{c|}{17.29} & \multicolumn{1}{c|}{0.6510} & \textbf{0.3975} & \textbf{34.68} & \textbf{103.1} \\ \hline
\end{tabular}%
}
\vspace{-6pt}
\end{table*}
\begin{figure*}[t!]
\begin{center}
\hspace*{-0.0\linewidth}\includegraphics[width=\textwidth]{fig/fid_gaussian_rgb_final.pdf}
\end{center}
\vspace{-0.7cm}
\captionsetup{font=small}
\caption{Verification of FAED in Structured3D dataset. It can be seen that FAED correlates well perceptual evaluation of human, as FAED increases as the data becomes more corrupted. For more detailed results, please refer to the suppl. material.}
\vspace{-0.6cm}
\label{fig:verification}
\end{figure*}
\noindent{}\textbf{Fréchet Distance} We treat the resulting $f_{latent}^{\prime\prime}$ as a vector and assume that it has a multi-dimensional Gaussian distribution. Then, we get the distribution of ground truths $\mathcal{N}(m, C)$ and that of generated samples $\mathcal{N}(\hat{m},\hat{C})$, and calculate the Fréchet distance $d$ between them as given by \cite{dowson1982frechet}:
\begin{equation}
\begin{split}
d^2(\mathcal{N}(m,&C),\mathcal{N}(\hat{m},\hat{C}))\\
&= ||m-\hat{m}||_2^2
+Tr(C+\hat{C}-2(C\hat{C})^{1/2}). \\[-4pt]
\end{split}
\end{equation}
We use $d^2$ as a perceptual distance metric where $m$ and $C$ denote mean and covariance, respectively.
\vspace{-4pt}
\section{Experimental Results}
\vspace{-3pt}
\noindent\textbf{Synthetic Dataset}
\label{subsec:dataset}
Structured3D dataset~\cite{zheng2019structured3d} provides various textures of indoor scenes with a $512\times 1024$ resolution.
We split the dataset into train, validation, and test set
where the numbers of data are 17468, 2183, and 2184, respectively.
In addition, with the corner locations
provided in the dataset, we manually generated layout depth maps of each 3D scene.
The residual depth maps are obtained by subtracting the layout depth from the GT depth map.
\noindent\textbf{Real Dataset}
We used a combination of two datasets: Matterport3D \cite{Matterport3D}, and 2D-3D-S dataset \cite{armeni2017joint}. Both datasets provide real-world indoor RGB-D panorama. Since this dataset does not provide sufficient number of annotated layout, it can't be used for training our framework and only used for test purpose.
We excluded data with too many of invalid pixels from test dataset, then its number of data is 603.
\noindent\textbf{Implementation Details}
For the details about our implementation, please refer to the supplementary material.
\vspace{-5pt}
\subsection{Verification of FAED}
\label{subsec:verification_faed}
\vspace{-3pt}
To show the effectiveness of FAED on measuring the perceptual quality of RGB-D panorama, we corrupt the Structured3D dataset \cite{zheng2019structured3d} in two ways: corrupting RGB images only and corrupting depth maps only.
Following \cite{heusel2017gans}, we corrupt the dataset by applying various types of noise: Gaussian blur, Gaussian noise, uniform patches, swirl, and salt and pepper noise.
Here, we only show the plots for Gaussian blur in Fig.~\ref{fig:verification} due to the lack of space. Other results can be found in suppl. material.
\textit{Note that the evaluation is done for RGB-D panorama, neither for RGB image alone nor for depth map alone.}
As shown in Fig. \ref{fig:verification}, the Fréchet distance for both RGB and depth panorama increases as the disturbance level (Gaussian blur) is increased.
We show that the same applies to the other four types of noises in the supplementary material.
\textit{This indicates the perceptual quality of RGB-D panorama becomes poorer as the FAED score increases.}
\begin{figure}[t]
\begin{center}
\hspace*{-0.0\linewidth}\includegraphics[width=\linewidth]{fig/pano_syn_res_new.pdf}
\end{center}
\vspace{-0.7cm}
\caption{Qualitative comparison to Sumantri et. al.~\cite{sumantri2020360}. While the result from~\cite{sumantri2020360} is blurry, our result is sharp and realistic.}
\label{fig:pano_syn_res}
\vspace{-15pt}
\end{figure}
\begin{table*}[h!]
\caption{Quantitative results of depth panorama synthesis on Structured3D dataset. Depth input type L/P means that we use LiDAR (L) and dense perspective depth sensor (P) in arbitrary configurations for the input. Full RGB image is used along with synthesized depth panorama for FAED calculation. \textbf{Bold} numbers indicate the best results.
}
\label{tab:results_depth}
\vspace{-8pt}
\tiny
\resizebox{\textwidth}{!}{%
\begin{tabular}{c|c|cc|cc|c|c}
\hline
\multirow{2}{*}{Category} & \multirow{2}{*}{Method} & \multicolumn{2}{c||}{Input type} & \multicolumn{2}{c|}{Depth metric} & Layout metric & Proposed metric \\ \cline{3-8}
& & \multicolumn{1}{c|}{RGB} & \multicolumn{1}{c||}{Depth} & \multicolumn{1}{c|}{AbsREL($\downarrow$)} & RMSE($\downarrow$) & 2D IoU($\uparrow$) & FAED($\downarrow$) \\ \Xhline{3\arrayrulewidth}
\multirow{4}{*}{Depth syn.} & CSPN \cite{Cheng_2020_TPAMI} & \multicolumn{1}{c|}{\multirow{5}{*}{Full}} & \multicolumn{1}{c||}{\multirow{5}{*}{L/P}} & \multicolumn{1}{c|}{0.0855} & 2214 & 0.8062 & 428.9 \\ \cline{2-2} \cline{5-8}
& NLSPN \cite{park2020non} & \multicolumn{1}{c|}{} & \multicolumn{1}{c||}{} & \multicolumn{1}{c|}{0.1268} & 2807 & 0.7333 & 836.1 \\ \cline{2-2} \cline{5-8}
& MSG-CHN \cite{Li_2020_WACV} & \multicolumn{1}{c|}{} & \multicolumn{1}{c||}{} & \multicolumn{1}{c|}{0.1764} & 3296 & 0.6724 & 896.4 \\ \cline{2-2} \cline{5-8}
& PENet \cite{hu2020PENet} & \multicolumn{1}{c|}{} & \multicolumn{1}{c||}{} & \multicolumn{1}{c|}{0.1740} & 3145 & 0.7033 & 906.0 \\ \cline{1-2} \cline{5-8}
& Ours & \multicolumn{1}{c|}{} & \multicolumn{1}{c||}{} & \multicolumn{1}{c|}{\textbf{0.0844}} & \textbf{1942} & \textbf{0.8286} & \textbf{131.5} \\ \hline
\end{tabular}%
}
\end{table*}
\begin{figure*}[t!]
\begin{center}
\hspace*{-0.0\linewidth}\includegraphics[width=\textwidth]{fig/inpainting_dc_res_1.pdf}
\end{center}
\vspace{-0.6cm}
\captionsetup{font=small}
\caption{(a) Visual results for RGB panorama synthesis on Structured3D dataset. Two methods, LaMa and CoMoGAN,
are visualized for comparison. (b) Visual results for depth panorama synthesis on Structured3D dataset.
CSPN is also visualized for comparison. More qualitative results can be found in suppl. material.
}
\vspace{-0.6cm}
\label{fig:inpainting_res}
\end{figure*}
\vspace{-2pt}
\subsection{RGB-D Panorama Synthesis}
\vspace{-4pt}
\begin{table}[t!]
\caption{Ablation study results of BIPS framework. The experiments in four rows take RGB-D input.
}
\label{tab:ablation}
\vspace{-8pt}
\footnotesize
\renewcommand{\tabcolsep}{17pt}
\begin{tabular}{c|cc}
\hline
\multirow{2}{*}{Method} & \multicolumn{2}{c}{Metric} \\ \cline{2-3}
& \multicolumn{1}{c|}{2D IoU($\uparrow$)} & FAED($\downarrow$) \\ \Xhline{3\arrayrulewidth}
IwDS (\cite{zhao2021large} + \cite{Cheng_2020_TPAMI}) & \multicolumn{1}{c|}{0.7561} & 640.9 \\ \hline
Ours w/o BFF & \multicolumn{1}{c|}{0.7859} & 381.4 \\ \hline
Ours w/o RDAL & \multicolumn{1}{c|}{0.7164} & 329.0 \\ \hline
Ours & \multicolumn{1}{c|}{\textbf{0.8158}} & \textbf{198.0} \\ \hline
\end{tabular}
\vspace{-13pt}
\end{table}
\begin{figure*}[t]
\begin{center}
\hspace*{-0.0\linewidth}\includegraphics[width=\linewidth]{fig/our_syn_res.pdf}
\end{center}
\vspace{-0.3cm}
\vspace{-8pt}
\caption{
Visualization of our synthesized RGB-D panorama results using RGB-D data in arbitrary configurations. (a) and (b) take both RGB and depth data, (c) takes only RGB and (d) takes only depth data. More results are visualized in suppl. materials.}
\label{fig:our_syn_res}
\vspace{-8pt}
\end{figure*}
\begin{figure*}[t]
\begin{center}
\hspace*{-0.0\linewidth}\includegraphics[width=\linewidth]{fig/ablation1.pdf}
\end{center}
\vspace{-0.3cm}
\vspace{-8pt}
\caption{
Visualization of ablation study results on Structured3D dataset. Result without BFF shows artifacts irrelevant to given input and result without RDAL infers distorted room layout while our final model synthesizes perceptual undistorted indoor room.
}
\label{fig:ablation}
\vspace{-15pt}
\end{figure*}
\begin{figure}[t]
\begin{center}
\hspace*{-0.0\linewidth}\includegraphics[width=0.98\linewidth]{fig/matter2.pdf}
\end{center}
\vspace{-0.5cm}
\caption{Visualization of our synthesized RGB-D panorama and 3D indoor model on Matterport3D dataset.}
\label{fig:matter}
\vspace{-18pt}
\end{figure}
\noindent\textbf{RGB Panorama Evaluation}
Table~\ref{tab:result_rgb} shows the quantitative comparison with the inpainting and outpainting methods on the Structured3D dataset. We use PSNR, SSIM and LPIPS to evaluate the quality of RGB panorama.
We also measure 2D corner error, where the 2D GT corner points are compared with the estimated 2D corner points using DuLa-Net~\cite{yang2019dula} on the synthesized RGB panorama.
We also use the proposed FAED to jointly evaluate the quality of RGB-D information.
As shown in Table~\ref{tab:result_rgb}, our method outperforms the image inpainting and outpainting methods: BRGM~\cite{marinescu2020bayesian}, CoModGAN~\cite{zhao2021large}, LaMa~\cite{suvorov2021resolution} and Boundless~\cite{boundless}, by a large margin for all metrics. For instance, our method outperforms the best inpainting method, CoModGAN, by an 4.6\% decrease of LPIPS score, 36.5\% drop of 2D corner error, and 22\% decline of FAED score. The effectiveness can also be visually verified in Fig.~\ref{fig:inpainting_res}(a).
Our method produces clearer RGB panorama images compared with LaMa producing blurry images. Although CoModGAN produces clear RGB outputs, it doesn't consider the indoor layout and semantic information of the furniture, \eg electric cooker is combined with bookshelves, as shown in Fig.~\ref{fig:inpainting_res}.
Therefore, its layout is semantically inconsistent with the input RGB region and its FAED score is higher than ours.
We also compare with the panorama synthesis method, Sumantri \etal~\cite{sumantri2020360}.
Our method shows slightly lower scores using the conventional metrics, PSNR and SSIM; however, it shows the much better LPIPS score (0.3975 vs 0.4190), 2D corner error (34.68 vs 50.76) and FAED score (103.1 vs 443.4), respectively. We argue that PSNR and SSIM merely measure local photometric similarity, and thus fail to well reflect the perceptual quality.
This can be verified from Fig.~\ref{fig:pano_syn_res} where we visually compare with \cite{sumantri2020360}. Our method synthesizes better textures and shows much higher visual quality. More results can be found in suppl. material.
\noindent\textbf{Depth Panorama Evaluation}
We compare our method with the image-guided depth synthesis methods on Structured3D dataset.
To evaluate the quality, we use AbsREL and RMSE, and the proposed FAED. We also use layout 2D IoU, as was done in~\cite{choi20203d}.
The details of the metrics and results can be found in the supplementary material.
Table~\ref{tab:results_depth} shows the quantitative comparison with the depth synthesis methods: CSPN~\cite{Cheng_2020_TPAMI}, NLSPN~\cite{park2020non}, MSG-CHN~\cite{Li_2020_WACV} and PENet~\cite{hu2020PENet}. In particular, our method outperforms on of the best depth synthesis method, CSPN, with much better AbsREL score (0.0844 vs 0.0855), RMSE (1942 vs 2214), 2D IoU (0.8286 vs 0.8062) and FAED score (131.5 vs 428.9).
With the proposed RDAL scheme, our method estimates the best layout depth, which is demonstrated by the highest layout 2D IoU.
This in turn, considerably affects the overall depth error in other metrics as well.
Figure.~\ref{fig:inpainting_res}(b) shows the qualitative comparison with CSPN~\cite{Cheng_2020_TPAMI}.
CSPN synthesizes the interior components,~\eg, beds, relatively well; however, the depth of planes (\eg, walls and ceiling) are not clear. Therefore, it cannot synthesize a valid layout,
failing to generate a realistic 3D indoor model.
By contrast, our synthesized depth panorama shows an undisturbed and clear layout.
\noindent{}\textbf{Evaluation on Real Dataset}
We evaluated our synthesized RGB-D panorama on real indoor scenes in Matterport3D and 2D-3D-S dataset. An output RGB-D panorama and its 3D indoor model are visualized in Fig.~\ref{fig:matter}.
Overall, our method synthesizes high-quality RGB-D panorama on real indoor scenes, unseen during training. Our synthesized depth panorama shows precise indoor layout and plausible residuals, generating a realistic 3D indoor model. For quantitative result, our method achieved better FAED score than IwDS (4645 vs 5099). Since the FAED score between synthetic and real dataset is 3517, it demonstrates that there exists distribution shift between the datasets and our result shows realistic RGB-D panorama and 3D indoor models consistently in both synthetic and real indoor scenes.
More results can be found in suppl. material.
\vspace{-8pt}
\subsection{Ablation Study and Analysis}
\vspace{-3pt}
\noindent\textbf{Inpainting w/ Depth Synthesis (IwDS)} One solution to obtain RGB-D panorama from partial RGB-D inputs is sequentially accomplishing RGB synthesis (inpainting) and depth synthesis.
To be specific, a RGB panorama is first synthesized from partial RGB input using the image inpainting method.
Then, depth panorama is synthesized by applying the depth synthesis method to the synthesized RGB panorama and partial depth input.
We chose CoModGAN \cite{zhao2021large} and CSPN \cite{Cheng_2020_TPAMI} for RGB and depth synthesis methods, which showed the highest FAED score in Table~\ref{tab:result_rgb} and Table~\ref{tab:results_depth}.
In Table~\ref{tab:ablation}, it can be seen that IwDS leads lower 2D IoU score and a much higher FAED score than our method.
This indicates that the two-stage, sequential synthesis of RGB-D panorama is less effective than our BIPS framework that fuses the bi-modal features, trained with one-stage, joint learning scheme. Also, IwDS fails to generate realistic 3D indoor models, with distorted indoor layouts and severe bumpy surfaces as shown in Fig.~\ref{fig:ablation}.
\noindent\textbf{Impact of BFF} We study the effectiveness of RGB-D panorama synthesis by removing the BFF branch in the generator.
In details, $G_{BFF}$ is replaced with a single branch network taking the concatenation of $G_{in}^{rgb}(I_{in}^{rgb})$ and $G_{in}^{depth}(I_{in}^{d})$.
As shown in Table~\ref{tab:ablation}, the 2D IoU drops and FAED score increases without BFF. Fig.~\ref{fig:ablation} shows that texture of the RGB-D output is not consistent with the given arbitrary RGB-D input. This reflects that BFF significantly contributes to well-process the bi-modal information
\noindent\textbf{Impact of RDAL} We further validate the effectiveness of RDAL by comparing the results without RDAL.
The number of output branches are reduced to two, and each are designed to learn RGB and total depth panorama, respectively.
As shown in Table~\ref{tab:ablation}, the 2D IOU score drops, and FAED score increases without RDAL. It shows that RDAL is critical for estimating precise indoor layout. The impact of RDAL is visually verified in Fig.~\ref{fig:ablation}. The result without RDAL shows distorted indoor layout while having fewer artifacts than ours w/o BFF. In summary, dividing the total depth into layout and residual depth helps to synthesize more structural 3D indoor model.
\vspace{-8pt}
\section{Conclusion}
\vspace{-3pt}
In this paper, we tackled a novel problem of synthesizing RGB-D indoor panoramas from arbitrary configurations of RGB and depth
inputs. Our method can synthesize high-quality RGB-D panoramas with the proposed BIPS framework by utilizing the bi-modal information and jointly training the layout and residual depth of indoor scenes.
Moreover,
a novel evaluation metric FAED was proposed and its validity was demonstrated. Extensive experiments show that our method achieves the SoTA RGB-D panorama synthesis performance.
\noindent \textbf{Limitation}
We mainly focused on
indoor scenes, and proposed RDAL is hardly applicable to outdoor scenes.
Future work will extend our method to various environments.
\clearpage
{\small
\bibliographystyle{ieee_fullname}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 4,480
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{
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\section{Introduction}The weight part of Serre's conjecture has been
much-studied over the last two decades, and while the original
problem has been resolved, a great deal remains to be proved in more general
settings. In the present paper we address the question of the weight
part of Serre's conjecture for totally real fields. Here one has the
Buzzard--Diamond--Jarvis conjecture \cite{bib:BDJ} and its various
generalisations, much of which has now been established
(cf. \cite{gee08serrewts}, \cite{blgg11-serre-weights-for-U2}). One
case that has not (so far as we are aware) been considered at all
over totally real fields is the case of forms of (partial) weight
one. This case is markedly different to the case of higher weights,
for the simple reason that mod $p$ modular forms of weight one
cannot necessarily be lifted to characteristic zero modular forms of
weight one; as the methods of \cite{gee08serrewts} and
\cite{blgg11-serre-weights-for-U2} are centered around modularity
lifting theorems, and in particular depend on the use of lifts to
characteristic zero modular forms, they cannot immediately say
anything about the weight one case.
In this paper we generalise a result of Gross \cite{MR1074305}, and
prove a companion forms theorem for Hilbert modular forms of parallel
weight one in the unramified $p$-distinguished case. To explain what this means,
and how it (mostly) resolves the weight one part of Serre's conjecture
for totally real fields, we return to the case of classical modular
forms. Serre's original formulation \cite{MR885783} of his
conjecture only considered mod $p$ modular forms which lift to
characteristic zero, and in particular ignored the weight one
case. However, Serre later observed that one could further refine his
conjecture by using Katz's definition \cite{MR0447119} of mod $p$
modular forms, and thus include weight one forms. He then conjectured
that a modular Galois representation should arise from a weight one
form (of level prime to $p$) if and only if the Galois representation
is unramified at $p$. The harder direction is to prove that the Galois
representation being unramified implies that there is a weight one
form; this was proved by Gross \cite{MR1074305}, under the further
hypothesis that the eigenvalues of a Frobenius element at $p$ are
distinct (i.e. we are in the $p$-distinguished case). It is this
result that we generalise in this paper, proving the following
theorem.
\begin{ithm}\label{thm: main result, introduction version}
Let $p>2$ be prime, let $F$ be a totally real field in which $p$ is
unramified, and let $\rhobar:G_F\to\operatorname{GL}_2(\overline{\F}_p)$ be an irreducible
modular representation such that $\rhobar|_{G_{F(\zeta_p)}}$ is
irreducible. If $p=3$ (respectively $p=5$), assume further that the projective image of
$\rhobar(G_{F(\zeta_p)})$ is not conjugate to $\operatorname{PSL}_2({\mathbb{F}}_3)$ (respectively $\operatorname{PSL}_2({\mathbb{F}}_5)$ or
$\operatorname{PGL}_2({\mathbb{F}}_5)$).
Suppose that
for each place $v|p$, $\rhobar|_{G_{F_v}}$ is unramified, and that
the eigenvalues of $\rhobar({\operatorname{Frob}}_v)$ are distinct.
Then there is a mod $p$ Hilbert modular form $f$ of
parallel weight $1$ and level prime to $p$ such that $\rhobar_f\cong\rhobar$.
\end{ithm}
(See Theorem \ref{thm: main result}, and see the body of the paper
for any unfamiliar notation or terminology.) The condition on
$\rhobar|_{G_{F(\zeta_p)}}$ is mild, and the only other hypothesis
which is not expected to be necessary (other than that $p$ is
unramified in $F$, which we assume for our geometric arguments) is
that the eigenvalues of $\rhobar({\operatorname{Frob}}_v)$ are distinct for all
$v|p$. This condition appears to be essential to our method, as we
explain below.
Our method of proof is a combination of modularity lifting theorem
techniques and geometric methods.
The first part of the argument, using modularity lifting theorems
to produce Hilbert modular forms of parallel weight $p$, was carried
out in \cite{gee051} under some additional hypotheses (in
particular, it was assumed that $\rhobar$ arose from an ordinary
Hilbert modular form), and in Section \ref{sec: BLGG} below we use
the techniques of \cite{BLGGT} (which involve the use of automorphy
lifting theorems for rank 4 unitary groups) to remove these
hypotheses. This gives us $2^n$ Hilbert modular forms of parallel
weight $p$ and level prime to $p$, where there are $n$ places of $F$
above $p$, corresponding to the different possible choices of
Frobenius eigenvalues at places above $p$. In Section \ref{section:
weight one} we take a suitable linear combination of these forms,
and show that it is divisible by the Hasse invariant of parallel weight $p-1$, by explicitly calculating the $p$-th power of the quotient. It is easy to show that the quotient is the sought-after Hilbert modular form of parallel weight one. If we do not assume that $\rhobar$ has
distinct Frobenius eigenvalues at each place dividing $p$, the
weight one form we obtain in this manner is actually zero.
In Section \ref{sec: Artin} we give an application of our
main theorem to Artin's conjecture, generalising the results (and
arguments) of \cite{MR1434905} to prove the following result, which
shows that the weak form of Serre's conjecture for totally real fields
implies the strong form of Artin's conjecture for totally odd
two-dimensional representations.
\begin{ithm}
Let $F$ be a totally real field. Assume that every irreducible,
continuous and totally odd representation
$\rhobar:G_F\to\operatorname{GL}_2(\overline{\F}_p)$ is modular, for every prime $p$. Then
every irreducible, continuous and totally odd representation
$\rho:G_F\to\operatorname{GL}_2({\mathbb{C}})$ is modular.
\end{ithm}
(See Theorem \ref{thm: Serre implies Artin}.) Finally, we remark that
it is possible that our results can be applied to Artin's conjecture
more directly (that is, without assuming Serre's conjecture), as an
input to modularity lifting theorems in parallel weight one; see the
forthcoming work of Calegari--Geraghty for some results in this
direction. Additionally, it would be of interest to generalise our
results to forms of partial weight one; the geometric techniques we
use in this paper amount to determining the intersection of the
kernels of the $\Theta$-operators of \cite{AG}, and it is possible
that a determination of the kernels of the individual
$\Theta$-operators could shed some light on this.
We are grateful to Shu Sasaki for suggesting that our results could be
used to generalise the arguments of \cite{MR1434905} to totally real
fields. We are also grateful to Kevin Buzzard for several helpful
conversations, and to Frank Calegari for asking a question which led
to our writing this paper.
\subsection{Notation} If $M$ is a field, we let $\overline{M}$ denote
an algebraic closure of $M$, and we let $G_M:={\operatorname{Gal}\,}(\overline{M}/M)$
denote its absolute Galois group. Let $p$ be a prime number, and let
$\varepsilon$ denote the $p$-adic cyclotomic character; our choice of
convention for Hodge--Tate weights is that $\varepsilon$ has all
Hodge--Tate weights equal to $1$. Let $F$ be a totally real field and
$f$ a cuspidal Hilbert modular eigenform of parallel weight $k$. If
$v$ is a finite place of $F$ which is coprime to the level of $f$,
then we have, in particular, the usual Hecke operator $T_v$
corresponding to the double coset \[\operatorname{GL}_2(\mathcal{O}_{F_v})
\begin{pmatrix}
\varpi_v&0\\0&1
\end{pmatrix}\operatorname{GL}_2(\mathcal{O}_{F_v}),\]where $\varpi_v$ is a uniformiser of $\mathcal{O}_{F_v}$,
the ring of integers of $F_v$.
There is a Galois representation $\rho_f:G_F\to\operatorname{GL}_2(\overline{\Q}_p)$
associated to $f$; we adopt the convention that if $v\nmid p$ is
as above, and ${\operatorname{Frob}}_v$ is an \emph{arithmetic} Frobenius element
of $G_{F_v}$ then ${\operatorname{tr}\,}\rho_f({\operatorname{Frob}}_v)$ is the $T_v$-eigenvalue of
$f$, so that in particular the determinant of $\rho_f$ is a finite
order character times $\varepsilon^{k-1}$.
We say that
$\rhobar:G_F\to\operatorname{GL}_2(\overline{\F}_p)$ is \emph{modular} if it arises as
the reduction mod $p$ of the Galois representation
$\rho_f:G_F\to\operatorname{GL}_2(\overline{\Q}_p)$ for some $f$.
\section{Modularity lifting in weight $p$}\label{sec: BLGG}\subsection{}In this section we apply the
modularity lifting techniques first used in \cite{gee051} to produce
companion forms in (parallel) weight $p$. We make use of the
techniques of \cite{BLGGT} in order to weaken the hypotheses
(for example, to avoid the necessity of an assumption of
ordinarity). In this section, we do not assume that $p$ is unramified
in $F$. Note that the definition of a mod $p$ modular form is recalled
in Section~\ref{section: weight one} below.
\begin{thm}\label{thm: lifting to weight p by blgg}
Let $p>2$ be prime, let $F$ be a totally real field, and let
$\rhobar:G_F\to\operatorname{GL}_2(\overline{\F}_p)$ be an irreducible modular
representation such that $\rhobar|_{G_{F(\zeta_p)}}$ is irreducible.
If $p=3$ (respectively $p=5$), assume further that the projective image of
$\rhobar(G_{F(\zeta_p)})$ is not conjugate to $\operatorname{PSL}_2({\mathbb{F}}_3)$ (respectively $\operatorname{PSL}_2({\mathbb{F}}_5)$ or
$\operatorname{PGL}_2({\mathbb{F}}_5)$).
Suppose that
for each place $v|p$, $\rhobar|_{G_{F_v}}$ is unramified, and in
fact suppose that \[\rhobar|_{G_{F_v}}\cong
\begin{pmatrix}
\lambda_{\alpha_{1,v}} &0\\0&\lambda_{\alpha_{2,v}}
\end{pmatrix}\]where $\lambda_x$ is the unramified character sending
an arithmetic Frobenius element to $x$. For each place $v|p$, let
$\gamma_v$ be a choice of one of $\alpha_{1,v}$,
$\alpha_{2,v}$. Let $N$ be an integer coprime to $p$ and divisible
by the Artin conductor of $\rhobar$. Then there is a mod $p$ Hilbert modular eigenform $f$ of
parallel weight $p$ such that:
\begin{itemize}
\item $f$ has level $\Gamma_1(N)$; in particular, $f$ has level prime
to $p$.
\item $\rhobar_f\cong\rhobar$.
\item $T_v f =\gamma_vf$ for each place $v|p$.
\end{itemize}
\end{thm}
\begin{proof} It suffices to prove that there is a (characteristic zero) Hilbert
modular eigenform $\mathcal{F}$ of parallel weight $p$ such that $\mathcal{F}$ has level
$N$, the Galois representation $\rho_{\mathcal{F}}$ associated to
$\mathcal{F}$ satisfies $\rhobar_{\mathcal{F}}\cong\rhobar$, and for each place
$v|p$ we have $T_v\mathcal{F}=\gammat_v \mathcal{F}$ for some lift $\gammat_v$ of
$\gamma_v$. (We remark that in the argument below, we will feel free
to let $\gammat_v$ denote \emph{any} lift of $\gamma_v$, rather than
a fixed lift.) By local-global compatibility at places dividing $p$
(cf. Theorem 4.3 of \cite{kisinpst}), it is enough to find a lift
$\rho$ of $\rhobar$ which is automorphic, which is minimally
ramified outside $p$, and has the further property that for each place
$v|p$ we have \[\rho|_{G_{F_v}}\cong
\begin{pmatrix}
\varepsilon^{p-1}\lambda_{x_v} & *\\ 0 & \lambda_{\gammat_v}
\end{pmatrix}\]for some $x_v$ and some $\gammat_v$ (such a
representation is automatically crystalline with Hodge--Tate weights
$0$, $p-1$ at each place $v|p$ and thus corresponds to a Hilbert
modular form of parallel weight $p$ and level prime to $p$).
The existence of such a representation $r$ is a straightforward
application of the results of \cite{blgg11-serre-weights-for-U2}, as
we now explain. This argument is very similar to the proof of
Proposition 6.1.3 of \cite{blggord}. Firstly, choose a quadratic
imaginary CM extension $F_1/F$ which splits at all places dividing
$p$ and all places where $\rhobar$ is ramified, and which is
linearly disjoint from $\overline{F}^{\ker\rhobar}(\zeta_p)$ over
$F$. Let $S$ denote a finite set of places of $F$, consisting of the
infinite places, and the union of set of places of $F$ at which
$\rhobar$ is ramified and the places which divide $p$. From now on
we will consider $\rhobar$ as a representation of $G_{F,S}$, the
Galois group of the maximal extension of $F$ unramified outside of
$S$. Let $\chi$ be the Teichm\"uller lift of
$\varepsilonbar^{1-p}\det\rhobar$.
Fix a finite extension $E/\Q_p$ with ring of integers $\mathcal{O}$ and
residue field ${\mathbb{F}}$ such that $\rhobar$ is valued in $\operatorname{GL}_2({\mathbb{F}})$. For
each finite place $v$ of $F$, let $R^\chi_{G_{F_v}}$ denote the
universal $\mathcal{O}$-lifting ring for lifts of $\rhobar|_{G_{F_v}}$ of
determinant $\chi\varepsilon^{p-1}$. By (for example) Lemma 3.1.8 of \cite{GG}, for
each place $v|p$ of $F$ there is a quotient
$R_{G_{F_v}}^{\chi,\gamma}$ of $R_{G_{F_v}}^\chi$ whose
$\overline{\Q}_p$-points correspond precisely to those lifts of
$\rhobar|_{G_{F_v}}$ which are conjugate to a representation of the
form \[\begin{pmatrix} \varepsilon^{p-1}\chi/\lambda_{\gammat_v} & *\\
0 & \lambda_{\gammat_v}
\end{pmatrix}\] for some $\gammat_v$ lifting $\gamma_v$. For each
finite place $v\in S$ with $v\nmid p$, let $\overline{R}_{G_{F_v}}^\chi$ be a
quotient of $R_{G_{F_v}}^\chi$ corresponding to an irreducible
component of $R_{G_{F_v}}[1/p]$, the points of which correspond to
lifts of $\rhobar|_{G_{F_v}}$ with the same Artin conductor as
$\rhobar|_{G_{F_v}}$. Let $R^{\chi,\gamma}$ denote the universal
deformation ring for deformations of $\rhobar$ of determinant
$\chi\varepsilon^{p-1}$, which have the additional property that for
each place $v|p$, the deformation corresponds to a point of
$R_{G_{F_v}}^{\chi,\gamma}$, and for each finite place $v\in S$,
$v\nmid p$, it corresponds to a point of $\overline{R}_{G_{F_v}}^{\chi}$. In
order to construct the representation $r$ that we seek, it is enough
to find a $\overline{\Q}_p$-point of $R^{\chi,\gamma}$ that is
automorphic. We will do this by showing that $R^{\chi,\gamma}$ is a
finite $\mathcal{O}$-algebra of dimension at least one (so that it has
$\overline{\Q}_p$-points), and that all its $\overline{\Q}_p$-points are automorphic.
We can and do extend $\rhobar|_{G_{F_1}}$ to a representation
$\rhobar:G_F\to\mathcal{G}_2({\mathbb{F}})$, where $\mathcal{G}_2$ is the group scheme
introduced in Section 2.1 of \cite{cht} (cf. Section 3.1.1 of
\cite{blggord}). In the notation of Section 2.3 of \cite{cht}, we
let $\widetilde{{S}}$ be a set of places of $F_1$ consisting of exactly one
place ${\widetilde{{v}}}$ above each place $v$ of $S$, and we let $\mathcal{S}$ denote the
deformation
problem \[(F_1/F,S,\widetilde{{S}},\mathcal{O},\rhobar,\varepsilon^{p-1}\chi,\{\overline{R}^\chi_{G_{F_{1,{\widetilde{{v}}}}}}\}_{v\in
S, v\nmid p},\{R_{G_{F_{1,{\widetilde{{v}}}}}}^{\chi,\gamma}\}_{v|p}).\] Let
$R_\mathcal{S}$ denote the corresponding universal deformation ring. Exactly
as in section 7.4 of \cite{GG}, the process of ``restriction to
$G_{F_1}$ and extension to $\mathcal{G}_2$'' makes $R^{\chi,\gamma}$ a
finite $R_\mathcal{S}$-module in a natural way. By Proposition 3.1.4 of
\cite{gee061} we have $\dim R^{\chi,\gamma}\ge 1$, so that (by
cyclic base change for $\operatorname{GL}_2$) it suffices to show that $R_\mathcal{S}$ is
finite over $\mathcal{O}$, and that all its $\overline{\Q}_p$-points are automorphic.
By Proposition A.2.1 of \cite{blgg11-serre-weights-for-U2} and our
assumptions on $\rhobar|_{G_{F(\zeta_p)}}$,
$\rhobar(G_{F(\zeta_p)})$ is adequate in the sense of
\cite{jack}. By Theorems 7.1 and 10.1 of \cite{jack}, it is enough
to check that $R_\mathcal{S}$ has an automorphic $\overline{\Q}_p$-point. We claim
that we can do this by applying Theorem A.4.1 of
\cite{blgg11-serre-weights-for-U2} to $\rhobar$. The only hypotheses
of {\em loc. cit.} that are not obviously satisfied are those
pertaining to potential diagonalizability. By Lemma 3.1.1 of
\cite{blgg11-serre-weights-for-U2}, we may choose a finite solvable
extension $F'/F$ of CM fields which is linearly disjoint from
$\overline{F}^{\ker\rhobar}(\zeta_p)$, such that $\rhobar|_{G_{F'}}$
has an automorphic lift which is potentially diagonalizable at all
places dividing $p$. All $\overline{\Q}_p$-points of each
$R_{G_{F_v}}^{\chi,\gamma}$ are potentially diagonalizable by Lemma
1.4.3 of \cite{BLGGT}, so Theorem A.4.1 of
\cite{blgg11-serre-weights-for-U2} produces a $\overline{\Q}_p$-point of
$R_{\mathcal{S}}$ which is automorphic upon restriction to $G_{F'}$. Since
$F'/F$ is solvable, the result follows by solvable base change
(Lemma 1.4 of \cite{BLGHT}).
\end{proof}
\section{Weight one forms}\label{section: weight one}\subsection{}
Let $p>2$ be a prime number. Let $F/\mathbb{Q}$ be a totally real
field of degree $d>1$, $\mathcal{O}_F$ its ring of integers, and
${\frak{d}}_F$ its different ideal. Let $\mathbb{S}=\{v|p\}$ be the set of all primes lying above $p$. We assume that $p$ is unramified in $F$. Let $N>3$ be an integer prime to $p$.
In this section we make our geometric arguments. We begin by
recalling some standard definitions. Let $K$ be a finite extension of
$\mathbb{Q}_p$ (which we will assume to be sufficiently large without further
comment), and let ${\mathcal{O}}_K$, $\kappa$ denote, respectively, its ring
of integers and its residue field. Let $X/{\mathcal{O}}_K$ be the Hilbert
modular scheme representing the functor which associates to an
${\mathcal{O}}_K$-scheme $S$, the set of all polarized abelian schemes with
real multiplication and $\Gamma_{00}(N)$-structure
$\underline{A}/S=(A/S,\iota,\lambda,\alpha)$ as follows:
\begin{itemize}
\item $A$ is an abelian scheme of relative
dimension $d$ over $S$;
\item the real multiplication $\iota\colon\mathcal{O}_F \hookrightarrow {\rm End}_S(A)$ is a ring
homomorphism endowing $A$ with an action of $\mathcal{O}_F$;
\item the map $\lambda$ is a polarization as in \cite{DP};
\item $\alpha$ is a rigid
$\Gamma_{1}(N)$-level structure, that is, $\alpha\colon \mu_N
\otimes_{\mathbb{Z}} {\frak{d}}_F^{-1} {\; \rightarrow \;} A$, an ${\mathcal{O}}_F$-equivariant
closed immersion of group schemes.
\end{itemize}
Let $X_K/K$, $\overline{X}/\kappa$ respectively denote the generic and the special fibres of $X$.
Let $\widetilde{X}$ denote a toroidal compactification of $X$. Similarly, we define $\widetilde{X}_K$ and $\widetilde{\overline{X}}$.
Let $Y$ be the scheme representing the functor which associates to an ${\mathcal{O}}_K$-scheme $S$, the set of all $(\underline{A}/S,C)=(A/S,\iota,\lambda,\alpha,C)$, where $(A/S,\iota,\lambda,\alpha)$ is as above, and $C$ is an ${\mathcal{O}}_F$-invariant
isotropic finite flat subgroup scheme of $A[p]$ of order $p^g$. Let $\widetilde{Y}$ denote a toroidal compactification of $Y$ obtained using the same choices of polyhedral decompositions as for $\overline{X}$. We introduce the notation $Y_K,\overline{Y},\widetilde{Y}_K,\widetilde{\overline{Y}}$ in the same way as we did for $X$. The ordinary locus in $\overline{X}$ is denoted by $\overline{X}^{ord}$. It is Zariski dense in $\overline{X}$.
There are two finite flat maps
\[
\pi_{1},\pi_2:\widetilde{Y} {\; \rightarrow \;} \widetilde{X},
\]
where $\pi_1$ forgets the subgroup $C$, and $\pi_2$ quotients out by $C$. We define the Atkin--Lehner involution $w:\widetilde{Y} \rightarrow \widetilde{Y}$ to be the map which sends $({\underline{A}},C)$ to $({\underline{A}}/C, A[p]/C)$; it is an automorphism of $\widetilde{Y}$. We have $\pi_2=\pi_1 \circ w$. We also define the Frobenius section $s:\widetilde{\overline{X}} \rightarrow \widetilde{\overline{Y}}$ which sends ${\underline{A}}$ to $({\underline{A}},{\rm Ker}({\operatorname{Frob}}_{A}))$. Our convention is to use the same notation to denote maps between the various versions of $X,Y$.
Let $\epsilon: \underline{\mathcal A}^{\rm univ} {\; \rightarrow \;} X$ be the universal abelian scheme. Let
\[
\underline{\Omega}=\epsilon_\ast \Omega^1_{\underline{\mathcal A}^{\rm
univ}/X}
\]
be the Hodge bundle on $X$. Since $p$ is assumed unramified in $F$, $\underline{\Omega}$ is a locally free $({\mathcal{O}}_F \otimes_\mathbb{Z} {\mathcal{O}}_X)$-module of rank one. We define $\underline{\omega}=\wedge^d \underline{\Omega}$. The sheaf $\underline{\omega}$ naturally extends to $\widetilde{X}$ as an invertible sheaf. Let $\epsilon^\prime: \underline{\mathcal B}^{\rm univ} {\; \rightarrow \;} Y$ be the universal abelian scheme over $Y$ with the designated subgroup $\mathcal C$. We have
\[
\pi_1^\ast\underline{\omega}=\wedge^d \epsilon_\ast \Omega^1_{{\mathcal B}^{\rm
univ}/Y},
\]
\[
\pi_2^\ast\underline{\omega}=\wedge^d \epsilon_\ast \Omega^1_{ ({\mathcal B}^{\rm
univ}/{\mathcal C})/Y }.
\]
Let
\[
\rm{pr}^\ast: \pi_1^\ast \underline{\omega} \rightarrow \pi_2^\ast\underline{\omega}
\]
denote the pullback under the natural projection ${\rm{pr}}: \underline{\mathcal B}^{\rm univ} \rightarrow \underline{\mathcal B}^{\rm univ}/{\mathcal C}$. We will often denote $\pi_1^\ast \underline{\omega}$ by $\underline{\omega}$.
Let $R$ be an ${\mathcal{O}}_K$-algebra. A (geometric) Hilbert modular form of parallel weight $k \in \mathbb{Z}$ and level $\Gamma_1(N)$ defined over $R$ is a section of $\underline{\omega}^k$ over $X\otimes_{{\mathcal{O}}_K} R$. Every such section extends to $\widetilde{X} \otimes_{{\mathcal{O}}_K} R$ by the Koecher principle. We denote the space of such forms by $M_k(\Gamma_1(N),R)$, and the subspace of cuspforms (those sections vanishing on the cuspidal locus) by $S_k(\Gamma_1(N),R)$. If $R$ is a $\kappa$-algebra, then elements of $M_k(\Gamma_1(N),R)$ are referred to as \emph{mod $p$ Hilbert modular forms}. Every such form is a section of $\underline{\omega}^k$ over $\overline{X}\otimes_{\kappa} R$, and extends automatically to $\widetilde{\overline{X}} \otimes_{\kappa} R$.
Given any fractional ideal ${\frak{a}}$ of ${\mathcal{O}}_F$, let $X_{\frak{a}}$ denote the subscheme of $X$ where the polarization module of the abelian scheme is isomorphic to $({\frak{a}},{\frak{a}}^+)$ as a module with notion of positivity. Then $X_{\frak{a}}$ is a connected component of $X$, and every connected component of $X$ is of the form $X_{\frak{a}}$ for some ${\frak{a}}$. The same statement is true for $Y_{\frak{a}}$, $Y$. Let
\[
Ta_{{\frak{a}}}=(\underline{\mathbb{G}_m\! \otimes\! {\frak{d}}_F^{-1})/q^{{\frak{a}}^{-1}}}
\]
denote a cusp on $X_{\frak{a}}$, where underline indicates the inclusion of standard PEL structure. Pick $c \in p^{-1}{\frak{a}}^{-1}-{\frak{a}}^{-1}$. Then
\[
Ta_{{\frak{a}},c}=(Ta_{\frak{a}},<\! q^c\!>)
\]
is a cusp on $Y_{\frak{a}}$, where $<\!q^c\!>$ denotes the ${\mathcal{O}}_F$-submodule of $Ta_{\frak{a}}[p]$ generated by $q^c$.
We now prove our main result, the following theorem.
\begin{thm}\label{thm: main result} Let $p>2$ be a prime which is
unramified in $F$, a totally real field. Let
$\rhobar:G_F\to\operatorname{GL}_2(\overline{\F}_p)$ be an irreducible modular
representation such that $\rhobar|_{G_{F(\zeta_p)}}$ is irreducible.
If $p=3$ (respectively $p=5$), assume further that the projective
image of $\rhobar(G_{F(\zeta_p)})$ is not conjugate to
$\operatorname{PSL}_2({\mathbb{F}}_3)$ (respectively $\operatorname{PSL}_2({\mathbb{F}}_5)$ or $\operatorname{PGL}_2({\mathbb{F}}_5)$).
Suppose that
for each prime $v|p$, $\rhobar|_{G_{F_v}}$ is unramified, and that
the eigenvalues of $\rhobar({\operatorname{Frob}}_v)$ are distinct.
Then there is a mod $p$ Hilbert modular form $h$ of
parallel weight $1$ and level prime to $p$ such that
$\rhobar_h\cong\rhobar$. Furthermore, $h$ can be chosen to have
level bounded in terms of the Artin conductor of $\rhobar$.
\end{thm}
\begin{proof}
For each $v\in \mathbb{S}$, let the eigenvalues of $\rhobar({\operatorname{Frob}}_v)$ be
$\gamma_{v,1}\ne\gamma_{v,2}$. Let $\mathfrak{N}$ denote the Artin
conductor of $\rhobar$, and $N>3$ an integer prime to $p$ and divisible by $\mathfrak{N}$. By Theorem \ref{thm: lifting to weight p
by blgg}, we see that for each subset $I\subset S$, there is a
mod $p$ Hilbert modular eigenform $f_I$ of weight $p$ and level
$\Gamma_1(N)$ such that $\rhobar_{f_I}\cong\rhobar$, and for each prime
$v\in \mathbb{S}$, we have $T_vf=\gamma_{v,1}f$ if $v\in I$, and
$T_vf=\gamma_{v,2}f$, otherwise. Since $\rhobar_{f_I}\cong\rhobar$,
we see that for each prime ${\frak{l}} \nmid Np$ of $F$, the $f_I$ are
eigenvectors for $T_{\frak{l}}$ with eigenvalues $\lambda_{\frak{l}}$ which are
independent of $I$. By a standard argument, using Proposition 2.3
of \cite{MR507462}, we can furthermore assume (at the possible
cost of passing to forms of level $N^2$) that for each prime
${\frak{l}}|N$, we have $T_{\frak{l}} f_I=0$ for all $I$.
We can and do assume that each $f_I$ is normalised, in the sense
that (in the notation of \cite{MR507462}) $c(\mathcal{O}_F,f_I)=1$. For
any $I\subset \mathbb{S}$, let $\gamma_I=\Pi_{v \in I}
\gamma_{v,1} \Pi_{v \not\in I} \gamma_{v,2}$; this is the $T_p$-eigenvalue of $f_I$. Set
\[
f=\sum_{I\subset S}(-1)^{|I|}\gamma_I f_I,
\]
\[
g=\sum_{I\subset S}(-1)^{|I|}f_I.
\]
We begin with a Lemma.
\begin{lemma}\label{Lemma: q-expansion} The section $\pi_1^\ast f-{\rm pr}^\ast \pi_2^\ast g$ of $\underline{\omega}^p$ on $\widetilde{Y}$ has $q$-expansion divisible by $p$ at every cusp of the form $Ta_{{\frak{a}},c}$.
\end{lemma}
\begin{proof} We let $\eta$ denote a generator of the sheaf $\underline{\omega}$ on the base of $Ta_{\frak{a}}$ or $Ta_{{\frak{a}},c}$. We first remark that by \cite[(2.23)]{MR507462}, if $h$ is a normalized Hilbert modular eigenform of
parallel weight $k$, and $h(Ta_{\frak{a}})=\sum_{\xi \in ({\frak{a}}^{-1})^+}
c_\xi q^\xi\eta^k$, then $c_\xi=c(\xi{\frak{a}},h)$ is the eigenvalue of the $T_{\xi{\frak{a}}}$ operator on $h$, for all $\xi\in ({\frak{a}}^{-1})^+$.
Write $f(Ta_{{\frak{a}}})=\sum_{\xi \in ({\frak{a}}^{-1})^+} a_\xi({\frak{a}}) q^\xi \eta^p$ and $g(Ta_{{\frak{a}}})=\sum_{\xi \in ({\frak{a}}^{-1})^+} b_\xi({\frak{a}}) q^\xi \eta^p$. We have:
\[
\pi_1^\ast f(Ta_{{\frak{a}},c})=f(Ta_{{\frak{a}}})=\sum_{\xi \in ({\frak{a}}^{-1})^+} a_\xi({\frak{a}}) q^\xi \eta^p,
\]
\[
{\rm pr}^\ast \pi_2^\ast g(Ta_{{\frak{a}},c})={\rm pr}^\ast g(Ta_{p{\frak{a}}})=\sum_{\xi \in p^{-1}({\frak{a}}^{-1})^+} b_\xi(p{\frak{a}}) q^\xi \eta^p.
\]
It is therefore enough to show that $b_\xi(p{\frak{a}})=0$ if $\xi \in
p^{-1}({\frak{a}}^{-1})^+-({\frak{a}}^{-1})^+$, and that $a_\xi({\frak{a}})\equiv
b_\xi(p{\frak{a}})\ {\rm mod}\ p$ for $\xi \in ({\frak{a}}^{-1})^+$.
For the first statement, let $v\in \mathbb{S}$ be such that $v$ does not divide $\xi p{\frak{a}}$. Then we can write
\[
b_\xi(p{\frak{a}})=\sum_{I\subset \mathbb{S}} (-1)^{|I|} c(\xi p{\frak{a}},f_I)=\sum_{v \not\in I}(-1)^{|I|}c(\xi p{\frak{a}},f_I) -\sum_{v \in I} (-1)^{|I|}c(\xi p{\frak{a}},f_I)=0,
\]
using $c(\xi\p{\frak{a}},f_I)=c(\xi p{\frak{a}},f_{I \cup \{v\}})$, since $v$
does not divide $\xi p {\frak{a}}$.
For the second statement, note firstly that for $\xi \in ({\frak{a}}^{-1})^+$ we can write
\[
b_\xi(p{\frak{a}})=\sum_{I \subset \mathbb{S}} (-1)^{|I|}c(\xi
p{\frak{a}},f_I),\]\[a_\xi({\frak{a}})= \sum_{I \subset \mathbb{S}}
(-1)^{|I|}\gamma_I c(\xi {\frak{a}},f_I).
\]
Now, if $h$ is a Hilbert modular eigenform, then for any integral
ideal ${\frak{m}}$ of ${\mathcal{O}}_F$, we have $c(p{\frak{m}},h)\equiv c((p),h)
c({\frak{m}},h)\ {\rm mod}\ p$. Since for any $I \subset \mathbb{S}$, we
have $c((p),f_I)=\gamma_I$, the result follows.
\end{proof}
For any section $h \in H^0(\widetilde{X},\underline{\omega}^k)$, we denote its image in $H^0(\widetilde{\overline{X}}, \underline{\omega}^k)$ by $\bar{h}$.
\begin{cor}\label{Corollary: equality of section on Xbar} We have the following equality of sections of $\underline{\omega}^p$ on $\widetilde{\overline{X}}$:
\[
s^\ast \pi_2^\ast \bar{f}=s^\ast w^\ast {\rm pr}^\ast \pi_2^\ast \bar{g}.
\]
\end{cor}
\begin{proof} Reducing the equation in Lemma \ref{Lemma: q-expansion}
mod $p$, we obtain an equality of sections on every irreducible
component of $\widetilde{\overline{Y}}$ which contains the reduction of a
cusp of the form $Ta_{{\frak{a}},c}$. These are exactly the irreducible
components of $ws(\widetilde{\overline{X}})$, since
$w(Ta_{{\frak{a}},c})=(Ta_{p{\frak{a}}},<\!\zeta\!>)=s(Ta_{p{\frak{a}}})$ (where
$<\!\zeta\!>$ is the ${\mathcal{O}}_F$-module generated by a $p$-th root of
unity $\zeta$). Pulling back under $w\circ s$, we obtain the desired equality on $\widetilde{\overline{X}}$.
\end{proof}
For any scheme $Z$ over $\kappa$, let ${\rm Fr}: Z {\; \rightarrow \;} Z^{(p)}$ denote the relative Frobenius morphism. Since $\widetilde{\overline{X}}$ has a model over $\mathbb{F}_p$, we have $\widetilde{\overline{X}}^{(p)}=\widetilde{\overline{X}}$. For any non-negative integer $k$, we define a morphism
\[
V: H^0(\widetilde{\overline{X}},\underline{\omega}^k) \rightarrow H^0(\widetilde{\overline{X}},\underline{\omega}^{kp})
\]
as follows: choose a trivialization $\{(U_i,\eta_i)\}$ for $\underline{\omega}$ on $\widetilde{\overline{X}}$. Let $f\in H^0(\widetilde{\overline{X}},\underline{\omega}^k)$ be given by $f_i \eta_i^k$ on $U_i$. Then, there is a unique section $V(f)$ in $H^0(\widetilde{\overline{X}},\underline{\omega}^{kp})$ whose restriction to $U_i$ is ${\rm Fr}^\ast (f_i) \eta_i^{kp}$.
Calculating on points, we see easily that for $\widetilde{\overline{X}}$, we
have $\pi_2\circ s={\rm Fr}$. Let $\bf{h}$ denote the Hasse invariant
of parallel weight $p-1$. It can be defined as follows: let $U$ be an open subset of $\overline{X}$ over which $\omega$ is trivial, and let $A_U$ denote the universal abelian scheme over $U$. Let $\eta$ be a non vanishing section of $\omega$ on $U$; it can be thought of as a section of $\Omega_{A_U/U}$. We let $\eta^{(p)}$ denote the induced section of $\Omega_{A_U^{(p)}/U}$. Let ${\rm Ver}: A_U^{(p)} \rightarrow A_U$ be the Verschiebung morphism. Then, there is a unique $\lambda \in {\mathcal{O}}_{\overline{X}}(U)$, such that ${\rm Ver}^\ast \eta=\lambda \eta^{(p)}$. We define a section of $\omega^{p-1}$ on $U$ via
\[
{\bf h}_{U,\eta}:=\lambda\eta^{p-1}.
\]
It is easy to see that there is a unique section of $\omega^{p-1}$ on $\overline{X}$, denoted ${\bf h}$, such that ${\bf h}_{|_U}={\bf h}_{U,\eta}$ for any choice of $(U,\eta)$ as above. See \cite[\S 7.11]{AG} for an equivalent construction.
\begin{prop} We have $V(\bar{f})=V({\bf h})\bar{g}$ as sections of $\underline{\omega}^{p^2}$ on $\overline{X}$. Furthermore, $\bar{f}$ is divisible by ${\bf h}$, and $\bar{f}/{\bf h}$ is a mod $p$ Hilbert modular form of parallel weight one defined over $\kappa$.
\end{prop}
\begin{proof} Let $U$ be an open subset of $\overline{X}$ over which $\underline{\omega}$ is trivializable, and $\eta$ a non-vanishing section of $\underline{\omega}$ over $U$. We claim that if ${\bf h}=\lambda \eta^{p-1}$ on $U$, then
\[
\lambda s^\ast \pi_2^\ast \eta= s^\ast w^\ast {\rm pr}^\ast \pi_2^\ast \eta.
\]
Evaluating both sides at a point corresponding to ${\underline{A}}$, we need to show that for the natural projection
\begin{eqnarray}\label{Equation: Verschiebung projection}
{\rm pr}: A/{{\rm Ker}({\rm Frob}_A)} \rightarrow A/A[p] \cong A,
\end{eqnarray}
we have ${\rm pr}^\ast \eta=\lambda \eta^{(p)}$, which follows from the definition of the Hasse invariant, since ${\rm pr}$ is the Verschiebung morphism of $A$.
Now, writing $\bar{f}=F \eta^p$ and $\bar{g}=G\eta^p$ on $U$, and using the above claim, over $U$, we can write
\[
\lambda^p s^\ast \pi_2^\ast \bar{f}=(s^\ast \pi_2^\ast F)(\lambda^p s^\ast \pi_2^\ast \eta^p)={\operatorname{Fr}}^\ast(F)( s^\ast w^\ast {\rm pr}^\ast \pi_2^\ast \eta^p).
\]
On the other hand, we have
\[
\lambda^ps^\ast w^\ast {\rm pr}^\ast \pi_2^\ast \bar{g}=\lambda^p(s^\ast w^\ast \pi_2^\ast G) (s^\ast w^\ast {\rm pr}^\ast \pi_2^\ast \eta^{p})=\lambda^pG(s^\ast w^\ast {\rm pr}^\ast \pi_2^\ast \eta^{p}).
\]
At a point corresponding to an {\it ordinary} abelian variety $A$, the section $s^\ast w^\ast {\rm pr}^\ast \pi_2^\ast \eta$ specializes to ${\operatorname{pr}\,}^\ast \eta$, where ${\operatorname{pr}\,}$ is as in (\ref{Equation: Verschiebung projection}), and is, hence, non vanishing. Corollary \ref{Corollary: equality of section on Xbar} now implies that over $\overline{X}^{ord} \cap U$ we have
\[
{\rm Fr}^\ast(F)=\lambda^p G={\rm
Fr^\ast}(\lambda)G,\]
the last equality because $\bf h$ is defined on a model of $\overline{X}$ over $\mathbb{F}_p$. Running over a trivializing open covering of $\overline{X}$ for $\omega$, we conclude that $V(\bar{f})=V({\bf
h})\bar{g}$ on $\overline{X}^{ord}$. Since $\overline{X}^{ord}$ is Zariski dense in $\overline{X}$, it follows that
\[
V(\bar{f})=V({\bf h})\bar{g}
\]
as sections of $\omega^{p^2}$ over $\overline{X}$.
Viewing $F/\lambda$ as a function on the ordinary part of $U$, we need
to show that it extends to all of $U$. Since $U$ is smooth over
$\kappa$, it is enough to show that the Weil divisor of $F/\lambda$
is effective. But the coefficients appearing in that divisor are the
coefficients of the Weil divisor of $G$ multiplied by $p$. Since $G$
has an effective Weil divisor, so does $F/\lambda$, and hence $F$ is
divisible by $\lambda$ on $U$. Repeating this argument over an open
covering of $\widetilde{\overline{X}}$, we obtain that $\bar{f}$ is divisible
by $\bf h$, and $\bar{f}/{\bf h}$ is a mod $p$ Hilbert modular form
of parallel weight one defined over $\kappa$, as required.
\end{proof}
We can now finish the proof of Theorem \ref{thm: main result}. The desired mod $p$ Hilbert modular form of parallel weight one $h$ is $\bar{f}/{\bf h}$. Since ${\bf h}$ has $q$-expansion $1$ at all unramified cusps, it follows that $h$ satisfies the desired assumptions.
\end{proof}
\section{Serre's Conjecture implies Artin's Conjecture}\label{sec:
Artin}\subsection{}In this final section we generalise the arguments of
\cite{MR1434905} to show that for a fixed totally real field $F$, the
weak form of Serre's conjecture for $F$ implies the strong form of
Artin's conjecture for two-dimensional totally odd representations
over $F$. To
be precise, the weak version of Serre's conjecture that we have in
mind is the following (cf. Conjecture 1.1 of \cite{bib:BDJ}, where it
is described as a folklore conjecture).
\begin{conj}\label{conj:Serre}
Suppose that $\rhobar:G_F\to\operatorname{GL}_2(\overline{\F}_p)$ is continuous,
irreducible and totally odd. Then $\rhobar\cong\rhobar_f$ for some
Hilbert modular eigenform $f$.
\end{conj}
Meanwhile, we have the following strong form of Artin's conjecture.
\begin{conj}
\label{conj:Artin}Suppose that $\rho:G_F\to\operatorname{GL}_2({\mathbb{C}})$ is continuous,
irreducible and totally odd. Then $\rho\cong\rho_f$ for the some
Hilbert modular eigenform $f$ (necessarily of parallel weight one).
\end{conj}
In order to show that Conjecture \ref{conj:Serre} implies Conjecture
\ref{conj:Artin}, we follow the proof of Proposition 1 of
\cite{MR1434905}, using Theorem \ref{thm: main result} in place of the
results of Gross and Coleman--Voloch used in \cite{MR1434905}. The
argument is slightly more involved than in \cite{MR1434905}, because
we have to be careful to show that the $p$-distinguishedness
hypothesis in Theorem \ref{thm: main result} is satisfied.
\begin{thm}\label{thm: Serre implies Artin}
Fix a totally real field $F$. Then Conjecture \ref{conj:Serre}
implies Conjecture \ref{conj:Artin}.
\end{thm}
\begin{proof}Suppose that $\rho:G_F\to\operatorname{GL}_2({\mathbb{C}})$ is continuous,
irreducible and totally odd. Then $\rho(G_F)$ is finite, so after
conjugation we may assume that $\rho:G_F\to\operatorname{GL}_2(\mathcal{O}_K)$, where
$\mathcal{O}_K$ is the ring of integers in some number field $K$. We will
show that there are a fixed integer $N$ and infinitely many rational
primes $p$ such that for each such $p$, if $\rhobar_p$ denotes the
reduction of $\rho$ mod $p$ (or rather, modulo a prime of $\mathcal{O}_K$
above $p$), then $\rhobar_p$ arises from the reduction mod $p$ of the
Galois representation associated to an eigenform in
$S_1(\Gamma_1(N),{\mathbb{C}})$, the space of cuspidal Hilbert modular forms of parallel weight one and level $\Gamma_1(N)$ over $\mathbb{C}$. Since
$S_1(\Gamma_1(N),{\mathbb{C}})$ is finite-dimensional, there are only finitely many
such eigenforms, so we see that one eigenform $f$ must work for
infinitely many $p$; but then it is easy to see that
$\rho\cong\rho_f$, as required.
Firstly, we claim that it suffices to prove that there is a fixed
$N$ and infinitely many primes $p$ such that $\rhobar\cong\rhobar_f$
for some eigenform $f\in S_1(\Gamma_1(N),\overline{\F}_p)$ (using the
notation of Section \ref{section: weight one}). To see this, note
that for all but finitely many primes $p$, the finitely generated ${\mathbb{Z}}$-module
$H^1(X,\underline{\omega})$ is $p$-torsion free, so that for all but
finitely many $p$ the reduction map
$H^0(X,\underline{\omega})\to
H^0(\overline{X},\underline{\omega})$ is surjective, and the
Deligne--Serre lemma (Lemma 6.11 of \cite{deligne-serre}) allows us
to lift from $S_1(\Gamma_1(N),\overline{\F}_p)$ to $S_1(\Gamma_1(N),{\mathbb{C}})$.
We are thus reduced to showing that there are infinitely many primes
$p$ for which $\rhobar_p$ satisfies the hypotheses of Theorem
\ref{thm: main result}. Firstly, note that there is at most one prime
$p$ for which $\rho|_{G_{F(\zeta_p)}}$ is reducible, so if we exclude
any such prime, as well as the (finitely many) primes dividing
$\#\rho(G_F)$, the primes which ramify in $F$, and the
primes less than $7$, then $\rhobar_p$ will satisfy the requirements
of the first paragraph of Theorem \ref{thm: main result}.
If we also exclude the finite many primes $p$ for which
$\rho|_{G_{F_v}}$ is ramified for some $v|p$, we see that it is enough
to show that there are infinitely many $p$ such that for all $v|p$,
$\rhobar_p({\operatorname{Frob}}_v)$ has distinct eigenvalues.
In fact, we claim that it is enough to see that there are infinitely
many $p$ such that for all $v|p$, $\rho({\operatorname{Frob}}_v)$ is not scalar. To
see this, suppose that $\rho({\operatorname{Frob}}_v)$ is not scalar, but
$\rhobar_p({\operatorname{Frob}}_v)$ is scalar. Then it must be the case that the
difference of the eigenvalues of $\rho({\operatorname{Frob}}_v)$ is divisible by some
prime above $p$. Now, there are only finitely many non-scalar elements
in $\rho(G_F)$, and for each of these elements there are only finitely
many primes dividing the difference of their eigenvalues, so excluding
this finite set of primes gives the claim.
Let ${\operatorname{proj}} \rho$ be the projective representation
${\operatorname{proj}}\rho:G_F\to\operatorname{PGL}_2({\mathbb{C}})$ obtained from $\rho$. We must show that
there are infinitely many primes $p$ such that for each place $v|p$ of
$F$, ${\operatorname{proj}}\rho({\operatorname{Frob}}_v)\ne 1$. Letting
$L=\overline{F}^{\ker{\operatorname{proj}}\rho}$, we must show that there are
infinitely many primes $p$ such that no place $v|p$ of $F$ splits
completely in $L$. Let $M$ be the normal closure of $F$ over ${\mathbb{Q}}$, and
$N$ the normal closure of $L$ over ${\mathbb{Q}}$. Since $\rho$ is totally odd,
we see that $M$ is totally real and $N$ is totally imaginary. Consider
a complex conjugation $c\in{\operatorname{Gal}\,}(N/{\mathbb{Q}})$. By the Cebotarev density
theorem there are infinitely many primes $p$ such that ${\operatorname{Frob}}_p$ is
conjugate to $c$ in ${\operatorname{Gal}\,}(N/{\mathbb{Q}})$, and it is easy to see that each such
prime splits completely in $M$ and thus in $F$, and that no place $v|p$ of $F$ splits
completely in $L$, as required.
\end{proof}
\bibliographystyle{amsalpha}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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3000 Security
Your Blog » 3000 Security
Previous: Facebook Makes Customers Buying Advertisements To Provide Social Safety Number
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Even though a lot of offices will have safety systems and firewalls in location to deter cyber attacks, there are hackers who are experienced receiving previous these sorts of barriers. Many occasions it's by means of spam mail or pop-ups. Only permit your staff access to the information they want to do their job and do not let them share passwords. Airport security lines are so lengthy that hundreds of fliers at a number of airports have reported missing their flights , and the head of the Transportation Security Administration recently warned passengers to continue to anticipate delays over the summer. Even though signing up for T.S.A. Precheck, a program that makes preflight risk assessments, is the most typical piece of guidance to fliers seeking to shorten their waits, there are other methods, according to Michael Holtz, the owner of SmartFlyer , a worldwide travel consultancy specializing in airfare. 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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
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| 4,326
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{"url":"http:\/\/codeforces.com\/blog\/entry\/65318","text":"Codeforces celebrates 10 years! We are pleased to announce the crowdfunding-campaign. Congratulate us by the link https:\/\/codeforces.com\/10years. \u00d7\n\n### tuwuna's blog\n\nBy\u00a0tuwuna, history, 12 months ago, ,\nHello, codeforces!\nRecently I came across many dynamic programming problems with trace such as:\n\nand many more\nSo I hope that you guys can give me some more dynamic programming problems with similar features (trace)","date":"2020-02-29 11:06:07","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2069643884897232, \"perplexity\": 3760.6232586021038}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-10\/segments\/1581875148850.96\/warc\/CC-MAIN-20200229083813-20200229113813-00423.warc.gz\"}"}
| null | null |
The Turkish Döner has been a European favorite for decades. At Dan-o's Döner, they recreate this delicious 'turning meat' using only all-Hawaiian, grass fed, antibiotic and hormone free beef stacked by hand on a spit daily. Slow roasted to tender perfection, the meat is then stuffed into an artisan bread pocket with fresh greens, tomatoes and a tangy yoghurt sauce. Committed to serving simply healthy food of the highest quality, Dan-o's makes their falafel and sauces in house and sources local ingredients whenever possible—guaranteeing freshness and helping to support the community. Döner kebabs, wraps, plates, salads and more.
|
{
"redpajama_set_name": "RedPajamaC4"
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| 4,934
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package com.kixeye.chassis.scala.transport.http
import org.springframework.web.method.support.{ModelAndViewContainer, HandlerMethodReturnValueHandler}
import org.springframework.core.MethodParameter
import scala.concurrent.Future
import org.springframework.web.context.request.NativeWebRequest
import org.springframework.web.context.request.async.{WebAsyncUtils, DeferredResult}
import scala.util.{Failure, Success}
import scala.concurrent.ExecutionContext.Implicits.global
class ScalaFutureReturnValueHandler extends HandlerMethodReturnValueHandler {
def supportsReturnType(returnType:MethodParameter) : Boolean = {
val clazz = returnType.getParameterType
classOf[Future[_]].isAssignableFrom(clazz)
}
def handleReturnValue(returnValue:AnyRef, returnType:MethodParameter, mavContainer:ModelAndViewContainer, webRequest:NativeWebRequest) : Unit = {
if (returnType == null) {
mavContainer.setRequestHandled(true)
return
}
val deferredResult = new DeferredResult[Any]()
val future:Future[_] = returnValue.asInstanceOf[Future[_]]
future onComplete {
case Success(args) => deferredResult.setResult(args)
case Failure(t) => deferredResult.setErrorResult(t)
}
WebAsyncUtils.getAsyncManager(webRequest).startDeferredResultProcessing(deferredResult, mavContainer)
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,379
|
\section{Introduction}
The behaviour of the structure functions of deep inelastic lepton-nucleon
scattering (DIS) at small values of the Bjorken variable $x_{\mbox{\scriptsize Bj}}$ has been
a topic of intense experimental and theoretical research in recent years.
The strong rise of the structure functions for $x_{\mbox{\scriptsize Bj}}\to 0$ observed at
HERA~\cite{hera} opened the way for a more detailed experimental study
of the small-$x_{\mbox{\scriptsize Bj}}$ limit of QCD. Today, many theoretical models try to
explain the behaviour of the structure functions in this limit.
In a very pragmatic perturbative approach, the well-known DGLAP dynamics
of the $Q^2$ evolution of structure functions~\cite{dglap} is taken
seriously in the small-$x_{\mbox{\scriptsize Bj}}$ region (cf., for example, the parametrizations
of~\cite{pdfs}). Given a sufficiently small $Q^2$ starting scale of the
perturbative evolution, the small-$x_{\mbox{\scriptsize Bj}}$ rise of structure functions can
even be described on the basis of valence-like parton distributions
(see~\cite{grv} and refs. therein). In this case, all of the small-$x_{\mbox{\scriptsize Bj}}$
rise is produced by perturbative QCD.
If, in a more modest approach, a constant behaviour or a soft growth for
$x_{\mbox{\scriptsize Bj}}\to 0$ is ascribed to the input distributions, the DGLAP evolution
allows for a good fit to the data even in the case of a larger $Q^2$
starting scale. This observation underlies successful analyses based on the
idea of double asymptotic scaling~\cite{das}. It is also at the heart of a
recent combined analysis of diffractive and inclusive structure
functions~\cite{bgh}, where a universal logarithmic growth of the input
distributions was assumed.
An obvious problem of the above, purely DGLAP-based approaches is the
presence of large $\ln(1/x_{\mbox{\scriptsize Bj}})$ corrections, which can spoil the usefulness
of the perturbation series as an asymptotic expansion. Using the BFKL
resummation method~\cite{bfkl} (see~\cite{lipr} for reviews and further
references), all leading $\ln(1/x_{\mbox{\scriptsize Bj}})$ contributions can be included in
the structure function analysis (see, e.g.,~\cite{f2a}). It is, at present,
not completely clear whether the predicted very strong power-like growth is
borne out by HERA data. Also, no final conclusions can yet be made
concerning the effect of the recently obtained next-to-leading order
results in the BFKL framework (see~\cite{nlo} and refs. therein) on
structure function analyses. Different methods of dealing with the
apparent large size of the corrections have been suggested~\cite{mnlo}.
Unfortunately, because of the problem of infrared diffusion~\cite{mue}, it
is not clear that the perturbative resummation of $\ln(1/x_{\mbox{\scriptsize Bj}})$ terms at
any given order in $\alpha_s$ can reveal the asymptotic behaviour. One
possibility to go beyond the above resummation schemes is the construction
of a high-energy effective action for reggeons (see~\cite{lip} and refs.
therein). Another possibility is the derivation of a small-$x_{\mbox{\scriptsize Bj}}$ evolution
equation in the framework of the semiclassical approach. This method goes
back to the treatment of hadron-hadron scattering in the functional
integral approach using the eikonal approximation introduced in~\cite{eik}.
For recent results concerning the energy dependence of cross sections in
this framework see, e.g.,~\cite{sc}.
A very different point of view is advertised in \cite{dl}, where, in
addition to the familiar soft pomeron, a phenomenological hard pomeron is
introduced to describe small-$x_{\mbox{\scriptsize Bj}}$ structure functions. A further
analysis~\cite{cdl}, motivated by the successful phenomenology
of~\cite{dl}, concludes that the appearance of new small-$x_{\mbox{\scriptsize Bj}}$
singularities due to $Q^2$ evolution is inconsistent with the analyticity
principle governing Regge theory and underlying the approach of~\cite{dl}.
Note also the successful analysis of various experimental cross sections
reported in~\cite{rue}, which combines ideas of~\cite{eik} and~\cite{dl}.
In spite of the large amount of work invested and the good description of
data achieved in most of the above approaches, our fundamental understanding
of the small-$x_{\mbox{\scriptsize Bj}}$ asymptotics in QCD is still not satisfactory. Therefore,
we propose yet another method to achieve this goal. In this article, we
will derive a connection between the small-$x_{\mbox{\scriptsize Bj}}$ behaviour of the
structure functions of DIS and the behaviour of correlation functions
in a certain effective field theory, which we consider both in Minkowski
and Euclidean space-time. The analytic continuation from Minkowski to
Euclidean space-time to be discussed below is similar in spirit to the one
described in \cite{meg} for the high-energy hadron-hadron scattering
amplitudes. However, the details are quite different and we will comment on
the connection between the two approaches.
For simplicity, we study in this article a scalar model field theory where
scalar currents replace the electromagnetic currents of real life, i.e.,
QCD. However, it will become clear that our methods allow a straightforward
generalization to QCD.
Our article is organized as follows. In Sect.~\ref{camp} we define the
model and discuss the properties of our scalar analogue of the virtual
Compton amplitude. In Sect.~\ref{mieu} we introduce a class of effective
Hamiltonians depending on a parameter $r$. We also make a rotation from
Minkowski to Euclidean space-time and show that the high-$Q^2$, $x_{\mbox{\scriptsize Bj}}\to 0$
limit corresponds to $r\to 0$. In Sect.~\ref{fi} the amplitude is written
as a functional integral with $r$-dependent action. In Sect.~\ref{ff} the
formalism is applied to a simple model of free fields. We show that -- at
least in the free-field limit -- we get a diverging correlation length in
our effective theory for $r\to 0$, i.e., a critical phenomenon. Finally,
two alternative continuations from Minkowski to Euclidean space-time are
outlined in Sect.~\ref{alt}. Section~\ref{conc} contains our conclusions.
\section{The model and the scalar analogue of the virtual Compton
amplitude}\label{camp}
\setcounter{equation}{0}
We consider a model with one real scalar field $\phi(x)$ and the classical
Lagrangian
\begin{equation}
{\cal L}(x)=\frac{1}{2}\,\partial_\mu\phi(x)\,\partial^\mu\phi(x)-\frac{m^2}
{2}\,\phi(x)^2-\frac{\lambda}{4!}\,\phi(x)^4\,,\label{lag}
\end{equation}
where $m$ and $\lambda$ are the unrenormalized mass and coupling parameter,
respectively. The momentum canonically conjugate to $\phi(x)$ is
\begin{equation}
\pi(x)=\frac{\partial{\cal L}}{\partial \dot{\phi}(x)}=\dot{\phi}(x)\,.
\end{equation}
The Hamiltonian and the third component $P^3$ of the momentum operator read
\begin{equation}
H=\int_{x^0=\mbox{\scriptsize const.}}d^3\vec{x}\left\{\frac{1}{2}\Pi(x)^2
+\frac{1}{2}\Big(\nabla\Phi(x)\Big)^2+\frac{m^2}{2}\Phi(x)^2+\frac{\lambda}
{4!}\Phi(x)^4\right\}\,,\label{hop}
\end{equation}
\begin{equation}
P^3=-\frac{1}{2}\int_{x^0=\mbox{\scriptsize const.}}d^3\vec{x}\,\left(\Pi(x)
\frac{\partial\Phi(x)}{\partial x^3}+\frac{\partial\Phi(x)}{\partial x^3}
\Pi(x)\right)\,.\label{pop}
\end{equation}
In Eqs.~(\ref{hop}) and (\ref{pop}) no vacuum expectation values are
subtracted. Note that we use lower- and upper-case letters for the
classical field variables and the corresponding operators respectively.
We assume that the theory has physical states with reasonable
spectrum\footnote{
Of course we know that the theory defined by Eq.~(\ref{lag}) is trivial if
the cutoff goes to infinity in four dimensions. The purist may always think of
a theory with a finite cutoff.}
etc. We will call `proton' the particle of lowest mass $M$. We introduce
now an `electromagnetic' coupling of our field to a scalar `photon' with
field $A(x)$:
\begin{equation} {\cal L}'(x)=-e\,J(x)\,A(x)\qquad\mbox{with}\qquad
J(x)=\Phi(x)^2\,.\label{je}
\end{equation}
This scalar current is our analogue of the electromagnetic current of QCD.
In the following we will study DIS, i.e., the cross section for the
absorption of the scalar `photon' on the scalar `proton' (Fig.~\ref{dis}).
\begin{figure}[ht]
\begin{center}
\vspace*{.2cm}
\parbox[b]{5cm}{\psfig{width=5cm,file=dis.eps}}\\
\end{center}
\refstepcounter{figure}\label{dis}
{\bf Figure \ref{dis}:} Diagram for the absorption of a scalar photon on
the scalar proton.
\end{figure}
We define the structure function for this reaction as
\begin{equation}
W(\nu,Q^2)=\sum_X\,\frac{1}{2}(2\pi)^3\delta^{(4)}(p'-p-q)\,\langle P(p)
|J(0)|X(p')\rangle\,\langle X(p')|J(0)|P(p)\rangle\,,\label{sf}
\end{equation}
where
\begin{equation}
Q^2=-q^2>0\qquad\mbox{and}\qquad \nu=pq/M>0\,.
\end{equation}
All the notation is standard. The conventions for the metric, normalization
of states etc. follow~\cite{nac}.
The object to study from a theoretical point of view is the virtual Compton
amplitude. To be precise, we will study the amplitude corresponding to the
retarded commutator (see, e.g,~\cite{kal}):
\begin{equation}
T_r(\nu,Q^2)=\frac{i}{2\pi}\int d^4x\,e^{iqx}\theta(x_0)\,\langle P(p)|
[J(x),J(0)]|P(p)\rangle\,.\label{tr}
\end{equation}
Here and in the remainder of the paper, we always assume that the connected
part of the relevant matrix element is taken, $\langle\cdots\rangle=
\langle\cdots\rangle_c$. It is easy to see that
\begin{equation}
\mbox{Im}\,T_r(\nu+i\varepsilon,Q^2)=\mbox{sgn}(\nu)\,W(|\nu|,Q^2)\label{imt}
\end{equation}
for $\nu$ real and $\varepsilon \to 0+$.
We consider now Eq.~(\ref{tr}) in the proton rest frame, where we can set
\begin{equation}
p=(M,\vec{0})\qquad,\qquad q=(\nu,\,\vec{e}_3\sqrt{\nu^2+Q^2}\,)\label{pq}
\end{equation}
with $\vec{e}_j\,\,(j=1,2,3)$ the spatial cartesian unit vectors.
Rotational invariance gives
\begin{equation}
\langle P(p)|J(\vec{x},x^0)J(0)|P(p)\rangle=\langle P(p)|J(\pm|\vec{x}|
\vec{e}_3,x^0)J(0)|P(p)\rangle\,.\label{rot}
\end{equation}
Inserting this in Eq.~(\ref{tr}) and using Eq.~(\ref{pq}) and the fact that
the commutator in Eq.~(\ref{tr}) vanishes outside the light cone, we find
\begin{equation}
T_r(\nu,Q^2)=-\frac{1}{\sqrt{\nu^2+Q^2}}\int\limits^\infty_0dx^0
\int\limits^{x^0}_{-x^0}dx^3x^3\,e^{ix^0\nu-ix^3\sqrt{\nu^2+Q^2}}\,
\langle P(p)[J(x^3\vec{e}_3,x^0),J(0)]|P(p)\rangle\,.\label{trm}
\end{equation}
In Eq.~(\ref{trm}) we have a convenient starting point for the analytic
continuation of $T_r(\nu,Q^2)$ into the upper half of the complex $\nu$
plane, keeping always $Q^2$ fixed. In fact, it is easy to see that the
integral in Eq.~(\ref{trm}) defines an analytic function for Im$\,\nu>0$
(cf.~Appendix~\ref{rac}). Using standard methods, one finds then that
$T_r(\nu,Q^2)$ can be extended to a function analytic in the whole $\nu$
plane except for poles and cuts on the real axis for $|\nu|\ge Q^2/2M$
(cf.~Fig.~\ref{nup}).
\begin{figure}[ht]
\begin{center}
\vspace*{.2cm}
\parbox[b]{7cm}{\psfig{width=7cm,file=nup.eps}}\\
\end{center}
\refstepcounter{figure}\label{nup}
{\bf Figure \ref{nup}:}
The analyticity structure of the virtual Compton amplitude $T_r(\nu,Q^2)$
in the $\nu$ plane. Singularities can only occur for real $\nu$, $|\nu|\ge
Q^2/2M$. The integral in Eq.~(\ref{trm}) is a representation of $T_r(\nu,
Q^2)$ for Im$\,\nu>0$.
\end{figure}
We are interested in the behaviour of $T_r(\nu,Q^2)$ for $\nu\to\infty$ on
the real axis. Instead of studying this directly, we will study $T_r(\nu,
Q^2)$ on the imaginary axis, i.e., for $\nu=i\eta,$ $\eta\to +\infty$. With
standard assumptions for the high-momentum behaviour of the amplitudes of
QFT (cf.~Appendix~\ref{rac}), we can apply the Phragm\'{e}n-Lindel\"of
theorem (see, e.g.,~\cite{pl}), which ensures that the asymptotic behaviour
on the real and imaginary axes are related by analytic continuation. Our
object of study is thus:
\begin{equation}
T_r(i\eta,Q^2)=\frac{i}{\sqrt{\eta^2-Q^2}}\int\limits^\infty_0dx^0
\int\limits^{x^0}_{-x^0}dx^3 x^3\,e^{-x^0\eta+x^3\sqrt{\eta^2-Q^2}}\,
\langle P(p)|[J(x^3\vec{e}_3,x^0),J(0)]|P(p)\rangle\,.
\end{equation}
It turns out to be convenient to generalize this amplitude slightly. Let
$\mu$ with Im$\,\mu\geq0$ be a complex parameter with dimension of mass and
define:
\begin{equation}
T_+(i\eta,Q^2,\mu)=\frac{2i}{\sqrt{\eta^2-Q^2}}\!\int\limits^\infty_0\!dx^0
\!\!\int\limits^{x^0}_{-x^0}\!dx^3x^3\,e^{x^0(i\mu-\eta)+x^3
\sqrt{\eta^2-Q^2}}\,\langle P(p)|J(x^3\vec{e}_3,x^0)J(0)|P(p)\rangle.
\label{tp}
\end{equation}
We have
\begin{equation}
T_r(i\eta,Q^2)=\mbox{Re}\,T_+(i\eta,Q^2,0)\,,\label{trtp}
\end{equation}
which is obvious for $\eta>Q$ and requires a little thought for $0<\eta\le
Q$ (cf.~Appendix~\ref{rac}).
In the next section we will represent $T_+(i\eta,Q^2,\mu)$ for Re$\,\mu<-M$
as a correlation function in an effective Euclidean field theory.
The amplitude $T_r(i\eta,Q^2)$ is then obtained from Eq.~(\ref{trtp}) after
analytic continuation of $T_+$ to $\mu=0$. We will also write
$T_+(i\eta,Q^2,0)$ as a correlation function in the corresponding
effective theory in Minkowski space-time.
\section{From Minkowski to Euclidean space}\label{mieu}
\setcounter{equation}{0}
Let us introduce new coordinates in Eq.~(\ref{tp}):
\begin{equation}
x^0=\xi\ \cosh\chi\quad,\quad x^3=\xi\ \sinh\chi
\end{equation}
with
\begin{equation}
0\leq\xi<\infty\quad,\quad-\infty<\chi<\infty\,.
\end{equation}
In this section we always consider $\eta>Q$.
Then we insert a sum over a complete set of states and perform the $\xi$
integration:
\begin{eqnarray}
&&\hspace*{-.5cm}
T_+(i\eta,Q^2,\mu)=\sum_X\frac{2i}{\sqrt{\eta^2-Q^2}}\int^\infty_{-\infty}
d\chi\,\sinh\chi\ \int^\infty_0d\xi\,\xi^2\label{tps}
\\
&&\hspace{.5cm}\times e^{-\xi\left[\left(\eta+i({p'}^0-M-\mu)\right)\cosh
\chi-(\sqrt{\eta^2-Q^2}+i{p'}^3)\sinh\chi\right]}\,\langle P(p)|J(0)|X(p')
\rangle\langle X(p')|J(0)|P(p)\rangle\,.\nonumber
\end{eqnarray}
The convergence of the $\xi$ integration in Eq.~(\ref{tps}) is guaranteed
since
\begin{equation}
\eta\ \cosh\chi-\sqrt{\eta^2-Q^2}\sinh\chi>0\,,
\end{equation}
and we get
\begin{eqnarray}
T_+(i\eta,Q^2,\mu)&=&\sum_X\frac{2i}{\sqrt{\eta^2-Q^2}}\int^\infty_{-\infty}
d\chi\ \sinh \chi\label{tpn}
\\
&&\times 2\left\{\left(\eta+i({p'}^0-M-\mu)\right)\cosh\chi-\left(
\sqrt{\eta^2-Q^2}+i{p'}^3\right)\sinh\chi\right\}^{-3}\nonumber
\\
&&\times\langle P(p)|J(0)|X(p')\rangle\langle
X(p')|J(0)|P(p)\rangle\,.\nonumber
\end{eqnarray}
Since ${p'}^0\geq |{p'}^3|$, we have also
\begin{equation}
({p'}^0-M-\mbox{Re}\,\mu)\cosh\chi-{p'}^3\sinh\chi>0
\end{equation}
for Re$\,\mu<-M$. This allows us to write Eq.~(\ref{tpn}) again as an
integral over a parameter~$\xi$:
\begin{eqnarray}
T_+(i\eta,Q^2,\mu)&=&\sum_X\frac{-2}{\sqrt{\eta^2-Q^2)}}
\int^\infty_{-\infty} d\chi\sinh\chi\ \int^\infty_0 d\xi\xi^2\label{tpl}
\\
&&\times\,e^{-\xi\left[({p'}^0-M-\mu-i\eta)\cosh\chi-({p'}^3-i
\sqrt{\eta^2-Q^2})\sinh\chi\right]}\nonumber
\\
&&\times\langle P(p)|J(0)|X(p')\rangle\langle X(p')|J(0)|P(p)\rangle
\nonumber
\\
\nonumber\\
&=&\frac{-2}{\sqrt{\eta^2-Q^2}}\int^\infty_{-\infty}d\chi\sinh\chi
\int^\infty_0d\xi\xi^2\nonumber
\\
&&\times\,e^{\xi\left[(\mu+i\eta)\cosh\chi-i\sqrt{\eta^2-Q^2}\sinh\chi
\right]}\,{\cal M}_E\,,\nonumber
\end{eqnarray}
where
\begin{equation}
{\cal M}_E=\langle P(p)|\,e^{\xi(H\cosh\chi-P^3\sinh\chi)}\,J(0)\,
e^{-\xi(H\cosh\chi-P^3\sinh\chi)}\,J(0)|P(p)\rangle\,.
\label{me}
\end{equation}
Effectively we have shifted the $\xi$-integration in Eq.~(\ref{tps})
from the real to the imaginary axis, $\xi\to -i\xi$. In Eq.~(\ref{me})
$H$ and $P^3$ denote the Hamilton operator and the third component of the
momentum operator of the original theory, Eqs.~(\ref{hop}) and (\ref{pop}),
respectively.
The matrix element ${\cal M}_E$ can now be interpreted as one of a
Euclidean field theory. For this we set
\begin{equation}
y^0=\xi\cosh\chi\qquad,\qquad y^3=\xi\sinh\chi\qquad,\qquad
y_\pm=y^0\pm y^3=\xi e^{\pm\chi}
\end{equation}
and
\begin{equation}
r=\frac{2y_-}{y_++y_-}=1-\frac{y^3}{y^0}\qquad,\qquad
\eta_\pm=\eta\pm\sqrt{\eta^2-Q^2}\,.\label{reta}
\end{equation}
We have
\begin{equation}
y_+\geq0,\quad y_-\geq0\qquad,\qquad 0\leq r\leq2\,.
\end{equation}
Furthermore we define an effective, $r$-dependent Hamiltonian:
\begin{equation}
H_{eff}(r)=H-(1-r)P^3\,.\label{heff}
\end{equation}
With this we can write
\begin{equation}
{\cal M}_E\equiv{\cal M}_E(y_0,r)=\langle P(p)|\,e^{y^0H_{eff}(r)}\,J(0)\,
e^{-y^0H_{eff}(r)}\,J(0)|P(p)\rangle\label{eme}
\end{equation}
and
\begin{eqnarray}
T_+(i\eta,Q^2,\mu)&\!\!\!=\!\!\!&
\frac{-1}{2\sqrt{\eta^2-Q^2}}\int^\infty_0 dy_+
\int^\infty_0dy_-(y_+-y_-)\,e^{\frac{1}{2}y_+(\mu+i\eta_-)+\frac{1}{2}
y_-(\mu+i\eta_+)}\,{\cal M}_E(y^0,r)\nonumber
\\
\label{tpme}\\
&\!\!\!=\!\!\!&
\frac{-2}{\sqrt{\eta^2-Q^2}}\int^\infty_0dy^0(y^0)^2\int^2_0dr(1-r)\,
e^{y^0[\mu+i(1-\frac{r}{2})\eta_-+i\frac{r}{2}\eta_+]}\,{\cal M}_E(y^0,r)
\,.\nonumber
\end{eqnarray}
We see from Eq.~(\ref{reta}) that for $\eta\to\infty, \ Q^2$ fixed,
we have $\eta_+\sim 2\eta$, $\eta_-\sim Q^2/(2\eta)$. Then the
oscillating term $\exp(i y^0r\eta_+/2)$ restricts the
$r$-integration to
\begin{equation}
r\mst{<}{\sim}\frac{1}{\eta y^0}\,.
\end{equation}
Thus, except for the small-$y^0$ range, $0\,{\scriptstyle \leq}\,y^0\mst{<}
{\sim}1/ \eta$, the behaviour of the matrix element ${\cal M}_E(y_0,r)$ for
$r\to 0$ will be essential. Going from $r=1$ to $r=0$ in Eq.~(\ref{heff})
corresponds, of course, to going from the ordinary Hamiltonian $H$ to the
light-cone Hamiltonian $H-P^3$.
In conventional light-cone calculations the theory is quantized directly
on a light-like subspace (for reviews and further refs. see~\cite{lc}).
However, we always stay away from the light cone by having $r\neq 0$.
For studies concerning the possibility to approach the light cone
continuously in the Hamiltonian method, we refer to~\cite{lcl}.
In Sect.~\ref{fi} below we will use the Lagrangian method and for us
the light-like limit concerns only the endpoint $r=0$ of the $r$
integration in Eq.~(\ref{tpme}).
Whereas for $r\in(0,2)$, the effective Hamiltonian $H_{eff}(r)$ has an
energy gap, this gap vanishes for $r=0$ and 2. We have
\begin{equation}
\mbox{min}\left\{\langle X|H_{eff}(r)|X\rangle-E_0\right\}=\sqrt{r(2-r)}\,
M\,,\label{min}
\end{equation}
where $E_0$ is the vacuum energy:
\begin{equation}
E_0=\langle 0|H_{eff}(r)|0\rangle=\langle 0|H|0\rangle\,,
\end{equation}
and the minimum is taken over all normalized states $|X\rangle$ orthogonal
to $|0\rangle$. Equation~(\ref{min}) is already indicative of a large
correlation length and a critical phenomenon for $r=0$ and we will give
more arguments for this in Sect.~\ref{ff}.
Instead of representing $T_+(i\eta,Q^2,\mu)$ as an integral over a
Euclidean matrix element ${\cal M}_E(y^0,r)$ in Eq.~(\ref{tpme}),
we can also represent it as an integral over the corresponding
Minkowskian matrix element ${\cal M}_E(y^0,r)={\cal M}_M(-iy^0,r)$:
\begin{equation}
T_+(i\eta,Q^2,\mu)=\frac{2i}{\sqrt{\eta^2-Q^2}}\int\limits^\infty_0dx^0
(x^0)^2\int\limits^2_0dr(1-r)\,e^{-x^0\left[-i\mu+(1-\frac{r}{2})\eta_-+
\frac{1}{2}r\eta_+\right]}\,{\cal M}_M(x^0,r).\label{tpmin}
\end{equation}
with
\begin{equation}
{\cal M}_M(x^0,r)=\langle P(p)|\,e^{+ix^0 H_{eff}(r)}\,J(0)\,e^{-ix^0
H_{eff}(r)}\,J(0)|P(p)\rangle\,.\label{mme}
\end{equation}
In Eq.~(\ref{tpmin}) there is no problem when setting $\mu=0$.
\section{Functional integral representation}\label{fi}
\setcounter{equation}{0}
In this section we will rewrite the matrix element of Eq.~(\ref{eme}) in
terms of a path integral, using standard procedures as in the conventional
case $H_{eff}=H$, i.e., $r=1$. We assume for simplicity that the states
$|P(p)\rangle$ have the quantum numbers of the $\Phi$ field, i.e., that the
$\Phi$ field is an interpolating field for these states. Then, according
to the basic principles of the LSZ reduction formalism, we have to
construct the operators
\begin{equation}
A(p,x^0)=i\int_{x^0=\mbox{\scriptsize const.}}d^3\vec{x}\,e^{ipx}\,\frac{
\stackrel{\leftrightarrow}{\partial}}{\partial x^0}\,\Phi(x)\,.
\end{equation}
We have then, in the weak sense,
\begin{equation}
\lim_{x^0\to\pm\infty}\frac{1}{\sqrt{Z}}A^\dagger(p,x^0)|0\rangle=|P(p)
^{out}_{in}\rangle=|P(p)\rangle\,,\label{lsz}
\end{equation}
where $Z$ is the wave function renormalization constant.
The Euclidean version of Eq.~(\ref{lsz}) for the proton with zero
three-momentum reads:
\begin{equation}
\frac{1}{\sqrt{Z}}\lim_{t\to\infty}\left(e^{-Ht}A^\dagger(0)|0\rangle
\right)e^{(M+E_0)t}=|P(p)\rangle\,,\label{lsze}
\end{equation}
where we set $A(0)\equiv A(p,0)$ with $p=(M,\vec{0})$. In terms
of the field operator and its conjugate canonical momentum, we have
\begin{eqnarray}
A(0)&=&\int_{x^0=0}d^3\vec{x}\left(i\Pi(x)+M\Phi(x)\right)\,,\label{adef}\\
A^\dagger(0)&=&\int_{x^0=0}d^3\vec{x}\left(-i\Pi(x)+M\Phi(x)\right)\,.
\label{addef}
\end{eqnarray}
Before rewriting the matrix element of Eq.~(\ref{eme}) in terms of a path
integral, let us recall the corresponding procedure in the conventional
case $H_{eff}=H$, i.e., $r=1$. Using Eq.~(\ref{lsze}) we have
\begin{equation}
{\cal M}_E(\tau,1)\!=\!\frac{1}{Z}\lim_{\tau_i\to-\infty\atop\tau_f\to+
\infty}\,e^{(\tau_f-\tau_i)(M+E_0)}\,\langle 0|A(0)\,e^{-(\tau_f-\tau)H}\,
\!J(0)\,e^{-(\tau-0)H}\,\!J(0)\,e^{-(0-\tau_i)H}\,A^\dagger(0)|0\rangle\,.
\label{emef}
\end{equation}
Now the standard procedure is to introduce alternating intermediate states
which are eigenstates of the field operators $\Pi$ and $\Phi$ with definite
classical field eigenvalues $\pi$ and $\phi$ on a sufficiently dense grid
in Euclidean time. The $\pi$ integrations can then be carried out
explicitly, leaving one with a product of $\phi$ integrations. In the limit
where the time slices become arbitrarily thin, this defines the Euclidean
path integral.
In realizing this procedure, all operators in Eq.~(\ref{emef}) are replaced
by functionals of $\pi$ and $\phi$. For $H$ and $J$, the relevant
expressions are given in Eqs.~(\ref{hop}) and (\ref{je}), for the
annihilation and creation operator $A$, $A^\dagger$ in Eqs.~(\ref{adef})
and (\ref{addef}).
The standard procedure outlined above gives the result
\begin{equation}
{\cal M}_E(\tau,1)=\frac{1}{Z}\lim_{\tau_i\to-\infty\atop\tau_f\to+\infty}
\,e^{(\tau_f-\tau_i)M}\,{\cal Z}^{-1}\int D\phi\, a(\tau_f)j(\tau)j(0)
a^\dagger(\tau_i)\,e^{-\int d^4x\,{\cal L}_E}\,,\label{emep}
\end{equation}
\begin{equation}
{\cal Z}=\int D\phi\,e^{-\int d^4x\,{\cal L}_E}\,,
\end{equation}
with the Euclidean Lagrangian
\begin{eqnarray}
{\cal L}_E&=&-i\pi(x)\dot{\phi}(x)+{\cal H}\\
&=&-i\pi(x)\dot{\phi}(x)+\frac{1}{2}\pi(x)^2+\frac{1}{2}\Big(\nabla\phi(x)
\Big)^2+\frac{m^2}{2}\phi(x)^2+\frac{\lambda}{4!}\phi(x)^4\,.\nonumber
\end{eqnarray}
Here the canonical momentum $\pi$ entering Eq.~(\ref{emep}) via $a$,
$a^\dagger$ and ${\cal L}_E$ has to be understood as a function of $\phi$.
In the Euclidean theory, the relation between $\phi$ and $\pi$ is defined
by
\begin{equation}
i\dot{\phi}=\frac{\partial{\cal H}}{\partial\pi}=\pi\,.\label{pf}
\end{equation}
In this way, Eq.~(\ref{emep}) and the expressions for $a$ and ${\cal L}_E$
follow directly from Eq.~(\ref{emef}) and the explicit form of the
Hamiltonian density ${\cal H}$.
The result at $r\neq 1$ can be obtained by following the standard procedure
for converting a matrix element into a functional integral expression
outlined above. It is easy to guess the correct answer by observing that
the effective Hamiltonian density is defined by the substitution
\begin{equation}
{\cal H}\,\,\longrightarrow\,\,{\cal H}_{eff}\,=\,{\cal H}+(1-r)\pi
\partial_3\phi\,.
\end{equation}
Thus, the expression for $\pi$ in terms of $\phi$ following from
Eq.~(\ref{pf}) now reads
\begin{equation}
i\dot{\phi}=\frac{\partial{\cal H}_{eff}}{\partial\pi}=\pi+(1-r)\,
\partial_3\phi\,.
\end{equation}
This is to be used when expressing $a$, $a^\dagger$ and the new effective
Lagrangian ${\cal L}_{E,\,eff}$ in terms of $\phi$ in Eq.~(\ref{emep}).
We summarize the results of this calculation, some details of which are given
in Appendix~\ref{fic}: the Euclidean matrix element of Eq.~(\ref{eme}) can
be calculated as
\begin{equation}
{\cal M}_E(\tau,r)=\frac{1}{Z}\lim_{\tau_i\to-\infty\atop\tau_f\to+\infty}
\,e^{(\tau_f-\tau_i)M}\,{\cal Z}^{-1}\int D\phi\, a(\tau_f)j(\tau)j(0)
a^\dagger(\tau_i)\,e^{-\int d^4x\,{\cal L}_{E,\,eff}}\,,\label{emer}
\end{equation}
\begin{equation}
{\cal Z}=\int D\phi\,e^{-\int d^4x\,{\cal L}_{E,\,eff}}\,,
\end{equation}
with
\begin{equation}
{\cal L}_{E,\,eff}=\frac{1}{2}\Big(\partial_0{\phi}(x)+i(1-r)\,\partial_3
\phi(x)\Big)^2+\frac{1}{2}\Big(\nabla\phi(x)\Big)^2+\frac{m^2}{2}\phi(x)^2+
\frac{\lambda}{4!}\phi(x)^4\,\label{el}
\end{equation}
and
\begin{eqnarray}
a(\tau_f)&=&\int_{x^0=\tau_f}d^3\vec{x}\,\Big(-\partial_0{\phi}
(x)-i(1-r)\,\partial_3\phi(x)+M\phi(x)\Big)\,,\label{af}\\
a^\dagger(\tau_i)&=&\int_{x^0=\tau_i}d^3\vec{x}\,\Big(\partial_0{\phi}
(x)+i(1-r)\,\partial_3\phi(x)+M\phi(x)\Big)\,,\label{afd}
\end{eqnarray}
\begin{equation}
j(\tau)=\phi^2(\vec{0},\tau)\,.
\end{equation}
Note that in the Euclidean path integral, Eq.~(\ref{emer}), the functionals
$a(\tau)$ and $a^\dagger(\tau)$ are not complex conjugate to each other and
${\cal L}_{E,\,eff}$ is not a real function for $r\neq 1$.
The matrix element Eq.~(\ref{emer}) is related to the high-energy limit of
the structure function $W$ via Eqs.~(\ref{imt}), (\ref{trtp}) and
(\ref{tpme}). The above Euclidean functional integral expression for
${\cal M}_E$ is one of the central results of this paper. We propose to
evaluate it using genuinely non-perturbative methods, e.g., lattice Monte
Carlo simulations.
Similarly, the Minkowskian matrix element of Eq.~(\ref{mme}) can be
expressed in terms of an appropriate Minkowskian functional integral
(cf.~Appendix~\ref{fic}).
\section{Free-field example}\label{ff}
\setcounter{equation}{0}
To illustrate the meaning of the formalism developed, let us consider the
simple example of free fields, i.e., the case $\lambda=0$.
Using Eqs.~(\ref{emef}), (\ref{af}) and (\ref{afd}), the matrix element is
expressed as
\begin{equation}
{\cal M}_E(\tau,r)=\frac{1}{Z}\lim_{\tau_i\to-\infty\atop\tau_f\to+\infty}
\,e^{(\tau_f-\tau_i)M}\,\int d^3\vec{x}_f\,d^3\vec{x}_i\left(
-\frac{\partial}{\partial\tau_f}+M\right)\left(\frac{\partial}{\partial
\tau_i}+M\right)G_{\phi jj\phi}(x_f,x,0,x_i)\,,\label{emeg}
\end{equation}
where
\begin{equation}
x_i=(\vec{x}_i,\tau_i)\quad,\quad x_f=(\vec{x}_f,\tau_f)\quad,\quad
x=(\vec{0},\tau)\,,
\end{equation}
and $G_{\phi jj\phi}$ is the connected Green function of two fields $\phi$
and two currents $j$ illustrated in Fig.~\ref{gf}. The terms with $x^3$
derivative disappear because of the $x^3$ integration.
\begin{figure}[ht]
\begin{center}
\vspace*{.2cm}
\parbox[b]{6.5cm}{\psfig{width=6.5cm,file=gf.eps}}\\
\end{center}
\refstepcounter{figure}\label{gf}
{\bf Figure \ref{gf}:} The Euclidean Green function required for the
calculation of ${\cal M}_E$.
\end{figure}
In the free-field case, Fig.~\ref{gf} contains only the two diagrams shown
in Fig.~\ref{td}, where the propagator following from the free part of the
Euclidean Lagrangian, Eq.~(\ref{el}), has to be used. It reads
\begin{equation}
G(x)=\int\frac{d^4k}{(2\pi)^4}\,e^{ikx}\,\frac{1}{k^TA_rk+m^2}=\frac{m}
{4\pi^2\sqrt{x^TA_r^{-1}x}}\,K_1\left(m\sqrt{x^TA_r^{-1}x}\right)\,,
\label{egf}
\end{equation}
where
\begin{equation}
A_r=\left(\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1-(1-r)^2&i(1-r)\\
0&0&i(1-r)&1\end{array}\right)\quad\mbox{with}\quad
x=\left(\begin{array}{c}x^1\\x^2\\x^3\\\tau\end{array}\right)\quad,\quad
k=\left(\begin{array}{c}k_1\\k_2\\k_3\\k_4\end{array}\right)\,.
\end{equation}
$K_1$ is the modified Bessel function, and $m=M$ in our free-field model. It
is easy to see that $x^TA_r^{-1}x\simeq 2r\tau^2$ for $x=(\vec{0},\tau)$
and $r\to 0$. According to Eq.~(\ref{egf}), this means that the correlation
length in the Euclidean time direction diverges and we are dealing with a
critical phenomenon.
\begin{figure}[ht]
\begin{center}
\vspace*{.2cm}
\parbox[b]{9cm}{\psfig{width=9cm,file=td.eps}}\\
\end{center}
\refstepcounter{figure}\label{td}
{\bf Figure \ref{td}:} The two diagrams contributing to the Euclidean
Green function $G_{\phi jj\phi}$ in the free-field case.
\end{figure}
To study in general the behaviour of $G(x)$ for $x\to\infty$ we set
\begin{equation}
x=R\hat{x}\qquad,\qquad R=|x|=\sqrt{x_1^2+x_2^2+x_3^2+\tau^2}
\end{equation}
and consider the limit $R\to\infty$ for fixed unit vector $\hat{x}$. We get
from Eq.~(\ref{egf}):
\begin{equation}
G(x)\longrightarrow\frac{1}{4\pi^2}\sqrt{\frac{\pi}{2}}\,M^2\left(M^2R^2
\hat{x}^TA_r^{-1}\hat{x}\right)^{-3/4}\!e^{-MR\sqrt{\hat{x}^TA_r^{-1}
\hat{x}}}\qquad\mbox{for}\qquad{R\to\infty}\,.
\end{equation}
Thus the decay of $|G(x)|$ as $R\to\infty$ is governed by exp$\left[-MR\,
\mbox{Re}\sqrt{\hat{x}^TA_r^{-1}\hat{x}}\,\right]$. This suggests to define
a correlation length depending on $\hat{x}$ as
\begin{equation}
\xi(\hat{x})=\left[M\,\mbox{Re}\sqrt{\hat{x}^TA_r^{-1}\hat{x}}\right]^{-1}
\,.
\end{equation}
We have, in the Euclidean time direction,
\begin{equation}
\xi(\vec{0},1)=\left[M\sqrt{r(2-r)}\right]^{-1}\label{xir} ~,
\end{equation}
and, in the space directions,
\begin{equation}
\xi(\vec{e}_j,0)=M^{-1}\,.
\end{equation}
Thus for $r\to 0$ the correlation in this free-field model becomes of long
range only in the time direction. There $\xi(\vec{0},1)$ diverges as
$1/\sqrt{r}$, i.e., in a manner characteristic of mean-field theories for
critical phenomena in statistical mechanics, identifying $r$ with $T-T_c$,
the deviation of the temperature from the critical value.
We also note the behaviour of $G(x)$, Eq.~(\ref{egf}), for $R\to 0$:
\begin{equation}
G(x)\longrightarrow\frac{1}{4\pi^2}\left(R^2\hat{x}A_r^{-1}\hat{x}
\right)^{-1}\qquad\mbox{for}\qquad R\to 0\,.
\end{equation}
In the Euclidean time direction this can be written as
\begin{equation}
G(\vec{0},\tau)\longrightarrow\frac{M^2}{4\pi^2}\left(\frac{\xi(\vec{0},1)}
{\tau}\right)^2\qquad\mbox{for}\qquad \tau\ll\xi(\vec{0},1)\,.\label{smt}
\end{equation}
This means that for times much smaller than the correlation length the
Green function in the free theory has a simple power behaviour, again
similar to what is found in the study of critical phenomena.
Now we describe the calculation of $T_+$ in Eq.~(\ref{tpme}) in the free-field
case. Changing the integration variables in Eq.~(\ref{tpme}) from $y_\pm$
to $y^0$ and $y^3$, using the expression of Eq.~(\ref{emeg}) for ${\cal
M}_E$, and calculating the Green function $G_{\phi jj\phi}$ according to
Fig.~\ref{td}, the amplitude $T_+$ reads
\begin{eqnarray}
T_+(i\eta,Q^2,\mu)&=&\frac{-1}{\pi^2\sqrt{\eta^2-Q^2}}\int_0^\infty dy^0
\int_{-y^3}^{y^3}dy^3\,y^3\,e^{\frac{1}{2}[(y^0+y^3)(\mu+i\eta_-)+
(y^0-y^3)(\mu+i\eta_+)]}\nonumber
\\
&&\times\left[e^{My^0}+e^{-My^0}\right]\frac{M}{\sqrt{(y^0)^2-(y^3)^2}}
K_1\left(M\sqrt{(y^0)^2-(y^3)^2}\right)\,.
\end{eqnarray}
Applying the identity
\begin{equation}
\frac{y^3M}{\sqrt{(y^0)^2-(y^3)^2}}K_1\left(M\sqrt{(y^0)^2-(y^3)^2}\right)
=\frac{\partial}{\partial y^3}K_0\left(M\sqrt{(y^0)^2-(y^3)^2}\right)\,,
\end{equation}
integrating by parts, and returning to the variables $y_\pm$, one finds
\begin{eqnarray}
T_+(i\eta,Q^2,\mu)&=&\frac{-i}{4\pi^2}\int_0^\infty dy_+
\int_0^\infty dy_-\,e^{\frac{1}{2}[y_+(\mu+i\eta_-)+y_-(\mu+i\eta_+)]}
\nonumber
\\
&&\times\left[e^{M(y_++y_-)/2}+e^{-M(y_++y_-)/2}\right]K_0\left(M
\sqrt{y_+y_-}\right)\,.
\end{eqnarray}
For sufficiently negative Re$\,\nu$, the integrals can be evaluated using
the relations 6.631.3, 9.224 and 6.224.1 of~\cite{gr}. The result is
\begin{equation}
T_+(i\eta,Q^2,\mu)=-\frac{i}{2\pi^2}\,\Big\{f(M)+f(-M)\Big\}
\end{equation}
with
\begin{equation}
f(M)=\frac{1}{\mu^2+2M\mu-Q^2+2i\eta(M\!+\!\mu)}\ln\left[\frac{1}{M^2}
\left\{(M\!+\!\mu)^2-Q^2+2i\eta(M\!+\!\mu)\right\}\right].
\end{equation}
When this expression is analytically continued to $\mu=0$, a careful
treatment of the imaginary part of the logarithms is essential. The
singularities of $T_+(i\eta,Q^2,\mu)$ in the complex $\mu$ plane are shown
in Fig.~\ref{sing}. The continuation in $\mu$ from Re$\,\mu<-M$ to $\mu=0$
has to be done along the real axis staying above the left hand
singularities.
\begin{figure}[ht]
\begin{center}
\vspace*{.2cm}
\parbox[b]{11cm}{\psfig{width=11cm,file=sing.eps}}\\
\end{center}
\refstepcounter{figure}\label{sing}
{\bf Figure \ref{sing}:} The singularities of $T_+(i\eta,Q^2,\mu)$ in the
complex $\mu$ plane. There are poles at $\pm M-i\tilde{\eta}_+$, $\pm M
-i\tilde{\eta}_-$ with $\tilde{\eta}_\pm=\eta\pm\sqrt{\eta^2-Q^2-M^2}$ and
logarithmic branch cuts starting at $\pm M-i\eta_+$ and $\pm M-i\eta_-$.
Here we assume $\eta^2>Q^2+M^2$.
\end{figure}
{}From Eq.~(\ref{trtp}) one finds the behaviour of the retarded amplitude
on the imaginary axis in the $\nu$ plane:
\begin{equation}
T_r(i\eta,Q^2)=\mbox{Re}\,T_+(i\eta,Q^2,0)=\frac{1}{2\pi}\left(\frac{1}
{Q^2-2i\eta M}+\frac{1}{Q^2+2i\eta M}\right)\,.
\end{equation}
The corresponding behaviour on the real axis follows from the analytic
continuation $i\eta\to\nu$ for $\nu$ real:
\begin{equation}
T_r(\nu,Q^2)=\frac{1}{2\pi}\left(\frac{1}{Q^2-2\nu M-i\varepsilon}+\frac{1}
{Q^2+2\nu M+i\varepsilon}\right)\,.
\end{equation}
This is in agreement with what one would have found by simply adding the
two diagrams for the forward scattering of a scalar proton and a scalar photon
in the original Minkowskian theory.
We will close this section with some speculative remarks. Looking at
Eq.~(\ref{tpme}) we see that for $\eta\to\infty$ the typical integration
range over ${\cal M}_E(y^0,r)$ is
\begin{equation}
0\,\,{\scriptstyle\leq}\,\,r\,\mst{<}{\sim}\,\frac{1}{\eta y^0}\,\,,
\label{rv}
\end{equation}
\begin{equation}
0\,\,{\scriptstyle\leq}\,\,y^0\,\mst{<}{\sim}\,\frac{2\eta}{Q^2}\equiv
y^0_m\,.
\end{equation}
Let us insert the mean value of $y^0$ of Eq.~(\ref{tpme}) into
Eq.~(\ref{rv}) to get as typical value for $r$:
\begin{equation}
\bar{r}=\frac{Q^2}{\eta^2}\,.
\end{equation}
Then we have two relevant scales for the $y^0$ integration in
Eq.~(\ref{tpme}): $y^0_m$ and the length scale of the decay of ${\cal M}_E
(y^0,\bar{r})$. Also in the general case of the theory with interactions
this should be governed by a correlation length $\xi(\bar{r})$ similar to
$\xi^{(0)}(\bar{r})\equiv\xi(\vec{0},1)$, Eq.~(\ref{xir}), in the free-field
case. Clearly the behaviour of the amplitude $T_+$ will depend
crucially on whether $y^0_m$ is smaller or bigger than $\xi(\bar{r})$.
In the free-field case we have
\begin{equation}
y^0_m\,\,\mst{<}{>}\,\,\xi^{(0)}(\bar{r})\qquad\mbox{for}\qquad Q^2\,\,
\mst{>}{<}\,\,8M^2\,.
\end{equation}
Here for large $Q^2$ and $\eta\to\infty$ the integration in
Eq.~(\ref{tpme}) probes only the region of ${\cal M}_E(y^0,r)$ where $y^0$
is smaller than the correlation length and thus where Eq.~(\ref{smt})
applies. We can speculate that in the theory with interaction we should
again be able to distinguish two regimes,
\begin{equation}
y^0_m\,\,\mst{<}{>}\,\,\xi(\bar{r})\,,\label{tre}
\end{equation}
where, from our experience with critical phenomena, we would expect
$\xi(\bar{r})$ to satisfy a scaling law for $\bar{r}\to 0$,
\begin{equation}
\xi(\bar{r})\simeq\frac{c}{M}(\bar{r})^{-\rho}\,,\qquad c=\mbox{const.}\,,
\qquad\rho>0\,,
\end{equation}
but not with the mean field exponent $\rho=1/2$ as in Eq.~(\ref{xir}).
For $0<\rho<1$ the dividing line between the two regimes of Eq.~(\ref{tre})
would then be roughly:
\begin{equation}
\eta=\frac{2M}{c}\left(\frac{Qc}{2M}\right)^{\frac{\scriptstyle 2-2\rho}
{\scriptstyle 1-2\rho}}\label{dl}
\end{equation}
and it is tempting to speculate that this could correspond to the dividing
line between hard $[y^0_m<\xi(\bar{r})]$ and soft $[y^0_m>\xi(\bar{r})]$
pomeron regimes. But much more work is needed before such a conjecture can
be substantiated.
Let us, nevertheless, assume for the moment that such a conjecture is true
and apply Eq.~(\ref{dl}) also in the physical region, replacing $\eta$ by
$\nu$. Then we should find a dividing line between hard and soft pomeron
effects in the structure functions in the $x_{\mbox{\scriptsize Bj}}$ versus $Q^2$ plane:
\begin{equation}
Q^2=\frac{4M^2}{c^2}(cx_{\mbox{\scriptsize Bj}})^{2-\frac{\scriptstyle 1}{\scriptstyle \rho}}\,.
\label{q2xf}
\end{equation}
This is illustrated in Fig.~\ref{q2x}. Thus, taking the limit $x_{\mbox{\scriptsize Bj}}\to 0$
at fixed $Q^2>0$ we would finally always go from the hard to the soft
regime for $0<\rho<1/2$ and vice versa for $1/2<\rho<1$.
\begin{figure}[ht]
\begin{center}
\vspace*{.2cm}
\parbox[b]{11.5cm}{\psfig{width=11.5cm,file=q2x.eps}}\\
\end{center}
\refstepcounter{figure}\label{q2x}
{\bf Figure \ref{q2x}:} Sketch of the regions of soft and hard pomeron
effects in the $x_{\mbox{\scriptsize Bj}}$--$Q^2$ plane using Eq.~(\ref{q2xf}).
\end{figure}
\section{Alternative analytic continuations to Euclidean space}\label{alt}
\setcounter{equation}{0}
It is clear that the form of the analytic continuation from the Minkowski
to the Euclidean theory discussed in the previous sections is by no means
unique. Other possible forms of analytic continuations from Minkowski to
Euclidean space can be derived: in this section we discuss two of these
alternative Euclidean formulations and compare them with the one of
Sect.~\ref{mieu}.
Working in the rest frame of the proton, consider the quantity
\begin{equation}
T(q^0,\vec{q}\,) = {i \over 2\pi} \int d^4x\,\theta (x^0) e^{iqx}
\langle P(p) \vert J(x) J(0) \vert P(p) \rangle\label{tdef}
\end{equation}
as an analytic function of $q^0$ with the spatial part $\vec{q}$ fixed and
real. Using standard methods, one finds
\begin{equation}
T(q^0,\vec{q}\,) = -\sum_X(2\pi)^2 \delta^{(3)} (\vec{q} - \vec{p}\,')
{1 \over q^0 +M - p'^0}\vert \langle P(p) \vert J(0) \vert X(p') \rangle
\vert^2\,,\label{nt}
\end{equation}
which reveals the cut along the positive real axis. The structure function
of Eq.~(\ref{sf}) is related to $T$ by
\begin{equation}
{\rm Im} [ T(q^0 + i\varepsilon,\vec{q}\,) ] = W(\nu,Q^2) ~,
\end{equation}
where $\varepsilon \to 0+$.
Now, consider $T(q^0,\vec{q}\,)$ on the positive imaginary axis, i.e., for
$q^0 = i\eta$ with $\eta > 0$. Using the identity
\begin{equation}
{1 \over i\eta+M-p'^0}=-\int_0^{+\infty} dx_4
e^{(i\eta +M-p'^0)x_4}
\end{equation}
(where the problematic lowest value of $p'^0$, $p'^0=M$, can be treated by
giving $\eta$ a small positive imaginary part), the following expression
for $T$ is obtained from Eq.~(\ref{nt}):
\begin{equation}
T(i\eta,\vec{q}\,) = {1 \over 2\pi} \displaystyle\int d^3\vec{x}
\int_0^{+\infty} dx_4 e^{i(\eta x_4 - \vec{q} \cdot \vec{x})}\langle P(p)
\vert J_E(\vec{x},x_4) J_E(0) \vert P(p) \rangle ~.\label{tje}
\end{equation}
Here $J_E(\vec{x},x_4)$ is the current of the conventional Euclidean
theory:
\begin{equation}
J_E(\vec{x},x_4) = e^{H x_4} J(0,\vec{x}) e^{-H x_4} ~.
\label{jedef}
\end{equation}
Using the methods of Sect.~\ref{camp} [cf.~Eqs.~(\ref{rot}) and
(\ref{trm})], invariance under spatial rotations can be employed to
further simplify the above expression for $T$.
To summarize, the amplitude $T$ on the real axis, which determines the
physical structure function, can be obtained from the one on the imaginary
axis by analytic continuation in $q^0$: $(q^0=i\eta)\,\to\,(q^0=\nu)$.
According to Eq.~(\ref{tje}), the latter one can be calculated from a
conventional Euclidean matrix element.
This approach is simpler than the one discussed in the previous sections
in that the Euclidean theory is based on the usual Hamiltonian $H$ and not
on the more complicated effective Hamiltonian of Eq.~(\ref{heff}). However,
in order to derive the large-$\nu$ behaviour of the structure function
$W(\nu,Q^2)$ at fixed $Q^2$, one needs the analytic continuation of
$T(q^0,\vec{q}\,)$ in $q^0$ for every value of $\vec{q}$. Only at this
point can one study the asymptotic limit $\nu \to \infty$, which involves
both $q^0\to\infty$ and $|\vec{q}\,|\to\infty$ in the physical region. This
analytic continuation in $q^0$ is expected to be more troublesome than
the $\mu$ continuation of Sect.~\ref{camp}, which is decoupled from the
high-energy limit.
We consider now a third possible form of analytic continuation from
Minkowski to Euclidean space, which is close in spirit to~\cite{meg}.
The basic object is still the virtual Compton amplitude Eq.~(\ref{tr}),
which we write now as:
\begin{equation}
T_r(\nu,Q^2)=\frac{1}{2}\left(\tilde{T}_+(q)+\tilde{T}_+^*(-q^*)\right)\,
\label{ntr}
\end{equation}
where
\begin{equation}
\tilde{T}_+(q)=\frac{i}{\pi}\int d^4x\,\theta(x^0)\theta((x^0)^2-(x^3)^2)
\,e^{iqx}\,\langle P(p)|J(x)J(0)|P(p)\rangle\,.
\end{equation}
Here we work in the rest system of the proton and choose now $q$ in the
form
\begin{equation}
q = (\nu,\vec{e}_\perp\sqrt{\nu^2 + Q^2}, 0)\,,
\end{equation}
with $\vec{e}_\perp$ a unit vector in the $(q^1,q^2)$ plane. With the
parametrization $x=(\xi\cosh\chi,\vec{x}_\perp,\xi\sinh\chi)$, we find
\begin{equation}
\tilde{T}_+(q)={i\over\pi}\int d^2\vec{x}_\perp\,e^{-i\vec{e}_\perp \cdot
\vec{x}_\perp\sqrt{\nu^2+Q^2}}\int_{-\infty}^{+\infty}d\chi\int_0^{+\infty}
d\xi \xi\,e^{i\nu\xi\cosh\chi}\langle P(p)\vert J(x)J(0)\vert P(p)
\rangle ~.
\end{equation}
We will show how to compute this quantity and its $\nu$ derivatives at
$\nu = 0$ using an analytic continuation from Minkowski to Euclidean
space. First of all, we write
\begin{equation}
\tilde{T}_+(q)\vert_{\nu =0}=\int d^2\vec{x}_\perp\,e^{-i\vec{q}_\perp \cdot
\vec{x}_\perp}\int_{-\infty}^{+\infty} d\chi A^{(1)}(\chi,\vec{x}_\perp) ~,
\end{equation}
where $\vec{q}_\perp=Q\vec{e}_\perp$ and the function $A^{(1)}$ is defined
by
\begin{eqnarray}
A^{(1)}(\chi,\vec{x}_\perp)&=&{i\over\pi}\int_0^{+\infty}d\xi\xi\langle
P(p)\vert J(x) J(0) \vert P(p) \rangle \nonumber
\\
&=& {-i \over\pi} \sum_X\langle P(p) \vert J(0,\vec{x}_\perp,0) \vert
X(p') \rangle \langle X(p') \vert J(0) \vert P(p) \rangle \nonumber
\\
& & \times {1 \over \left[ (p'^0 - M) \cosh\chi - p'^3 \sinh\chi - i
\varepsilon\right]^2} ~,
\end{eqnarray}
where finally the limit $\varepsilon \to 0+$ is taken. The singularity
structure in the complex $\chi$ plane is such that the function can be
continued to the imaginary axis, $\chi\to i\theta$ where, however, the
$\theta$ range is restricted by $\theta\in(-\pi/2,\pi/2)$. In this region,
$A^{(1)}$ is related to a Euclidean matrix element,
\begin{eqnarray}
A^{(1)}(i\theta,\vec{x}_\perp) &=&
{-i \over\pi} \displaystyle\int_0^{\infty} d\xi \xi
\langle P(p) \vert J_E(x_E) J_E(0) \vert P(p) \rangle\nonumber \\
&=& {-i \over\pi} \displaystyle\sum_X
\langle P(p) \vert J(0,\vec{x}_\perp,0) \vert X(p') \rangle
\langle X(p') \vert J(0) \vert P(p) \rangle \nonumber \\
& & \times {1 \over \left[ (p'^0 - M) \cos\theta - ip'^3 \sin\theta
-i\varepsilon\right]^2} ~,
\end{eqnarray}
where $x_E=(\vec{x}_\perp, \xi \sin\theta, \xi \cos\theta)$ is a Euclidean
four-vector and the Euclidean current $J_E(x_E)$ is defined by
Eq.~(\ref{jedef}).
More generally, the expression for the $n$-th derivative of $\tilde{T}_+$
with respect to $\nu$, evaluated at $\nu = 0$, reads
\begin{equation}
\partial^n_\nu\tilde{T}_+(q)\vert_{\nu =0}=\sum_{l=0}^n\int d^2
\vec{x}_\perp e^{-i\vec{q}_\perp \cdot \vec{x}_\perp} C_l^n(\vec{q}_\perp\!
\cdot\!\vec{x}_\perp,Q^2)\int_{-\infty}^{+\infty} d\chi (\cosh\chi)^l A^{(l+1)}
(\chi,\vec{x}_\perp) ~,\label{cl}
\end{equation}
with explicitly calculable coefficients $C_l^n$ and functions $A^{(l)}$
defined by
\begin{eqnarray}
A^{(l)}(\chi,\vec{x}_\perp)&=&{i\over\pi}\int_0^{\infty} d\xi \xi^l
\langle P(p) \vert J(x) J(0) \vert P(p) \rangle\nonumber \\
& & = {(-i)^l l! \over\pi}\sum_X\langle P(p) \vert J(0,\vec{x}_\perp,0)
\vert X(p') \rangle\langle X(p') \vert J(0) \vert P(p) \rangle \nonumber \\
&&\times {1 \over \left[ (p'^0 - M) \cosh\chi - p'^3 \sinh\chi - i\varepsilon
\right]^{l+1}} ~.
\end{eqnarray}
As in the case $l = 1$, the values of this function for real $\chi$ can be
obtained from
\begin{eqnarray}
A^{(l)}(i\theta,\vec{x}_\perp)&=&{(-i)^l \over\pi} \int_0^\infty d\xi
\xi^l\langle P(p) \vert J_E(x_E) J_E(0) \vert P(p) \rangle\nonumber \\
& & = {(-i)^l l! \over\pi} \sum_X\langle P(p) \vert J(0,\vec{x}_\perp,0)
\vert X(p') \rangle \langle X(p') \vert J(0) \vert P(p) \rangle \nonumber\\
&& \times {1 \over \left[ (p'^0 - M) \cos\theta - ip'^3 \sin\theta
-i\varepsilon \right]^{l+1}} ~.
\end{eqnarray}
by the analytic continuation $i\theta \to \chi$.
To summarize, one first computes $A^{(l)}(i\theta,\vec{x}_\perp)$ for $l=1,
\ldots, n+1$ and $\theta\in(-\pi/2,\pi/2)$ in the Euclidean field theory (for
example, on the lattice). Then, the value of $\partial^n_\nu \tilde{T}_+(q)
\vert_{\nu = 0}$ can be obtained from Eq.~(\ref{cl}) using the analytic
continuations of the $A^{(l)}$ to the real axis. Thus, using
Eq.~(\ref{ntr}) and a Taylor expansion of $\tilde{T}_+$ around $\nu = 0$,
the behaviour of $T_r(\nu,Q^2)$ at small $\nu$ (corresponding to large
$x_{\mbox{\scriptsize Bj}}$) can be studied. The values of $\partial^n_\nu T_r(\nu,Q^2)\vert_{
\nu = 0}$ can then be related to integrals of the structure function
$W(\nu, Q^2)$ using dispersion relations in $\nu$. Assuming for simplicity
no subtractions this reads:
\begin{equation}
T_r(\nu,Q^2)=\frac{1}{\pi}\int_{Q^2/2M}^\infty d\nu'\,W(\nu',Q^2)\left[
\frac{1}{\nu'-\nu-i\varepsilon}+\frac{1}{\nu'+\nu+i\varepsilon}\right]\,,
\end{equation}
\begin{equation}
\partial^n_\nu T_r(\nu,Q^2) \vert_{\nu = 0}=\frac{n!}{\pi}
\int_{Q^2/2M}^\infty d\nu' {W(\nu', Q^2) \over (\nu')^{n+1}}[1+(-1)^n]\,,
\qquad (n=0,1,2,...)\,.
\end{equation}
Again, the advantage with respect to the method of Sect.~\ref{mieu} is
the use of the conventional Hamiltonian in the Euclidean theory. The
disadvantage is the limited sensitivity to the region of small $x_{\mbox{\scriptsize Bj}}$.
\section{Conclusions}\label{conc}
\setcounter{equation}{0}
In this paper, a fundamentally new approach to the long-standing problem of
small-$x_{\mbox{\scriptsize Bj}}$ structure functions in DIS has been developed. It is based on
the well-known relation of the small-$x_{\mbox{\scriptsize Bj}}$ limit of DIS and the high-energy
limit of forward virtual Compton scattering. Instead of taking the energy
of the forward virtual Compton amplitude to infinity along the real axis,
we propose to consider the limit of large imaginary energy. According to
the theorems of Phragm\'{e}n and Lindel\"of type, the asymptotic behaviour
in both directions is related by analytic continuation.
A slight generalization of the above virtual Compton amplitude with
imaginary energy, which contains an additional mass variable $\mu$ for
convergence, can be written as an integral over a matrix element in an
effective Euclidean field theory. Using standard methods, this matrix
element is expressed in terms of a Euclidean functional integral with a
simple effective Lagrangian, which is given explicitly. The essential
proposal of our paper is to attempt an evaluation of this functional
integral using genuinely non-perturbative methods, e.g., lattice
Monte-Carlo simulations. Finally, an analytic continuation to $\mu=0$ and
to the real axis in the complex energy plane should allow the extraction
of the desired asymptotic small-$x_{\mbox{\scriptsize Bj}}$ limit of DIS structure functions.
To illustrate how our approach works, we have explicitly performed all
necessary steps in a simple model with free scalar fields. In this case,
the Euclidean path integral is given by two tree-level Feynman diagrams and
the subsequent analytic continuations in $\mu$ and the energy variable can
be carried out explicitly. As expected, the final result for the structure
function is in agreement with a direct diagrammatic calculation in
Minkowski space.
We have shown that in the free-field case the high-energy limit of the
virtual Compton amplitude is governed by the behaviour of the effective
Euclidean theory near the critical point $r=0$, where $r$ is our parameter
defined in Eq.~(\ref{reta}). We have then assumed that also in the
effective theory with interaction a critical point occurs at $r=0$ and
discussed the possible consequences of this for the hard and soft pomeron
regimes of the structure function.
We do not claim that we have found the optimal method for an analytic
continuation of high-energy amplitudes. In fact, in Sect.~\ref{alt} of this
paper we introduce two alternative possibilities. They have the advantage
that the Euclidean field theory obtained is based on the conventional
Hamiltonian as opposed to the effective Hamiltonian required in the
original approach. However, in both cases it appears to be more difficult
to recover the small-$x_{\mbox{\scriptsize Bj}}$ limit of structure functions from the final
result of the calculation.
A lot of work remains to be done before phenomenologically relevant
information can be extracted from the approach suggested. Note first that
all of the discussion in the present paper is based on a model with a
scalar `photon' coupled to scalar partons. This has to be extended to the
realistic case of a vector photon and QCD. However, we do not expect any
fundamental problems with this generalization.
Furthermore, the feasibility of a lattice calculation or any alternative
non-per\-tur\-bative treatment of our Euclidean path integral expression has
to be evaluated. Note that our effective Lagrangian contains an imaginary
part, which, even though it does not raise any fundamental problems, may
lead to technical difficulties on the lattice. Note also that the
subsequent analytic continuation back to the physical region could prove
highly non-trivial.
On a more fundamental level, one has to ask whether better methods for the
treatment of the small-$x_{\mbox{\scriptsize Bj}}$ limit of DIS in a Euclidean theory exist. We
have attempted to address this question in our cursory discussion of
alternative methods of analytic continuation. However, we are not able to
give a general answer at present.
Given the above reservations, the importance of our results lies in their
potential to relate small-$x_{\mbox{\scriptsize Bj}}$ cross sections in DIS to quantities
derivable from an effective Euclidean field theory. One can then hope to
understand the limit $x_{\mbox{\scriptsize Bj}}\to 0$ in terms of the critical behaviour in this
Euclidean theory using all the tools which have been developed in
statistical mechanics for the study of criticality. Also one can hope
to calculate the relevant quantities on the lattice. This goal is
fundamental since lattice calculations remain practically the only
non-perturbative method in QFT that can be derived strictly from first
principles. Thus, it is certainly worthwhile to continue the exploration of
possibilities to obtain high-energy or small-$x_{\mbox{\scriptsize Bj}}$ cross sections from
Euclidean quantities.\\[.4cm]
{\bf Acknowledgements}\\[.1cm]
The authors are grateful to A. Donnachie, H.G. Dosch, P.V. Landshoff,
F. Lenz and H.Ch. Pauli for useful discussions.
\section*{Appendix}
\begin{appendix}
\section{Considerations concerning the analytic continuation of amplitudes
in the $\nu$ plane}\label{rac}
\setcounter{equation}{0}
\renewcommand{\theequation}{\ref{rac}.\arabic{equation}}
Here we will first discuss the analytic continuation of $T_r(\nu,Q^2)$,
Eq.~(\ref{trm}), from real values of $\nu$ into the half plane Im$\,\nu>0$,
where we have
\begin{equation}
\mbox{Im}\,\nu>\mbox{Im}\,\sqrt{\nu^2+Q^2}\ge 0\,.\label{die}
\end{equation}
Proof: the second inequality is obvious. The first inequality holds for
imaginary $\nu$. By continuity, the inequality can only be violated if
there exists some $\nu$ in the upper half plane such that
\begin{equation}
\mbox{Im}\,\nu=\mbox{Im}\,\sqrt{\nu^2+Q^2}\,.
\end{equation}
Thus, for some $a\in I\!\!R$,
\begin{equation}
\sqrt{\nu^2+Q^2}=\nu+a\,.
\end{equation}
Squaring this equation, one finds
\begin{equation}
Q^2=2\nu a+a^2\,,
\end{equation}
which can not be fulfilled for non-zero $Q$ and Im$\,\nu>0$. Therefore, the
first inequality in Eq.~(\ref{die}) holds everywhere in the upper half
plane and our proof is complete.
With Eq.~(\ref{die}) we find that the factor exp$(ix^0\nu-ix^3\sqrt{\nu^2+
Q^2})$ in Eq.~(\ref{trm}) decreases exponentially for Im$\,\nu>0$ as
$x^0\to\infty$ with $|x^3|/x^0\le 1$. Thus the integral in Eq.~(\ref{trm})
should be well convergent and define an analytic function in $\nu$ for
Im$\,\nu>0$. There is still the possibility of $T_r(\nu,Q^2)$ having a cut
on the imaginary $\nu$ axis for $0\le\mbox{Im}\,\nu\le Q$ due to the
explicit factor $\sqrt{\nu^2+Q^2}$ in Eq.~(\ref{trm}). But using
Eq.~(\ref{rot}) it is easy to see that the values of $T_r(\nu,Q^2)$ when
approaching the imaginary axis from both sides are equal. Then the ``edge of
the wedge'' theorem (cf., e.g., \cite{eotw}) guarantees that $T_r(\nu,Q^2)$ is
also analytic for $0<\mbox{Im}\,\nu<Q$. The point $\nu=iQ$ could still be
an isolated singularity but this is incompatible with the square root in
Eq.~(\ref{trm}). This concludes our discussion of the analyticity of
$T_r(\nu,Q^2)$ for Im$\,\nu>0$.
The discussion of the analyticity of $T_+(\nu,Q^2,\mu)$ defined as in
Eq.~(\ref{tp}) but with $i\eta$ replaced by $\nu$ is analogous. The proof
of Eq.~(\ref{trtp}) for $0<\eta<Q$ is straightforward using
Eq.~(\ref{rot}).
In the remainder of this appendix we will discuss the connection between
the limits $\nu\to\infty$ either on the real or the positive imaginary
axis. We will outline one possibility of specifying the requirements for
guaranteeing that the analytic continuation of the asymptotic behaviour of
the amplitude from the real to the imaginary axis is possible.
The retarded amplitude $T_r(\nu,Q^2)$ is an analytic function of $\nu$ with
cuts along the positive and negative real axis (Fig.~\ref{nup}). Let us
assume that there exists a function $f(\nu)$ analytic for Im$\,\nu>0$ such
that $f(\nu)\neq 0$ for Im$\,\nu\ge 0$, and
\begin{equation}
R(\nu)\equiv \frac{T_r(\nu,Q^2)}{f(\nu)}\label{rdef}
\end{equation}
is a bounded function, $|R(\nu)|\le\,$const. for Im$\,\nu\ge 0$. (Since
$Q^2$ is kept fixed we suppress this argument in $R(\nu)$ and $f(\nu)$.)
Let us furthermore assume that
\begin{equation}
\lim_{\eta\to\pm\infty}R(\eta)=C_{\pm}\,.\label{cpm}
\end{equation}
Then the Phragm\'{e}n-Lindel\"of theorem (see theorem 5.64 of~\cite{pl})
states that $C_+=C_-$ and that $R(\nu)$ approaches the same limit $C_+$
along any ray $\nu=\eta\exp(i\phi)$, $0\le\phi\le\pi$, $\phi=$\,const.,
$\eta\to +\infty$. Thus we have also on the imaginary axis
\begin{equation}
\lim_{\eta\to +\infty}R(i\eta)=C_+\,.\label{cpl}
\end{equation}
Suppose now that from the study of $T_r(i\eta,Q^2)$, e.g., by lattice
calculations, we can deduce the asymptotic behaviour for $\eta\to\infty$,
construct a suitable function $f(i\eta)$ and deduce the value of the
constant $C_+$ [Eq.~(\ref{cpl})] with $C_+\neq 0$.
Typically one would try to fit lattice data to functions reflecting our
general expectations concerning the high-energy behaviour of amplitudes
in QFT like $f(\nu)=(\nu-\nu_0)^\alpha$ or $f(\nu)=(\nu-\nu_0)^\alpha
\ln(\nu-\nu_0)$. Here $\alpha$ should be taken as a real constant and
$\nu_0$ as a constant with Im$\,\nu_0<0$. With the assumptions specified in
Eqs.~(\ref{rdef}) and (\ref{cpm}) we get for the physical amplitude on the
real axis:
\begin{equation}
T_r(\nu,Q^2)\,\longrightarrow\,C_+f(\nu)\qquad\mbox{for}\qquad\nu\to\infty
\,.
\end{equation}
To summarize: if we {\it assume} that the limit of $T_r(\nu,Q^2)$ for
$\nu\to\infty$, $0\le\mbox{arg}\,\nu\le\pi$ is governed by a suitable
analytic function $f(\nu)$, then this function can be {\it determined} from
the study of $T_r(\nu,Q^2)$ on the positive imaginary axis.
We have only outlined here the simplest assumptions making the analytic
continuation of the high-energy limits on the real and imaginary axes
possible. No doubt, using the methods of~\cite{cm} one can relax these
assumptions and still get useful relations between the two limits.
\section{The functional integrals for ${\cal M}_E$ and ${\cal M}_M$}
\label{fic}
\setcounter{equation}{0}
\renewcommand{\theequation}{\ref{fic}.\arabic{equation}}
In this appendix we give the details of the derivation of Eq.~(\ref{emer}).
We start with Eq.~(\ref{eme}) and using Eq.~(\ref{lsze}) rewrite it as
\begin{eqnarray}
{\cal M}_E(\tau,r)&\!\!\!\!\!=\!\!\!\!&\frac{1}{Z}\lim_{\tau_i\to-\infty
\atop\tau_f\to+\infty}\lim_{\tau_i'\to-\infty\atop\tau_f'\to+\infty}\,
e^{(\tau_f-\tau_i)M}\,\langle 0|\,e^{-(\tau_f'-\tau_f)H_{eff}(r)}\,A(0)\,
e^{-(\tau_f-\tau)H_{eff}(r)}\,\label{mea}\\
\nonumber\\
&&\times J(0)\,e^{-(\tau-0)H_{eff}(r)}\,J(0)\,e^{-(0-\tau_i)H_{eff}(r)}\,
A^\dagger(0)\,e^{-(\tau_i-\tau_i')H_{eff}(r)}\,|0\rangle\Bigg/
e^{-(\tau_f'-\tau_i')E_0}\,.\nonumber
\end{eqnarray}
Here we have introduced further times $\tau_i'$, $\tau_f'$ with $\tau_i'
<\tau_i<\tau_f<\tau_f'$ and the limits in Eq.~(\ref{mea}) are to be taken
in the order indicated there.
Let $|\phi\rangle$ be eigenstates of the field operator $\Phi(x)$ at
$x^0=0$:
\begin{equation}
\Phi(\vec{x},0)|\phi\rangle=\phi(\vec{x})|\phi\rangle\,,
\end{equation}
where $\phi(\vec{x})$ are classical functions. We have
\begin{equation}
\int D\phi\,|\phi\rangle\langle\phi|={\bf 1}\,.\label{one}
\end{equation}
The basic relation of the path integral formalism~\cite{pi}
discussed in many textbooks (see, e.g.,~\cite{wein}) is in our case
\begin{eqnarray}
\langle \phi^{(2)}|\,e^{-\Delta\tau\,H_{eff}(r)}\,|\phi^{(1)}\rangle &=&
\int D\pi^{(2)}\,e^{i\int d^3\vec{x}\left[\pi^{(2)}(\vec{x})\left(\phi^{(2)}
(\vec{x})-\phi^{(1)}(\vec{x})\right)+i\Delta\tau\,{\cal H}_r\left(\pi^{(2)}
(\vec{x}),\phi^{(2)}(\vec{x})\right)\right]}\nonumber
\\
&&+{\cal O}(\Delta\tau^2)\,,\label{pif}
\end{eqnarray}
where the measure includes a factor $1/(2\pi)$ for each $\pi^{(2)}(\vec{x}
)$ integration. Here $\pi^{(2)}(\vec{x})$ is the classical momentum field
and ${\cal H}_r$ the classical Hamilton density corresponding to $H_{eff}
(r)$:
\begin{equation}
{\cal H}_r(\pi,\phi)=\frac{1}{2}\pi(\vec{x})^2+(1-r)\pi(\vec{x})
\partial_3\phi(\vec{x})+\frac{1}{2}\left(\vec{\nabla}\phi(\vec{x})\right)^2
+\frac{1}{2}m^2\phi(\vec{x})^2+\frac{\lambda}{4!}\phi(\vec{x})^4\,.
\end{equation}
Next we choose a grid on the time interval $[\tau_i',\tau_f']$: $\tau_i'
\equiv\tau^{(0)}<\tau^{(1)}<\tau^{(2)}\cdots<\tau^{(N)}\equiv\tau_f'$,
where also $\tau_i$, 0, $\tau$, $\tau_f$ should occur as intermediate
points $\tau^{(j)}$. We discuss the factor exp$[-(\tau_f'-\tau_i')E_0]$
which we rewrite using Eqs.~(\ref{one}) and (\ref{pif}) as:
\begin{eqnarray}
e^{-(\tau_f'-\tau_i')E_0}&=&\langle 0|\,e^{-(\tau_f'-\tau_i')H_{eff}(r)}|0
\rangle
\\
&=&\langle 0|e^{-(\tau^{(N)}-\tau^{(N-1)})H_{eff}(r)}\,\cdots\,
e^{-(\tau^{(1)}-\tau^{(0)})H_{eff}(r)}\,|0\rangle\nonumber
\\
&=&\int\prod_{j=0}^N D\phi^{(j)}\,\langle 0|\phi^{(N)}\rangle\langle
\phi^{(N)}|\,e^{-(\tau^{(N)}-\tau^{(N-1)})H_{eff}(r)}\,|\phi^{(N-1)}
\rangle\nonumber
\\
&&\cdots\langle\phi^{(1)}|\,e^{-(\tau^{(1)}-\tau^{(0)})H_{eff}(r)}\,|
\phi^{(0)}\rangle\langle\phi^{(0)}|0\rangle\,,\nonumber
\end{eqnarray}
\begin{eqnarray}
e^{-(\tau_f'-\tau_i')E_0}&=&\lim_{N\to\infty\atop\Delta\tau\to 0}
\int\prod_{j=0}^N D\phi^{(j)}\prod_{j=1}^N D\pi^{(j)}\langle 0|\phi^{(N)}
\rangle\label{efi}
\\
&&\hspace*{-3cm}
\times\prod_{j=1}^N e^{i\int d^3\vec{x}^{(j)}\left[\pi(\vec{x}^{(j)},\tau^{(j)})
\left(\phi(\vec{x}^{(j)},\tau^{(j)})-\phi(\vec{x}^{(j)},\tau^{(j-1)})\right)
+i(\tau^{(j)}-\tau^{(j-1)}){\cal H}_r(\pi(\vec{x}^{(j)},\tau^{(j)}),
\phi(\vec{x}^{(j)},\tau^{(j)})\right]}\langle\phi^{(0)}|0\rangle\,.
\nonumber
\end{eqnarray}
Here we set $\phi^{(j)}(\vec{x})\equiv\phi(\vec{x},\tau^{(j)})$ and
$\pi^{(j)}(\vec{x})\equiv\pi(\vec{x},\tau^{(j)})$.
Now the integration over the $\pi$ fields in Eq.~(\ref{efi}) can be
performed since the integral is of Gaussian type. In the limit
$N\to\infty$, $\Delta\tau\to 0$ we get
\begin{equation}
e^{-(\tau_f'-\tau_i')E_0}={\cal C}\int D\phi\,e^{-\int_{\tau_i'}^{\tau_f'}
d\tau\int d^3\vec{x}\,{\cal L}_{E,\,eff}(\vec{x},\tau)}\,,
\end{equation}
where ${\cal L}_{E,\,eff}$ is given in Eq.~(\ref{el}) and ${\cal C}$ is a
constant (which is infinite). Performing the same steps for the matrix
element in the numerator in Eq.~(\ref{mea}) and taking the limit
$\tau_i'\to -\infty$, $\tau_f'\to+\infty$ we get the expression for
${\cal M}_E(\tau,r)$ of Eq.~(\ref{emer}). If we perform the analogous
steps for the Minkowskian matrix element, Eq.~(\ref{mme}), we get:
\begin{equation}
{\cal M}_M(t,r)=\frac{1}{Z}\lim_{t_i\to-\infty\atop t_f\to+\infty}
\,e^{i(t_f-t_i)M}\,{\cal Z}^{-1}\int D\phi\, a(t_f)j(t)j(0)a^\dagger
(t_i)\,e^{i\int d^4x\,{\cal L}_{M,\,eff}}\,,
\end{equation}
\begin{equation}
{\cal Z}=\int D\phi\,e^{i\int d^4x\,{\cal L}_{M,\,eff}}\,,
\end{equation}
with
\begin{equation}
{\cal L}_{M,\,eff}=\frac{1}{2}\Big(\partial_0{\phi}(x)-(1-r)\,\partial_3
\phi(x)\Big)^2-\frac{1}{2}\Big(\nabla\phi(x)\Big)^2-\frac{m^2}{2}\phi(x)^2-
\frac{\lambda}{4!}\phi(x)^4\,
\end{equation}
and
\begin{eqnarray}
a(t_f)&=&\int_{x^0=t_f}d^3\vec{x}\,\Big(i\partial_0{\phi}
(x)-i(1-r)\,\partial_3\phi(x)+M\phi(x)\Big)\,,\\
a^\dagger(t_i)&=&\int_{x^0=t_i}d^3\vec{x}\,\Big(-i\partial_0{\phi}
(x)+i(1-r)\,\partial_3\phi(x)+M\phi(x)\Big)\,.
\end{eqnarray}
\end{appendix}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 8,724
|
The writing of academic essays has been going on seemingly forever. As a student you should understand that the various stages involved in writing an academic essay have pretty much remained unchanged again seemingly forever. You would be making a serious mistake to try and reinvent the wheel. Know what the important stages of writing an academic essay are and follow them religiously. Also many students buy essays to make their life easy. And by all means make your actual writing as interesting and as relevant as possible as far as the structure is concerned; learn it and use it.
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|
{
"redpajama_set_name": "RedPajamaC4"
}
| 88
|
Q: How to know when AVPlayerItem is playing I am having a problem with AVPlayerItem and AVQueuePlayer. Currently i have a lot of music files which are 1-2 sec long and a queue Player for playing them in sequence.
What I want is to know when a music file has just started playing and not when it has finished playing(via AVPlayerItemDidPlayToEndTimeNotification).
This is because i want to run a function when a new file is loaded and played.
My code:
for (NSUInteger i = 0; i < [matchedAddr count]; i++)
{
NSString *firstVideoPath = [[NSBundle mainBundle] pathForResource:[matchedAddr objectAtIndex:i] ofType:@"wav"];
//NSLog(@"file %@",firstVideoPath);
avitem=[AVPlayerItem playerItemWithURL:[NSURL fileURLWithPath:firstVideoPath]];
[[NSNotificationCenter defaultCenter] addObserver:self
selector:@selector(currentItemIs:)
name:AVPlayerItemDidPlayToEndTimeNotification
object:avitem];
[filelist addObject:avitem];
}
player = [AVQueuePlayer queuePlayerWithItems:filelist];
[player play];
- (void)currentItemIs:(NSNotification *)notification
{
NSString *asd=[seqArray objectAtIndex:currentColor];
currentColor=currentColor+1;
AVPlayerItem *p = [notification object];
[p seekToTime:kCMTimeZero];
if([asd isEqual:@"1"])
{
[UIView animateWithDuration:0.01 animations:^{
one.alpha = 0;
} completion:^(BOOL finished) {
[UIView animateWithDuration:0.01 animations:^{
one.alpha = 1;
}];
}];
}
}
As you can see,the currentItemIs void is called but it runs when the track has finished playing.I want to be called when the track is at the beginning.
EDIT:
Updated version of Winston's snippet:
NSString * const kStatusKey = @"status";
[avitem addObserver:self
forKeyPath:kStatusKey
options:NSKeyValueObservingOptionInitial | NSKeyValueObservingOptionNew
context:@"AVPlayerStatus"];
- (void)observeValueForKeyPath:(NSString *)path
ofObject:(id)object
change:(NSDictionary *)change
context:(void *)context {
if (context == @"AVPlayerStatus") {
AVPlayerStatus status = [[change objectForKey:NSKeyValueChangeNewKey] integerValue];
switch (status) {
case AVPlayerStatusUnknown: {
}
break;
case AVPlayerStatusReadyToPlay: {
// audio will begin to play now.
NSLog(@"PLAU");
[self playa];
}
break;
}
}
}
A: First you need to register your AVPlayerItem as an observer:
[self.yourPlayerItem addObserver:self
forKeyPath:kStatus
options:NSKeyValueObservingOptionInitial | NSKeyValueObservingOptionNew
context:AVPlayerStatus];
Then on your player Key Value Observer method you need to check for AVPlayerStatusReadyToPlay status, like so:
- (void)observeValueForKeyPath:(NSString *)path
ofObject:(id)object
change:(NSDictionary *)change
context:(void *)context {
if (context == AVPlayerStatus) {
AVPlayerStatus status = [[change objectForKey:NSKeyValueChangeNewKey] integerValue];
switch (status) {
case AVPlayerStatusUnknown: {
}
break;
case AVPlayerStatusReadyToPlay: {
// audio will begin to play now.
}
break;
}
}
A: Following should work:
Observe the Player's State:
let playerItem: AVPlayerItem = AVPlayerItem(asset: videoPlusSubtitles, automaticallyLoadedAssetKeys: requiredAssetKeys)
playerItem.addObserver(self, forKeyPath: #keyPath(AVPlayerItem.status), options: [], context: nil)
player = AVPlayer(playerItem: playerItem)
Respond to a State Change:
override func observeValue(forKeyPath keyPath: String?, of object: Any?, change: [NSKeyValueChangeKey : Any]?, context: UnsafeMutableRawPointer?) {
if keyPath == #keyPath(AVPlayerItem.status) {
let status: AVPlayerItem.Status
if let statusNumber = change?[.newKey] as? NSNumber {
status = AVPlayerItem.Status(rawValue: statusNumber.intValue)!
} else {
status = .unknown
}
// Switch over status value
switch status {
case .readyToPlay:
print("Player item is ready to play.")
break
case .failed:
print("Player item failed. See error")
break
case .unknown:
print("Player item is not yet ready")
break
@unknown default:
fatalError()
}
}
}
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,249
|
\section{Introduction}
Thermal transport in silicon based materials has been extensively studied by classical molecular dynamics (MD) simulations \cite{volz2000prb,henry2008jctn,donaido2009prl,donaido2010nl,lampin2012apl,howell2012jcp,xiong2014prb,saaskilahti2016aipa,cartoix2016apl,zaoui2017prb,zhou2017nl,dong2018prb}. The results strongly depend on the empirical interatomic potential used. Quantitatively accurate empirical potentials for covalently bonded solids such as silicon are many-body in nature and cannot be expressed as sums of pairwise interactions. Among the various many-body empirical potentials, the Tersoff potential \cite{tersoff1988prb,tersoff1989prb} is the most frequently used for silicon. In addition to the original parametrizations by Tersoff \cite{tersoff1988prb,tersoff1989prb}, this potential has also been modified and/or re-parametrized by many other authors \cite{erhart2005prb,kumagai2007cms,Pun2017prb}. Although the Tersoff potential has a relatively simple form and low computational cost compared to many other many-body potentials, it can capture the essence of quantum-mechanical bonding \cite{brener2005}, justifying its widespread use in modeling \cite{mota1998prb,albe2002prb_1,albe2002prb,nord2003jpcm,erhart2006jpcm,munetoh2007cms,muller2007jpcm,powell2007prb,Henriksson2009prb,los2017prb,Byggmastar2018jpcm}.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=\columnwidth]{kappa_bar.eps}
\caption{Thermal conductivity of diamond silicon at 700 K and zero pressure from experiments \cite{Glassbrenner1964pr} and some commonly used empirical potentials using the homogeneous nonequilibrium molecular dynamics method \cite{Fan2019prb} as implemented in the GPUMD code \cite{fan2017cpc,gpumd}. Isotope scattering is taken into account here. See text for details.}
\label{figure:sw_tersoff}
\end{center}
\end{figure}
There are however some features that cannot be consistently reproduced by Tersoff-like potentials, such as heat conductivity in the solid phase. In particular, in Fig. \ref{figure:sw_tersoff} we show the thermal conductivity of the standard diamond silicon structure at 700 K (where quantum effects can be neglected) and zero pressure predicted by using the previous Tersoff-like potentials as well as the one introduced in this work. None of the previous ones gives a reasonable match to the reference experimental value of $51$ W/mK. The Tersoff potentials parametrized by Tersoff \cite{tersoff1989prb} and Erhart and Albe \cite{erhart2005prb} (the one named as Si-II which was suggested to be better for simulation with elemental silicon) predict comparable values and overshoot the experimental value by about $80\%$, while the modified Tersoff potentials by Kumagai \textit{et al.} \cite{kumagai2007cms} (the one called MOD in this reference) and by Pun and Mishin \cite{Pun2017prb} underestimate the experimental value by a factor of 2 and 5, respectively. The fact that the Tersoff-like potentials can predict very different thermal conductivity values suggests that accurate prediction of the thermal conductivity could be achieved with an appropriate functional form and parametrization.
To achieve this goal, we propose here a minimal Tersoff potential for silicon. Here, by ``minimal'' we mean that every parameter in the potential is essential and there is no redundancy. In the original Tersoff potential \cite{tersoff1989prb}, there are 11 parameters. The version used by Erhart and Albe \cite{erhart2005prb} has the same number of parameters, although some functions have been written in a different but equivalent way. In the modified Tersoff potential by Kumagai \textit{et al.} \cite{kumagai2007cms}, 16 parameters were used, and the latest version by Pun and Mishin \cite{Pun2017prb} used 17. Here, instead of going with this trend of increasing the number of fitting parameters and the complexity of the potential, we do the opposite. With extensive fitting trials with the help of a genetic algorithm, we find that three parameters in the Tersoff potential can be eliminated without adversely affecting the quality of the fitting. A set of optimized parameters were found by fitting the minimal Tersoff potential against energy, virial, and force data from quantum density functional theory (DFT) \cite{hohenberg1964pr,kohn1965pr} calculations for many configurations. Our optimized potential predicts a thermal conductivity which only overshoots the experimental value by about $20\%$ at 700 K.
This paper is organized as follows. In Sec. \ref{section:potential}, we introduce the functional form of the minimal Tersoff potential. In Sec. \ref{section:fitting}, we present the details of the training data and the fitting method. In Sec. \ref{section:optimized}, we evaluate the optimized potential in terms of elastic constants, phonon dispersion, and thermal conductivity. In Sec. \ref{section:summary} we present our summary and conclusions.
\section{Potential model\label{section:potential}}
\subsection{The Tersoff potential}
We first briefly introduce the Tersoff potential in the form published by Tesoff in 1989 \cite{tersoff1989prb}. This is equivalent to the form used by Erhart and Albe in 2005 \cite{erhart2005prb}.
The total potential energy (cohesive energy) $U$ for a system with $N$ atoms is written as a sum the site potentials:
\begin{equation}
U = \sum_{i=1}^N U_{i}.
\end{equation}
The site potential for atom $i$ is formally written as
\begin{equation}
U_{i}=\frac{1}{2} \sum_{j\neq i}^N U_{ij},
\end{equation}
where the potential between atoms $i$ and $j$ is
\begin{equation}
U_{ij}= f_{\rm C}(r_{ij}) \left[ f_{\rm R}(r_{ij}) - b_{ij} f_{\rm A}(r_{ij}) \right].
\end{equation}
This is the general form of the Tersoff potential. Here, $f_{\rm C}(r_{ij})$ is the pairwise cutoff function, $f_{\rm R}(r_{ij})$ and $f_{\rm A}(r_{ij})$ are respectively the pairwise repulsive and attractive functions, and $b_{ij}$ (not equal to $b_{ji}$ in general) is the bond order for the $ij$ bond. Many-body effects are totally embodied in the bond order. The repulsive and attractive functions take the following forms:
\begin{equation}
f_{\rm R}(r_{ij}) = A e^{-\lambda r_{ij}};
\label{equation:f_R}
\end{equation}
\begin{equation}
f_{\rm A}(r_{ij}) = B e^{-\mu r_{ij}},
\label{equation:f_A}
\end{equation}
where $A>0$, $\lambda>0$, $B>0$, $\mu>0$ are fitting parameters.
The bond order $b_{ij}$ is expressed as
\begin{equation}
b_{ij}=\left(1+\zeta_{ij}^n\right)^{-1/2n};
\end{equation}
\begin{equation}
\zeta_{ij}=\sum_{k\neq i,j}^N f_C({r_{ik}}) g(\theta_{ijk}),
\end{equation}
where $n>0$ is a fitting parameter. A larger $\zeta_{ij}$ gives a smaller $b_{ij}$ and a weaker bond. When $\zeta_{ij}=0$, $b_{ij}$ attains a maximum value of one. The angular function is chosen as
\begin{equation}
g^{\rm T}(\theta_{ijk}) = \gamma
\left(
1 + \frac{c^2}{d^2} - \frac{c^2}{d^2 + \left( \cos\theta_{ijk} - h \right)^2}
\right),
\label{equation:g_tersoff}
\end{equation}
where $\gamma$, $c$, $d$ and $h$ are fitting parameters and $\theta_{ijk}$ is the bond angle formed by the $ij$ and $ik$ bonds.
In the expressions of $U_{ij}$ and $\zeta_{ij}$, there is a cutoff function $f_{\rm C}(r)$ which takes the following form:
\begin{equation}
f_{\rm C}(r) =
\begin{cases}
1, & r\leq R_1; \\
\frac{1}{2}\left[ 1+\cos\left(\pi\frac{r-R_1}{R_2-R_1}\right)\right], & R_1<r<R_2; \\
0, & r\geq R_2.
\end{cases}
\label{equation:fc_tersoff}
\end{equation}
Here, $R_1>0$ and $R_2>R_1$ are the inner and outer cutoff distances, respectively.
The cutoff distances $R_1$ and $R_2$ are usually not optimized systematically but are chosen by hand instead. Therefore, there are 9 fitting parameters for the Tersoff potential: $A$, $B$, $\lambda$, $\mu$, $\gamma$, $n$, $c$, $d$, $h$.
\subsection{The minimal Tersoff potential}
We note that in most Tersoff potentials, $c^2/d^2\gg 1$, $d^2\gg 1$, and $\gamma \ll 1$. Under these conditions, $g^{\rm T}(\theta_{ijk}) \approx \gamma c^2/d^4 \left( \cos\theta_{ijk} - h \right)^2$. Defining $\beta=\gamma c^2/d^4$, we obtain
\begin{equation}
g(\theta_{ijk}) = \beta \left( \cos\theta_{ijk} - h \right)^2.
\label{equation:g}
\end{equation}
An advantage of Eq. (\ref{equation:g}) over Eq. (\ref{equation:g_tersoff}) is that the fitting parameter $\beta$ takes a value of the order of unity, while those in the original Tersoff potential take values differing by orders of magnitude. Therefore, our new angular function is much easier to fit.
As in most previous Tersoff potentials, we do not fit $R_1$ and $R_2$ but chose their values by hand. We choose $R_1=2.8$ \AA ~and $R_2=3.2$ \AA, but they can be modified as needed. None of the training data involve atom pairs with distances within the two cutoffs. One of the drawbacks of the bond-order potentials is the abrupt cutoff function, which results in abnormally large forces when two atoms are within the two cutoff distances. Screened bond-order potentials \cite{Pastewka2008prb,Pastewka2013prb,perriot2013prb} have been proposed overcome this drawback. Because our focus here is on the elastic and thermal properties of diamond silicon, we do not consider these advanced cutoff schemes.
In our numerical implementation, we do not fit the parameters $A$, $B$, $\lambda$, and $\mu$ directly, but instead translate them to another set of equivalent parameters $D_0$, $\alpha$, $r_0$, and $S$ as done by Erhart and Albe \cite{erhart2005prb}:
\begin{equation}
A=\frac{D_0}{S-1} \exp\left(\alpha r_0\sqrt{2S} \right);
\end{equation}
\begin{equation}
B=\frac{D_0S}{S-1} \exp\left(\alpha r_0\sqrt{2/S} \right);
\end{equation}
\begin{equation}
\lambda= \alpha\sqrt{2S};
\end{equation}
\begin{equation}
\mu= \alpha\sqrt{2/S}.
\end{equation}
The advantage of using the parameters $D_0$, $\alpha$, $r_0$, and $S$ in the fitting process is that they all have values of the order of unity (when energy is in units of eV and length is in units of \AA), which makes it easier to set up ranges for their allowed values. Physically, $S$ is the slope parameter in the Pauling plot (bond energy versus bond length). When $S=2$, the combination of the repulsive and attractive functions in Eqs. (\ref{equation:f_R}) and (\ref{equation:f_A}) reduces to the Morse function. In our fitting trials, we always got $S \approx 2$ (up to $0.1\%$ deviation only) and we thus fix $S= 2$ and do not treat it as a fitting parameter. Therefore, there are only 6 fitting parameters for our minimal Tersoff potential: $D_0$, $\alpha$, $r_0$, $\beta$, $n$, $h$. To our knowledge this is a Tersoff-like potential with the smallest number of fitting parameters proposed so far.
\section{Fitting database and fitting method \label{section:fitting}}
\subsection{DFT calculations for the training data}
DFT calculations are performed using the Vienna Ab initio Simulation Package (VASP) \cite{Kresse1996prb} that employs a plane-wave basis (we chose a kinetic energy cutoff of 600 eV) and the projector augmented wave (PAW) method \cite{blochl1994prb,kresse1999prb}. A $\Gamma$-centered uniform $k$-point grid with $16 \times 16 \times 16$ $k$-points is employed in the total energy calculations for a cubic unit cell with 8 atoms and a similar $k$-point density is used for other unit cells. When atom positions are to be optimized, the stopping criteria is to make the force on each atom smaller than $10^{-4}$ eV/\AA. Spin is considered in all the calculations. As for the exchange-correlation energy functional, we have compared the following three variants: local spin density approximation (LSDA) \cite{perdew1992prb2}, generalized-gradient approximation \cite{perdew1992prb} as parametrized by Perdew, Burke, and Ernzerhof (GGA-PBE) \cite{perdew1996prl}, and a revised GGA-PBE (GGA-PBEsol) \cite{perdew2008prl}. We first performed a calculation with the atom positions allowed to be optimized. The calculated lattice constant and the corresponding cohesive energy for the diamond structure using different functionals are listed in Table \ref{table:lattice_and_cohesive}. While GGA-PBE gives the most accurate cohesive energy compared with the experimental data, GGA-PBEsol gives the most accurate lattice constant. As we will shift the energy before fitting the potential parameters (see below), we chose to use the results from GGA-PBEsol in the fitting.
\begin{table}[htb]
\centering
\caption{Lattice constants ($a$) and cohesive energies ($E_{\rm c}$) for diamond silicon calculated by using different exchange-correlation functionals. }
\begin{tabular}{lll}
\hline
Functional & $a$ (\AA) & $E_{\rm c}$ (eV/atom) \\
\hline
\hline
LSDA & $5.403$ & $-5.35$ \\
\hline
GGA-PBE & $5.469$ & $-4.61$ \\
\hline
GGA-PBEsol & $5.436$ & $-4.93$ \\
\hline
Experimental & $5.43$ & $-4.63$ \\
\hline
\hline
\end{tabular}
\label{table:lattice_and_cohesive}
\end{table}
After obtaining the ground state structure, we create unit cells with triaxial, biaxial, and uniaxial deformations. For each deformation type, we consider strains $\epsilon$ from $-10\%$ to $10\%$, with smaller steps around the ground state. For each structure, we calculate the total energy and virial tensor without optimizing the atom positions (single-point calculations). The calculated cohesive energy (from GGA-PBEsol) for the ground state deviates from the experimental value to some degree. This might be related to the difficulty of accurately determining the energy of an isolated atom. In order to obtain an empirical potential that can reproduce the experimental value of the cohesive energy, we shift all the DFT energies by a constant value such that the ground state cohesive energy is $-4.63$ eV per atom. Similar corrections were made by Kumagai \textit{et al.} \cite{kumagai2007cms}.
To increase the the diversity of bond angles and coordination numbers in the training database, we also consider a few (artificial or real) allotropes of silicon: simple cubic crystal, body-centered cubic crystal, face-centered cubic crystal, and two-dimensional silicene at their ground states with zero stress. Apart from energy and virial, we also include the forces in the training database. To this end, we use the Tersoff potential \cite{tersoff1989prb} to generate five configurations at 100, 200, 300, 400, and 500 K, and calculate the force on each atom using DFT. The system here is a cubic cell consisting of 64 atoms with periodic boundary conditions in all directions.
\subsection{Genetic algorithm as the fitting method}
Simultaneously optimizing all the parameters is a challenging task for conventional fitting methods, but a metaheuristic such as the genetic algorithm (GA) is well suited to handle it. The GA is a global optimization method and has been successfully used in some previous works to optimize complex potentials with many parameters \cite{larsson2013jcc,kumagai2007cms,rohskopf2017npj}. Other global optimization methods such as the particle swarm optimization method has also been used to fit empirical potentials \cite{kandemir2016nt}. Here, we use the GA to optimize all the parameters in our potential simultaneously.
In our optimization problem, the fitness function (also called objective or cost function) to be minimized is a weighted sum of the errors for energy, virial and force:
\begin{equation}
Z(x) = w_{\rm e} Z_{\rm e}(x) + w_{\rm v} Z_{\rm v}(x) + w_{\rm f} Z_{\rm f}(x).
\end{equation}
Here $x$ represents a solution of the optimization problem, which is an array consisting of the potential parameters:
\begin{equation}
x=[D_0, \alpha, r_0, \beta, n, h].
\end{equation}
For energy, we define the fitness function as
\begin{equation}
Z_{\rm e}(x) = \left(\frac{\sum_n|E(n) - E^{\rm DFT}(n) |^2}{\sum_n |E^{\rm DFT}(n)|^2} \right)^{1/2},
\end{equation}
where $E(n)$ and $E^{\rm DFT}(n)$ are the energies of the $n$-th structure calculated from the empirical potential and DFT, respectively. Similarly, the fitness function for virial is defined as
\begin{equation}
Z_{\rm v}(x) = \left(\frac{\sum_n\sum_{\mu\nu}|\sigma_{\mu\nu}(n) - \sigma_{\mu\nu}^{\rm DFT}(n) |^2}{\sum_n \sum_{\mu\nu} |\sigma^{\rm DFT}_{\mu\nu}(n)|^2} \right)^{1/2},
\end{equation}
where $\sigma_{\mu\nu}(n)$ and $\sigma^{\rm DFT}_{\mu\nu}(n)$ are the $\mu\nu$ virial component of the $n$-th structure calculated from the empirical potential and DFT, respectively. The $\mu\nu$ summation is over the nonequivalent elements of the second-rank virial tensor. The fitness function for force is
\begin{equation}
Z_{\rm f}(x) = \left(\frac{\sum_n\sum_{i}|\vect{f}_{i}(n) - \vect{f}^{\rm DFT}_i(n) |^2}{\sum_n \sum_{i} |\vect{f}^{\rm DFT}_{i}(n)|^2} \right)^{1/2},
\end{equation}
where $\vect{f}_{i}(n)$ and $\vect{f}^{\rm DFT}_{i}(n)$ are the force on the $i$-th atom in the $n$-th structure calculated from the empirical potential and DFT, respectively. The above fitness function is similar to those used in the potfit \cite{brommer2015msmse} and POPS \cite{rohskopf2017npj} packages.
The weighting factors $w_{\rm e}$, $w_{\rm v}$ and $w_{\rm f}$ can be adjusted to control the relative emphasis on the targeting properties. A smaller $Z$ corresponds to a better solution. This unambiguous criteria is the basis for applying the GA.
The workflow of the GA we used is as follows:
\begin{enumerate}
\item Initialization. Create $N_{\rm pop}$ individual solutions $\{x_i\}_{i=1}^{N_{\rm pop}}$, which form a population with population size $N_{\rm pop}$. In this work, we use a real-valued chromosome representation, where each gene in a chromosome represents a potential parameter. Therefore, there are $N_{\rm pop}$ chromosomes in each generation, and each chromosome has $6$ genes. The translation between the genotype and the phenotype is very simple: each gene takes a value within $[0, 1]$, which is translated to a potential parameter according to two limiting values we set for that parameter.
\item Loop over $N_{\rm gen}$ generations
\begin{enumerate}
\item Evaluate the fitness functions $Z(x_i)$ for all the individuals $x_i$ in the population, sorting them according to the fitness values.
\item Keep the best solution (the elite) in each generation without altering it.
\item Select $N_{\rm par}$ individuals with better fitness (smaller $Z$ values) as parents and discarding the remaining ones.
\item Perform the crossover genetic operation on the $N_{\rm par}$ selected parents, producing $N_{\rm pop}-N_{\rm par}$ new individuals (children) such that the population size is recovered.
\item Randomly choose some genes in some chromosomes with a given probability and mutate them, i.e., change their values randomly.
\end{enumerate}
\end{enumerate}
After trial and error, we found that the following parameters are good choices: $N_{\rm pop}=200$, $N_{\rm par}=100$, $N_{\rm gen}=1000$, and a mutation rate linearly decreasing from $0.2$ to zero during the genetic evolution.
\subsection{GPU implementation}
While the GA is generally capable of finding globally optimized potential parameters, it requires evaluating the fitness function many times. It is therefore desirable to make an efficient computer implementation.
Recently, efficient implementation of force evaluation routines in graphics processing units (GPU) has been made for general many-body potentials \cite{fan2017cpc,gpumd}. However, it has also been demonstrated that the computational speed sensitively depends on the simulation cell size. In the calculations here, we only need to use a small simulation cell containing $N_{\rm a}=64$ silicon atoms to incorporate all the interactions. For a system as small as this, a naive GPU implementation barely results in a speedup compared to a CPU implementation. To overcome this difficulty, we note that in each generation, we have $N_{\rm pop}$ individuals, each corresponding to $N_{\rm c}$ configurations. We thus have $N_{\rm pop}N_{\rm c}$ configurations in each generation, which are independent of each other. Therefore, we can use a single CUDA kernel to calculate the physical properties (energy, force, and virial) of part or all of the configurations. The effective system size for the CUDA kernel is thus large enough to achieve a considerable speedup. With our efficient GPU code, performing one optimization with $1000$ generations only takes a few minutes using a Tesla P100 graphics card. This allows us to do a huge number of fitting trials. The fitting code is called GPUGA and it is publicly available \cite{gpuga}.
\begin{table}
\centering
\caption{Optimized parameters of the minimal Tersoff potential for silicon systems.}
\begin{tabular}{llrrr}
\hline
Parameter & Units & Value\\
\hline
\hline
$D_0$ & eV & $3.21481$\\
\hline
$\alpha$ & \AA$^{-1}$ & $1.43134$\\
\hline
$r_0$ & \AA & $2.23801$\\
\hline
$\beta$ & Dimensionless & $0.282818$ \\
\hline
$n$ & Dimensionless & $0.602568$\\
\hline
$h$ & Dimensionless & $-0.641048$\\
\hline
$R_1$ & \AA & $2.8$ \\
\hline
$R_2$ & \AA & $3.2$ \\
\hline
\hline
\end{tabular}
\label{table:optimized_parameters}
\end{table}
\begin{figure*}[htb]
\begin{center}
\includegraphics[width=1.8\columnwidth]{fitting.eps}
\caption{(a) Force, (b) energy, and (c) virial as calculated from the minimal Tersoff potential compared with the training data from DFT. In the legend, ``triaxial'' means deforming the three axes of a cubic unit cell by the same amount, ``biaxial'' means deforming two axes only and ``uniaxial'' means deforming one axis only. The lattice constant $a$ in (b) and (c) refers to the deformed value.}
\label{figure:fitting}
\end{center}
\end{figure*}
\subsection{The optimized minimal Tersoff potential }
The optimized parameters for the minimal Tersoff potential are listed in Table \ref{table:optimized_parameters}. Energy, virial, and force calculated using the optimized potential are compared with the DFT training data in Fig. \ref{figure:fitting}. The force and virial stress from the empirical potential were calculated using the formulas in Ref. \cite{fan2015prb}. The agreement with DFT results is reasonably good. The errors for energy and virial are of the order of $1\%$. The cohesive energy and lattice constant calculated using the optimized potential are $-4.63$ eV per atom and $5.434$ \AA, respectively. The error for force is relatively large. It is possible to reduce this error, but at the expense of increasing the errors for energy and virial, resulting in unreasonable elastic constants.
To see how the current potential differs from previous Tersoff-like potentials, we plot the angular function $g(\theta)$ and the bond order function $b(\theta)$ for a single triplet in Fig. \ref{figure:g}. Our angular function resembles the spline function constructed by Schall \textit{et al.} based on energies in structures with some special bond angles \cite{Schall2008prb}.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=\columnwidth]{g_and_b.eps}
\caption{The angular function $g$ and bond order $b_{ij}$ as a function of the bond angle $\theta_{ijk}$ in a single triplet $ijk$ for the Tersoff-like potentials considered in this work (see text for details).}
\label{figure:g}
\end{center}
\end{figure}
\section{Evaluation of the optimized minimal Tersoff potential \label{section:optimized}}
In this section, we evaluate the optimized minimal Tersoff potential in terms of mechanical and thermal properties. We implement this potential into the efficient open-source GPUMD package \cite{fan2017cpc,gpumd} and use this package to do all the MD simulations. We will compare the results with some of the existing Tersoff-type potentials \cite{tersoff1989prb,erhart2005prb,kumagai2007cms,Pun2017prb}.
\subsection{Elastic constants}
\begin{table}
\centering
\caption{Elastic constants (in units of GPa) of diamond silicon from experiments, DFT calculations, and various empirical potentials.
}
\begin{tabular}{lrrrrr}
\hline
Method/Potential & Taken from & $C_{11}$& $C_{12}$ & $C_{44}$ & $C_{12}-C_{44}$ \\
\hline
\hline
Experimental \cite{mcskimin1951pr} & \cite{mcskimin1951pr} & $167.4$ & $65.2$ & $79.6$ & $-14.4$ \\
\hline
SW \cite{stillinger1985prb} & \cite{Pun2017prb} & $151.4$ & $76.4$ & $56.4$ & $20$\\
\hline
Tersoff \cite{tersoff1988prb} & \cite{kumagai2007cms} & $142.5$ & $75.4$ & $69.0$ & $6.4$\\
\hline
Erhart (Si-II) \cite{erhart2005prb} & \cite{erhart2005prb} & $167$ & $65$ & $72$ & $-7$ \\
\hline
Kumagai \cite{kumagai2007cms} & \cite{kumagai2007cms} & $166.4$ & $65.3$ & $77.1$ & $-11.8$ \\
\hline
Pun \cite{Pun2017prb} & \cite{Pun2017prb} & $172.6$ & $64.6$ & $81.3$ & $-16.7$ \\
\hline
mini-Tersoff & here & $148$ & $65$ & $75$ & $-10$ \\
\hline
DFT & here & $156$ & $62$ & $74$ & $-12$ \\
\hline
\hline
\end{tabular}
\label{table:elastic}
\end{table}
The elastic constants calculated using stress-strain relations at zero temperature are presented in Table \ref{table:elastic}. Our minimal Tersoff potential can predict the correct sign of $C_{12}-C_{44}$, while the SW potential \cite{stillinger1985prb} and the Tersoff-1988 potential \cite{tersoff1988prb} fail. The other potentials \cite{erhart2005prb,kumagai2007cms,Pun2017prb} all describe the elastic properties very well. From Table \ref{table:elastic} and Fig. \ref{figure:sw_tersoff}, we see that there is no clear correlation between the elastic constants and the thermal conductivity. The good elastic properties of our minimal Tersoff potential is implied by the good fit to the energy and virial data in many deformed structures, as shown in Fig. \ref{figure:fitting}.
\subsection{Phonon dispersion}
\begin{figure*}[htb]
\begin{center}
\includegraphics[width=2\columnwidth]{phonon.eps}
\caption{Phonon dispersion of diamond silicon from the various empirical potentials (red solid lines) compared with experimental data (blue dots) \cite{holt1999prl}. }
\label{figure:phonon}
\end{center}
\end{figure*}
To properly describe the phonon transport properties, an adequate description of the phonon dispersion curves is needed. Figure \ref{figure:phonon} shows the phonon dispersions calculated using harmonic lattice dynamics with the second order force constants being calculated from the various empirical potentials using the finite displacement method, compared with experimental data \cite{holt1999prl} from X-Ray transmission scattering. Here the \verb"phonon" executable within the GPUMD package \cite{gpumd} is used. All of the empirical potentials give a reasonable description for the acoustic branches. However, except for the Tersoff-1989 potential \cite{tersoff1989prb} and our minimal Tersoff potential, all the other potentials give rise to too large a cutoff frequency for the optical branches. Overall, our minimal Tersoff potential gives the best description for the phonon dispersion of diamond silicon among all the empirical potentials considered here.
\subsection{Thermal conductivity}
We next calculate the thermal conductivity $\kappa$ using the efficient homogeneous nonequilibrium molecular dynamics (HNEMD) method \cite{evans1982pla} for many-body potentials \cite{Fan2019prb}. In this method, one generates a non-equilibrium heat current by adding a small external driving force and measure the heat current, which is directly proportional to the thermal conductivity. For details on the HNEMD method, see Ref. \cite{Fan2019prb}.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=\columnwidth]{kappa_T.eps}
\caption{Thermal conductivity of diamond silicon as a function of temperature from the various potentials. Isotope scattering is included here. Experimental data are from Ref. \cite{Glassbrenner1964pr}.}
\label{figure:kappa_T}
\end{center}
\end{figure}
We use a simulation cell with 8000 silicon atoms (with periodic boundaries in all three directions) and consider temperatures from 300 to 1000 K, all with zero pressure. To be consistent with experiments, isotope scattering is considered by randomly choosing the mass of a silicon atom according to the following abundance distribution: $92.2\%$ $^{28}$Si, $4.7\%$ $^{29}$Si, and $3.1\%$ $^{30}$Si.
The results obtained by the various Tersoff-like potentials are shown in Fig. \ref{figure:kappa_T} and are compared with experimental data \cite{Glassbrenner1964pr}. Results for $T=700$ K have also been shown in Fig. \ref{figure:sw_tersoff}. It is clear that our minimal Tersoff potential gives results closest to the experimental data. At high temperatures where quantum effects are not important, our predictions are only about $20\%$ \emph{larger} than the experimental values. However, our predicted thermal conductivity at $T=300$ K is slightly \emph{smaller} than the experimental value. This indicates the presence of quantum effects at low temperatures, as we will discuss below.
To explore the influence of quantum effects, we calculate the thermal conductivity by iteratively solving the Peierls-Boltzmann transport equation (PBTE). In our calculations, we consider both three-phonon and four-phonon scatterings \cite{gu2019prb} and temperature-dependent interatomic force constants \cite{hellman2013prb}. In this method, both classical and quantum statistics for the phonon population can be conveniently considered. As in the case of MD simulations, isotope scattering is also considered. For details, see Ref. \cite{gu2019prb}.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=\columnwidth]{kappa_quantum.eps}
\caption{Thermal conductivity as a function of temperature from the minimal Tersoff potential using MD simulation data and from PBTE calculations with classical and quantum statistics. Isotope scattering is included here. Experimental data are from Ref. \cite{Glassbrenner1964pr}. }
\label{figure:kappa_quantum}
\end{center}
\end{figure}
Figure \ref{figure:kappa_quantum} shows the classical and quantum thermal conductivity from the PBTE calculations using the minimal Tersoff potential, compared to the MD and experimental data. The thermal conductivity from PBTE calculations with classical statistics is slightly larger than that from MD, but they have a similar $T$ dependence. When quantum statistics is used in the PBTE calculations, the thermal conductivity at $T=300$ K increases by about $10 \%$. At temperatures above the Debye temperature (640 K), there is essentially no difference between the classical and quantum results. There are two competing quantum effects \cite{turney2009prb}: quantum statistics gives smaller modal heat capacities but larger phonon scattering times compared to classical statistics. In the temperature range considered here, the second effect is stronger, leading to underestimated $\kappa$ using classical statistics. Albeit, this overall effect is quite small (about $10 \%$) even at a temperature that is half of the Debye temperature. The point here is that if quantum corrections can be made to the classical MD results, the thermal conductivity at $T=300$ will be larger instead of smaller than the experimental value. Overall, we can conclude that our minimal Tersoff potential gives the best prediction for the thermal conductivity of diamond silicon among all the empirical potentials considered here.
\section{Summary and Conclusions\label{section:summary}}
In summary, we have proposed a minimal Tersoff empirical potential for diamond silicon and obtained a set of optimized parameters by fitting the potential against first-principles data using the genetic algorithm. The DFT data include energy and virial in many deformed structures and force in a few structures at finite temperatures. The optimized minimal Tersoff potential well describes the elastic constants, phonon dispersion, and thermal conductivity of diamond silicon simultaneously. Using classical statistics underestimates the thermal conductivity by an amount of about $10\%$ compared to using quantum statistics at room temperature. Both the fitting method and the optimized potential are made freely accessible from open-source codes we developed \cite{gpumd,gpuga}. The methods developed here are promising for constructing empirical potentials for new materials with good descriptions of the elastic and thermal properties.
\begin{acknowledgments}
ZF and TA-N acknowledge the supports from the National Science Foundations of China (NSFC) (No. 11974059) and from the Academy of Finland Centre of Excellence program QTF (Project 312298) and the computational resources provided by Aalto Science-IT project and Finland's IT Center for Science (CSC). YW, PQ and YS acknowledge the support from the financial support of National Key Research and Development Program of China (2016YFB0700500). XG acknowledges the support from the National Science Foundations of China (NSFC) (No. 51706134)
\end{acknowledgments}
|
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Republicans divided as Janet Nguyen launches…
Republicans divided as Janet Nguyen launches surprise bid for Tyler Diep's Assembly seat in 2020
Former party leader Scott Baugh says Diep is too liberal, while Diep decries GOP 'purity tests.'
Former State Sen. Janet Nguyen, seen here speaking at a groundbreaking in Los Alamitos, filed a last-minute challenge to Assemblyman Tyler Diep in the 72nd District race. (Photo by Brittany Murray, Press-Telegram/SCNG)
By Brooke Staggs | bstaggs@scng.com | Orange County Register
In a move that took Republican insiders by surprise, former GOP State Senator Janet Nguyen is challenging moderate GOP Assemblyman Tyler Diep for his 72nd Assembly District seat in 2020.
The looming primary battle is sparking division among party leadership, as the GOP struggles to find its footing in an increasingly Democratic region where Donald Trump's brand of Republicanism is a tough sell.
Former Orange County GOP chair Scott Baugh prompted Nguyen to run with a Dec. 5 email to local party leaders that blasted Diep's voting record on issues such as charter schools and his recent comments in support of organized labor, which Baugh termed "a step ladder into the penthouse of the leftist elite."
"He brought this fight to us by campaigning as a conservative and betraying us in Sacramento," Baugh said in a follow-up email obtained by the Register. "There is a rat in our cellar and I am turning on the light."
But by Friday, Dec. 13, some leading Californian Republicans had jumped to Diep's defense. California Republican Party Chairwoman Jessica Patterson, Senate Republican Leader Shannon Grove and Assembly Republican Leader Marie Waldron issued a joint statement calling Nguyen's bid "a distraction" that "plays directly into the Democrat speaker's playbook."
"We call on everyone who is committed to the party to put differences aside and join us in keeping this district Republican," the women wrote.
In an emailed response to local GOP leaders, first-term Assemblyman Diep blamed Baugh for Democrat Harley Rouda's 2018 win in the formerly Republican-held 48th Congressional seat. The result came after Baugh challenged longtime GOP Rep. Dana Rohrabacher in the 2018 primary.
"Our Assembly Republican caucus is now down to just 18 members. We had 32 members just 12 years ago," Diep of Westminster said. "Infighting and purity tests are not going to make us stronger."
It's unclear who the GOP might have to beat for the party to hold AD-72. Democrat Josh Lowenthal initially took out paperwork to challenge Diep to a rematch after losing the district seat to him by 3.2 percentage points in 2018, but he didn't follow through. Instead, records show two other Democrats are hoping to win the seat, cancer scientist Diedre Nguyen and civil rights activist Bijan Mohseni.
The standoff between the two Vietnamese Americans in a district that includes Little Saigon was the biggest surprise to emerge in the past week as ballots take shape for Orange County's 2020 primary contests.
A final list of candidates on the ballot March 3 for every race that touches Orange County will be set Dec. 26, when the Secretary of State releases its certified list. But local candidates had to file paperwork with the Orange County Registrar of Voters by Dec. 6, with the deadline extended until Wednesday, Dec. 11 for one county race where the incumbent decided not to run for reelection. And unless litigation or some other rare circumstance comes into play, election officials said the county's list of candidates should stick.
Nguyen filed her paperwork on Dec. 6, a day after Baugh sent his first email about Diep.
The Fountain Valley resident has been eyeing a new position since she narrowly lost her 2018 reelection bid to Democrat Tom Umberg. She tried and failed earlier this year to win appointment to a regional water board seat. She also considered a congressional run, and she has active campaign committees for a 2020 county supervisor seat and a 2022 run for the state senate.
Nguyen has proven to be a strong fundraiser in past election cycles, spending more than $2 million in contributions during her 2018 state senate bid.
Diep raised $309,650 in the first half of the year for his 2020 election campaign, according to Secretary of State records, with $280,648 in cash at the end of the last reporting cycle June 30.
Diep has earned a reputation as a moderate Republican during his first year in Sacramento. He voted in support of a bill that removes mandatory sentence enhancements for some repeat criminals and as he's spoken out against President Donald Trump's immigration policies. Since voter registration data shows the GOP is losing ground in the area, and many recent immigrants or relatives of immigrants live in the district, those stances could position Diep to win back his seat.
But Baugh accused Diep of preparing to leave the Republican party. And he argued in one of this emails to fellow county Republicans that it wasn't fair for the party to stand by Diep while it abandons 73rd District Assemblyman Bill Brough "for private indiscretions that he disputes."
Brough is facing allegations of sexual assault and an investigation by state ethics officials over his use of campaign funds. Brough has repeatedly denied wrongdoing in both cases and is running for reelection, though state and local GOP leadership has thrown its support behind Republican challenger Laurie Davies.
california-politics
orange-county-politics
Brooke Staggs
Brooke Edwards Staggs covers state and federal politics through an Orange County lens, plus the politics, business and culture of cannabis in California. Journalism has led Staggs to a manhunt in Las Vegas, a zero gravity flight over Queens and a fishing village in Ghana. The Big Bear native is addicted to education. She earned her bachelors degree in English from California Baptist University, then got her master's in education as she taught high school English in the Inland Empire. After four years in the classroom, she left in 2006 to be a student again herself, earning a masters degree in journalism from New York University while interning and freelancing for a variety of publications. She sees journalism as another form of teaching, helping readers make informed decisions and better understand the world around them. Staggs spent five years as a staff writer then city editor at the Daily Press in Victorville. She joined the Orange County Register in January 2013, covering several Orange County communities before taking on the marijuana beat in February 2016 and the politics beat in April 2019. That work has earned her first-place wins in the Best of the West, California Journalism Awards and Orange County Press Club competitions. On occasion, she also teaches community college and ghostwrites nonfiction books. Staggs loves dancing and new adventures. She hates water slides and injustice. If she doesn't get right back to you, there's a good chance she's sitting with her DJ husband on a plane or train or boat destined for somewhere – anywhere – they've never been.
Follow Brooke Staggs @JournoBrooke
|
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| 3,459
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Ранчо лас Палмас има више значења:
Ранчо лас Палмас (Гвадалупе), насеље у савезној држави Чивава у Мексику
Ранчо лас Палмас (Дуранго), насеље у савезној држави Дуранго у Мексику
Ранчо лас Палмас (Бенито Хуарез), насеље у савезној држави Гереро у Мексику
Ранчо лас Палмас (Сан Хуан Козокон), насеље у савезној држави Оахака у Мексику
Ранчо лас Палмас (Венустијано Каранза), насеље у савезној држави Пуебла у Мексику
Ранчо лас Палмас (Мазатлан), насеље у савезној држави Синалоа у Мексику
Ранчо лас Палмас (Танкоко), насеље у савезној држави Веракруз у Мексику
Ранчо лас Палмас (Виља Гарсија), насеље у савезној држави Закатекас у Мексику
|
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"redpajama_set_name": "RedPajamaWikipedia"
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site_title: Foo Bar
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"redpajama_set_name": "RedPajamaGithub"
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| 7,670
|
Q: Can't display the data entered in form in database The user enters the data in the form. But the data entered in the form doesn't get displayed in the Database.
views.py
def add(request):
if request.method=='POST':
form=FilesCreate(request.POST)
if form.is_valid():
form.save()
return render(request,'plagiarism/page1.html',{'form':FilesCreate()})
def add2(request):
if request.method=='POST':
form2=FilesCreate2(request.POST)
if form2.is_valid():
form2.save()
return render(request,'plagiarism/page2.html',{'form':FilesCreate2})
models.py
from django.db import models
class File1(models.Model):
#user=models.ForeignKey(User)
firstfile=models.CharField(max_length=1000, default="")
#secondfile=models.CharField(max_length=1000)
def __str__(self):
return self.firstfile
plagiarism/page1.html
<h1>Enter your first file</h1>
<form action="file2/" method="post">
{% csrf_token %}
{% for field in form %}
{{field}}
<input type="submit" value="Submit file1"/>
{% endfor %}
</form>
plagiarism/page2.html (displays page after clicking submit in page 1)
<h1>Enter your second file</h1>
<form action="plagiarism/file2/result/" method="post">
{% csrf_token %}
{% for field in form %}
{{field}}
<input type="submit" value="Get Results"/>
{% endfor %}
</form>
{% block h1 %}
{% endblock %}
<body>
plagiarism/page3.html (displays page after clicking submit in page 2)
<h1> Here is your Result </h1>
<h2>
{{data}}
</h2>
</body>
forms.py
from django.forms import ModelForm
from django import forms
from plagiarism.models import File1,File2
class FilesCreate(ModelForm):
class Meta:
model=File1
exclude=()
widgets={'firstfile':forms.Textarea(attrs={'cols':50,'rows':100})}
example.py
from django.shortcuts import render
def getresult(request):
data=95.5
return render(request,'plagiarism/page3.html',{'data': data})
urls.py
from django.conf.urls import url
from . import views
from . import example3
urlpatterns=[
url(r'^$',views.add,name='add'),
url(r'file2/$',views.add2,name='add2'),
url(r'file2/result/$',example3.getresult,name='getresult')
]
A: You seem to want a kind of wizard, where you process a form and it redirects you to the next, but you're not doing the basics of form processing well. For simple form handling, you can do this:
urls.py
from django.conf.urls import url
from . import views
from . import example3
urlpatterns=[
url(r'^$',views.add,name='add'),
url(r'file2/result/$', example3.getresult, name='getresult')
]
In the template, you are calling file2 with the form's action, but you really want to call the same page, to process the form with the add view:
plagiarism/page1.html
<h1>Enter your first file</h1>
<form method="post">
{% csrf_token %}
{% for field in form %}
{{field}}
{% endfor %}
<input type="submit" value="Submit file1"/>
</form>
Note the missing action attribute in the <form> element.
When you visit the root of the website, the add view will be called with a GET request. When you submit the form, the same add view will be called, with a POST request, which will then be processed:
views.py
def add(request):
if request.method == 'POST':
form = FilesCreate(request.POST)
if form.is_valid():
form.save()
return HttpResponseRedirect(reverse('getresult'))
else:
form = FilesCreate()
return render(request,'plagiarism/page1.html',{'form': form})
Note the HttpResponseRedirect, which redirects to a new page on success, and the else, which creates an empty form for the first time you visit the page (i.e. request.method is not POST, it is GET). This way, if the form isn't valid, the last line will render it bound to the data that was submitted and display the errors.
This should get you the data into the database, which was your first goal. If you want to go to another form upon submission, you can redirect there (instead of the result page) and do the same as above in the view add2.
There used to be a Django Form Wizard, but you can see this project to do multi-step forms.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,677
|
Boophis goudotii är en groddjursart som beskrevs av Johann Jakob von Tschudi 1838. Boophis goudotii ingår i släktet Boophis och familjen Mantellidae. IUCN kategoriserar arten globalt som livskraftig. Inga underarter finns listade.
Källor
Externa länkar
Stjärtlösa groddjur
goudotii
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 2,149
|
Українсько-палестинські відносини — відносини між Україною та Палестиною.
Палестина (в особі Організації визволення Палестини) визнала незалежність України 2 січня 1992 року. Дипломатичні відносини було встановлено 2 листопада 2001 року, коли у Києві відкрили Посольство Палестини.
Історія
В листопаді 1996 року Президент України Леоніда Кучми відвідав з офіційним візитом Палестинську Національну Адміністрацію (ПНА), в рамках якого у Рамаллаї було проведено переговори з головою ПНА Ясером Арафатом. У квітні 1999 року голова ПНА Ясер Арафат відвідав Київ, провів переговори з Президентом України Леонідом Кучмою.
Близько трьох тисяч палестинців здобули освіту в українських вишах.
Див. також
Українсько-ізраїльські відносини
Примітки
Українсько-палестинські відносини
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 8,360
|
Q: Defining the dimension of a convex set In Stephen Boyd's optimization book, it says
"We define the dimension of an affine set C as the dimension of the
subspace V = C−x0,where x0 is any element of C"
I have two questions regarding this:
*
*Why do we need to introduce the subspace to define the dimension of the affine set ?
*Based on my understanding, I am guessing the subspace is a subset which is a vector space and is closed under linear combinations [link]
So the subspace is also an affine set. This leads to a circular argument for defining the dimension of an affine set. I would appreciate some clarity regarding the above points.
A: The dimension of a linear subspace is well-defined (refer to any linear algebra text); as you noted it is a subset of a vector space that is itself a vector space (closed under linear combinations).
Boyd is defining the dimension of an affine set by producing a related set $C-x_0$ that happens to be a linear subspace, and then referring to the established definition of dimension for linear subspaces. There is no circular argument here.
The set $C-\{x_0\}$ is not a subset of $C$; geometrically, it is shifting/translating the affine space until it touches the origin.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,384
|
Q: UWP crashes when entering in a User Name and password this is my first post. I will try to get all of the relevant info. I am developing a UWP for my BS Capstone class. I have a mainpage that gives the user the choice to enter in a user name and password and log in, or enter a user name and password and register so they will be able to log in. I have some exceptions in there in the event that a user is not registered, a dialog will inform them they need to register.
The problem is when I enter in a user name and password that I know is not registered, the app crashes.
I am using VS 2015 and an Azure SQL database. The only clue i have to whats wrong is the output shows the following message.
Exception thrown: 'System.Net.Http.HttpRequestException' in mscorlib.ni.dll
Also, I have the connection string in the App.Xaml.cs tab as
public static MobileServiceClient MobileService = new
MobileServiceClient("http://tale-server1.database.windows.net");
Finally, when trying to register a new user, the Catch exception fires of:
catch (Exception em)
{
var dialog = new MessageDialog("An Error Occured: " +
em.Message);
await dialog.ShowAsync();
}
My Mainpage code is below.
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.InteropServices.WindowsRuntime;
using Windows.Foundation;
using Windows.Foundation.Collections;
using Windows.UI.Xaml;
using Windows.UI.Xaml.Controls;
using Windows.UI.Xaml.Controls.Primitives;
using Windows.UI.Xaml.Data;
using Windows.UI.Xaml.Input;
using Windows.UI.Xaml.Media;
using Windows.UI.Xaml.Navigation;
using Microsoft.WindowsAzure.MobileServices;
using System.Threading.Tasks;
using Windows.UI.Popups;
using Windows.Storage;
using System.Net.Http;
using Newtonsoft.Json;
using SQLite;
using SQLite.Net;
using SQLite.Net.Async;
using Microsoft.WindowsAzure.MobileServices.Sync;
using Microsoft.WindowsAzure.MobileServices.SQLiteStore;
using SQLitePCL;
// The Blank Page item template is documented at
http://go.microsoft.com/fwlink/?LinkId=402352&clcid=0x409
namespace TALE_Capstone
{
/// <summary>
/// An empty page that can be used on its own or navigated to within a
Frame.
/// </summary>
public sealed partial class MainPage : Page
{
public MainPage()
{
this.InitializeComponent();
}
public int IsAuth { get; set; }
//[DataTable("User_Cred")]
public class User_Cred
{
public string id { get; set; }
public string userName { get; set; }
public string Password { get; set; }
}
private IMobileServiceSyncTable<User_Cred> todoGetTable =
App.MobileService.GetSyncTable<User_Cred>();
private async Task InitLocalStoreAsync()
{
if (!App.MobileService.SyncContext.IsInitialized)
{
var store = new MobileServiceSQLiteStore("Tale-DB");
store.DefineTable<User_Cred>();
await App.MobileService.SyncContext.InitializeAsync(store);
}
await SyncAsync();
}
private async Task SyncAsync()
{
await App.MobileService.SyncContext.PushAsync();
await todoGetTable.PullAsync("User_Cred",
todoGetTable.CreateQuery());
}
async public void submitAuthBtn_Click(object sender, RoutedEventArgs e)
{
await InitLocalStoreAsync();
GetAuthentication();
}
async public void GetAuthentication()
{
try
{
//IMobileServiceTable<User_Cred> todoTable = App.MobileService.GetTable<User_Cred>();
List<User_Cred> items = await todoGetTable
.Where(User_Cred => User_Cred.userName == UserNameEnter.Text)
.ToListAsync();
IsAuth = items.Count();
// Return a List UI control value back to the form
foreach (var value in items)
{
var dialog = new MessageDialog("Welcome Back " + value.userName);
await dialog.ShowAsync();
}
if (IsAuth > 0)
{
var dialog = new MessageDialog("You are Authenticated");
await dialog.ShowAsync();
}
else
{
var dialog = new MessageDialog(" Account Does Not Exist, please Register to get Started.");
await dialog.ShowAsync();
}
}
catch (Exception em)
{
var dialog = new MessageDialog("An Error Occured: " + em.Message);
await dialog.ShowAsync();
}
}
async private void submitAuthBtn_Copy_Click(object sender, RoutedEventArgs e)
{
try
{
User_Cred itemReg = new User_Cred
{
userName = UserNameEnter.Text,
Password = PWEnter.Text
};
await App.MobileService.GetTable<User_Cred>().InsertAsync(itemReg);
var dialog = new MessageDialog("Thank you for Registering! Lets begin");
await dialog.ShowAsync();
}
catch (Exception em)
{
var dialog = new MessageDialog("An Error Occured: " + em.Message);
await dialog.ShowAsync();
}
}
}
}
Any help would be appreciated!
Conrad
A: According to your description, I assumed that you are connecting your UWP app with the Azure Mobile App backend and Azure SQL database for storing data. AFAIK, the initialization of MobileServiceClient would look like as follows:
MobileServiceClient MobileService = new MobileServiceClient("https://{your-appname}.azurewebsites.net");
I would recommend you could follow this tutorial and download the sample client project to check this issue. Also, you could leverage fiddler and collect the network traces when you connect your uwp app with azure mobile app to get the detailed error message, then you could narrow this issue or you could update your question with the detailed error for us to locate this issue.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,692
|
Q: How do I use a local Objective-C file in a pod class file I'm editing? I have a library that I'm using through Cocoapods, and I'm modifying it slightly. I have a class I've created in my normal project (outside of Cocoapods) that I want to use in the Cocoapod, but when I try to import the file it says that file doesn't exist.
As pods are seemingly achieved through a separate project within the same workspace, I assume that's the reason why I can't access it. How would I access it, however? Do I have to import the file separately into the Pods project and then maintain two separate versions? Or is there a better way?
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 8,045
|
Elena Erin's World of Mayhem
Elena Erin as of right now is living a socialite's life between New York City and London. Full steam ahead, she has performed throughout New York, hit number 2 CBC Radio, been featured on major Spotify editorial playlists (New Music Friday Canada/Fresh Finds), yields 8k monthly listeners on Spotify alone, and has eclipsed over a million streams cumulatively across the various platforms. It would almost seem like this was "all of a sudden" given the whirlwind pace she is moving at right now. However, the remarkable part of it all is actually how far she has come to where she is now. And not just talking about the beginning of her discography that dates back to September of 2018. No, prior to even that, the small-town Canadian girl has actually been playing classical piano since six years old! Started writing songs at ten years old. Attended Berklee College of Music. Indeed, from growing up on a cattle farm in rural Canada to Berklee to New York to now back and forth between London, one could only imagine the trials, tribulations, and stories that have come about from that journey. Well, imagine as much as you wish, but Elena Erin actually provides a great deal of insight and storytelling behind it with her latest album, "Holy Tender Artist," released earlier this year in July. Musically, my initial first impressions would be that I recommend her music for fans of Gwen Stefani, Cyndi Lauper or Laura Branigan.
As I've noticed with many talented people, as gifted as she has been since such a young age, she still possessed a great deal of apprehension about singing her own songs, until one defining moment:
While in a studio session in New York in 2016, I sang on a demo and the producers decided to keep my voice on the track, saying I had a unique voice and should sing my own songs.
Elena Erin
Elena took that advice and ran with it. Effectively, that is what "Holy Tender Artist" is an accounting of. It is telling the tale, so to speak, of a homeschooled small town girl with big city dreams meeting the realities of a dangerous, scandalous and cruel world. She refers to the album's lead off track "Almost Famous" as a pinnacle of the overarching storyline. Featuring real-life phone conversations with her best friend, and ending with the self-assuring whisper to herself of: "You're still Holy, you're still tender, and no matter how much you try to escape it, you'll always be an artist," Erin is painting a vivid picture for her audience about her path to self discovery. Her Spotify bio summarizes:
This album is highlighted by royalty, sex, exploration, vulnerability, and in-your-face New York style of storytelling from her time there.
The official music video for the track "Mayhem World" was just released last month. Where "Almost Famous" is perhaps the figurative exposition of the album, "Mayhem World" is effectively one of the key conflicts in the plot. It is a song chronicling the woes of a lover who is at odds with the feeling of longing to be closer to someone that is also just as damaged in a similar way. Both put up emotional walls keeping anyone from getting close to them. Hence, keeping both of them siloed in their own worlds of mayhem. It's such a strange thing isn't it? How people can be together yet still so alone. Elena Erin admits that the song is penned from a perspective of vulnerability. The standout line of the song being, "nobody knows what it's like to hold us closer." As if to acknowledge that both parties take part in pushing each other away. The video depicts Erin sitting at a bar, having drinks and drowning in sorrow waiting for a call, a text, or some kind of communication from someone before leaving without resolve upset and sad. Clearly, the tragic part of the saga.
"The song is about talking to someone you are really into, thinking they feel the same way, and then realizing that they aren't going to text you back. It's about an unrequited love of sorts." Elnea Erin
Holy Tender Artist (which "Mayhem World" is featured on) is about: Friendship, Heartbreak, and self-discovery are the main themes. The biggest one is the love that comes from friendship. A lot of songs are about romantic love that doesn't really last or work out, but then there are songs like "We Could Grow Old Together," where I sing about growing old and traveling with my best friend.
Don't forget to support this project and to follow on Instagram, Facebook, Twitter, TikTok, YouTube, and Spotify. It also helps to stream and share their music; you can obviously find it in the following Playlists: Fresh Singles, Indie Only, Female Rising Stars, and 12 New Songs This Week.
Remember that you can always find me here AMS Radio for all my social media and collaborations.
Published by Audio Mirage Studios
View all posts by Audio Mirage Studios
Female Rising Stars, New Music by Genre, Pop
Introducing to...
Dream of a Man in a Top Hat – "The Destination"
Unknown But Essentials (Nov 2022)
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 5,623
|
\section{Why model language dynamics?}
There has been a surge in enthusiasm for modelling human social behaviour over the past few years. Language dynamics is particularly popular, both among a community of modellers (who typically have a background in statistical physics \cite{cas09}) and latterly with linguists and psychologists too \cite{cri03,hru09}. However, there also seems to be some lingering discontent regarding the lack of contact between formal models on the one hand, and empirical data on the other.
For example, Castellano, Loreto and Fortunato state early on in their excellent review of mathematical models for social dynamics \cite{cas09} that ``there is a striking imbalance between empirical evidence and theoretical modelization, in favor of the latter. \ldots The introduction of a profusion of theoretical models has been justified mainly by vague plausibility arguments, with no direct connection to measurable facts. '' (p593 of \cite{cas09}). Simply put, the models in question may display rather beautiful physics, but have limited empirical utility due to featuring impoverished treatments of both the behaviour transmitted between agents and of the agents themselves.
Although some resistance to the quantitive modelling of language dynamics has been reported among certain linguists (see \cite{mar09}), it seems nevertheless a reasonable endeavour \emph{as long as} one does not attempt to recreate single instances of historical change with a computational model. For, as Hruschka \textit{et al} observe, ``[g]iven the stochastic nature of language change, trying to predict individual trajectories and particular histories would be a fool's errand'' (p466 of \cite{hru09}). Instead, these authors advance the use of \emph{null models} as a means to disentangle the various possible factors that may account---in a statistical sense---for general patterns of language change. It is this idea that I pursue in the present work as a means to proceed towards the laudable and important goal of aligning mathematical models of social dynamics with relevant empirical data.
The main purpose of a null model is to provide the probability distribution of observable outcomes due to (in principle all) factors other than the one of interest to an experimenter. Most often a null model incorporates finite sample-size effects and allows one to determine when a difference between two measured values is significant. However, it is legitimate to include other processes into a null model as long as it is: (i) sufficiently tractable that the required distribution can calculated; (ii) contains sufficiently few free parameters that it is falsifiable; and (iii) intimately related to a specific theoretical hypothesis. This last point is key, because otherwise rejecting the null model is uninformative. Further discussion of these three requirements is given in an online appendix to this article.
The remainder of this work is devoted to the proposition that \emph{neutral evolution} (to be defined in the next section) is a viable null model for the dynamics of linguistic variation in a speech community. In particular, I will show that it is strongly intertwined with the (hotly debated) role of \emph{identity} in language use and change, and to a lesser extent the relevance of meaning to the trajectory of change. Thus, rejection of the null model has important consequences for theories of language change. I also survey some available empirical evidence for and against neutral evolution as a mechanism for language change. Finally, despite the simplicity of neutral evolution as a mathematical model, I will also demonstrate that there are a number of properties that remain to be established, and thus serve as open problems in the statistical physics of social dynamics.
\section{All roads lead to neutral evolution}
\label{sec:neut}
\emph{Neutral evolution} (also known as \emph{genetic drift} \cite{cro70}, \emph{neutral theory} \cite{hub01} and \emph{random copying} \cite{ben07} in various contexts where it appears) is a process that one is ineluctably drawn to whenever the changes occur due to \emph{replication} acting alone (i.e., without selection) are considered. Replication sits at the heart of any evolutionary process, and this includes cultural evolutionary processes such as the dynamics of language, wherein a speaker replicates linguistic utterances she has previously heard used to convey a desired meaning. A model that includes only this process of replication seems like a good starting point in a quest for a null model of language dynamics.
\subsection{The simplest models of replication}
\label{sec:moran}
A simple model of replication in a linguistic context can be formulated as follows. A speaker has a memory of $N$ occasions where a particular meaning ${\cal M}$ was conveyed. On $n_v$ occasions, a \emph{token} of a particular linguistic structure $v$ was used ($v=1,2,3,\ldots$). When next called upon to convey the same meaning, she picks one of the $N$ stored tokens with equal probability, and replicates it. She retains a record of this utterance in her store by replacing one of the existing tokens (again chosen at random) with a token of the variant she just produced. See Figure~\ref{fig:moran}. In a population genetics context, this particular model is known as the Moran model \cite{mor58}. We will examine various extensions and generalisations, including interactions with other speakers, below.
\begin{figure}[hb]
\centerline{
\psfig{file=moran.eps,width=5cm}
}
\vspace*{8pt}
\caption{\label{fig:moran} A single update in the Moran model. One of the tokens (filled circles) is selected at random and duplicated. One existing token is randomly chosen and deleted so that the total number of stored tokens remains constant over time. The illustrated update leads to the variant represented by the darker shading increasing in frequency relative to that represented by the lighter shading.}
\end{figure}
If $N$ is large, and $x_v$ measures the probability that the speaker uses variant $v$ to convey ${\cal M}$, it is well established that the probability distribution of $x_v$ is governed by the Fokker-Planck (or Kolmogorov, or diffusion) equation
\begin{equation}
\label{ne}
\frac{\partial}{\partial t} P(x_v, t) = \frac{\partial^2}{\partial x_v^2} x_v(1-x_v) P(x_v, t)
\end{equation}
if one unit of time corresponds to $N^2$ token production events. This is the defining equation of genetic drift \cite{cro70}, a process that has been studied intensively by population geneticists since the 1930s. One can find extensive discussion of how this important equation is derived and solved in the literature (see e.g., \cite{cro70,ewe04,bly07} and references therein), so I will not repeat this unnecessarily here.
The dynamical rules used above to define this model are completely arbitrary. One would be correct in levelling Castellano \textit{et al}'s criticism of being ``justified mainly by vague plausibility arguments, with no direct connection to measurable facts'' at this model. However, we launch our defence of neutral evolution as a null model for language dynamics with the observation that \emph{very many models in which replication takes place at a rate that does not depend on the replicator's structure are also described by the diffusion equation (\ref{ne})}.
Let us first add other speakers to the mix. This can be achieved by introducing a separate Moran-type population for each speaker. At any given interaction, two speakers are chosen to interact, and a token is sampled from each store. Copying a sampled token and replacing it within the same store that the sample was taken from corresponds to a speaker ``listening to herself''---that is, reinforcing her own behaviour. Additionally, one speaker can place a copy of the other speaker's token in his store: this corresponds to a speaker modifying their behaviour to match more closely that of the interlocutor. We can assign different probabilities to events of copying tokens between stores---see Figure~\ref{fig:multimoran}. This allows different speakers to be influenced to a greater or lesser extent by different members of the community: as we will discuss in the next section, variation of these probabilities between speakers relates to acts of identity and related phenomena in sociolinguistics.
\begin{figure}[hb]
\centerline{
\psfig{file=multimoran.eps,width=8cm}
}
\vspace*{8pt}
\caption{\label{fig:multimoran} A multi-speaker generalisation of the Moran model. Here, two speakers $i$ and $j$ interact, each sampling a token from their stores. With probability $p_{ij}$ speaker $i$ retains a copy of speaker $j$'s sampled token in his store (displacing an existing token from store $i$). With probability $p_{ji}$ converse applies. The standard Moran update (wherein a sampled token is reinserted into a speaker's own store) is always performed for both speakers.}
\end{figure}
This multi-speaker generalisation of the Moran model is a version of the \emph{Utterance Selection Model} \cite{bax06}, a mathematical instantiation of the evolutionary model for language change proposed by Croft \cite{cro00}. Translated into population genetics language, this is genetic drift in a subdivided population \cite{rou04}. Under certain technical assumptions on the network of interactions between speakers \cite{bly10,bly11}, which seems to amount to the network having the `small-world' property (i.e., a short distance between any pair of speakers, relative to the size of the network, a property believed to be true of real social networks), equation (\ref{ne}) can \emph{still} be used to describe the dynamics of a linguistic variant, albeit under a different definition of time unit, and a weighted average of the usage frequency in place of $x_v$.
Different models for the storage of tokens in memory can be employed, and still give rise to an equation of the form (\ref{ne}). For example, one can relax the rigid one-in, one-out policy that is enforced in the Moran model; alternatively, one can replace more than one token in each update, or even a number drawn from a distribution \cite{ewe04}. This number can further depend on the age of the speaker: if the age distribution in the community remains stationary as individuals age, it has been found that Eq.~(\ref{ne}) continues to describes the dynamics of a variant (again with a suitably defined unit of time) \cite{bax11}. It seems likely that any combination of the the above effects would serve only to change the characteristic timescale of Eq.~(\ref{ne}).
The essential ingredient of an evolutionary process that leads to an equation of the form (\ref{ne}) is the uniform sampling of stored tokens in producing an utterance. This amounts to an assumption that the different variants $v$ of a linguistic variable are functionally and socially equivalent. In the above, we have described the process in terms of different forms with a common meaning. This may apply to synonyms of the same word, different ways of conveying a grammatical function (like the future tense), or different phonetic realisations of a vowel (such as the `a' in the word `trap'). This is the type of variation typically considered by sociolinguists (see, e.g.,~\cite{lab01}). Fundamentally different dynamics emerge when the sampling is nonuniform. The simplest way to achieve this is if mutations are possible---that is, once a stored token is chosen, there is some probability that a different token is actually uttered. This could model the case of attempting to convey a meaning that differs slightly from ${\cal M}$, or the fact that due to articulatory or auditory constraints, a speaker is not able to produce the intended token. The main effect of mutations on the Moran model is that it supports a stationary state in which multiple variants coexist \cite{cro70,ewe04}. In all models that are described by (\ref{ne}), every variant bar one eventually goes extinct. The effect of mutations could (and should) be incorporated into a null model if, for example, there is evidence that variation is being generated as the language evolves.
Fundamentally different behaviour also arises when the probability a variant is used is a nonlinear function of its frequency in the store. Generically, such nonlinearities can be interpreted as a form of selection, and hence departure from a neutral model---which may or may not include mutation as appropriate to the empirical context---would normally be taken to indicate that selection played a role in shaping the structure of a population. In the context of language dynamics, two selection mechanisms are often advocated. Some take the view that one variant may be inherently more `functional' than another (e.g., because it is more easily articulated)---see e.g.~\cite{net99}. Croft \cite{cro00} however argues that such functional factors are better represented by mutation processes generating variation: it is then left to \emph{social factors} (such as one variant being associated with a prestigious group of speakers) to propagate some variants at the expense of others. Gotelli and McGill \cite{got06} argues that in population genetics, where reproduction and mutation rates can be independently measured, neutral evolution (as encapsulated by Eq.~(\ref{ne}) or one of the extensions that incorporates mutation) can be used as a null model corresponding to the hypothesis that there is no selection acting. However, in an ecological context these parameters are less accessible---and in cultural evolutionary applications also certainly cannot be directly observed. Therefore more work is needed to convince ourselves that neutral evolution can be used as a null model for language dynamics.
\subsection{A more concrete basis in cognition}
In a recent paper, Reali and Griffiths \cite{rea09} (hereafter, RG) forged an important link between explicit models of learning and neutral evolution. The agents in these models are \emph{Bayesian learners}. Given some prior beliefs regarding how languages might in principle be structured, and (incomplete) data obtained from interactions with other language users, a Bayesian learner draws a rational inference as to the structure of the language used in his speech community. An advantage of this approach is that it is closely aligned with empirical research in psychology: Bayesian learning is one of the paradigms that have been used to understand the behaviour of human subjects in a number of laboratory-based experiments (see e.g., the special issue beginning with Ref.~\cite{smi08}).
The crucial step taken by RG was to integrate Bayesian learning into the \emph{iterated learning} paradigm of Kirby and coworkers \cite{smi03}. Iterated learning generically describes the situation where an agent's task is to learn a structure that has been learned before. RG operationalise this with a \emph{diffusion chain}, wherein the first agent is assumed already to have learned a language. This agent then uses the language, and the second agent in the chain infers its structure from the utterances that are produced. Once this second agent has reached a certain age, the first agent is removed from the system, and the second agent produces utterances in the presence of a third agent and so on.
As the nomenclature suggests, the learning algorithm in this model exploits Bayes' theorem. The learner's seeks to determine the frequency $x_v$ that variant $v$ is used to convey meaning ${\cal M}$ by the teacher. If $N$ tokens are heard in total, $n_v$ of which are of variant $v$, the learner constructs the probability distribution for the frequency $x_v$ via Bayes' rule
\begin{equation}
P(x_v | n_v) \propto P(n_v | x_v) P(x_v)
\end{equation}
in which the constant of proportionality is fixed by summing over all possible $v$. On the right-hand side of this expression are the \emph{prior} $P(x_v)$ and the likelihood $P(n_v | x_v)$. The prior encapsulates the learner's prior beliefs about the set of possible language structures. For example, this could be uniform: anything goes. Alternatively, it could favour values of $x_v$ close to zero and one, thereby building in a preference for languages in which speakers consistently use one particular variant to convey the meaning, as opposed to switching freely between them. Another possibility is the opposite preference. RG allow for all these possibilities by adopting a Dirichlet distribution for the prior:
\begin{equation}
P(x_v) \propto x_v^{\gamma-1} (1-x_v)^{\gamma -1} \;.
\end{equation}
If $\gamma=1$, the prior is uniform; consistency is favoured (disfavoured) for $0 < \gamma<1$ ($\gamma>1$).
The function $P(n_v | x_v)$ is the probability the learner ascribes to the event that $n_v$ tokens of variant $v$ are uttered \emph{assuming} that the speaker's usage frequency is known to be $x_v$. As in the Utterance Selection Model \cite{bax06}, RG assume a binomial distribution of $N$ trials (tokens) with a success probability $x_v$. Having constructed the posterior distribution $P(x_v)$, RG assume that the learner takes its mean to fix an actual value of $x_v$ to use for his own token productions. As a consequence of these particular choices, RG find that $x_v$ is governed by a neutral evolutionary dynamics within which mutations between any pair of variants occurs at a constant rate proportional to $\gamma$. More precisely, one has for large $N$ the Fokker-Planck equation
\begin{equation}
\label{nem}
\frac{\partial}{\partial t} P(x_v, t) = \frac{2\gamma}{k} \frac{\partial}{\partial x_v} (k x_v-1) P(x_v, t) + \frac{\partial^2}{\partial x_v^2} x_v(1-x_v) P(x_v, t)
\end{equation}
where $k$ is the total number of possible linguistic variants conveying the meaning ${\cal M}$ and one unit of time corresponds to $2N$ generations of learners.
This derivation of a neutral evolutionary dynamics from a specific model of cognition provides a firmer basis for the use of neutral evolution as a null model for language dynamics. It is however true that the direct mapping to a standard neutral evolutionary model depends somewhat crucially on the choice of the prior, the likelihood function, the way the learner selects $x_v$ from the posterior and the fact that one agent learns only from another in a single batch, with the linguistic behaviour remaining fixed after this learning period is over. As noted in the previous section, a rather large number of changes can be made to the Moran model, whilst still being well-described by the diffusion equation (\ref{ne}). This is also when mutations are present. It is therefore plausible that there exist other combinations of Bayesian inference and iterated learning may also lead to a model for the language dynamics of the form (\ref{nem}), although this has not yet been established.
\subsection{Linguistic theories and neutral evolution}
In sociohistorical linguistics, one is often interested in the question of why a language change (e.g., a change in word order) occurred. A variety of fundamental mechanisms have been proposed. For example, the theory of \emph{accommodation} \cite{gil73} describes a process in which interacting speakers become more alike in their linguistic behaviour. Speakers who frequently interact with one another would be expected to be more similar than those who rarely converse. A theory that allows for accommodation alone as a mechanism for change may only make reference to different interaction frequencies between pairs of speakers in explaining any observed change process.
In terms of the multi-speaker Moran process introduced in Section~\ref{sec:moran}, an accommodation-only theory allows for different pairs of speakers to be chosen to interact (have their stores sampled), but the probability that a token is copied from the first to the second speaker must equal that of copying from the second to the first. The weight assigned to another speaker's utterances depends on the identity of neither speaker nor hearer.
Contrasting theories are those that are based on \emph{prestige} \cite{lab01} or \emph{acts of identity} \cite{lep85}. Here the identity of speaker and listener may both play in role in determining (a) how much weight a listener gives to a speaker's utterances at the time they are produced and (b) whether, at the time of production, a speaker favours one variant over another due to the identity of speakers who are associated with it. An example of an act of identity would be a speaker emulating the linguistic behaviour of a socially prestigious group, perhaps acquiring some of this prestige in the process, or at least identifying themselves as aligning with this group as opposed to any other.
The role of identity as a an explanatory factor in language change has been disputed in some quarters. Most notably, Trudgill argues that, in cases of new-dialect formation in emerging societies, the notion of a new national identity played no part in the language changes that took place \cite{tru04,tru08}. Trudgill argues that all such changes took place through the process of accommodation alone, although this is a matter of some debate as the responses to the discussion paper \cite{tru08} demonstrate.
Accommodation- and identity-based theories for language change very nearly map onto neutral and non-neutral models of replication respectively. This can be understood by considered symmetry relations between different variants and between different speakers. By denying a bias towards or against a particular variant at the time of token retrieval (option (b) above), any process of sampling of stored variants that is not invariant under their relabelling is excluded. Additionally preventing anything other than interaction frequency affecting token storage demands an invariance under relabelling of speakers as well as variants. Baxter \textit{et al} \cite{bax06,bax09} observe that the frequency speaker $i$ interacts with speaker $j$ is necessarily equal to the frequency speaker $j$ interacts with speaker $i$. However, the weight ascribed to speaker $i$'s utterances by speaker $j$ need not equal the converse. An accommodation-only theory, however, does mandate an equality of these weights. Baxter \textit{et al} \cite{bax08} showed that as a consequence of this symmetry, the social network structure does not affect the choice of time units that yields Eq~(\ref{ne}) (or, if mutations are included, Eq.~(\ref{nem})). The only demographic factor affecting the unit of time is the overall size of the speech community. The fact that this quantity is directly observable greatly simplifies the application of neutral models to real instances of language change.
The one place where neutral theory and accommodation-based theories diverge is that a linear sampling of the stored tokens is excluded from the former but not necessarily from the latter. It is therefore possible that one could reject the null hypothesis that a change occurred due to neutral evolution, but this needn't rule out an accommodation-only explanation. We will return to this point below when we examine the case of the New Zealand English language dialect.
\subsection{Is neutral evolution null enough?}
In the introduction we set out three basic requirements that must be satisfied for a model to enjoy a null status. (These are discussed in more detail in the online appendix). First, it must be simple enough that the entire distribution of outcomes it predicts can be calculated. Second, any parameters in the null model must be independently measurable. Finally, the null model must describe all possible outcomes of a theory that excludes a theoretically interesting factor. I now argue that neutral evolution broadly satisfies these requirements as a null model for language dynamics, albeit with a few caveats.
\paragraph{Simple enough?} In mathematical terms, the null models of interest here correspond to Eq.~(\ref{ne}), if mutation is thought not to be relevant, Eq.~(\ref{nem}), if it is. The full time-dependent solutions of these equations for arbitrarily many variants and starting from any initial conditions are available \cite{cro70,gri79,bax07,bly10}. In principle, therefore, the distribution of any function of variant frequencies can be calculated.
\paragraph{No free parameters?} The question of whether the null model contains free parameters is more vexing. First we have to decide if mutation appears to be present, or not, and if so, at what rate this is occurring. If there is no evidence for the spontaneous generation of new variants during the period of interest, it would be appropriate to use the mutation-free version of the null model. It still remains to determine how the unit of time in which Eq.~(\ref{ne}) is defined is related to real time. In the following section we outline one attempt at this.
When mutation is judged to be relevant, one also needs to measure the mutation rate, ideally independently of the data set which is to be tested against the null model. One way to do this may be through laboratory experiments, e.g., by estimating the parameter $\gamma$ appearing in Reali and Griffith's model (as was done for example in \cite{rea09cog}). Alternatively, for certain mutation models, there exist ways to test for departure from neutral evolution that do not require knowledge of either time units or mutation rates \cite{ewe04}. Such tests may be a useful tool in the analysis of cultural evolutionary processes.
\paragraph{Theoretically interesting?} The hypothesis that a language change occurred through neutral evolution alone is very nearly theoretically interesting. There is a close---but not quite exact---mapping between neutral evolutionary processes and those that exclude prestige or identity effects. There are, however, two corner cases to contend with. First, the class of neutral models exceeds that allowed by accommodation-only theories, in that it allows for speaker identity to play a role at the time a token is retained in a store. If possible, one must exclude from the null model those instances where such unwanted effects are present. The second issue is that accommodation allows for certain nonlinear effects that are not part of a standard neutral evolutionary theory. If a null model that excludes these nonlinearities were rejected, one would need to check that it would not subsequently be accepted when the nonlinearities are introduced.
\bigskip
In short, despite its imperfections, I regard neutral evolution to be \emph{sufficiently} simple, parameter-free and theoretically interesting to act as a null model for language dynamics.
\section{Neutral evolution versus empirical reality}
\label{sec:apps}
I now examine empirical evidence for and against the null model of neutral evolution as a mechanism for language change, beginning with those cases where the data do not allow the null hypothesis to be rejected.
\subsection{The New Zealand English dialect}
Baxter \textit{et al} \cite{bax09} used neutral evolution as a null model for the formation of the New Zealand English (NZE) language dialect, as documented in the comprehensive work of Gordon \textit{et al} \cite{gor04}, and upon which Trudgill's accommodation-based theory for new-dialect formation was based \cite{tru04}. Briefly, NZE was formed as a consequence of waves of immigrants from Britain and Ireland arriving in New Zealand in the mid-19th century. This placed speakers of different regional dialects of English into contact with one another, and over the subsequent two generations, a considerable amount of variation within the speech community was eliminated.
Trudgill \cite{tru04} discusses in detail several linguistic variables (e.g., phonetic realisations of vowel sounds appearing in a class of words). In each of the cases discussed, one of the variants present in the initial condition is `fixed' in the present-day dialect (i.e., used consistently by all speakers in the community). An estimate of the initial frequency for each successful variant is provided in \cite{tru04}.
Using neutral evolution as to model Trudgill's theory (further constrained to preclude any speaker-based weighting of variants beyond interaction frequency effects), the prediction is that if a variant $v$ is present at a frequency $x_v$ in the initial condition it will fix with probability $x_v$. To decide whether the observed outcome is consistent with the neutral hypothesis, Baxter et al \cite{bax09} note that with the particular set of frequencies provided by Trudgill \cite{tru04}, the observed outcome (in which two variants initially in the minority fixed), had a likelihood that is about one tenth of the most probable outcome. That is, if multiple parallel NZE dialects were to form from the same initial condition, ten cases where all the majority variants fixed would be matched by one case where the observed outcome occurred. This does not appear to be sufficiently rare for the null hypothesis to be rejected.
Another way to quantify the likelihood of the observed outcome under the neutral hypothesis is to apply a type of `exact test' (see e.g.~\cite{sla94}). The idea here is to calculate the cumulative probability of all possible events that have a smaller probability of being realised than the observed event. Again, using the frequency data of \cite{tru04}, the combined probability within the neutral theory of all possible New Zealand English dialects that are less likely than that observed is $74\%$. This is too large for the null hypothesis of neutrality to be rejected. Moreover, models that admit nonuniform sampling of stored tokens, but in a way that is invariant under relabelling of variants or speakers, have been found in general to be a \emph{worse} fit to the NZE frequency data than the linear model \cite{bly09}. This leads us to believe that neutral evolution is indeed an appropriate null model for new-dialect formation.
\subsection{The Zipf word distribution}
It is well established that the distribution of word frequencies in a language have a Zipf (power-law) distribution. That is, $x_k \sim 1/k^{\sigma}$, where $k$ is the rank of the word ($k=1$ is the most frequent word, $k=2$ the second most frequent etc.), and $\sigma$ is some exponent, usually found to be close to unity \cite{zip49}. Reali and Griffiths \cite{rea09} have argued that this distribution is to be expected from neutral theory.
To model this situation, RG consider each variant to be a distinct word, and allow in principle an infinite number of them. That is, when a mutation occurs, a hitherto unused word enters the vocabulary. This corresponds to the \emph{infinite alleles model} in population genetics \cite{ewe04}. In this model, words simply continue to be used at approximately their current frequency, subject to finite sample size fluctuations and the occasional introduction of new words.
Recall that within the formulation of the null model presented in Section~\ref{sec:moran}, each variant that exists is taken to have a \emph{single} common meaning ${\cal M}$. Thus the actual \emph{meaning} of words, and in particular, any relationship between word meanings (e.g., synonymy) plays no role in this model. That is, two words with the same meaning are considered to be competing in the same space as two words with completely different meanings. RG do not comment on this aspect of their analysis, nor do they refer to a theory that suggests that words with different meanings should (or should not) compete in this way. Therefore, if the neutral model is found to predict a Zipf distribution of word frequencies (or not), it is somewhat unclear how this finding should be interpreted.
What RG do find can be summarised as follows. They first take a sample of size $N=33399$, since that corresponds to the size of a widely-used corpus of child-directed speech \cite{ber84}. On simulating the neutral model with a suitable choice of parameters in the prior, RG find they are able to reproduce the power law with exponent $\sigma = 1.70$ believed to well describe this corpus. This finding is at odds with that of Fontanari and Perlovsky \cite{fon70} who argue that the variant abundance distribution (when variants are rank ordered) has an exponential tail rather than a power law. Interestingly, these authors cite a earlier work by Tullo and Hurford \cite{tul03} that proposes neutral evolution as a more appropriate null model for a word distribution than an earlier contender that comprised only random emission of symbols and spaces. This illustrates again the important question of what counts as interesting when designing a null model (see online appendix).
Fontanari and Perlovsky provide one explanation as to why a power-law distribution might be inferred from simulations like those performed by RG, namely finite sample-size effects. The method used in \cite{fon70} appears to probe the full distribution more efficiently than brute-force methods. However, it is not stated precisely how these finite-size effects would lead to a power law, and whether the samples used to determine empirical word distributions fall into this finite-size regime. Closer scrutiny of the role of sample size is needed to resolve this conflict.
\subsection{Rate of lexical replacement as a function of frequency}
In a prominent paper, Lieberman \emph{et al} \cite{lie07} established that the rate at which an irregular verb was regularised decreases with its usage frequency. Whilst linguists have long understood the importance of frequency in terms of linguistic structure (see e.g., \cite{byb01} for a collection of articles on this topic), Lieberman \emph{et al}'s contribution was to state the functional form of a relationship that could be inferred from empirical data. Specifically, they found that replacement rate of an irregular verb is inversely proportional to the square-root of its frequency. Reali and Griffiths \cite{rea09} have argued that this functional form is also to be expected from neutral theory.
To apply neutral evolution to this situation, RG took each variant to be a different verb, and asked the question: given that a particular verb is used with frequency $x$, how long does it take to go extinct within the infinite-alleles model? It was then assumed that when a verb went extinct, it would be replaced by a regular form with the same meaning. The regularisation rate was then taken to be the reciprocal of the extinction time. Simulating this process, and plotting the results as a function of the initial frequency, an inverse square-root relationship between initial frequency and replacement rate was found. However, a mathematical analysis, also presented in \cite{rea09} shows that the inverse square-root law is not exact for neutral evolution (although it is a reasonable fit across a certain range of frequencies). More stringent statistical tests are needed to determine conclusively whether the data for verb regularisation really is compatible with neutral theory.
What is perhaps more concerning about this formulation is that all other verbs that coexist with the one that is outgoing have the same status. What is not included in this model is the fact that the regular and irregular form of some verb are competing with each to be used for a common meaning, while the regular forms of two different verbs are not necessarily in competition with each other (at least not in the same way). Again, it is important to relate the model more directly to linguistic theories for how verbs compete with one another.
\subsection{The trajectory of an innovation}
It is widely recognised among linguists that when a new convention usurps an existing one, the frequency of the innovation follows an `S-curve' trajectory, starting slowly, then gathering pace, before slowing down again as the old form dies out. In their remarkable work, Reali and Griffiths \cite{rea09}, further claim that neutral evolution exhibits such a phenomenon.
To arrive at this conclusion, RG note an important subtlety. An equation like (\ref{ne}) describes all possible future trajectories starting from an initial condition. In particular, the time at which a variant fixes is a random variable. However, in an instance of observed change, this time is a known quantity. RG thus argue that one should \emph{condition} on fixation occurring at a particular time. When this is done, one finds that the \emph{mean} trajectory of the incoming variant, averaged over multiple realisations of the process, follows an S-curve.
However, this does not quite correspond to the empirical situation, in which only one realisation of the process is observed. Here what is needed is the \emph{probability} of the observed trajectory within the subsensemble of changes that fix at the same time. As far as I are aware, calculation of this quantity is an outstanding technical challenge. Until this is achieved, it is hard to know whether conditioning neutral evolution on a given fixation time is sufficient to generate an S-curve with high probability in individual stochastic realisations of the dynamics.
\subsection{The rate of new-dialect formation}
We conclude by returning to the example of New Zealand English. In addition to the final structure of the new dialect, Baxter \textit{et al} \cite{bax09} also considered the formation time, noting that it was completed in a remarkably short period (approximately $50$ years) given the size of the speech community (some $100,000$ or more speakers). We recall from Equation (\ref{ne}) that all timescales are proportional to a single characteristic timescale. In the restricted class of neutral evolutionary models that correspond to the accommodation-only theory advanced by Trudgill \cite{tru04,tru08}, Baxter \textit{et al} found that this characteristic timescale is proportional to the community size, and does not depend on its structure. The origin of this surprising structure independence is in the symmetry between pairs of speakers that is implied by the accommodation-only theory. That is, if in any one interaction, each speaker accommodates towards the other by the same degree, only the community size matters. Community structure may play a role if this symmetry is relaxed and could, for instance, explain the variance of linguistic diversity with community structure noted by Lupyan and Dale \cite{lup10}, though we do not discuss this possibility further here.
Even within the accommodation-only scenario, there remains one important factor that does contribute into the emergent timescale for language change. This is the time it takes a speaker to forget a stored token. If the community is large, this time must be short to allow the change to proceed at the observed pace. However, it cannot be arbitrarily short: it certainly can't be shorter than the time between any two utterances. Experiments on infants \cite{rov95} suggest that any reasonable estimate for this time should in fact exceed two days. Already, given the size of the speech community, this leads to a characteristic timescale for the formation of the new dialect that vastly exceeds the two generations that was actually observed. Whilst there remains considerable uncertainty in the appropriate choice for the shorter timescale in this model, it seems likely that the null hypothesis of neutral evolution driving the formation of New Zealand English can be rejected.
\section{Challenges for the future}
In this work I have critically addressed the question of how to apply simple models of language dynamics to relevant empirical data. As an alternative to the construction of models whose microscopic rules appear to be informed largely by guesswork, I advocate a systematic approach based around a null model which, when rejected, implies a theory of a fundamentally different kind to the corresponding null hypothesis. I have further proposed that neutral evolution, as defined in Section~\ref{sec:neut}, is an appropriate null model for language dynamics, in that it mostly satisfies the requirements set out in the introduction.
The main selling point is that this model is robustly arrived at from diverse starting points that have one particular feature in common: the only factor affecting language dynamics is the frequency that different variant forms for a particular meaning are used by a speaker's interlocutors. At the most basic level this corresponds to a \emph{usage-based} theory for language dynamics in which linguistic structures that emerge are mostly determined by interactions with other language users (see e.g., \cite{tom03}). (These theories contrast with \emph{generative} approaches which typically ascribe a much greater importance to innate aspects of cognition in predetermining the structure of languages). Another factor in favour of neutral evolution as a null model is that it excludes such complicating factors as the meaning of words or the social status of interlocutors. Finally, this model is well studied, particularly in the population genetics literature, and many of its predictions are precisely known.
The evidence that some aspects of language dynamics might be accounted for by neutral evolution was reviewed in Section~\ref{sec:apps}. Here it was found that neutral evolutionary models corresponding to a theory for language change driven purely by accommodation could quantitatively describe the structure of the New Zealand English language dynamics but not the speed at which it was formed. Although there were free parameters in the model used for this analysis, these conclusions were found to be independent over the range of values they could reasonably take (see \cite{bax09} for full details). On the other hand, the quantitative support for neutral evolution provided by Reali and Griffiths \cite{rea09}, namely compatibility with word-frequency distributions and lexical replacement rates, involved parameter fitting in both cases. According to Gotelli and McGill \cite{got06} parameter fitting is problematic because it biases the null hypothesis in favour of being accepted. Meanwhile, as we noted above in the case of verb regularisation, it is not always clear what the null hypothesis corresponding to neutral evolution is. This is of crucial importance in understanding the theoretical consequences of rejecting the null model.
From the discussion of Section~\ref{sec:apps} it is apparent that applying a model even as simple as neutral evolution to empirical data can be difficult in practice. In part this can be due to the nature of available data: it is always difficult to test a theory when data are limited. This, however, is a state of affairs that suggests effort should be expended on the collection of more relevant data, rather than on the development and study of new models, echoing the sentiment of Castellano \textit{et al} referred to in the introduction. An important contribution that modellers can make here is to determine precisely \emph{what} data would most effectively yield the deepest insights into the fundamental mechanisms driving language dynamics.
We have, however, also seen that despite the venerability of neutral evolution, a number of technical challenges stand in the way of its being fully understood. The space of models that has been shown to be characterised at some level by neutral evolution is growing on a daily basis. As was discussed in Section~\ref{sec:neut}, many modifications can be made to the most simple neutral models whose only effect is to change its single characteristic timescale. What is missing is a precise understanding of what factors lead to a fundamentally different dynamics, and what these factors correspond to in terms of linguistic theory. The relationship between simple models for language dynamics and Bayesian learning uncovered by Reali and Griffiths looks like particularly fertile ground for future enquiry. As we have noted, the robustness of neutral evolution as a model for language dynamics when adopting more abstract starting points suggests that a wide range of combinations of Bayesian and iterated learning should ultimately deliver a neutral evolutionary dynamics of some type or other. Further experimental research, interpreted with the Bayesian learning formalism, would also appear to be useful in constraining parameters that appear in models of language dynamics.
Even within the simplest models, i.e., those described by Equations (\ref{ne}) and (\ref{nem}), some basic properties seem at best poorly appreciated and at worst unknown to us at this time. For example, the nature of the distribution of variant frequencies within neutral evolution needs to be more widely appreciated. Perhaps more importantly, Reali and Griffiths emphasise the effects of conditioning the distribution of trajectories generated by neutral evolution on certain observed properties. This seems to have received very little attention within the modelling community, a fact that prevents certain empirical properties of language change (like the trajectory followed by an innovation) from being satisfactorily analysed.
Closer study of change trajectories is one way in which departure from neutral behaviour may be detected. Much sociolinguistic research is concerned with the manner by which one linguistic variant usurps another, these processes sometimes taking up to several hundred years (as, for example, in the case of the marking of the future tense in Brazilian Portuguese English \cite{pop07}). Such records of the past are typically unavailable for ecological changes and it may be that there are new ways to detect the presence of selection by examining the time-course of change. Meanwhile, there are a number of statistical tests to non-neutral diversity patterns in communities sampled at a single point in time (mostly based on Ewens' sampling formula and its relatives \cite{ewe04,eti05}). To my knowledge, such tests have yet to be applied to cultural evolutionary data.
In short, to achieve the goal of linking models to data, I argue not for more models and certainly not for the cuteness of a model's behaviour being the sole factor in an evaluation of its importance. Instead what I believe is needed are null models that incorporate all possible factors that are excluded by an interesting, nontrivial and relevant theoretical viewpoint. For those cases where one wishes to identify social identity or meaning as being significant in a language change, neutral evolution seems to fit the bill. No doubt there are other null models that are relevant to other key questions about language dynamics, but I think it is fair to say that considerable effort must be expended if we are to draw these out of the vast array of models that have been presented in the statistical mechanics literature so far.
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\section{The purpose of GNI}
Geometric numerical integration (GNI) emerged as a major thread in numerical mathematics some 25 years ago. Although it has had antecedents, in particular the concerted effort of the late Feng Kang and his group in Beijing to design structure-preserving methods, the importance of GNI has been recognised and its scope delineated only in the 1990s.
But we are racing ahead of ourselves. At the beginning, like always in mathematics, there is the definition and the rationale of GNI. The rationale is that all-too-often mathematicians concerned with differential equations split into three groups that have little in common. Firstly, there are the applied mathematicians, the model builders, who formulate differential equations to describe physical reality. Secondly, there are those pure mathematicians investigating differential equations and unravelling their qualitative features. Finally, the numerical analysts who flesh out the numbers and the graphics on the bones of mathematical formulation. Such groups tended to operate in mostly separate spheres and, in particular, this has been true with regards to computation. Discretisation methods were designed (with huge creativity and insight) to produce rapidly and robustly numerical solutions that can be relied to carry overall small error. Yet, such methods have often carried no guarantee whatsoever to respect qualitative features of the underlying system, the very same features that had been obtained with such effort by pure and applied mathematicians.
Qualitative features come basically in two flavours, the {\em dynamical\/} and the {\em geometric.\/} Dynamical features -- sensitivity with respect to initial conditions and other parameters, as well as the asymptotic behaviour -- have been recognised as important by numerical analysts for a long time, not least because they tend to impinge directly on accuracy. Thus, sensitivity with respect to initial conditions and perturbations comes under `conditioning' and the recovery of correct asymptotics under `stability', both subject to many decades of successful enquiry. Geometric attributes are invariants, constants of the flow. They are often formulated in the language of differential geometry (hence the name!) and mostly come in three varieties: {\em conservation laws,\/} e.g.\ Hamiltonian energy or angular momentum, which geometrically mean that the solution, rather than evolving in some large space $\BB{R}^d$, is restricted to a lower-dimensional manifold $\mathcal{M}$, {\em Lie point symmetries,\/} e.g.\ scaling invariance, which restrict the solution to the tangent bundle of some manifold, and quantities like {\em symplecticity\/} and {\em volume,\/} whose conservation corresponds to an evolution on the cotangent bundle of a manifold. {\em The design and implementation of numerical methods that respect geometric invariants is the business of GNI.\/}
Since its emergence, GNI has become the new paradigm in numerical solution of ODEs, while making significant inroads into numerical PDEs. As often, yesterday's revolutionaries became the new establishment. This is an excellent moment to pause and take stock. Have all the major challenges been achieved, all peaks scaled, leaving just a tidying-up operation? Is there still any point to GNI as a separate activity or should it be considered as a victim of its own success and its practitioners depart to fields anew -- including new areas of activity that have been fostered or enabled by GNI?
These are difficult questions and we claim no special authority to answer them in an emphatic fashion. Yet, these are questions which, we believe, must be addressed. This short article is an attempt to foster a discussion. We commence with a brief survey of the main themes of GNI {\em circa\/} 2015. This is followed by a review of recent and ongoing developments, as well as of some new research directions that have emerged from GNI but have acquired a life of their own.
\section{The story so far}
\subsection{Symplectic integration}
The early story of GNI is mostly the story of symplectic methods. A Hamiltonian system
\begin{equation}
\label{Hamiltonian}
\dot{\MM{p}}=-\frac{\partial H(\MM{p},\MM{q})}{\partial\MM{q}},\qquad \dot{\MM{q}}=\frac{\partial H(\MM{p},\MM{q})}{\partial \MM{p}},
\end{equation}
where $H:\BB{R}^{2d}\rightarrow\BB{R}$ is a {\em Hamiltonian energy,\/} plays a fundamental role in mechanics and is known to possess a long list of structural invariants, e.g.\ the conservation of the Hamiltonian energy. Yet, arguably its most important feature is the conservation of the {\em symplectic form\/} $\sum_{k=1}^d \D\MM{p}_k\wedge\D\MM{q}_k$ because symplecticity is equivalent to Hamiltonicity -- in other words, every solution of a Hamiltonian system is a symplectic flow and every symplectic flow is Hamiltonian with respect to an appropriate Hamiltonian energy \cite{hairer06gni}.
The solution of Hamiltonian problems using symplectic methods has a long history, beautifully reviewed in \cite{hairer03gni}, but modern efforts can be traced to the work of Feng and his collaborators at the Chinese Academy of Sciences, who have used generating-function methods to solve Hamiltonian systems \cite{feng89ccd}. And then, virtually simultaneously, \citeasnoun{lasagni88crk}, \citeasnoun{sanzserna88rks} and \citeasnoun{suris88pss} proved that certain Runge--Kutta methods, including the well-known Gauss--Legendre methods, preserve symplecticity and they presented an easy criterion for the symplecticity of Runge--Kutta methods. GNI came of age!
Subsequent research into symplectic Runge--Kutta methods had branched out into a number of directions, each with its own important ramifications outside the Hamiltonian world:
\begin{itemize}
\item {\em Backward error analysis.\/} The idea of backward error analysis (\reflectbox{BEA}) can be traced to Wilkinson's research into linear algebra algorithms in the 1950ties. Instead of asking ``what is the numerical error for our problem", Wilkinson asked ``which nearby problem is solved {\em exactly\/} by our method?". The difference between the original and the nearby problem can tell us a great deal about the nature of the error in a numerical algorithm.
A generalisation of \reflectbox{BEA} to the field of differential equations is fraught with difficulties. Perhaps the first successful attempt to analyse Hamiltonian ODEs in this setting was by \citeasnoun{neishtadt84sms} and it was followed by many, too numerous to list: an excellent exposition (like for many things GNI) is the monograph of \citeasnoun{hairer06gni}. The main technical tool is the B-series, an expansion of composite functions in terms of forests of rooted trees, originally pioneered by \citeasnoun{butcher63csr}. (We mention in passing that the Hopf algebra structure of this {\em Butcher group\/} has been recently exploited by mathematical physicists to understand the renormalisation group \cite{connes99lqt} -- as the authors write, ``We regard Butcher's work on the classification of numerical integration methods as an impressive example that concrete problem-oriented work can lead to far-reaching conceptual results''.) It is possible to prove that, subject to very generous conditions, the solution of a Hamiltonian problem by a symplectic method, implemented with constant step size, is exponentially near to the {\em exact\/} solution of a nearby Hamiltonian problem for an exponentially long time. This leads to considerably greater numerical precision, as well as to the conservation on average (in a strict ergodic sense) of Hamiltonian energy.
B-series fall short in a highly oscillatory and multiscale setting, encountered frequently in practical Hamiltonian systems. The alternative in the \reflectbox{BEA} context is an expansion into {\em modulated Fourier series\/} \cite{hairer00lte}.
\item {\em Composition and splitting.}
Many Hamiltonians of interest can be partitioned into a sum of kinetic and potential energy, $H(\MM{p},\MM{q})=\MM{p}^\top M\MM{p}+V(\MM{q})$. It is often useful to take advantage of this in the design of symplectic methods. While conventional symplectic Runge--Kutta methods are implicit, hence expensive, {\em partitioned Runge--Kutta methods,\/} advancing separately in the `direction' of kinetic and potential energy, can be explicit and are in general much cheaper. While perhaps the most important method, the St\"ormer--Verlet scheme \cite{hairer03gni}, has been known for many years, modern theory has led to an entire menagerie of composite and partitioned methods \cite{sanzserna94nhp}.
Splitting methods\footnote{Occasionally known in the PDE literature as {\em alternate direction methods.\/}} have been used in the numerical solution of PDEs since 1950s. Thus, given the equation $u_t=\mathcal{L}_1(u)+\mathcal{L}_2(u)$, where the $\mathcal{L}_k$s are (perhaps nonlinear) operators, the idea is to approximate the solution in the form
\begin{equation}
\label{splitting}
u(t+h)\approx {\mathrm e}^{\alpha_1 h\mathcal{L}_1} {\mathrm e}^{\beta_1 h\mathcal{L}_2} {\mathrm e}^{\alpha_2 h\mathcal{L}_1} \cdots {\mathrm e}^{\alpha_s h\mathcal{L}_1} {\mathrm e}^{\beta_s\mathcal{L}_2}u(t),
\end{equation}
where $v(t_0+h)=:{\mathrm e}^{h \mathcal{L}_1}v(t_0)$ and $w(t_0+h)=:{\mathrm e}^{h \mathcal{L}_2}w(t_0)$ are, formally, the solutions of $\dot{v}=\mathcal{L}_1(v)$ and $\dot{w}=\mathcal{L}_2(w)$ respectively, with suitable boundary conditions. The underlying assumption is that the solutions of the latter two equations are either available explicitly or are easy to approximate, while the original equation is more difficult.
A pride of place belongs to {\em palindromic compositions\/} of the form
\begin{equation}
\label{palindromic}
{\mathrm e}^{\alpha_1 h\mathcal{L}_1} {\mathrm e}^{\beta_1 h\mathcal{L}_2} {\mathrm e}^{\alpha_2 h\mathcal{L}_1} \cdots {\mathrm e}^{\alpha_q h\mathcal{L}_1}{\mathrm e}^{\beta_q h\mathcal{L}_2}{\mathrm e}^{\alpha_q h\mathcal{L}_1} \cdots {\mathrm e}^{\alpha_2 h\mathcal{L}_1} {\mathrm e}^{\beta_1 h\mathcal{L}_2} {\mathrm e}^{\alpha_1 h\mathcal{L}_1},
\end{equation}
invariant with respect to a reversal of the terms. They constitute a {\em time-symmetric map,\/} and this has a number of auspicious consequences. Firstly, they are always of an even order. Secondly -- and this is crucial in the GNI context -- they respect both structural invariants whose integrators are closed under composition, i.e.\ form a group (for example integrators preserving volume, symmetries, or first integrals), as well as invariants whose integrators are closed under symmetric composition, i.e.\ form a symmetric space (for example integrators that are self-adjoint, or preserve reversing symmetries). A basic example of \R{palindromic} is the second-order {\em Strang composition\/}
\begin{displaymath}
{\mathrm e}^{\frac12 h\mathcal{L}_1} {\mathrm e}^{h\mathcal{L}_2}{\mathrm e}^{\frac12 h \mathcal{L}_1} ={\mathrm e}^{h(\mathcal{L}_1+\mathcal{L}_2)} +\O{h^3}.
\end{displaymath}
Its order -- and, for that matter, the order of any time-symmetric method -- can be boosted by the {\em Yoshida device\/} \cite{yoshida90cho}. Let $\Phi$ be a time-symmetric approximation to ${\mathrm e}^{t\mathcal{L}}$ of order $2P$, say. Then
\begin{displaymath}
\Phi((1+\alpha)h)\Phi(-(1+2\alpha)h)\Phi((1+\alpha)h),\qquad \mbox{where}\qquad \alpha=\frac{2^{1/(2P+1)}-1}{2-2^{1/(2P+1)}}
\end{displaymath}
is also time symmetric and of order $2P+2$. Successive applications of the Yoshida device allow to increase arbitrarily the order of the Strang composition, while retaining its structure-preserving features. This is but a single example of the huge world of splitting and composition methods, reviewed in \cite{mclachlan02sm}.
\item {\em Exponential integrators.}
Many `difficult' ODEs can be written in the form $\dot{\MM{y}}=A\MM{y}+\MM{b}(\MM{y})$ where the matrix $A$ is `larger' (in some sense) than $\MM{b}(\MM{y})$ -- for example, $A$ may be the Jacobian of an ODE (which may vary from step to step). Thus, it is to be expected that the `nastiness' of the ODE under scrutiny -- be it stiffness, Hamiltonicity or high oscillation -- is somehow `hardwired' into the matrix $A$. The exact solution of the ODE can be written in terms of the variation-of-constants formula,
\begin{equation}
\label{VoC}
\MM{y}(t+h)={\mathrm e}^{hA}\MM{y}(t)+\int_0^h {\mathrm e}^{(h-\xi)A}\MM{b}(\MM{y}(t+\xi))\D\xi,
\end{equation}
except that, of course, the right-hand side includes the unknown function $\MM{y}$. Given the availability of very effective methods to compute the matrix exponential, we can exploit this to construct {\em exponential integrators,\/} explicit methods that often exhibit favourable stability and structure-preservation features. The simplest example, the {\em exponential Euler\/} method, freezes $\MM{y}$ within the integral in \R{VoC} at its known value at $t$, the outcome being the first-order method
\begin{displaymath}
\MM{y}_{n+1}={\mathrm e}^{hA}\MM{y}_n+A^{-1}({\mathrm e}^{hA}-I)\MM{b}(\MM{y}_n).
\end{displaymath}
The order can be boosted by observing that (in a loose sense which can be made much more precise) the integral above is discretised by the Euler method, which is a one-stage explicit Runge--Kutta scheme, discretising it instead by multistage schemes of this kind leads to higher-order methods \cite{hochbruck10ei}.
Many Hamiltonian systems of interest can be formulated as second-order systems of the form $\ddot{\MM{y}}+\Omega^2\MM{y}=\MM{g}(\MM{y})$. Such systems feature prominently in the case of highly oscillatory mechanical systems, where $\Omega$ is positive definite and has some large eigenvalues. Variation of constants \R{VoC} now reads
\begin{Eqnarray*}
\left[\!
\begin{array}{c}
\MM{y}(t+h)\\
\dot{\MM{y}}(t+h)
\end{array}
\!\right]&=& \left[
\begin{array}{cc}
\cos(h\Omega) & \Omega^{-1}\sin(h\Omega)\\
-\Omega\sin(h\Omega) & \cos(h\Omega)
\end{array}
\right] \left[\!
\begin{array}{c}
\MM{y}(t)\\
\dot{\MM{y}}(t)
\end{array}
\!\right]\\
&&\mbox{}+\int_t^{t+h} \left[
\begin{array}{cc}
\cos((h-\xi)\Omega) & \Omega^{-1}\sin((h-\xi)\Omega)\\
-\Omega\sin((h-\xi)\Omega) & \cos((h-\xi)\Omega)
\end{array}
\right] \! \left[
\begin{array}{c}
\MM{0}\\
\MM{g}(\MM{y}(t+\xi))
\end{array}
\right]\!\D\xi
\end{Eqnarray*}
and we can use either standard exponential integrators or exponential integrators designed directly for second-order systems and using Runge--Kutta--Nystr\"om methods on the nonlinear part \cite{wu13spa}.
An important family of exponential integrators for second-order systems are {\em Gautschi-type methods\/}
\begin{equation}
\label{Gautschi}
\MM{y}_{n+1}-2\MM{y}_n+\MM{y}_{n-1}=h^2\Psi(h\Omega) (\MM{g}_n-\Omega^2\MM{y}_n),
\end{equation}
which are of second order. Here $\Psi(x)=2(1-\cos x)/x$ while, in Gautschi's original method, $\MM{g}_n=\MM{g}(\MM{y}_n)$ \cite{hochbruck10ei}. Unfortunately, this choice results in resonances and a better one is $\MM{g}_n=\MM{g}(\Phi(h\Omega)\MM{y}_n)$, where the {\em filter\/} $\Phi$ eliminates resonances: $\Phi(0)=I$ and $\Phi(k\pi)=0$ for $k\in\BB{N}$. We refer to \cite{hochbruck10ei} for further discussion of such methods in the context of symplectic integration.
\item {\em Variational integrators.} {\em Lagrangian formulation\/} recasts a large number of differential equations as minima of nonlinear functionals. Thus, for example, instead of the Hamiltonian problem $M\ddot{\MM{q}}+\MM{\nabla} V(\MM{q})=\MM{0}$, where the matrix $M$ is positive definite, we may consider the equivalent variational formulation of minimizing the positive-definite nonlinear functional $L(\MM{q},\dot{\MM{q}})=\frac12 \dot{\MM{q}}^\top M\dot{\MM{q}}-V(\MM{q})$. With greater generality, Hamiltonian and Lagrangian formulations are connected via the familiar Euler--Lagrange equations and, given the functional $L$, the corresponding second-order system is
\begin{displaymath}
\frac{\partial L(\MM{q},\dot{\MM{q}})}{\partial\MM{q}}-\frac{\D}{\D t} \left[\frac{\partial L(\MM{q},\dot{\MM{q}})}{\partial \dot{\MM{q}}}\right]=\MM{0}.
\end{displaymath}
The rationale of variational integrators parallels that of the {\em Ritz method\/} in the theory of finite elements. We first reformulate the Hamiltonian problem as a Lagrangian one, project it to a finite-dimensional space, solve it there and transform back. The original symplectic structure is replaced by a finite-dimensional symplectic structure, hence the approach is by design symplectic \cite{marsden01dmv}.
\end{itemize}
\subsection{Lie-group methods}
Let $\mathcal{G}$ be a Lie group and $\mathcal{M}$ a differentiable manifold. We say that $\Lambda:\mathcal{G}\times\mathcal{M}\rightarrow\mathcal{M}$ is a {\em group action\/} if\\[4pt]
a.~$\Lambda(\iota,y)=y$ for all $y\in\mathcal{M}$ (where $\iota$ is the identity of $\mathcal{G}$) and \\[2pt]
b.~$\Lambda(p,\Lambda(q,y))=\Lambda(p\cdot q,y)$ for all $p,q\in\mathcal{G}$ and $y\in\mathcal{M}$.\\[4pt]
If, in addition, for every $x,y\in\mathcal{M}$ there exists $p\in\mathcal{G}$ such that $y=\Lambda(p,x)$, the action is said to be transitive and $\mathcal{M}$ is a {\em homogeneous space,\/} acted upon by $\mathcal{G}$.
Every Lie group acts upon itself, while the orthogonal group $\CC{O}(n)$ acts on the $(n-1)$-sphere by multiplication, $\Lambda(p,y)=py$. The orthogonal group also acts on the {\em isospectral manifold\/} of all symmetric matrices similar to a specific symmetric matrix by similarity, $\Lambda(p,y)=pyp^\top$. Given $1\leq m\leq n$, the {\em Grassmann manifold\/} $\BB{G}(n,m)$ of all $m$-dimensional subspaces of $\BB{R}^n$ is a homogeneous space acted upon by $\CC{SO}(m)\times\CC{SO}(n-m)$, where $\CC{SO}(m)$ is the special orthogonal group -- more precisely, $\BB{G}(n,m)=\CC{SO}(n)/(\CC{SO}(m)\times\CC{SO}(n-m))$.
Faced with a differential equation evolving in a homogeneous space, we can identify its flow with a group action: Given an initial condition $y_0\in\mathcal{M}$, instead of asking ``what is the value of $y$ at time $t>0$'' we might pose the equivalent question ``what is the group action that takes the solution from $y_0$ to $y(t)$?''. This is often a considerably more helpful formulation because a group action can be further related to an {\em algebra action.\/} Let $\GG{g}$ be the Lie algebra corresponding to the matrix group $\mathcal{G}$, i.e.\ the tangent space at $\iota\in\mathcal{G}$, and denote by $\GG{X}(\mathcal{M})$ the set of all Lipschitz vector fields over $\mathcal{M}$. Let $\lambda:\GG{g}\rightarrow\GG{X}(\mathcal{M})$ and $a:\BB{R}_+\times\mathcal{M}\rightarrow\GG{g}$ be both Lipschitz. In particular, we might consider
\begin{displaymath}
\lambda(a,y)=\frac{\D}{\D s} \Lambda(\rho(s,y),y)\,\rule[-6pt]{0.75pt}{18pt}_{\,s=0},
\end{displaymath}
where $\Lambda$ is a group action and $\rho:\BB{R}_+\rightarrow\mathcal{G}$, $\rho(s,y(s))=\iota+a(s,y(s))s+\O{s^2}$ for small $|s|$. The equation $\dot{y}=\lambda(a(t,y),y)$, $y(0)=y_0\in\mathcal{M}$ represents {\em algebra action\/} and its solution evolves in $\mathcal{M}$. Moreover,
\begin{equation}
\label{alg_action}
y(t)=\Lambda(v(t),y_0)\qquad \mbox{where}\qquad \dot{v}=a(t,\Lambda(v,y_0))v,\quad v(0)=\iota\in\mathcal{G}
\end{equation}
is a {\em Lie-group equation.\/} Instead of solving the original ODE on $\mathcal{M}$, it is possible to solve \R{alg_action} and use the group action $\Lambda$ to advance the solution to the next step: this is the organising principle of most {\em Lie-group methods\/} \cite{iserles00lgm}. It works because a Lie-group equation can be solved in the underlying Lie algebra, which is a {\em linear space.\/} Consider an ODE\footnote{Or, for that matter, a PDE, except that formalities are somewhat more complicated.} $\dot{y}=f(y)$, $y(0)\in\mathcal{M}$, such that $f:\mathcal{M}\rightarrow\GG{X}$ -- the solution $y(t)$ evolves on the manifold. While conventional numerical methods are highly unlikely to stay in $\mathcal{M}$, this is not the case for Lie-group methods. We can travel safely between $\mathcal{M}$ and $\mathcal{G}$ using a group action. The traffic between $\mathcal{G}$ and $\GG{g}$ is slightly more complicated and we need to define a {\em trivialisation,\/} i.e.\ an invertible map taking smoothly a neighbourhood of $0\in\GG{g}$ to a neighbourhood of $\iota\in\mathcal{G}$ and taking zero to identity. The most ubiquitous example of trivialisation is the exponential map, which represents the solution of \R{alg_action} as $v(t)={\mathrm e}^{\omega(t)}$, where $\omega$ is the solution of the {\em dexpinv equation\/}
\begin{equation}
\label{dexpinv}
\dot{\omega}=\sum_{m=0}^\infty \frac{\CC{B}_m}{m!} \CC{ad}^m_{a(t,{\mathrm e}^\omega)}\omega,\qquad \omega(0)=0\in\GG{g}
\end{equation}
\cite{iserles00lgm}. Here the $\CC{B}_m$s are Bernoulli numbers, while $\CC{ad}^m_b$ is the {\em adjoint operator\/} in $\GG{g}$,
\begin{displaymath}
\CC{ad}_b^0 c=c,\qquad \CC{ad}_b^m c=[b,\CC{ad}_b^{m-1}c],\quad m\in\BB{N},\qquad b,c\in\GG{g}.
\end{displaymath}
Because $\GG{g}$ is closed under linear operations and commutation, solving \R{dexpinv} while respecting Lie-algebraic structure is straightforward. Mapping back, first to $\mathcal{G}$ and finally to $\mathcal{M}$, we keep the numerical solution of $\dot{y}=f(t)$ on the manifold.
Particularly effective is the use of explicit Runge--Kutta methods for \R{dexpinv}, the so-called Runge--Kutta--Munthe-Kaas (RKMK) methods \cite{munthekass98rkm}. To help us distinguish between conventional Runge--Kutta methods and RKMK, consider the three-stage, third-order method with the Butcher tableau\footnote{For traditional concepts such as Butcher tableaux, Runge-Kutta methods and B-series, the reader is referred to \cite{hairer93sod}.}
\begin{equation}
\label{RK3}
\begin{array}{c|ccc}
0 & \\
\frac12 & \frac12\\[2pt]
1 & -1 & 2\\\hline
& \frac16 & \frac23 & \frac16\rule{0pt}{13pt}
\end{array}.
\end{equation}
Applied to the ODE $\dot{y}=f(t,y)$, $y(t_n)=y_n\in\mathcal{M}$, evolving on the manifold $\mathcal{M}\subset\BB{R}^d$, it becomes
\begin{Eqnarray*}
&&k_1=f(t_n,y_n),\\
&& k_2=f(t_{n+\frac12},y_n+\Frac12 hk_1),\\
&& k_3=f(t_{n+1},y_n-hk_1+2hk_2),\\
&&\Delta=h(\Frac16 k_1+\Frac23 k_2+\Frac16 k_3),\\[3pt]
y_{n+1}&=&y_n+\Delta.
\end{Eqnarray*}
Since we operate in $\BB{R}^d$, there is absolutely no reason for $y_{n+1}$ to live in $\mathcal{M}$. However, once we implement \R{RK3} at an algebra level (truncating first the dexpinv equation \R{dexpinv}),
\begin{Eqnarray*}
&&k_1=a(t_n,\iota),\\
&&k_2=a(t_{n+\frac12},{\mathrm e}^{hk_1/2}),\\
&&k_3=a(t_{n+1},{\mathrm e}^{-hk_1+2hk_2}),\\
&&\Delta=h(\Frac16 k_1+\Frac23 k_2+\Frac16 k_3),\\[3pt]
\omega_{n+1}&=&\Delta+\Frac16 h[\Delta,k_1]\\
y_{n+1}&=&\Lambda({\mathrm e}^{\omega_{n+1}},y_n),
\end{Eqnarray*}
the solution is guaranteed to stay in $\mathcal{M}$.
An important special case of a Lie-group equation is the linear ODE $\dot{v}=a(t)v$, where $a:\BB{R}_+\rightarrow\GG{g}$. Although RKMK works perfectly well in a linear case, special methods do even better. Perhaps the most important is the {\em Magnus expansion\/} \cite{magnus54esd}, $v(t)={\mathrm e}^{\omega(t)}v(0)$, where
\begin{Eqnarray}
\nonumber
\omega(t)&=& \int_0^t a(\xi)\D \xi -\frac12 \int_0^t\!\int_0^{\xi_1} [a(\xi_2),a(\xi_1)]\D\xi_2\D\xi_1 \\
\label{Magnus}
&&\mbox{}+\frac14 \int_0^t \! \int_0^{\xi_1} \! \!\int_0^{\xi_2} [[a(\xi_3),a(\xi_2)],a(\xi_1)]\D\xi_3\D\xi_2\D\xi_1\\
\nonumber
&&+\frac{1}{12} \int_0^t\!\int_0^{\xi_1}\!\!\int_0^{\xi_2}[a(\xi_3),[a(\xi_2),a(\xi_1)]]\D\xi_3\D\xi_2\D\xi_1+\cdots.
\end{Eqnarray}
We refer to \cite{iserles99sld,iserles00lgm,blanes09mes} for explicit means to derive expansion terms, efficient computation of multivariate integrals that arise in this context and many other implementation details. Magnus expansions are important in a number of settings when preservation of structure is not an issue, not least in the solution of linear stochastic ODEs \cite{lord08esi}.
There are alternative means to expand the solution of \R{dexpinv} in a linear case, not least the {\em Fer expansion,\/} that has found recently an important application in the computation of Sturm--Liouville spectra \cite{ramos15nss}.
Another approach to Lie-group equations uses {\em canonical coordinates of the second kind\/} \cite{owren01imb}.
\subsection{Conservation of volume}
An ODE $\dot{\MM{x}}=\MM{f}(\MM{x})$ is divergence-free if $\MM{\nabla} \cdot \MM{f}(\MM{x})=0$. The flows of divergence-free ODEs are volume-preserving (VP). Volume is important to preserve, as it leads to KAM-tori, incompressibility, and, most importantly, is a crucial ingredient for ergodicity. Unlike symplecticity, however, phase space volume can generically {\it not} be preserved by Runge--Kutta methods, or even by their generalisations, B-series methods. This was proved independently in \cite{chartier07pfi} and in \cite{iserles07bmc}. Since B-series methods cannot preserve volume, we need to look to other methods.
There are essentially two known numerical integration methods that preserve phase space volume. The first volume-preserving method is based on splitting \cite{feng95vpa}. As an example, consider a 3D volume preserving vector field:
\begin{Eqnarray}
\dot{x} &=& u(x,y,z) \nonumber \\
\label{3D}
\dot{y} &=& v(x,y,z) \\
\dot{z} &=& w(x,y,z) \nonumber
\end{Eqnarray}
with
\begin{displaymath}
u_x + v_y + w_z = 0.
\end{displaymath}
We split this 3D VP vector field into two 2D VP vector fields as follows
\begin{equation}
\label{VP1}
\begin{array}{lcl}
\displaystyle \dot{x} = u(x,y,z), &\qquad\quad& \displaystyle \dot{x} = 0,\\[6pt]
\displaystyle \dot{y} = -\int\! u_x(x,y,z)\D y, && \displaystyle \dot{y} = v(x,y,z) + \int\! u_x(x,y,z) \D y,\\[12pt]
\displaystyle \dot{z} = 0; && \displaystyle \dot{z} = w(x,y,z).
\end{array}\hspace*{20pt}
\end{equation}
The vector field on the left is divergence-free by construction, and since both vector fields add up to (2.1), it follows that the vector field on the right is also volume-preserving.
Having split the original vector field into 2D VP vector fields, we need to find VP integrators for each of these 2D VP vector fields. But that is easy, since 2D VP vector fields are essentially equivalent to 2D Hamiltonian vector fields (with the extra dimension `frozen'), and all symplectic methods (e.g. symplectic Runge--Kutta methods) are volume-preserving for Hamiltonian vector fields.
The above splitting method is easily generalised to $n$ dimensions, where one splits into $n-1$ 2D VP vector fields, and integrates each using a symplectic Runge--Kutta method.
An alternative VP integration method was discovered independently by Shang and by Quispel \cite{shang94gfv,quispel95vpi}. We again illustrate this method in 3D.
We will look for an integrator of the form
\begin{Eqnarray}
x_1 &=& g_1(x_1',x_2,x_3) \nonumber \\
\label{VPint}
x_2' &=& g_2(x_1',x_2,x_3) \\
x_3' &=& g_1(x_1',x_2',x_3) \nonumber
\end{Eqnarray}
where (here and below) $x_i= x_i(nh)$, and $x_i'=x_i((n+1)h)$. The reason the form \R{VPint} is convenient, is because any such map is VP iff
\begin{equation}\label{VPintcon}
\frac{\partial x_1}{\partial x_1'} = \frac{\partial x_2'}{\partial x_2}\frac{\partial x_3'}{\partial x_3}.
\end{equation}
To see how to construct a VP integrator of the form \R{VPint}, consider as an example the ODE
\begin{Eqnarray}
\dot{x}_1 &=& x_2 + x_1^2 + x_3^3 \nonumber \\
\label{3D2}
\dot{x}_2 &=& x_3 + x_1x_2 + x_1^4 \\
\dot{x}_3 &=& x_1 - 3x_1x_3 + x_2^5 \nonumber
\end{Eqnarray}
It is easy to check that it is divergence-free.
\bigskip \noindent Now consistency requires that any integrator for \R{3D2} should satisfy
\begin{Eqnarray}
x_1' &=& x_1 + h( x_2 + x_1^2 + x_3^3) + \O{h^2} \nonumber \\
\label{consis1}
x_2' &=& x_2 + h(x_3 + x_1x_2 + x_1^4) + \O{h^2} \\
x_3' &=& x_3 + h(x_1 - 3x_1x_3 + x_2^5) + \O{h^2} \nonumber
\end{Eqnarray}
and therefore
\bigskip \noindent
\begin{Eqnarray}
x_1 &=& x_1' - h( x_2 + x_1'^2 + x_3^3) + \O{h^2} \\
\label{consis2}
x_2' &=& x_2 + h(x_3 + x_1'x_2 + x_1'^4) + \O{h^2} \\
x_3' &=& x_3 + h(x_1' - 3x_1'x_3 + x_2'^5) + \O{h^2}
\end{Eqnarray}
Since we are free to choose any consistent $g_2$ and $g_3$ in \R{VPint}, provided $g_1$ satisfies \R{VPintcon}, we choose the terms designated by $\O{h^2}$ in (2.15) and (2.16) to be identically zero. Equation \R{VPintcon} then yields
\begin{equation}\label{VPegcon}
\frac{\partial x_1}{\partial x_1'} = (1+hx_1')(1-3hx_1').
\end{equation}
This can easily be integrated to give
\begin{equation}\label{VPintconsol}
x_1 = x_1' - hx_1'^2 - h^2x_1'^3 + k(x_2,x_3;h).
\end{equation}
where the function $k$ denotes an integration constant that we can choose appropriately. The simplest VP integrator satisfying both (2.14) and \R{VPintconsol} is therefore:
\begin{Eqnarray}
x_1 &=& x_1' - h( x_2 + x_1'^2 + x_3^3) -h^2x_1'^3 \nonumber \\
\label{egint}
x_2' &=& x_2 + h(x_3 + x_1'x_2 + x_1'^4) \\
x_3' &=& x_3 + h(x_1' - 3x_1'x_3 + x_2'^5) \nonumber
\end{Eqnarray}
A nice aspect of the integrator \R{egint} (and \R{VPint}) is that it is essentially only implicit in one variable. Once $x_1'$ is computed from the first (implicit) equation, the other two equations are essentially explicit.
\bigskip \noindent Of course the method just described also generalises to any divergence-free ODE in any dimension.
\subsection{Preserving energy and other first integrals}
As mentioned, Hamiltonian systems exhibit two important geometric properties simultaneously, they conserve both the symplectic form and the energy. A famous no-go theorem by \citeasnoun{ge88lph} has shown that it is generically impossible to construct a geometric integrator that preserves both properties at once. One therefore must choose which one of these two to preserve in any given application. Particularly in low dimensions and if the energy surface is compact, there are often advantages in preserving the energy.
An energy-preserving B-series method was discovered in \cite{quispel08nce} cf.\ also \cite{mclachlan99gid}.
For any ODE $\dot{\MM{x}} = \MM{f}(\MM{x})$, this so-called average vector field method is given by
\begin{equation}\label{defavf}
\frac{\MM{x}'-\MM{x}}{h} = \int_{0}^{1}\MM{f}(\xi \MM{x}' + (1-\xi)\MM{x})\D\xi.
\end{equation}
If the vector field $\MM{f}$ is Hamiltonian, i.e. if there exists a Hamiltonian function $H(\MM{x})$ and a constant skew-symmetric matrix $S$ such that $\MM{f}(\MM{x}) = S\nabla H(\MM{x})$, then it follows from \R{defavf} that energy is preserved, i.e. $H(\MM{x}')=H(\MM{x})$.
While the B-series method \R{defavf} is energy-preserving for any Hamiltonian $H$, it can be shown that no Runge--Kutta method is energy-preserving for all $H$. For a given {\it polynomial} $H$ however, Runge--Kutta methods preserving that $H$ do exist \cite{iavtrig09hos}. This can be seen as follows.
Note that the integral in \R{defavf} is one-dimensional. This means that e.g.\ for cubic vector fields (and hence for quartic Hamiltonians) an equivalent method is obtained by replacing the integral in \R{defavf} using Simpson's rule:
\begin{equation}\label{simp}
\int_{0}^{1} g(\xi)\D\xi \approx \frac{1}{6}\left[g(0) + 4g(\Frac{1}{2}) + g(1)\right]\!.
\end{equation}
yielding the Runge--Kutta method
\begin{equation}\label{RKsimp}
\frac{\MM{x}'-\MM{x}}{h} = \frac{1}{6}\left[\MM{f}(\MM{x}) + 4\MM{f}\left(\frac{\MM{x}+\MM{x}'}{2}\right) + \MM{f}(\MM{x}')\right]\!,
\end{equation}
preserving all quartic Hamiltonians.
We note that \R{defavf} has second order accuracy. Higher order generalisations have been given in \cite{hairer10epv}. We note that the average vector field method has also been applied to a slew of semi-discretised PDEs in \cite{celledoni12per}.
While energy is one of the most important constants of the motion in applications, many other types of first integrals do occur. We note here that all B-series methods preserve all linear first integrals, and that all symplectic B-series methods preserve all quadratic first integrals. So, for example, the implicit midpoint rule
\begin{displaymath}
\frac{\MM{x}'-\MM{x}}{h} = \MM{f}\!\left(\frac{\MM{x}+\MM{x}'}{2} \right)
\end{displaymath}
(which is symplectic) preserves all linear and quadratic first integrals. There are however many cases not covered by any of the above.
How does one preserve a cubic first integral that is not energy? And what about Hamiltonian systems whose symplectic structure is not constant? It turns out that generically, any ODE $\dot{\MM{x}} = \MM{f}(\MM{x})$ that preserves an integral $I(\MM{x})$, can be written in the form
\begin{equation}\label{gendeform}
\dot{\MM{x}} = S(\MM{x})\MM{\nabla} I(\MM{x}),
\end{equation}
where $S(\MM{x})$ is a skew-symmetric matrix\footnote{Note that in general $S(\MM{x})$ need not satisfy the so-called Jacobi identity.}.
An integral-preserving discretisation of \R{gendeform} is given by
\begin{equation}
\label{gendeintgrtr}
\frac{\MM{x}'-\MM{x}}{h} = \bar{S}(\MM{x},\MM{x}') \bar{\nabla}I(\MM{x},\MM{x}'),
\end{equation}
where $\bar{S}(\MM{x},\MM{x}')$ is any consistent approximation to $S(\MM{x})$ (e.g. $\bar{S}(\MM{x},\MM{x}')=S(\MM{x})$), and the {\em discrete gradient\/} $ \bar{\MM{\nabla}}I$ is defined by
\begin{equation}
\label{dgdefn1}
(\MM{x}'-\MM{x}) \cdot \bar{\MM{\nabla}}I(\MM{x},\MM{x}') = I(\MM{x}') - I(\MM{x})
\end{equation}
and
\begin{equation}
\label{dgdefn2}
\lim_{\Mm{x}' \rightarrow \Mm{x}} \bar{\MM{\nabla}}I(\MM{x},\MM{x}') = \MM{\nabla} I(\MM{x}).
\end{equation}
There are many different discrete gradients that satisfy \R{dgdefn1} and \R{dgdefn2}. A particularly simple one is given by the Itoh--Abe discrete gradient, which for example in 3D reads
\begin{equation}\label{ItohAbe}
\bar{\nabla}I(\MM{x},\MM{x}') = \left[
\begin{array}{c}
\displaystyle \frac{I(x_1',x_2,x_3) - I(x_1,x_2,x_3)}{x_1'-x_1} \\[10pt]
\displaystyle \frac{I(x_1',x_2',x_3) - I(x_1',x_2,x_3)}{x_2'-x_2} \\[10pt]
\displaystyle \frac{I(x_1',x_2',x_3') - I(x_1',x_2',x_3)}{x_3'-x_3}
\end{array}
\right]\!.
\end{equation}
Other examples of discrete gradients, as well as constructions of the skew-symmetric matrix $S(\MM{x})$ for a given vector field $\MM{f}$ and integral $I$ may be found in \cite{mclachlan99gid}.
We note that the discrete gradient method can also be used for systems with any number of integrals. For example an ODE $\dot{\MM{x}}=\MM{f}(\MM{x})$ possessing two integrals $I(\MM{x})$ and $J(\MM{x})$ can be written
\begin{equation}\label{ode2ints}
\dot{x}_i = S_{ijk}(\MM{x}) \frac{\partial I(\MM{x})}{\partial x_j} \frac{\partial J(\MM{x})}{\partial x_k},
\end{equation}
where the summation convention is assumed over repeated indices and $S(\MM{x})$ is a completely antisymmetric tensor. A discretisation of \R{ode2ints} which preserves both $I$ and $J$ is given by
\begin{equation}\label{disc2ints}
\frac{x_i' - x_i}{h} = \bar{S}_{ijk}(\MM{x},\MM{x}') \bar{\nabla}I(\MM{x},\MM{x}') \,\rule[-4pt]{0.5pt}{16pt}_{\,j} \bar{\nabla}J(\MM{x},\MM{x}') \,\rule[-4pt]{0.5pt}{16pt}_{\,k}
\end{equation}
with $\bar{S}$ any completely skew approximation of $S$ and $\bar{\nabla}I$ and $\bar{\nabla}J$ discrete gradients as defined above.
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\section{Five recent stories of GNI}
The purpose of this section is not to present a totality of recent research into GNI, a subject that would have called for a substantially longer paper. Instead, we wish to highlight a small number of developments with which the authors are familiar and which provide a flavour of the very wide range of issues on the current GNI agenda.
\subsection{Highly oscillatory Hamiltonian systems}
High oscillation occurs in many Hamiltonian systems. Sometimes, e.g.\ in the integration of equations of celestial mechanics, the source of the problem is that we wish to compute the solution across a very large number of periods and the oscillation is an artefact of the time scale in which the solution has physical relevance. In other cases oscillation is implicit in the multiscale structure of the underlying problem. A case in point are the (modified) {\em Fermi--Pasta--Ulam (FPU) equations,\/} describing a mechanical system consisting of alternating stiff harmonic and soft nonlinear springs. The soft springs impart fast oscillation, while the hard springs generate slow transfer of energy across the system: good numerical integration must capture both!
A good point to start (which includes modified FPU as a special case) is the second-order ODE
\begin{equation}
\label{HiOscODE}
\ddot{\MM{q}}+\Omega^2\MM{q}=\MM{g}(\MM{q}),\qquad t\geq0,\qquad \MM{q}(0)=\MM{u}_0,\quad \dot{\MM{q}}(0)=\MM{v}_0,
\end{equation}
where $\MM{g}(\MM{q})=-\MM{\nabla}U(\MM{q})$ and
\begin{displaymath}
\Omega= \left[
\begin{array}{cc}
O & O\\
O & \omega I
\end{array}
\right]\!,\quad \omega\gg1,\qquad \MM{q}= \left[
\begin{array}{c}
\MM{q}_0\\\MM{q}_1
\end{array}
\right]\!,\qquad \MM{q}_0\in\BB{R}^{n_0},\;\;\MM{q}_1\in\BB{R}^{n_1}.
\end{displaymath}
An important aspect of systems of the form \R{HiOscODE} is that the exact solution, in addition to preserving the total Hamiltonian energy
\begin{equation}
\label{HamEn}
H(\MM{p},\MM{q})=\frac12 (\|\MM{p}_1\|^2+\omega^2 \|\MM{q}_1\|^2)+\frac12 \|\MM{p}_0\|^2 +U(\MM{q}_0,\MM{q}_1),
\end{equation}
where $\dot{\MM{q}}=\MM{p}$, also preserves the {\em oscillatory energy\/}
\begin{equation}
\label{OscEn}
I(\MM{p},\MM{q})=\frac12 \|\MM{p}_1\|^2+\frac{\omega^2}{2} \|\MM{q}_1\|^2
\end{equation}
for intervals of length $\O{\omega^N}$ for any $N\geq1$. This has been proved using the {\em modulated Fourier expansions\/}
\begin{displaymath}
\MM{q}(t)=\sum_{m=-\infty}^\infty {\mathrm e}^{{\mathrm i} m\omega t} \MM{z}_m(t).
\end{displaymath}
The solution of \R{HiOscODE} exhibits oscillations at frequency $\O{\omega}$ and this inhibits the efficiency of many symplectic methods, requiring step size of $\O{\omega^{-1}}$, a situation akin to stiffness in more conventional ODEs. However, by their very structure, exponential integrators (and in particular Gautschi-type methods \R{Gautschi}) are particularly effective in integrating the linear part, which gives rise to high oscillation. The problem with Gautschi-type methods, though, might be the occurrence of resonances and we need to be careful to avoid them, both in the choice of the right filter (cf.\ the discussion in Subsection~2.1) and step size $h$.
Of course, one would like geometric numerical integrators applied to \R{HiOscODE} to exhibit favourable preservation properties with respect to both total energy \R{HamEn} and oscillatory energy \R{OscEn}. Applying modulated Fourier expansions to trigonometric and modified trigonometric integrators, this is indeed the case provided that the step size obeys the {\em non-resonance condition\/} with respect to the frequency $\omega$,
\begin{displaymath}
|\sin(\Frac12 mh\omega)|\geq c h^{1/2},\qquad m=1,\ldots,N,\quad N\geq2,
\end{displaymath}
cf.\ \citeasnoun{hairer09olt}.
All this has been generalised to systems with multiple frequencies, with the Hamiltonian function
\begin{displaymath}
H(\MM{p},\MM{q})=\overbrace{\frac12 \sum_{j=1}^s \left(\|\MM{p}_j\|^2+\omega_j^2\|\MM{q}_j\|^2\right)}^{\CC{oscillatory}}+\overbrace{\frac12\|\MM{p}_0\|^2+U(\MM{q})}^{\CC{slow}},
\end{displaymath}
where
\begin{displaymath}
\MM{p}= \left[
\begin{array}{c}
\MM{p}_0\\\MM{p}_1\\\vdots\\\MM{p}_s
\end{array}
\right]\!,\quad \MM{q}=\left[
\begin{array}{c}
\MM{q}_0\\\MM{q}_1\\\vdots\\\MM{q}_s
\end{array}
\right]\!,\qquad 0<\min_{j=1,\ldots,s}\omega_j,\quad 1\ll \max_{j=1,\ldots,s}\omega_j
\end{displaymath}
for both the exact solution \cite{gauckler13eso} and for discretisations obtained using trigonometric and modified trigonometric integrators \cite{cohen15lta}.
Further achievements and open problem in the challenging area of marrying symplectic integration and high oscillation are beautifully described in \cite{hairer14cgi}.
\subsection{Kahan's `unconventional' method}
A novel discretisation method for quadratic ODEs was introduced and studied in \cite{kahan93unm}. This new method discretised the vector field
\begin{equation}\label{kahan1}
\dot{x}_i = \sum_{j,k}^{}a_{ijk}x_jx_k + \sum_{j}^{}b_{ij}x_j + c_i
\end{equation}
as follows,
\begin{equation}\label{kahan2}
\frac{x_i'-x_i}{h} = \sum_{j,k}^{}a_{ijk} \left(\frac{x_jx_k' + x_j'x_k}{2}\right) + \sum_{j}^{}b_{ij} \left( \frac{x_j + x_j'}{2} \right) + c_i.
\end{equation}
Kahan called the method \R{kahan2} `unconventional', because it treats the quadratic terms different from the linear terms. He also noted some nice features of \R{kahan2}, e.g. that it often seemed to be able to integrate through singularities.
\bigskip \noindent \textbf{Properties of Kahan's method:}
\begin{enumerate}
\item {\it Kahan's method is (the reduction of) a Runge--Kutta method.}
\citeasnoun{celledoni13gpk} showed that \R{kahan2} is the reduction to quadratic vector fields of the Runge--Kutta method
\begin{equation}\label{kahan3}
\frac{\MM{x}'-\MM{x}}{h} = 2 \MM{f}\left(\frac{\MM{x} + \MM{x}'}{2}\right) - \frac{1}{2} \MM{f}(\MM{x}) - \frac{1}{2} \MM{f}(\MM{x}')
\end{equation}
This explains {\em inter alia\/} why Kahan's method preserves all linear first integrals.
\item {\it Kahan's method preserves a modified energy and measure.}
For any Hamiltonian vector field of the form
\begin{equation}\label{hamode}
\dot{\MM{x}} = \MM{f}(x) = S\MM{\nabla} H(\MM{x}),
\end{equation}
with cubic Hamiltonian $H(\MM{x})$ and constant symplectic (or Poisson) structure $S$, Kahan's method preserves a modified energy as well as a modified measure exactly \cite{celledoni13gpk}.
The modified volume is
\begin{equation}\label{modvol}
\frac{\D x_1 \wedge \dots \wedge \D x_n}{\det \!\left( I - \frac{1}{2}hf'(\MM{x}) \right)},
\end{equation}
while the modified energy is
\begin{equation}\label{modenergy}
\tilde{H}(\MM{x}) := H(\MM{x}) + \frac{1}{3}h \MM{\nabla} H(\MM{x})^\top \!\left(I - \frac{1}{2}hf'(\MM{x}) \right)^{-1} \!\MM{f}(\MM{x}).
\end{equation}
\item {\it Kahan's method preserves the integrability of many integrable systems of quadratic ODEs.}
Beginning with the work of Hirota and Kimura, subsequently extended by Suris and collaborators \cite{petrera11ihk}, and by Quispel and collaborators \cite{celledoni13gpk,celledoni14ipk,vanderkamp14iss}, it was shown that Kahan's method preserves the complete integrability of a surprisingly large number of quadratic ODEs.
\end{enumerate}
\bigskip \noindent Here we list some 2D vector fields whose integrability is preserved by Kahan's method:
\begin{itemize}
\item Quadratic Hamiltonian systems in 2D:
\noindent The 9-parameter family
\begin{equation}\label{9paramfam}
\left[ \begin{array}{c}
\dot{x} \\ \dot{y} \end{array} \right] =
\left[ \begin{array}{c}
bx^2 + 2cxy +dy^2 +fx + gy + i \\ -ax^2 - 2bxy - cy^2 - ex -fy -h \end{array} \right]\!;
\end{equation}
\item Suslov systems in 2D:
\noindent The 9-parameter family
\begin{equation}\label{suslov}
\left[ \begin{array}{c}
\dot{x} \\ \dot{y} \end{array} \right] = l(x,y)
\left[ \begin{array}{cc} 0 & 1 \\ -1 & 0
\end{array} \right] \nabla H(x,y),
\end{equation}
where $l(x,y) = ax+by+c$; $H(x,y) = dx^2 + exy +fy^2 + gx + hy + i$;
\item Reduced Nahm equations in 2D:
\noindent Octahedral symmetry:
\begin{equation}\label{nahm1}
\left[\begin{array}{c}
\dot{x} \\ \dot{y} \end{array} \right] =
\left[ \begin{array}{c}
2x^2 - 12y^2 \\ -6x^2 - 4y^2 \end{array} \right]\!;
\end{equation}
Icosahedral symmetry:
\begin{equation}\label{nahm2}
\left[ \begin{array}{c}
\dot{x} \\ \dot{y} \end{array} \right] =
\left[\begin{array}{c}
2x^2 - y^2 \\ -10xy + y^2 \end{array} \right]\!.
\end{equation}
\end{itemize}
The modified energy and measure for the Kahan discretisations of these 2D systems, as well as of many other (higher-dimensional) integrable quadratic vector fields are given in \cite{petrera11ihk,celledoni13gpk,celledoni14ipk}.
Generalisations to higher degree polynomial equations using polarisation are presented in \cite{celledoni15dpv}.
\subsection{Applications to celestial mechanics}
GNI methods particularly come into their own when the integration time is large compared to typical periods of the system. Thus long-term integrations of e.g. solar-type systems and of particle accelerators typically need symplectic methods. In this subsection we focus on the former\footnote{A very readable early review of integrators for solar system dynamics is \cite{morbidelli02mis}, cf also \cite{morbidelli02mcm}}.
One of the first symplectic integrations of the solar system was done in \cite{sussman92ces} where it was confirmed that the solar system has a positive Lyapunov exponent, and hence exhibits chaotic behaviour cf \cite{laskar03css}.
More recently these methods have been improved and extended \cite{mclachlan95cmp,duncan98mts,laskar11nos,blanes15nfs}. Several symplectic integrators of high order were tested in \cite{farres13hps}, in order to determine the best splitting scheme for long-term studies of the solar system.
These various methods have resulted in the fact that numerical algorithms for solar system dynamics are now so accurate that they can be used to define the geologic time scales in terms of the initial conditions and parameters of solar system models (or vice versa).
\subsection{Symmetric Zassenhaus splitting and the equations of quantum mechanics}
Equations of quantum mechanics in the semiclassical regime represent a double challenge of structure conservation and high oscillation. A good starting point is the linear Schr\"odinger equation
\begin{equation}
\label{LSE}
\frac{\partial u}{\partial t}={\mathrm i}\varepsilon \frac{\partial^2 u}{\partial x^2}-{\mathrm i}\varepsilon^{-1} V(x)u
\end{equation}
(for simplicity we restrict our discourse to a single space dimension), given in $[-1,1]$ with periodic boundary conditions. Here $V$ is the potential energy of a quantum system, $|u(x,t)|^2$ is a position density of a particle and $0<\varepsilon\ll1$ represents the difference in mass between an electron and nuclei. It is imperative to preserve the unitarity of the solution operator (otherwise $|u(\,\cdot\,,t)|^2$ is no longer a probability function), but also deal with oscillation at a frequency of $\O{\varepsilon^{-1}}$. A conventional approach advances the solution using a palindromic splitting \R{palindromic}, but this is suboptimal for a number of reasons. Firstly, the number of splittings increases exponentially with order. Secondly, error constants are exceedingly large. Thirdly, quantifying the quality of approximation in terms of the step-size $h$ is misleading, because there are three small quantities at play: the step size $h$, $N^{-1}$ where $N$ is the number of degrees of freedom in space discretisation (typically either a spectral method or spectral collocation) and, finally, $\varepsilon>0$ which, originating in physics rather than being a numerical artefact, is the most important. We henceforth let $N=\O{\varepsilon^{-1}}$ (to resolve the high-frequency oscillations) and $h=\O{\varepsilon^\sigma}$ for some $\sigma>0$ -- obviously, the smaller $\sigma$, the larger the time step.
\citeasnoun{bader14eas} have recently proposed an alternative approach to the splitting of \R{LSE}, of the form
\begin{equation}
\label{Zassenhaus}
{\mathrm e}^{{\mathrm i} h (\varepsilon \partial_x^2-\varepsilon^{-1} V)}\approx {\mathrm e}^{\mathcal{R}_0}{\mathrm e}^{\mathcal{R}_1} \cdots {\mathrm e}^{\mathcal{R}_s}{\mathrm e}^{\mathcal{T}_{s+1}}{\mathrm e}^{\mathcal{R}_s} \cdots {\mathrm e}^{\mathcal{R}_1} {\mathrm e}^{\mathcal{R}_0}
\end{equation}
such that $\mathcal{R}_k=\O{\varepsilon^{\alpha_k}}$, $\mathcal{T}_{s+1}=\O{\varepsilon^{\alpha_{s+1}}}$, where $\alpha_0\leq \alpha_1<\alpha_2<\alpha_3<\cdots$ -- the {\em symmetric Zassenhaus splitting.\/} Here $\partial_x=\partial / \partial x$.
The splitting \R{Zassenhaus} is derived at the level of differential operators (i.e., prior to space discretisation), applying the symmetric Baker--Campbell--Hausdorff formula to elements in the free Lie algebra spanned by $\partial_x^2$ and $V$. For $\sigma=1$, for example, this yields
\begin{Eqnarray*}
\mathcal{R}_0&=&-\Frac12\tau\varepsilon^{-1}V=\O{1},\\
\mathcal{R}_1&=&\Frac12\tau\varepsilon \partial_x^2=\O{1},\\
\mathcal{R}_2&=&\Frac{1}{24}\tau^3\varepsilon^{-1}(\partial_xV)^2+\Frac{1}{12} \tau^3\varepsilon \{(\partial_x^2V)\partial_x^2+\partial_x^2[(\partial_x^2V)\,\cdot\,]\}=\O{\varepsilon^2},\\
\mathcal{R}_3&=&-\Frac{1}{120}\tau^5\varepsilon^{-1}(\partial_x^2 V)(\partial_xV)^2 -\Frac{1}{24}\tau^3\varepsilon (\partial_x^4V) +\Frac{1}{240}\tau^5\varepsilon \left(7\{(\partial_x^2V)^2\partial_x^2 \right.\\
&&\mbox{}+\partial_x^2[(\partial_x^2V)^2\,\cdot\,] +\{(\partial_x^3V)(\partial_xV)\partial_x^2\left.\mbox{}+\partial_x^2[(\partial_x^3V)(\partial_xV)\,\cdot\,]\}\right)\\
&& +\Frac{1}{120}\tau^5\varepsilon^{-3} \{(\partial_x^4V)\partial_x^4+\partial_x^4[(\partial_x^4V)\,\cdot\,]\}=\O{\varepsilon^4},
\end{Eqnarray*}
where $\tau={\mathrm i} h$. Note that all the commutators, ubiquitous in the BCH formula, have disappeared: in general, the commutators in this free Lie algebra can be replaced by linear combinations of derivatives, with the remarkable property of {\em height reduction:\/} each commutator `kills' one derivative, e.g.
\begin{displaymath}
[V,\partial_x^2]=-(\partial^2_x V)-2(\partial_xV)\partial_x,\qquad [[V,\partial_x^2],\partial_x^2]=(\partial_x^4V)+4(\partial_x^3V)\partial_x+4(\partial_x^2V)\partial_x^2.
\end{displaymath}
Once we discretise with spectral collocation, $\mathcal{R}_0$ becomes a diagonal matrix and its exponential is trivial, while ${\mathrm e}^{\mathcal{R}_1}\MM{v}$ can be computed in two FFTs for any vector $\MM{v}$ because $\mathcal{R}_1$ is a Toeplitz circulant. Neither $\mathcal{R}_2$ nor $\mathcal{R}_3$ possess useful structure, except that they are {\em small!\/} Therefore we can approximate ${\mathrm e}^{\mathcal{R}_k}\MM{v}$ using the Krylov--Arnoldi process in just 3 and 2 iterations for $k=2$ and $k=3$, respectively, to attain an error of $\O{\varepsilon^6}$ \cite{bader14eas}.
All this has been generalised to time-dependent potentials and is applicable to a wider range of quantum mechanics equations in the semiclassical regime.
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\section{Beyond GNI}
Ideas in one area of mathematical endeavour often inspire work in another area. This is true not just because new mathematical research equips us with a range of innovative tools but because it provides insight that casts new light not just on the subject in question but elsewhere in the mathematical universe. GNI has thus contributed not just toward its own goal, better understanding of structure-preserving discretisation methods for differential equations, but in other, often unexpected, directions.
\subsection{GNI meets abstract algebra}
The traditional treatment of discretisation methods for differential equations was wholly analytic, using tools of functional analysis and approximation theory. (Lately, also tools from algebraic topology.) GNI has added an emphasis on geometry and this leads in a natural manner into concepts and tools from abstract algebra. As often in such mathematical dialogues, while GNI borrowed much of its conceptual background from abstract algebra, it has also contributed to the latter, not just with new applications but also new ideas.
\begin{itemize}
\item {\em B-series and beyond.\/} Consider numerical integration methods that associate to each vector field $\MM{f}$ a map $\MM{\psi}_h(\MM{f})$. A method $\MM{\psi}_h$ is called $g$-covariant\footnote{Also called equivariant.} if the following diagram commutes,
\begin{center}
\begin{picture}(250,135)
\thicklines
\put (-20,0) {$\tilde{\MM{x}}=\MM{\psi}_h(\MM{f})(\MM{x})$}
\put (50,2) {\vector(1,0){140}}
\put (200,0) {$\tilde{\MM{y}}=\MM{\psi}_h(\tilde{\MM{f}})(\MM{y})$}
\put (15,110) {\vector(0,-1){95}}
\put (225,110) {\vector(0,-1){95}}
\put (-5,118) {$\dot{\MM{x}}=\MM{f}(\MM{x})$}
\put (47,120) {\vector(1,0){148}}
\put (210,118) {$\dot{\MM{y}}=\tilde{\MM{f}}(\MM{y})$}
\put (100,8) {$\MM{x}=\MM{g}(\MM{y})$}
\put (100,126) {$\MM{x}=\MM{g}(\MM{y})$}
\end{picture}
\end{center}
It follows that if $g$ is a symmetry of the vector field $f$ and $\psi$ is $g$-covariant, then $\psi$ preserves the symmetry $g$. It seems that this concept of covariance for integration methods was first introduced in \cite{mclachlan95cps} and \cite{mclachlan98nit}.
It is not hard to check that all B-series methods are covariant with respect to the group of affine transformations. A natural question to ask then, was ``are B-series methods the only numerical integration methods that preserve the affine group?". This question was open for many years, until it was answered in the negative by \cite{munthekaas15abs}, who introduced a more general class of integration methods dubbed ``aromatic Butcher series", and showed that (under mild assumptions) this is the most general class of methods preserving affine covariance. Expansions of methods in this new class contain both rooted trees (as in B-series), as well as products of rooted trees and so-called $k$-loops \cite{iserles07bmc}.
Whereas it may be said that to date the importance of aromatic B-series has been at the formal rather than at the constructive level, these methods may hold the promise of the construction of affine-covariant volume-preserving integrators.
\item {\em Word expansions.\/} Classical B-series can be significantly generalised by expanding in {\em word series\/} \cite{murua15wsd}. This introduced an overarching framework for Taylor expansions, Fourier expansions, modulated Fourier expansions and splitting methods. We consider an ODE of the form
\begin{equation}
\label{word_series}
\dot{\MM{x}}=\sum_{a\in\mathcal{A}} \lambda_a(t) \MM{f}_a(\MM{x}),\qquad \MM{x}(0)=\MM{x}_0,
\end{equation}
where $\mathcal{A}$ is a given {\em alphabet.\/} The solution of \R{word_series} can be formally expanded in the form
\begin{displaymath}
\MM{x}(t)=\sum_{n=0}^\infty \sum_{\Mm{w}\in\mathcal{W}_n} \alpha_{\Mm{w}}(t) f_{\Mm{w}}(\MM{x}_0),
\end{displaymath}
where $\mathcal{W}_n$ is the set of all words with $n$ letters from $\mathcal{A}$. The coefficients $\alpha_{\Mm{w}}$ and functions $\MM{f}_{\Mm{w}}$ can be obtained recursively from the $\lambda_a$s and $\MM{f}_a$s in a manner similar to B-series. Needless to say, exactly like with B-series, word series can be interpreted using an algebra over rooted trees.
The concept of word series is fairly new in numerical mathematics but it exhibits an early promise to provide a powerful algebraic tool for the analysis of dynamical systems and their discretisation.
\item {\em Extension of Magnus expansions.\/} Let $\mathcal{W}$ be a {\em Rota--Baxter algebra,\/} a commutative unital algebra equipped with a linear map $R$ such that
\begin{displaymath}
R(x)R(y)=R(R(x)y+xR(y)+\theta xy),\qquad x,y\in\mathcal{W},
\end{displaymath}
where $\theta$ is a parameter. The inverse $\partial$ of $R$ obeys
\begin{displaymath}
\partial(xy)=\partial(x)y+x\partial(y)+\theta\partial(x)\partial(y)
\end{displaymath}
and is hence a generalisation of a derivation operator: a neat example, with clear numerical implications, is the backward difference $\partial(x)=[x(t)-x(t-\theta)]/\theta$. \citeasnoun{ebrahimifard09amf} generalised Magnus expansions to this and similar settings, e.g.\ dendriform algebras. Their work uses the approach in \cite{iserles99sld}, representing individual `Magnus terms' as rooted trees, but generalises it a great deal.
\item {\em The algebra of the Zassenhaus splitting.\/} The success of the Zassenhaus splitting \R{Zassenhaus} rests upon two features. Firstly, the replacement of commutators by simpler, more tractable expressions and, secondly, height reduction of derivatives under commutation. \citeasnoun{singh15ath} has derived an algebraic structure $\GG{J}$ which, encoding these two features, allows for a far-reaching generalisation of the Zassenhaus framework. The elements of $\GG{J}$ are operators of the form $\langle f\rangle_k =f\circ\,\partial_x^k+\partial_x^k\circ f$, where $k\in\BB{Z}_+$ and $f$ resides in a suitable function space. $\GG{J}$ can be endowed with a Lie-algebraic structure and, while bearing similarities with the Weyl algebra and the Heisenberg group, is a new and intriguing algebraic concept.
\end{itemize}
\subsection{Highly oscillatory quadrature}
Magnus expansions \R{Magnus} are particularly effective when the matrix $A(t)$ oscillates rapidly. This might seem paradoxical -- we are all conditioned to expect high oscillation to be `difficult' -- but actually makes a great deal of sense. Standard numerical methods are based on Taylor expansions, hence on {\em differentiation,\/} and their error typically scales as a high derivative of the solution. Once a function oscillates rapidly, differentiation roughly corresponds to multiplying amplitude by frequency, high derivatives become large and so does the error. However, the Magnus expansion does not differentiate, it {\em integrates!\/} This has an opposite effect: the more we integrate, the smaller the amplitude and the series \R{Magnus} converges more rapidly. Indeed, often it pays to render a linear system highly oscillatory by a change of variables, in a manner described in \cite{iserles02ged}, and then solve it considerably faster and cheaper. Yet, once we contemplate the discretisation of \R{Magnus} for a highly oscillatory matrix function $A(t)$, we soon come up another problem, usually considered difficult, if not insurmountable: computing multivariate integrals of highly oscillatory functions.
In a long list of methods for highly oscillatory quadrature (HOQ) {\em circa\/} 2002, ranging from the useless to the dubious, one method stood out: \citeasnoun{levin82pco} proposed to calculate univariate integrals by converting the problem to an ODE and using collocation. This was the only effective method around, yet incompletely understood.
The demands of GNI gave the initial spur to the emergence in the last ten years to a broad swath of new methods for HOQ: Filon-type methods, which replace the {\em non-oscillatory\/} portion of the integrand by an interpolating polynomial \cite{iserles05eqh}, improved Levin-type methods \cite{olver06qmh} and the method of numerical stationary phase of \citeasnoun{huybrechs06eho}. The common characteristic of all these methods is that they are based on asymptotic expansions. This means that high oscillation is no longer the enemy -- indeed, the faster the oscillation, the smaller the error!
Highly oscillatory integrals occur in numerous applications, from electromagnetic and acoustic scattering to fluid dynamics, quantum mechanics and beyond. Their role in GNI is minor. However, their modern numerical theory was originally motivated by a problem in GNI. This is typical to how scholarship progresses and it is only natural that HOQ has severed its GNI moorings and has become an independent area on its own.
\subsection{Structured linear algebra}
GNI computations often lead to specialised problems in numerical linear algebra. However, structure preservation has wider impact in linear algebraic computations. Often a matrix in an algebraic problem belongs to an algebraic structure, e.g.\ a specific Lie algebra or a symmetric space, and it is important to retain this in computation -- the sobriquet ``Geometric Numerical Algebra'' might be appropriate! Moreover, as in GNI so in GNA, respecting structure often leads to better, more accurate and cheaper numerical methods. Finally, structured algebraic computation is often critical to GNI computations.
\begin{itemize}
\item Matrix factorization is the lifeblood of numerical algebra, the basis of the most effective algorithms for the solution of linear systems, computation of eigenvalues and solution of least-squares problems. A major question in GNA is ``Suppose that $A\in\mathcal{A}$, where $\mathcal{A}$ is a set of matrices of given structure. Given a factorization $A=BC$ according to some set of rules, what can we say about the structure of $B$ or $C$?''. \citeasnoun{mackey05sfs} addressed three such `factorization rules': the {\em matrix square root,\/} $B=C$, the {\em matrix sign,\/} where the elements of $B$ are $\pm1$, and the {\em polar decomposition,\/} with unitary $B$ and positive semidefinite $C$. They focussed on sets $\mathcal{A}$ generated by a sesquilinear form $\langle\,\cdot\,,\,\cdot\,\rangle$. Such sets conveniently fit into two classes:
\begin{enumerate}
\item[(a)] Automorphisms $G$, such that $\langle G\MM{x},G\MM{y}\rangle=\langle\MM{x},\MM{y}\rangle$, generate a {\em Lie group;\/}
\item[(b)] Self-adjoint matrices $S$, such that $\langle S\MM{x},\MM{y}\rangle=\langle \MM{x},S\MM{y}\rangle$, generate a {\em Jordan algebra;\/} and
\item[(c)] Skew-adjoint matrices $H$ such that $\langle H\MM{x},\MM{y}\rangle=-\langle\MM{x},H\MM{y}\rangle$, generate a {\em Lie algebra.\/}
\end{enumerate}
It is natural to expect that conservation of structure under factorization would depend on the nature of the underlying inner product. The surprising outcome of \cite{mackey05sfs} is that, for current purposes, it is sufficient to split sesquilinear forms into just two classes, unitary and orthosymmetric, each exhibiting similar behaviour.
\item Many algebraic eigenvalue problems are structured, the simplest example being that the eigenvalues of a symmetric matrix are real and of a skew-symmetric are pure imaginary: all standard methods for the computation of eigenvalues respect this. However, many other problems might have more elaborate structure, and this is the case in particular for nonlinear eigenvalue problems. An important example, with significant applications in mechanics, is
\begin{equation}
\label{QuadEig}
(\lambda^2 M+\lambda G+K)\MM{x}=\MM{0},
\end{equation}
where both $M$ and $K$ are symmetric, while $G$ is skew symmetric. The eigenvalues $\lambda$ of \R{QuadEig} exhibit {\em Hamiltonian\/} pattern: if $\lambda$ is in the spectrum then so are $-\lambda,\bar{\lambda}$ and $-\bar{\lambda}$.\footnote{To connect this to the GNI narrative, such a pattern is displayed by matrices in the {\em symplectic Lie algebra\/} $\Gg{sp}(2n)$.} As often in numerical algebra, \R{QuadEig} is particularly relevant when the underlying matrices are large and sparse.
Numerical experiments demonstrate that standard methods for the computation of a quadratic eigenvalue problems may fail to retain the Hamiltonian structure of the spectrum but this can be obtained by bespoke algorithms, using a symplectic version of the familiar Lanczos algorithm, cf.\ \cite{benner07slc}.
This is just one example of the growing field of structured eigenvalue and inverse eigenvalue problems.
\item The exponential from an algebra to a group: Recall Lie-group methods from Section~2.2: a critical step, e.g.\ in the RKMK methods, is the exponential map from a Lie algebra to a Lie group. Numerical analysis knows numerous effective ways to approximate the matrix exponential \cite{moler03ndw}, yet most of them fail to map a matrix from a Lie algebra to a Lie group! There is little point to expand intellectual and computational effort to preserve structure, only to abandon the latter in the ultimate step, and this explains the interest in the computation of the matrix exponential which is assured to map $A$ in a Lie algebra to an element in the corresponding Lie group.
While early methods have used structure constants and, for maximal sparsity, Lie-algebraic bases given by space-root decomposition \cite{celledoni01mam}, the latest generation of algorithms is based upon {\em generalised polar decomposition} \cite{munthekaas01gpd}.
\end{itemize}
\section*{Acknowledgments}
This work has been supported by the Australian Research Council. The authors are grateful to David McLaren for assistance during the preparation of this paper, as well as to Philipp Bader, Robert McLachlan and Marcus Webb, whose comments helped to improve this paper.
\bibliographystyle{agsm}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 7,847
|
GARY RANDALL
A/G McKenna--Let God's People Go
In another place, at another time, Moses, speaking for God, told a repressive government that refused to allow the Hebrew people to worship their God in truth, action and conscience, "Let my people go so they can worship me." (Ex. 9:1 NIV)
I speak only as a concerned citizen, a retired pastor and a Christian brother to the Stormans family, "Please, Mr. Attorney General, let God's people go."
Please do not drag them through yet another court and ultimately to the Supreme Court in order to suppress their religious objection to selling "Plan B," or what they and many believe to be "The Abortion Pill" in their pharmacy.
You and the state have said they must violate their conscience and religious beliefs and sell the pills in order "to provide timely access to medicines for people who need them."
Judge Leighton has ruled that in fact, "The state's true goal was to suppress religious objection by druggists---not promote timely access."
The Stormans have been publicly tried for their religious beliefs and the right to practice them in their own pharmacy. The personal cost to the Stormans family is nearly $500,000, stress and humiliation.
The Governor, Planned Parenthood, NARAL and the Seattle Times editorial board are all urging that, "The state should appeal" and take it all the way if necessary.
Please don't do it.
However, should you yield to these forceful voices and continue to litigate against the Stormans family, please look up to the top of the eastern pediment of the US Supreme Court Building as you enter. You will note that Herman A. McNeil has carved the likeness of Moses in the center of the pediment.
Please know that he will likely be looking down on the proceedings---and so will a lot of people of faith and conscience in Washington State.
Be Vigilant. Be Discerning. Be Prayerful. Be Active. Be Blessed.
Anonymous 7:23 AM, February 27, 2012
What a hypocrite! When the California AG refused to appeal the ruling striking down Prop 8, Gary and his friends denounced him.
Joel 8:40 AM, February 27, 2012
See, the left isn't actually opposed to discrimination, they just want to decide who gets discriminated against.
Gary isn't a hypocrite. He is consistently oppossed to gay marriage and consistently pro-life. Thank you for your stand Gary.
Anonymous 11:14 AM, February 27, 2012
I agree with Rick Santorem, separation of church and state makes me sick!
Anonymous 12:00 PM, February 27, 2012
11:14 Nice try lefty.
Anonymous 2:13 PM, February 27, 2012
Huh? Rick's not a lefty. He's our next president, and he's right, seperation of church and state is WRONG.
Amen again! Thanks Gary and staff.
So, in other words Gary isn't a hipocrite, he is just a practitioner of outcome based ethics. If the ends suit him, the means are ethical.
What? Its not unethical to pursue your goal within the confines of the law. Which is everyone's right. Even yours.
Craig in Lacey
Tom Niewulis 5:23 AM, February 28, 2012
The confusion regarding the AG's actions are a testimony to how he is influenced by others in regard to political expediency and how he seemingly views the responsibility of his office.
By this I must remind all that when the initial law suit was filed regarding National Health care by several state in 2010, the AG stood against his office position and the governor to join the law suit. Now this was not of his own doing but under the pressure of several of Wa States strong Constitutional Conservative. It can be argued that since this was a "Federal" bill, the AG was safe to engage in a suit contrary to the beliefs of the governor.
Yet, the AG could argue that this is a State issue and that he must support the governor in her pursuit to again force her immorality on every citizen through legislation and the courts. For the AG one would hope that the moral inconsistency that he is exhibiting in standing against the federal legislation that incorporates "Plan B" and yet supports it at the state level would keep a moral man up at night.
Our Founders established or form of governance for a moral and virtuous people. Such that the rule of law would have consistencies. Yet, the States have the capacity to establish stronger positions than the Fed but can NEVER obviate the moral definitions of an individual Citizen. Hence the protection of ones religious conscience, self expression and many other God given Rights protected in both the federal and state Constitutions.
It seems that we have those in governance that are willing to trample Rights for the implementation of practices that cater to the few and are willing to obviate the core foundations of what established this nation, allowing it to rise to greatness through the blessings of God.
Nice post, thanx
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 2,344
|
Q: Why memory warnings with 4 MB utilization and 320 MB free? I'm testing on an iPhone 4 running iOS 7.1 attached to Xcode 5.1.1. I don't understand why I am getting memory warnings and even crashes when instruments shows my app is only using a few megabytes and there is plenty of memory free (see attached). Any ideas?
Update:
In instruments, as I suspected, I found no leaks, but the "Anonymous VM" size seems unduly large and filled with image data. Each table cell in my app displays a JPEG. Perhaps I should be pre-scaling these images and that is the cause of the large Anonymous VM size... More investigation to be done.
A: It turned out images displayed in UIImageViews in each and every table cell were being stored in memory at their full size, not the scaled size (size of the UIImageView). This only showed up in the "Anonymous VM" in Instruments (since iOS only stores references to your images in your application heap and the actual image caches are in system memory it seems), not in the basic memory usage displayed in Xcode. I resolved the issue by pre-scaling my images before putting them into the UIImageViews of the table view cells. There were no leaks.
A: Instrument is sometimes imprecise about the real memory used. The best way to measure is to print the memory usage on the console.
I found the code on this thread: Programmatically retrieve memory usage on iPhone
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,107
|
This tutorial shows you how to work with the Review and Comment features in Acrobat X. See what the all-new Acrobat DC can do for you.
Learn how to do a PDF review or document review using Acrobat X.
In this infographic, learn how to do a PDF review or document review using either a network folder, web server folder, or SharePoint workspace (Windows only) in Acrobat X.
Specify your shared reviews location (Network folder, Web server folder, or SharePoint workspace for Windows only) and click Next.
Choose Send using Adobe Acrobat.
Click Review Deadline and enter a date when comments can no longer be published and click Send.
* Setting up a shared review using Acrobat.com has been discontinued.
I have a newer version of Adobe pro, and the review funcitonality seems to be missing in my tools pane. I can send it throught the view tab, if I select review, but it does not allow me to modify the deadline. I also don't see how we send comments, i.e. what does the recipient select to return their comments? Is this disabled on my version, or do I need to do something to make this enabled?
What point version of Acrobat 9 are you running (what OS)? Are you saying that the email message to the reviewers doesn't not include a link to the folder when you select this option? What does it say about the server in Tracker (View > Tracker)?
I am also using adobe acrobat professional 9 pro to create shared review from my internal server. But, whenever I provide the sharepoint link, it is not able to show the respective folders to link the review process.
I have complete access rights and the internal sharepoint server. Can you please suggest what might be wrong here…?
Make sure everyone in the review is using the very latest point updates for Acrobat - there were some issues with Shared Reviews in earlier point updates.
When sending documents for review, any user added to our exchange-2010 server as a new user , Acrobat cannot resolve the email address. We have had to add a workaround by forwarding the message after it is received (we always add ourselves to the recipient list). Any suggestions?
This shouldn't be an problem when you set up a Shared Review. Only the comments are moving back and forth between reviewers and the original file - so there aren't any save/read only issues.
for a pdf created for Shared Reviews that is saved on an internal network, if one person has the pdf file open and another person tries to open that file, does that second person get a warning that the file is in use or that it's read only? My concern is that if one person has the file open and then a 2nd person opens it and makes changes, that second person won't be able to save changes (unless they make a copy of the file, which defeats the whole purpose of having comments in 1 doc). Can you pls clarify what happens when a pdf doc is open and someone else tries to open/edit it? Thanks!
Unfortunately shared reviews are designed to be a manual process initiated on the desktop. There are probably other types of software that integrate PDF documents and can automate this process to some extent.
that's nice, but what happens when you have more than 100 files to send for shared review?
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 9,489
|
You can provide mock values in a terse manner via static providers. Pass in
an array of tuple pairs (array pairs) into the `provide` method. For each pair,
the first element should be a matcher for matching the effect and the second
effect should be the mock value you want to provide. You can use effect creators
from `redux-saga/effects` as matchers or import matchers from
`redux-saga-test-plan/matchers`. The benefit of using Redux Saga Test Plan's
matchers is that they also offer partial matching. For example, you can use
`call.fn` to match any calls to a function without regard to its arguments.
```js
import { call, put, select } from 'redux-saga/effects';
import { expectSaga } from 'redux-saga-test-plan';
import * as matchers from 'redux-saga-test-plan/matchers';
import api from 'my-api';
import * as selectors from 'my-selectors';
function* saga() {
const id = yield select(selectors.getId);
const user = yield call(api.fetchUser, id);
yield put({ type: 'RECEIVE_USER', payload: user });
}
it('provides a value for the API call', () => {
return expectSaga(saga)
.provide([
// Use the `select` effect creator from Redux Saga to match
[select(selectors.getId), 42],
// Use the `call.fn` matcher from Redux Saga Test Plan
[matchers.call.fn(api.fetchUser), { id: 42, name: 'John Doe' }],
])
.put({
type: 'RECEIVE_USER',
payload: { id: 42, name: 'John Doe' },
})
.run();
});
```
## Matchers
Inside the `redux-saga-test-plan/matchers` module, there are matchers for most
of the effect creators available in Redux Saga. You can reference effect
creators in Redux Saga's docs
[here](http://redux-saga.github.io/redux-saga/docs/api/index.html#effect-creators).
- `actionChannel(pattern, [buffer])`
- `apply(context, fn, args)`
- `call([context, fn], ...args)`
- `call(fn, ...args)`
- `cancel(task)`
- `cancelled()`
- `cps([context, fn], ...args)`
- `cps(fn, ...args)`
- `flush(channel)`
- `fork([context, fn], ...args)`
- `fork(fn, ...args)`
- `getContext(prop)`
- `join(task)`
- `put(action)`
- `putResolve(action)`
- `race(effects)`
- `select(selector, ...args)`
- `setContext(props)`
- `spawn([context, fn], ...args)`
- `spawn(fn, ...args)`
- `take(pattern)`
- `takeMaybe(pattern)`
## Partial Matchers
Sometimes you're not interested in matching a `call` effect with exact arguments
or a `put` effect with a particular action payload.
Instead you only want to match a `call` to a particular function or match a
`put` with a particular action type. You can handle these situations with
partial matchers.
The following assertions have a `like` method along with convenient helper
methods for partially matching assertions:
- `actionChannel`
- `apply`
- `call`
- `cps`
- `fork`
- `put`
- `put.resolve`
- `select`
- `spawn`
**NOTE:** the `like` method requires knowledge of the properties on effects such
as the `fn` property of `call` and the `action` property of `put`. Essentially,
`like` allows you to match effects with certain properties without worrying
about the other properties. Therefore, you can match a `call` by `fn` without
worrying about the `args` property.
In addition to `like`, there are other some common helper methods like `fn` and
`actionType` available, appropriate to the kind of effect:
| Method | Description |
| ------ | ----------- |
| `actionChannel.pattern` | Match `actionChannel` by `pattern`. Useful if you use custom `buffers` with `actionChannel`. |
| `apply.fn` | Match `apply` by `fn`. |
| `call.fn` | Match `call` by `fn`. |
| `cps.fn` | Match `cps` by `fn`. |
| `fork.fn` | Match `fork` by `fn`. |
| `put.actionType` | Match `put` by `action.type`. |
| `put.resolve.actionType` | Match `put.resolve` by `action.type`. |
| `select.selector` | Match `select` by `selector` function. |
| `spawn.fn` | Match `spawn` by `fn`. |
## Ordering
Providers are checked from left to right (or top to down depending on how you
look at it). The first provider to match an effect is used, skipping subsequent
providers. If no providers match, then the effect is handled by Redux Saga as
normal.
```js
import { call, put, select } from 'redux-saga/effects';
import * as matchers from 'redux-saga-test-plan/matchers';
import api from 'my-api';
import * as selectors from 'my-selectors';
function* saga() {
const user = yield call(api.findUser, 1);
const dog = yield call(api.findDog);
const greeting = yield call(api.findGreeting);
const otherData = yield select(selectors.getOtherData);
yield put({
type: 'DONE',
payload: { user, dog, greeting, otherData },
});
}
const fakeUser = { name: 'John Doe' };
const fakeDog = { name: 'Tucker' };
const fakeOtherData = { foo: 'bar' };
it('takes multiple providers and composes them', () => {
return expectSaga(saga)
.provide([
[matchers.call.fn(api.findUser), fakeUser],
[matchers.call.fn(api.findDog), fakeDog],
[select(selectors.getOtherData), fakeOtherData],
])
.put({
type: 'DONE',
payload: {
user: fakeUser,
dog: fakeDog,
greeting: 'hello',
otherData: fakeOtherData,
},
})
.run();
});
```
## Throw Errors
You can simulate errors with static providers via the `throwError` function from
the `redux-saga-test-plan/providers` module. When providing an error, wrap it
with a call to `throwError` to let Redux Saga Test Plan know that you want to
simulate a thrown error.
```js
import { call, put } from 'redux-saga/effects';
import * as matchers from 'redux-saga-test-plan/matchers';
import { throwError } from 'redux-saga-test-plan/providers';
import api from 'my-api';
function* userSaga(id) {
try {
const user = yield call(api.fetchUser, id);
yield put({ type: 'RECEIVE_USER', payload: user });
} catch (e) {
yield put({ type: 'FAIL_USER', error: e });
}
}
it('handles errors', () => {
const error = new Error('error');
return expectSaga(userSaga)
.provide([
[matchers.call.fn(api.fetchUser), throwError(error)],
])
.put({ type: 'FAIL_USER', error })
.run();
});
```
## Static Providers with Dynamic Values
Static providers can provide dynamic values too. Instead of supplying a static
value, you can supply a function that produces the value. This function takes as
arguments the matched effect as well as a `next` function. Additionally, you
must wrap the function with a call to the `dynamic` function from the
`redux-saga-test-plan/providers` module. Inside the provider function, you can
inspect the effect further and return a mock value or return a call to the
`next` function. Returning a call to the `next` function will tell Redux Saga
Test Plan to try the next provider, similar to a middleware stack. If there are
no more providers, then Redux Saga Test Plan will let Redux Saga handle the
effect.
```js
import { call, put } from 'redux-saga/effects';
import { expectSaga } from 'redux-saga-test-plan';
import * as matchers from 'redux-saga-test-plan/matchers';
import { dynamic } from 'redux-saga-test-plan/providers';
const add2 = a => a + 2;
function* someSaga() {
const x = yield call(add2, 4);
const y = yield call(add2, 6);
const z = yield call(add2, 8);
yield put({ type: 'DONE', payload: x + y + z });
}
const provideDoubleIf6 = ({ args: [a] }, next) => (
// Check if the first argument is 6
a === 6 ? a * 2 : next()
);
const provideTripleIfGt4 = ({ args: [a] }, next) => (
// Check if the first argument is greater than 4
a > 4 ? a * 3 : next()
);
it('works with dynamic static providers', () => {
return expectSaga(someSaga)
.provide([
[matchers.call.fn(add2), dynamic(provideDoubleIf6)],
[matchers.call.fn(add2), dynamic(provideTripleIfGt4)],
])
.put({ type: 'DONE', payload: 42 })
.run();
});
```
## Other Examples
### Parallel Effects via `all`
Providers work on effects yielded inside an `all` effect:
```js
import { put, select, all } from 'redux-saga/effects';
import { expectSaga } from 'redux-saga-test-plan';
import { selectors } from 'my-selectors';
function* saga() {
const [name, age] = yield all([
select(selectors.getName),
select(selectors.getAge),
]);
yield put({ type: 'USER', payload: { name, age } });
}
it('provides values for effects inside arrays', () => {
return expectSaga(saga)
.provide([
[select(selectors.getName), 'Tucker'],
[select(selectors.getAge), 11],
])
.put({
type: 'USER',
payload: { name: 'Tucker', age: 11 },
})
.run();
});
```
### Providing in Forked/Spawned Sagas
Providers work for effects in forked/spawned sagas too.
```js
import { call, fork, put } from 'redux-saga/effects';
import { expectSaga } from 'redux-saga-test-plan';
import * as matchers from 'redux-saga-test-plan/matchers';
import api from 'my-api';
function* fetchUserSaga() {
const user = yield call(api.fetchUser);
yield put({ type: 'RECEIVE_USER', payload: user });
}
function* forkingSaga() {
yield fork(fetchUserSaga);
}
function* spawningSaga() {
yield spawn(fetchUserSaga);
}
it('provides values in forked sagas', () => {
return expectSaga(forkingSaga)
.provide([
[matchers.call.fn(api.fetchUser), fakeUser],
])
.put({ type: 'RECEIVE_USER', payload: fakeUser })
.run();
});
it('provides values in spawned sagas', () => {
return expectSaga(spawningSaga)
.provide([
[matchers.call.fn(api.fetchUser), fakeUser],
])
.put({ type: 'RECEIVE_USER', payload: fakeUser })
.run();
});
```
## More Examples
For some more contrived examples of providers, look in the
[repo tests](https://github.com/jfairbank/redux-saga-test-plan/tree/master/__tests__/expectSaga/providers).
## Caveats
For providers to work, `expectSaga` will necessarily wrap forked/spawned sagas
with an intermediary generator called `sagaWrapper` in order to intercept
effects. To ensure that your saga receives back a task object with a correct
`meta.name` property, Redux Saga Test Plan will attempt to rename the `sagaWrapper`
function to the name of a forked saga. This works in almost all JavaScript
environments but will fail in PhantomJS. Therefore, you **can't** depend on the
task `meta.name` property being correct in PhantomJS.
|
{
"redpajama_set_name": "RedPajamaGithub"
}
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|
Q: CDF of first passage time for Poisson dam/shot noise with constant amplitude jumps and exponential decay I'm looking for a CDF (either exact or approximation) of the first passage time, $T$, of a storage process $\{X(t); 0 \leq t < \infty \},$ with constant (unit) input jumps occurring in a Poisson process with mean rate of $\lambda$ jumps per unit time, an exponential decay rate, alpha $X(t)$, and initial value $X(0) = x_0$.
I found several references in the literature of similar problems where the inputs are compound Poisson, i.e. both the intervals between successive inputs and the input amplitudes are exponentially distributed, e.g.:
*
*Harrison, J.M & Resnick, S (1976) The stationary distribution and
first exit probabilites of a storage process with general release
rate. Mathematics of Operations Res. 1, 347-358.
*Yeo, G.F. (2010) Rediscoveries of a first passage time result for
dams and shot noise. Mathematical Scientist vol. 35, no. 1, 18-22
as well as an example of input and release amplitudes both constant:
*
*Moran, P.A.P. (1959) The Theory of Storage 79-81.
But I haven't been able to find the case of constant amplitude inputs and exponential decay.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,496
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Stand Up: HBS Marks 50 Years of Women
New York Times best-selling author, HBS alumna, and Facebook COO Sheryl Sandberg was the keynote speaker at the recent W50 Summit, a two-day conference celebrating 50 years of women in the Harvard M.B.A. program.
Photograph by Katherine Taylor/Harvard News Office
HBS dean Nitin Nohria told the audience he considers himself a feminist and supports a culture that reflects equality for women in the workplace.
Robin Ely discussed a new HBS survey that aims to "open a dialogue" about gender and work.
Photograph b Kris Snibbe/Harvard News Office
In 1963, eight women crossed the Charles River to crack a barrier that had stood for more than half a century at Harvard, becoming the first of their gender to enroll in the Business School's two-year M.B.A. program. Fifty years and 11,000 female graduates later, women make up about 40 percent of today's incoming M.B.A. classes. An equal number of men and women graduate with honors, and their current dean, Nitin Nohria, considers himself a feminist.
Yet when Facebook chief operating officer Sheryl Sandberg '91, M.B.A. '95—the keynote speaker at the recent W50 Summit, a two-day conference celebrating 50 years of women in the M.B.A. program—asked a group of about 800 alumnae gathered in Burden Hall to stand if they had ever vocalized wanting to become CEO of their own companies, almost no one did.
"I'm here today to do one thing: to give every woman in this audience not just the permission, but the encouragement to stand up next time that question is asked," said Sandberg, author of the New York Times best-selling book Lean In. "Not just to be CEO of the company you are in, but to do anything you might not think you can do…anything you might be afraid to do. I want to do that for the men in this room today as well, but I want to do it especially for the women, because the blunt truth is, men still rule the world."
Throughout the two-day conference, alumnae gathered in small groups to discuss topics like "Negotiate What You Need to Succeed: A Workshop for Women," "Getting onto Boards Bootcamp," and "Using Business Acumen to Effect Social Change." They heard from such business-world leaders as former Time Inc. chief Ann Moore, M.B.A. '78, and Gail McGovern, the president and CEO of the American Red Cross, as well as from prominent faculty members, including Arbuckle professor of business administration Rosabeth Moss Kanter. A Women's Place, a new film on the history of women at HBS, was screened on Thursday evening.
The W50 Summit was a time for celebration as well as thoughtful reflection, but also a moment for HBS women to ponder the future and think of ways to create a culture in which they can be truly equal to men in the workplace. As President Drew Faust noted in her opening address, women are far from reaching parity with their male peers: they comprise only 4 percent of Fortune 500 Company CEOs, run less than 10 percent of America's venture capital firms, and hold just 26 percent of full professorships across the country and about 20 percent of top government posts.
How to define success when it comes to the education of women—whether at Harvard Business School, or in the United States, or globally—remains a pressing question, Faust noted, before offering three reasons why it should remain a crucial concern. "First, we educate women because it is fair—a level field, as we aspire to include women as full and equal participants in society," she said.
We educate women also because it is smart: women are one half of our human resources, and we increasingly see the beneficial effects of educated women in all realms of life and in every part of the world. Finally, we educate women because it is transformative. Not only boosting incomes and economies, education elevates us, diffusing differences, opening common ground, and making the most of all of our human capacities.
Faust discussed the history of the first women to enter HBS, praising their entry into "a kind of other world that was up to that point reserved for men." (She mentioned a 1963 Crimson article on women at HBS that stated: "perfume wafted through the corridors, and some men complained.") The women at HBS set out to succeed, Faust said, whether it meant studying harder than their male peers, doing without on-campus housing until 1969, or petitioning for a women's lounge in McCulloch Hall.
On the first day of the conference, Wilson professor of business administration Robin Ely, the senior associate dean for culture and community at HBS, took the podium at Burden Hall to discuss a new survey—Life and Leadership After HBS. It aims to "open a dialogue" about gender and work, to gain insight into the realities, decisions, and tradeoffs that the school's men and women make regarding work and family life. (Of the 26,000 alumni contacted, 6,458 completed the survey; their HBS affiliations ranged from the M.B.A. and doctoral programs to executive education programs and early offerings such as the Harvard-Radcliffe Program in Business Administration.)
Answers to such questions as "What factors impede women's advancement?" and "What do our Alumni value?" indicated that less than a tenth of Generation X and Baby Boomer women left the workforce to care for children full-time. That finding debunks the common perception that female Harvard M.B.A. graduates are staying home in order to raise children—though it doesn't explain the dearth of women CEOs.
Ely, in presenting the survey's findings, engaged the audience in a dialogue about those factors that impede women's advancement to leadership roles. "There is a whole set of experiences that look less like women opting out, and more like women being pushed out, by organizations that demand a 24/7 work schedule," she said. "Women are being pulled out by a culture that promulgates a compelling—some might say guilt-inducing—image of mothering that is hard to live up to while you are trying to hold a job."
Ann Moore spoke on the importance of staying sane in the workplace, encouraging women to get enough sleep, exercise, empower their assistants, and do little things like taking a five-minute break: all "mind-clearing tricks to break the logjam in your life." The former Time leader said that as Americans are starting to see signs of a financial recovery, she worries "we didn't seem to learn much" from disasters like Hurricane Katrina or the collapse of Lehman Brothers, and is disappointed that this country has not made better progress in bridging the gender and pay gaps that exist in top leadership positions.
She asked, "Are we wiser and better prepared to deal with new challenges going forward?" Challenging her audience, she declared:
I don't know about you, but I'm not spending my twilight years playing catch-up again. I got through HBS in the '70s when there wasn't even a proper ladies room in Aldrich Hall. I played basketball in the '60s with that stupid three-dribble rule. I had to go out of state for college, because my state school, UVA, was all male. I spent my lifetime catching up—I caught up. So let's not slip behind again.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 7,447
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\section{Introduction}
\label{intro}
Lattice gauge field theory provides universal framework for analysis of systems with infinite degrees of freedom with corresponding local and global symmetry. It allows to develop new theoretical concepts for the condensed and soft matter physics. From other other hand such systems allow direct experimental study of new nontrivial properties of the gauge field theory, what can be applied to QCD and confinement understanding. One of the most interesting and unusual subjects to which a field theory approach can be applied is the protein research.
Currently, the most ambitious computational approaches to modelling the structure of proteins are based on classical molecular dynamics that allows us to describe the processes of protein folding in the case of short and fast folding proteins only~\cite{Feddolino}. For a realistic description of the tertiary and quaternary structures on large spatial and temporal scales computing power by 5-6 orders of magnitude greater than is technically achievable now is needed~\cite{Lindor}.
To overcome the computational problems and to make possible the practical modelling of the properties of proteins and their complexes over large time scales, a number of models based on a rough physical assumptions has been developed. These models, increasing the speed of calculations, systematically exclude the contributions to the total atomic force fields, which are assumed to be insignificant. For example, the force field UNRES~\cite{unres} gives a very detailed, but still approximate expression for the potential energy, which includes fifteen different terms in conjunction with a simplified geometry. The considerable success of various approximate approaches allows us to raise the question - what are the factors that really important to describe the free energy? In particular, is there a systematic method to approximate the force fields, based on first principles that can reproduce the correct structure of proteins? Such a classification scheme as the CATH~\cite{cath} (http://www.cathdb.info/) and SCOP~\cite{scop} (http://scop.mrc-lmb.cam.ac.uk/scop/), who develop a taxonomic approach to describe the topology of protein available database PDB, found that despite the differences in their amino acid structures, the number of different shapes is limited. Such empirical data provide a conceptual framework for new methods for structure prediction. Within these methods folded protein structure assembled by combining fragments obtained from homologously related proteins already described in PDB. Since the number of conformations, which may be in a particular sequence is very limited, the basic idea is that various fragments, which have been described in the PDB, can be used as the designer of the building blocks for creating the folded protein. The whole structure can be obtained by coupling these fragments in the three-dimensional conformation, frequently via the energy function by comparison with similar homology by its control structures from PDB. According to the generally accepted tests Critical Assessment for Structural Prediction (http://www.predictioncenter.org/index.cgi), at the moment this type of practices have the greatest predictive power for the conformation of the protein. However, the disadvantage of these methods is the lack of sound energy function, which greatly complicates their application for research of dynamic aspects, including the processes of folding, and especially the nature of and reasons for the transition to incorrect protein folding.
Furthermore, all of these approaches are based on data from experimental studies on synchrotron radiation sources. Currently, there is a revolutionary development of experimental techniques sources of hard gamma radiation. Now the third generation synchrotron sources such as ESFR and PETRA, next-generation sources are such facilities as the European X-ray Free Electron Laser at DESY, providing high-precision studies of the structure of proteins. However, these studies are hampered by the need for protein crystallisation. There are significant differences in the molecular structure of various proteins, and the resulting crystals are extremely fragile. Moreover, crystallisation of proteins in most cases is impossible. This leads to the fact that the number of protein structures studied by three orders of magnitude smaller than the number of known protein sequences. As a result, the gap between the number of known sequences, and studied structures remains high. In addition, the study of protein-protein interactions in the search for the causes of diseases of protein misfolding, and protein studies of conformational changes upon environment influence on receptor subunits requires much greater precision and can not be solved on the crystallised proteins. Thus, the particular relevance numerical modelling of the tertiary and quaternary structure of the protein and its dynamics in external fields in terms of collective degrees of freedom derived from first principles.
One of the solutions of the problem can be obtained with the help of coarse grain modelling within effective field theory, which allows a natural way to introduce the collective degree of freedom and nonlinear topological structures based on fundamental principles of gauge symmetry. The corresponding field theory model is based on local symmetry of proteins that will dynamically define tertiary structure of proteins~\cite{Niemi_lecture}.
\section{Local symmetry of proteins}
\label{symmetry}
Protein local symmetry is defined by amino-acids and protein backbone bonds structure. The covalent bond between amino acids central carbon atom $C_{\alpha}$ and carbon in the carboxyl group $C^\prime$ has very low rotation energy. Rotation energy of the rest of the bonds in the amino-group is high and neighbour $C_\alpha$ and all peptide bond atoms between them are in the same plane. Taking it into account we can consider the protein backbone as a freely rotating discrete chain of such planes. A such chain formally can be described by a discreet (1+1) manifold with $U(1)$ local symmetry. Correspondingly, the gauge phase can be associated with rotational angle of the $C_{\alpha}$ and $C^\prime$ bond. In the water medium the protein local $U(1)$ symmetry is broken due to hydrophobic and hydrophilic forces that lead to the amino acids alignment inside (hydrophobic) or outside (hydrophilic) of the protein secondary structure.
The discussed symmetry breaking exhibits chirality as a consequence of the amino acids geometry. The $C_\alpha$ atom is in a $sp^3$ hybridise state, thus its covalent bonds form a regular tetrahedron with R-group, $H$, $N$ and $C^\prime$ atoms at vertices. If there is no one pair of equivalent groups at the vertices, then this structure is obviously chiral. All of the amino acids that generate a protein are chiral with left orientation except glycine, which is non-chiral due to hydrogen atom as the R-group. This symmetry breaking leads to chirality of the polypeptide ground state structures. For example, all $\alpha$-helices are right handed.
The angles between the covalent bonds of the peptide bonds atoms have large fluctuation energy and are almost constant. Thus, the backbone bending angle fluctuates near a fixed value determined by the stable secondary structures of the protein (alpha-helix, beta-sheets and so forth). Thus, we can consider protein as a chain with almost constant bending.
The considered above local symmetry breaking and chirality folds the freely rotating constant bending chain into to the correct protein structure.
The considered properties of the proteins can be formally described by an appropriate geometric description of protein.
A such model can be formulated within the approach that use description of the local geometry of proteins based on the formalism of discrete Frenet coordinates~\cite{Niemi_lecture}. Under this formalism proteins are considered as one-dimensional discrete uniformity, which determined the free energy functional, defined solely by the angles of curvature and torsion.
The Frenet Frame rotation can be presented by the following transformation:
\begin{eqnarray}
\frac{d}{ds}\left(\begin{array}{c} {\bf e}_1 \\ {\bf e}_2\\{\bf t}\end{array} \right) = \left(\begin{array}{ccc} 0 & (\tau+\eta_s) & -\kappa cos(\eta)\\ (\tau+\eta_s) & 0 & \kappa sin(\eta) \\ \kappa cos(\eta) & -\kappa sin(\eta)& 0\end{array}\right)\times \left( \begin{array}{c}{\bf e}_1 \\ {\bf e}_2\\{\bf t} \end{array} \right)
\end{eqnarray}
Upon rotation of the local coordinate system doublet of dynamic variables is transformed just as two-dimensional Abelian Higgs multiplet.
This transformation can be rewritten as a gauge U(1) transformation of the scalar field:
\begin{eqnarray}
\kappa \sim \phi \to \kappa e^{-i\eta}\equiv \phi e^{-i\eta}\\
\tau \sim A_i \to \tau + \eta_s \equiv A_i+ \eta_s
\end{eqnarray}
Here the bending ($\kappa \sim \phi $) and torsion ($\tau \sim A_i$) are introduced as scalar and gauge filed correspondingly.
Thus, the Abelian Higgs Model Hamiltonian takes the form:
\begin{eqnarray}
H=\int\limits_0^L ds(|(\partial_s+ie\tau)\kappa|^2+\lambda(|\kappa|^2-m^2)^2+a\tau-\frac{c}{2}\tau^2) \label{Hmlt}
\end{eqnarray}
where $s$ is the natural parameter of the curve. The Chern-Simons term $a\tau$ is introduced to ensure chirality of proteins that leads to domination of the right hand alpha-helices, the $\tau^2$ Proca mass term follows from the partial gauge symmetry breaking. As the results we obtain ground states of the protein backbone as the theory vacua with different topological sectors:
$\alpha$-helices (broken chiral symmetry, negative parity):
\begin{eqnarray*}
\begin{cases} \kappa\simeq \frac{\pi}{2} \\ \tau\simeq 1 \end{cases}
\end{eqnarray*}
$\beta$-strands (restored chiral symmetry, positive parity):
\begin{eqnarray*}
\begin{cases} \kappa\simeq 1 \\ \tau\simeq \pi \end{cases}
\end{eqnarray*}
Loops can be considered as spatial transition between different ground states. To get explicit geometrical description of the transitions, one can apply following $Z_2$ symmetry transition of the bending and torsion:
\begin{eqnarray}
\kappa \to -\kappa \\
\tau \to \tau+\pi.
\end{eqnarray}
Such transition leaves the geometrical structure of a one-dimensional curve unchanged and introduce inflection points in the protein chain where the curve becomes flat. These inflection points are stable topological structure that cannot be removed by a continuous transformation. Such inflection points are defined by the exact soliton solutions of the real part of the Hamiltonian (\ref{Hmlt})~\cite{Niemi2}:
\begin{eqnarray}
\kappa(s)=m tanh(m\sqrt{\lambda}(s-s_0))
\label{Soliton}\end{eqnarray}
with energy:
\begin{eqnarray}
E=\int ds (\kappa_s^2+\lambda(\kappa^2-m^2)^2-a\tau-b\kappa^2\tau+\frac{c}{2}\tau^2+\frac{d}{2}\kappa^2\tau^2)
\label{FreeEn} \end{eqnarray}
This approach allows parametrisation of the protein backbone structure by superposition of the one-dimensional solitons (kinks) with high accuracy~\cite{Niemi2}, and dynamical properties of the protein chain is defined by the corresponding soliton dynamics.
.
\section{Monte-Carlo numerical simulations of the protein structure}
\label{MonteCarlo}
To obtain the soliton structure that describes protein topology and dynamics, one have to define positions of the inflection points that fit protein tertiary structure and find soliton parameters that correspond to the global minimum of the free-energy~(\ref{FreeEn}).
\begin{figure}[h]
\centering
\includegraphics[width=12cm,clip]{img07}
\caption{Front-end for the protein structure visualisation and analysis toolkit. Upper panel - torsion and bending angels, lower panel - parameters for the protein soliton structure.}
\label{WebSite1}
\end{figure}
The inflection point can be defined by a visual analysis of the protein topology. For this propose a special toolkit for protein structure visualisation and analysis was developed~\cite{WebSite}.
On the figure~(\ref{WebSite1}) the front end of the toolkit is presented. In this example the torsion and bending of the Myoglobin (1ABS) is presented before and after definition of all inflection points.
The free energy~(\ref{FreeEn}) exhibits two energy scales. The higher energy scale is related to the bending $\kappa$ and presented by terms that have exclusively $\kappa$ contribution. Values of the $\kappa$, that correspond to classical minimum of the free-energy, are defined by the corresponding exact solution~(\ref{Soliton}). As the first approximation we obtain parameters of the equation~(\ref{Soliton}) that fit the particular protein backbone bending with all inflection points taken into account.
The lower energy scale is related to the terms that depend off the torsion $\tau$. An extremum condition of the free-energy gives the following values of the torsion:
\begin{eqnarray}
\tau = \frac{a+b\kappa^2}{c+d\kappa^2}
\label{SolTrosion}\end{eqnarray}
Protein free energy can have multiple local extrema that satisfy this relation. Thus, as the next approximation we obtain parameters of the expression~(\ref{SolTrosion}) that fit the protein backbone torsion and correspond the global minimum of the free-energy, using combination of the simulated annealing and gradient descent methods.
As the result we get precise description of the protein structure. For example we get three-dimensional structure of the Myoglobin with RMSD less then $1A$~(figure \ref{Myoglobin}.).
\begin{figure}[h]
\centering
\includegraphics[width=11cm,clip]{Myoglobin}
\caption{Left panel - native three-dimensional structure of the Myoglobin from PDB. Right panel - structure reproduced by with the present approach as superpositIon of topological solitons.}
\label{Myoglobin}
\end{figure}
This approach allows not only geometrical description of the protein three dimensional structure, but its dynamics as well. To make simulation of the protein structure thermal dynamics we apply Glauber heating algorithm~\cite{Myoglobin1,Myoglobin2}.
On each step of the heating algorithm we put a fluctuation of the torsion or bending at a random amino acid in a way that the new value of the torsion has the form:
\begin{eqnarray}
\tau_i^\prime = \tau_i + 1.4 R
\end{eqnarray}
and new value of the bending has the following form:
\begin{eqnarray}
\kappa_i^\prime = \kappa_i + 0.06 R
\end{eqnarray}
where $R$ - is a random number with normal distribution with the central value equal $0$ and dispersion equal $1$.
The corresponding configuration is accepted with the probability:
\begin{eqnarray}
P=\frac{e^{-(E^\prime - E)/T}}{1+e^{-(E^\prime - E)/T}},
\label{GlaubProb}\end{eqnarray}
where $T$ - Glauber temperature, $E$- free-energy of the protein chain before the fluctuation, $E^\prime$ - the free-energy after the fluctuation. If the configuration accepted, then the value of $\tau_i$ or $\kappa_i$ is substituted by $\tau^\prime_i$ or $\kappa^\prime_i$ correspondingly. If the configuration is not accepted then value of the angle remains same as on previous step. Then, temperature changes on a small value and on the next step the procedure is repeated.
\begin{figure}[h]
\centering
\includegraphics[width=10cm,clip]{1ABSv2}
\caption{Myoglobin radius of gyration dependence on the Glauber temperature. The x-axis - radius of gyration in Angstroms, the y-axis is the number of step in heating/cooling procedure}
\label{heating}
\end{figure}
\begin{figure}[h]
\centering
\includegraphics[width=10cm,clip]{map}
\caption{The torsion angle deviation from the values at the Myoglobin native state (colour bar) site by site. The x-axis - logarithm of the Glauber temperature, the y-axis is the number of the amino-cid}
\label{f-helix}
\end{figure}
The result of calculation for the Myoglobin is presented at the figure~\ref{heating}.
The simulation is performed in the Glauber temperature range from $10^{-18}$ to $10^{-4}$, with fifteen million steps. As it follows from the expression~(\ref{GlaubProb}), the acceptance rate of the steps, were energy increases on the value larger than temperature, will be exponentially suppressed. Due to this, there is no thermal changes of the higher energy scale $\kappa$-terms of~(\ref{FreeEn}). As the result all thermal fluctuations are produced by torsion.
The radius of gyration temperature dependence shows that thermal unfolding of the obtained myoglobin soliton configuration goes through several stages. At low temperature we have native configuration, then at $T=10^{-14}$ there is a crossover to the intermediate state - molten globule. At higher temperature - $T=10^{-9}$ there is a crossover from molten globule to the self-avoiding random walk (SARW). During the cooling process, myoglobin soliton structure folds from SARW state to the native state through the same stages. Calculation of the root-mean-square deviation of atomic positions (RMSD) presented at figure~\ref{RMSD} shows that after cooling the myoglobin soliton configuration folds to the exactly same native conformation with RMSD less than 1 Angstrom. Thus, we can conclude that obtained free-energy minimum corresponds the stable native conformation of the protein.
\begin{figure}[h]
\centering
\includegraphics[width=10cm,clip]{RMSD}
\caption{Temperature dependence of the root-mean-square deviation of atomic positions from the native state.}
\label{RMSD}
\end{figure}
To understand nature of the molten globule state, we analyse torsion angle fluctuations during heating and cooling processes for each amino-acid site. The result of the numerical simulations is presented at figure~\ref{f-helix}.
The figure shows that molten globule state appears due thermal unfolding of a short part of the backbone chain. The part is located at cites from 84 to 96, what exactly corresponds to the alpha-helix F. Thus myoglobin molten globule has unfolded F-helix with the rest of the structure exactly same as at native state.
\section{Conclusions}
\label{results}
Analogy between gauge fields and protein chain Frenet frames geometry allow us to use full power of the field theory approach to study not only protein structure in terms of the collective degrees of freedom, but also dynamics at different thermodynamical conditions and in external fields. Gauge and chiral symmetry breaking provides new concept of the protein structure study in terms of topological solitons superpositions, what allows us to reproduce protein secondary and tertiary structure with accuracy better than 1 Angstrom. Analysis of protein dynamics within field theory Monte-Carlo simulations shows that the gauge symmetry restoration at particular protein clusters provides fundamental mechanism of the protein folding to different conformations, what can be directly related to the biological function of the protein. For example, myoglobin thermal unfolding to the molten globule and folding back occurs due to unfolding and folding of the F-helix, which is bound with the heme-group. What can explain mechanism of the oxygen storage and release in myoglobin.
{\bf Acknowledgement:}The work was supported by the Federal Target Programme
for Research and Development in Priority Areas
of Development of the Russian Scientific and Technological
Complex for 2014-2020 (The unique identifier of the Contract RFMEFI58415X0017, contract number 14.584.21.0017).
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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Dr. Marcie Dudeck
Dr. Julie Erickson
Dr. Lance Hawley
Dr. Danielle Katz
Dr. Naomi Koerner
Rotem Regev, M.A.
Dr. Alexandra Soliman
Sandra Fournier
Alexander R. Daros
Dean Carcone
Director Dr. Neil A. Rector, Ph.D
ABOUT CBT
Molecular role of gene
booking@medicenter.com
© 2018 Forest Hill Centre for Cognitive Behavioural Therapy All Rights Reserved
MANKATO, Minn. -- In announcing Latavius Murray's right ankle surgery on March 22, the Minnesota Vikings released a statement saying he would "fully recover and be available for training camp."
More than four months later, however, Murray remains on the physically unable to perform list and thus ineligible to practice. Brett Favre Jerseys He said Monday there is "no timetable" for his return, but expressed confidence he could be ready for the regular season even if he misses training camp -- a view that coach Mike Zimmer does not appear to share.
"He is a smart guy," Zimmer said, "but he needs to get out there."
Murray has missed the first five days of camp, and if his return is imminent, he provided no indications Monday. As we noted over the weekend, rookie Dalvin Cook has taken the early lead to start in what was expected to be an interesting camp competition. Harrison Smith Jerseys Although the Vikings' original statement said he would be ready for training camp -- presumably from the beginning -- Murray said Monday: "As of right now, I'm not behind or anything."
Murray had a similar procedure on his left ankle earlier in his career but said he has not been able to use that experience to predict recovery from his most recent.
"You can't treat any injury the same," he said. Stefon Diggs Jerseys "Even if it's the same surgery, you can't treat the recovery process the same way. Everyone is different and so I'm just trusting the process."
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 9,381
|
{"url":"https:\/\/kseebsolutions.guru\/2nd-puc-basic-maths-question-bank-chapter-7-ex-7-3\/","text":"Students can Download Basic Maths Exercise 7.3 Questions and Answers, Notes Pdf, 2nd PUC Basic Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.\n\n## Karnataka 2nd PUC Basic Maths Question Bank Chapter 7 Ratios and Proportions Ex 7.3\n\nPart \u2013 A\n\n2nd PUC Basic Maths Ratios and Proportions Ex 7.3 Three Marks Questions and Answers ( 3 \u00d7 4 = 12)\n\nQuestion 1.\nIf \u20b9 150 maintains a family of 4 persons for 30 days. How long 7600 maintain a family of 6 persons?\n\nQuestion 2.\n300 workers can finish a work in 8 days. How many workers will finish the same work in 5 days.\n\nWorkers and days are in inverse proportion 300 : x = 5 : 8\nx = $$\\frac{300 \\times 8}{5}$$ = 480 workers\n\nQuestion 3.\n5 carpenters can earn \u20b9540 in 6 days working 9 hours a day. How much will 8 carpenters can earn in 12 days working 6 hours a day?\n\nDays and amount are in direct proportion, hours and amount are in direct proportion\n\nQuestion 4.\nA mixture contains milk and water in the ratio 6:1 on adding 5 litres of water, the ratio of milk and water becomes 7 : 2, find the quantity of milk in the original mixture.\nQuantity of milk is 6x and water is 1x, 5 liters of water is added, the new ratio is 7:2\n$$\\frac{6 x}{x+5}=\\frac{7}{2}$$\n12x = 7x + 35 \u21d2 5x = 35\nx = 7\nThe quantity of milk is 6(x) = 6 (7) = 42\n\nPart \u2013 B\n\n2nd PUC Basic Maths Ratios and Proportions Ex 7.3 Five Mark Questions and Answers\n\nQuestion 1.\nA jar contains two liquids X and Y in the ration 7:5. When 6 litres of the mixture is drawn and the jar in filled with the same quantity of Y, the ratio of Xand Y becomes 7:9. Find the quantity X in the jar initially,\nLet quantity of liquid X is 7x and Y is 5x 6 liters of the mixture is drawn.\ni.e.,$$\\frac{7 \\times 6}{12}=\\frac{7}{2}$$ litres of X is removed\n$$\\frac{5 \\times 6}{12}=\\frac{5}{2}$$ litres of Y is removed\n\u2234 The remaining quantity of X and Y is 7x \u2013 $$\\frac{7}{2}$$ and 5x \u2013$$\\frac{5}{2}$$ respectively.\n6 litres of Y is added to get ratio 7:9.\n\nQuestion 2.\nTwo taps fill a cistern separately in 20 minutes and 40 minutes respectively and a drain pipe can drain off 30 litres per minute. If all the three pipes are opened, the cistern fills in 72 minutes what is the capacity of the cistern?\nTime taken by tap A is 20 min\n\u2234 $$\\frac{1}{20}$$b of the Cistern is filled by tap A\nSimilarly $$\\frac{1}{40}$$ of the Cistern is filled by tap B\nBoth the taps can fill $$\\frac{1}{20}+\\frac{1}{40}=\\frac{3}{40}$$\n\u201c204040 A drain tap can drain 30 liters per minute the cistern is filled in 60 minute.\n\nThe drain tap can drain in 17 minutes in 1minute it drains 30 litres\nIn 17 minutes it drains 30 \u00d7 17litres\n\u2234 The capacity of the cistern = 510 litres\n\nQuestion 3.\nIf ten persons can do a job in 60 days. In how many days can twenty persons do the same job?\n\nPersons & days are in inverse proportion\n\u2234 10:20 = x : 60\nX= $$\\frac{60 \\times 10}{20}$$ = 30days 20\n\nQuestion 4.\nA can do a piece of work in 20 days, B in 30 days and C in 60 days. All of them began to work together. However, A left the job after 6 days and B quit work 6 days before the completion of work. How many days\ndid the work last?\nIn 1 day the work done by A, B & C is\n\nIn 6 days the work done is $$\\frac{6}{10}=\\frac{3}{5}$$\nRemainin work is $$1-\\frac{3}{5}=\\frac{2}{5}$$ of the work\nLet the number of days to complete the work be x.C does $$\\frac{x}{60}$$ of the work & B does $$\\frac{x-6}{30}$$ of the work in x days\n\nQuestion 5.\n8 men and 16 women can finish a job in 6 days | but 12 men & 24 women can finish it in 8 days. How many days will 26 men and 20 women take to finish the job?\n8 men & 16 women can finish a Job in 6 days\n\u2234 In 1 day the work done is of 48men and 96 women.\n12 men & 24 women can finish a job in 8 days. In 1 day the work done is of 96 men & 192 women.\n\u2234 48 men + 96 women = 96 men + 192 women\n26M + 20W = 52W + 20W = 72W\nLet the required number of days be x.\n192 : 72 = x : 5\nX = $$\\frac{192 \\times 5}{72}=\\frac{45}{3}$$ = 15 days\n\nQuestion 6.\n4 men and 12 boys can do a piece of work in 5 \u2026 days by working 8 hours per day. In how many days 2 men & 4 boys can do the same piece of work working 12 hours a day.\nGiven 4 m = 12 B\n1 m = 3 B\n2men & 4 boys = 6 boys + 4 boys = 10 boys\n\nBoys & days are in inverse proposition days & hours are in inverse proportion.\n\u2234 10 : 12 :: 5 : x 12 : 8\nx = $$\\frac{12 \\times 8 \\times 5}{10 \\times 12}=$$ = 4days.\n\nQuestion 7.\nA railway train 100 metres long is running at the speed of 30 kmph. In what time will it pass (i) a man standing near the line (ii) a bridge 100 metres long?\nd = 100m Speed = 30km ph\nSpeed = $$\\frac{\\mathrm{d}}{\\mathrm{t}}$$\n\nLength of the bridge is 100m\nd = 100 + 100 = 200\nt = $$\\frac{200 \\times 18}{30 \\times 5}$$ = = 24 Sec.\n\nQuestion 8.\nThe driver of car is traveling at a speed of 36 kmph and spots a bus 80 metres ahead of him. After 1 hour the bus is 120 metres behind the car. What is the speed of the bus?\n\u2234 t = $$\\frac{200}{36-x}$$\n1 = $$\\frac{200}{(36-x) 1000}$$","date":"2023-04-01 13:18:27","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.4820564091205597, \"perplexity\": 1043.8147418409055}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296950030.57\/warc\/CC-MAIN-20230401125552-20230401155552-00407.warc.gz\"}"}
| null | null |
[Beowulf] Reminder: Today is "Beowulf User Group Tuesday!"
Reminder: Today is "Beowulf User Group Tuesday!"
Both East and West coast user's groups are meeting today.
"Eliminating Complexity in Creating HPC/Computing/Networking Platforms"
network with other Linux HPC professionals.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 799
|
\section{Introduction}
Abbott, Altenkirch, Ghani, Hancock, McBride and Morris's containers
\cite{AAG:conspt,AGHMM:indc} are a representation of a wide class of
set functors (datatypes) in terms of shapes and positions. We could
say that they are a form of syntax for datatypes as semantic
entities. Polynomials \`a la Gambino and Hyland \cite{GH:weltdp} are a
close variation of containers. They are nice in particular because
they can be made to work in a very general setting (categories with
pullbacks) \cite{Web:polcp}, but the definitions and proofs get very
involved very early on.
Ahman, Chapman and Uustalu \cite{ACU:wheicc} introduced directed
containers to make explicit the additional structure of those
containers whose set functor interpretation carries a comonad
structure. Typical examples of such functors with a comonad structure
are node-labelled tree datatypes. The counit extracts the root label
of a tree while the comultiplication relabels every node with the
whole subtree rooted by that node. In a directed container every
position in a shape determines another shape, the subshape
corresponding to this position. Ahman, Chapman and Uustalu
\cite{ACU:wheicc} also spelled out the polynomial version of directed
containers (directed polynomials), but did not put it to any use.
In this paper, we revisit directed polynomials and take advantage of
them to make some observations about the structure of the category of
directed containers. In particular, we develop some new constructions
on directed containers and some specializations of directed
containers.
Specifically, we see that the category of directed containers is
isomorphic to the category of small categories and (what we here call)
relative split pre-opcleavages of a certain type. We consider the
opposite category construction (for a datatype of node-(i.e.,
subtree-)labelled trees, the corresponding datatype of
context-labelled trees) and the concept of a groupoid (of which zipper
datatypes are typical examples).
The significance of containers for functional programming consists
primarily in providing a tool for generic programming with both datatypes
in general as well as with datatypes with special structure. But containers
are also particularly well-suited for analyzing special classes of datatypes
from a combinatorial perspective. For instance, the concepts of directed
containers and distributive laws of directed containers enable us to
recognize and enumerate the comonad structures that are available on
different functors, the distributive laws that exist between these
comonads etc.
This paper is organized as follows. First, in Section~\ref{sect:dcontainers}, we briefly review
containers and directed containers. Then, we go to polynomials and
directed polynomials in Section~\ref{sect:dpolynomials}, recognizing that a directed polynomial is just a small category while a directed polynomial morphism is not a functor, but something different and considerably more involved. Next, in Section~\ref{sect:coproductandtensor}, we consider the coproduct of two directed
containers and a certain tensor of two directed containers as constructions of categories. Finally, we
analyze opposite categories and groupoids as directed containers in Sections~\ref{sect:oppositedcontainer} and~\ref{sect:bdcontainers}, respectively.
Throughout the paper, we use syntax similar to that of the
dependently-typed functional programming language Agda. In particular,
when declaring the type of a function, we mark the arguments that are
derivable in most contexts as implicit by enclosing them/their types
in braces. In applications of the function, we either omit these
arguments or provide them in braces. In infix applications of
functions, we place the implicit arguments (if we want to provde them)
after the function symbol.
\section{Directed Containers}
\label{sect:dcontainers}
We begin with a brief recap of containers and directed containers.
\subsection{Containers}
A \emph{container} is given by a set $S$ (of shapes) and a $S$-indexed
family of sets $P$ (of positions).
Any container $(S, P)$ interprets into a set functor $\csem{S, P}$,
defined on objects as $\csem{S, P}\, X =_{\mathrm{df}} \Sigma s : S.\, P\, s \to X$ and
on morphisms as $\csem{S, P}\, f\, (s, v) =_{\mathrm{df}} (s, \lambda p.\, f\, (v\, p))$.
A \emph{container morphism} between $(S, P)$ and $(S', P')$ is given
by maps $t : S \to S'$ and \linebreak $q : \Pi s : S.\, P'\, (t\, s) \to P\, s$,
correspondingly interpreting
into a natural transformation $\csem{t, q}$ between
the functors $\csem{S, P}$ and $\csem{S', P'}$, defined as
$\csem{t, q}\, (s, v) =_{\mathrm{df}} (t\,s, \lambda p.\, v\, (q\, s\, p))$.
Containers and container morphisms form a monoidal category
$\mathbf{Cont}$. The interpretation $\csem{-}$ is a fully faithful monoidal
functor from $\mathbf{Cont}$ to $[\mathbf{Set},\mathbf{Set}]$, with the monoidal structures
given by the composition of containers and the composition of set
functors, respectively.
We emphasize the fully-faithfulness of $\csem{-}$: it means that all natural
transformations between functors representable by containers are
representable as container morphisms and uniquely so.
\subsection{Directed Containers}
Directed containers are containers with additional structure.
A \emph{directed container} is a container $(S, P)$ together with maps
${\downarrow} : \Pi s : S.\, P\, s \to S$ (the subshape corresponding to a
position), $\o : \Pi \ia{s : S}.\, P\, s$ (the root position in a shape), ${\oplus} : \Pi \ia{s
: S}.\, \Pi p : P\, s.\, P\, (s \downarrow p) \to P\, s$ (translation of
subshape positions into the global shape) such that
\[
\begin{array}{c}
s \downarrow \o = s \\
s \downarrow (p \oplus p') = (s \downarrow p) \downarrow p' \\
p \oplus \o = p \\
\o \oplus p = p \\
(p \oplus p') \oplus p'' = p \oplus (p' \oplus p'')
\end{array}
\]
where the 4th displayed equation is welltyped thanks to the 1st (to type the
left-hand side we need $p : P\, (s \downarrow \o)$ while to type the
right-hand side we need $p : P\, s$) and the 5th thanks to the 2nd (to
type the left-hand side we need $p'' : P\, (s \downarrow (p \oplus p'))$ while
to type the right-hand side we need $p'' : P\, ((s \downarrow p) \downarrow p)$). In
the special case $S = 1$, the equations simply require that $(P\, {\ast},
\o\, \ia{{\ast}}, {\oplus}\, \ia{{\ast}})$ is a monoid.
Any directed container $(S, P, {\downarrow},\o, {\oplus})$ interprets into a comonad $\dcsem{S, P, {\downarrow},
\o, {\oplus}} =_{\mathrm{df}} (D, \varepsilon, \delta)$ on $\mathbf{Set}$, with $D =_{\mathrm{df}} \csem{S, P}$,
$\varepsilon\, (s, v) =_{\mathrm{df}} v\, (\o\, \ia{s})$, $\delta\, (s, v) =_{\mathrm{df}} (s,
\lambda p.\, (s \downarrow p, \lambda p'.\, v\, (p \oplus \ia{s}\, p')))$.
A \emph{directed container morphism} between $(S, P, \downarrow, \o, \oplus)$
and $(S', P', {\mathbin{\downarrow'}}, \o', {\mathbin{\oplus'}})$ is a container morphism $(t, q)$
between $(S, P)$ and $(S', P')$ such that
\[
\begin{array}{c}
t\, (s \downarrow q\, s\, p) = t\, s \mathbin{\downarrow'} p \\
\o\, \ia{s} = q\, s\, (\o'\, \ia{t\, s}) \\
q\, s\, p \oplus \ia{s}\, q\, (s \downarrow q\, s\, p)\, p' = q\, s\, (p \mathbin{\oplus'} \ia{t\, s}\, p')
\end{array}
\]
where the 3rd displayed equation is welltyped as the 1st holds (to type the
left-hand side we need $p' : P'\, (t\, (s \downarrow q\, s\, p))$ while to type the
right-hand side we need $p' : P'\, (t\, s \mathbin{\downarrow'} p)$). In the special
case $S = S' = 1$, which trivializes $t$, the map $q\, {\ast}$ is a
monoid morphism between $(P'\, {\ast}, \o'\, \ia{{\ast}}, {\mathbin{\oplus'}}\, \ia{{\ast}})$ and $(P\, {\ast}, \o\, \ia{{\ast}}, {\oplus}\, \ia{{\ast}})$---in the opposite
direction compared to the directed container morphism.
A directed container morphism $(t,q)$ between $(S, P, \downarrow, \o, \oplus)$
and $(S', P', {\mathbin{\downarrow'}}, \o', {\mathbin{\oplus'}})$
interprets into a comonad morphism
between $\dcsem{S, P, \downarrow, \o, \oplus}$ and $\dcsem{S', P', {\mathbin{\downarrow'}}, \o',
{\mathbin{\oplus'}}}$, given by $\dcsem{t, q} =_{\mathrm{df}} \csem{t, q}$.
Directed containers and directed container morphisms form a category
$\mathbf{DCont}$. The interpretation
$\dcsem{-}$ is a fully faithful functor from $\mathbf{DCont}$ to
$\Comonad{\mathbf{Set}}$. In fact, $\dcsem{-}$ is a pullback of $\csem{-}$ along
$U : \Comonad{\mathbf{Set}} \to [\mathbf{Set},\mathbf{Set}]$, meaning that directed
containers are precisely those containers whose set functor interpretation
carries a comonad structure.
Here are some simple examples of directed containers.
Taking $S =_{\mathrm{df}} 1$, $P\, {\ast} =_{\mathrm{df}} \mathsf{Nat}$, ${\ast} \downarrow p =_{\mathrm{df}} {\ast}$, $\o
=_{\mathrm{df}} 0$, $p \oplus p' =_{\mathrm{df}} p + p'$, we get a directed container
interpreting into the stream comonad: $D\, X =_{\mathrm{df}} \Sigma {\ast} : 1.\,
\mathsf{Nat} \to X \cong \mathsf{Str}\, X$. The counit extracts the head element from
a stream while the comultiplication turns a stream into a stream of
its suffixes.
Taking $S =_{\mathrm{df}} \mathsf{Nat}$, $P\, s =_{\mathrm{df}} [0..s]$, $s \downarrow p =_{\mathrm{df}} s - p$,
$\o =_{\mathrm{df}} 0$, $p \oplus p' =_{\mathrm{df}} p + p'$, we get a directed container
interpreting into the nonempty list comonad: $D\, X =_{\mathrm{df}} \Sigma s :
\mathsf{Nat}.\, [0..s] \to X \cong \mathsf{NEList}\, X$. The counit extracts the head
element from a nonempty list while the comultiplication turns a
nonempty list into a nonempty list of its suffixes.
If we instead take $S =_{\mathrm{df}} \mathsf{Nat}$, $P\, s =_{\mathrm{df}} [0..s]$, $s \downarrow p =_{\mathrm{df}}
s$, $\o =_{\mathrm{df}} 0$, $p \oplus \ia{s}\, p' =_{\mathrm{df}} (p + p')
\mathbin{\mathrm{mod}} (s + 1)$, we get a directed container
interpreting into a different comonad on the nonempty list
functor. The counit extracts the head element from a nonempty list
while the comultiplication turns a nonempty list into a nonempty list
of its cyclic shifts.
Finally, taking $S$ to be any given set and $P\, s =_{\mathrm{df}} 1$, we get a
directed container interpreting into the reader comonad $D\, X =_{\mathrm{df}}
\Sigma s : S.\, 1 \to X \cong S \times X$. Taking $S$ to be any given
set, $P\, s =_{\mathrm{df}} S$, $s \downarrow s' =_{\mathrm{df}} s'$, $\o\, \ia{s} =_{\mathrm{df}} s$ and
$s' \oplus \ia{s}\, s'' =_{\mathrm{df}} s''$, the directed container obtained
interprets into the array comonad $D\, X =_{\mathrm{df}} \Sigma s : S.\, S \to X
\cong S \times (S \to X)$.
\section{Directed Containers as Categories}
\label{sect:dpolynomials}
We now proceed to polynomials and directed polynomials.
\subsection{Containers as Polynomials}
Polynomials are an alternative view of containers where the $S$-indexed
family $P$ of positions is replaced with a single set
$\bar{P}$ that collects all positions across all shapes. This set must be
fibred over $S$ in the sense of coming together with a map $\mathsf{s} : \bar{P}
\to S$ that tells which shape each position belongs to.
A \emph{polynomial} is hence given by two sets $S$ and $\bar{P}$ and a map
$\mathsf{s}: \bar{P} \to S$.
Containers can be converted into polynomials and vice versa by $\bar{P}
=_{\mathrm{df}} \Sigma s : S.\, P\, s$, $\mathsf{s}\, (s, p) =_{\mathrm{df}} s$ resp.\ $P\, s
=_{\mathrm{df}} \Sigma p : \bar{P}.\, \ia{\mathsf{s}\, p = s}$.\footnote{Elements of $P\, s$ are dependent pairs with an equality proof as the second component. We mark this component as implicit by enclosing its type in braces in the definition of $P\, s$ and omit it in actual pairs of this type. We apply the same practice also to other similar dependent tuple types.} This gives us a bijection up to
isomorphism between the collections of containers and polynomials.
In a morphism between polynomials, instead of an $S$-indexed family of
maps $q\, s : P'\ (t\, s) \to P\, s$, we have a single map $\bar{q}$
sending elements of $\bar{P}'$ to $\bar{P}$ which is defined only for those
$p : \bar{P}'$ whose shape is in the image of $t : S \to S'$, i.e., $t\, s
= \mathsf{s}'\, p$ for some $s : S$. This $s$ must be explicitly supplied, as
it is not uniquely determined by $p$, unless $t$ is
injective. Moreover, the shape for the position returned by $\bar{q}$ on
$(s, p)$ must be $s$, i.e., $\mathsf{s}\, (\bar{q}\, (s, p)) = s$.\footnote{These
considerations concern general polynomial morphisms, which is what
we need. In works on polynomials, it is commonplace to consider only
linear polynomial morphisms. They are much easier to handle, but too
restrictive for our purposes.}
A \emph{polynomial morphism} between $(S, \bar{P}, \mathsf{s})$ and $(S', \bar{P}',
\mathsf{s}')$ is therefore given by maps $t : S \to S'$ and $\bar{q} : (\Sigma s :
S.\, \Sigma p : \bar{P}'.\, \ia{t\, s = \mathsf{s}'\, p}) \to \bar{P}$ such that $\mathsf{s}\,
(\bar{q}\, (s, p)) = s$. Polynomials and polynomial morphisms form a
category $\mathbf{Poly}$.
Container morphisms and polynomial morphisms are interconverted by
$\bar{q}\, (s, p) =_{\mathrm{df}} q\, s\, p$ resp.\ $q\, s\, p =_{\mathrm{df}} \bar{q}\, (s,
p)$. These conversions extend the bijection up to isomorphism between
the collections of containers and polynomials to an equivalence
between the categories $\mathbf{Cont}$ and $\mathbf{Poly}$ of containers resp.\
polynomials.
\subsection{Directed Containers as Directed Polynomials as Small
Categories}
Let us apply a similar change of view (from ``indexed'' to ``fibred'')
to directed containers. We arrive at the following result.
A \emph{directed polynomial} is given by sets $S$, $\bar{P}$ and maps
$\mathsf{s}, \t : \bar{P} \to S$, $\mathsf{id} : \ia{S} \to P$, ${;} : (\Sigma p : \bar{P}.\,
\Sigma p' : \bar{P}.\, \ia{\t\, p = \mathsf{s}\, p'}) \to \bar{P}$ such that $\mathsf{s}\, (\mathsf{id}\,
\ia{s}) = s$, $\mathsf{s}\, (p \mathbin{;} p') = \mathsf{s}\, p$ and
\[
\begin{array}{c}
\t\, (\mathsf{id}\, \ia{s}) = s \\
\t\, (p \mathbin{;} p') = \t\, p' \\
p \mathbin{;} \mathsf{id}\, \ia{s} = p \\
\mathsf{id}\, \ia{s} \mathbin{;} p = p \\
(p \mathbin{;} p') \mathbin{;} p'' = p \mathbin{;} (p' \mathbin{;} p'')
\end{array}
\]
Similarly to the situation with directed containers, here the 4th
displayed equation is welltyped because the 1st equation holds and the
5th equation is welltyped because the 2nd equation holds. (But the
more basic nondisplayed equations need also to be used.)
A directed container is converted into a directed polynomial by $\bar{P}
=_{\mathrm{df}} \Sigma\, s : S.\, P\, s$, $\mathsf{s}\, (s, p) =_{\mathrm{df}} s$, $\t\, (s, p)
=_{\mathrm{df}} s \downarrow p$, $\mathsf{id}\, \ia{s} =_{\mathrm{df}} (s, \o\, \ia{s})$, $(s, p)
\mathbin{;} (s \downarrow p, p') =_{\mathrm{df}} (s, p \oplus \ia{s}\, p')$.
A conversion in the opposite direction is given by $P\, s =_{\mathrm{df}} \Sigma
p : \bar{P}.\, \ia{\mathsf{s}\, p = s}$, $s \downarrow p =_{\mathrm{df}} \t\, p$, $\o\, \ia{s} =_{\mathrm{df}}
\mathsf{id}\, \ia{s}$, $p \oplus \ia{s} p' =_{\mathrm{df}} p \mathbin{;} p'$. These
conversions form a bijection up to isomorphism between the collections
of directed containers and directed polynomials.
It is easy to notice that the data and laws of a directed polynomial
are just those of a small category: shapes are objects, positions are
morphisms, $\mathsf{s}$ and $\t$ give the source and target of a morphism, $\mathsf{id}$ and
${;}$ are the identities and composition. We learn that the reason why
a directed container is like a monoid, albeit not quite, is that it is
a proper generalization of a monoid, and a well-known proper
generalization at that, a small category!
What are the implications of this? Can it be that the category of
directed containers is nothing but the category $\mathbf{Cat}$ of small
categories and functors? That would be a hasty conclusion. We should
diligently spell out what a directed container morphism amounts to. It
is this.
A \emph{directed polynomial morphism} between $E = (S, \bar{P}, \mathsf{s}, \t,
\mathsf{id}, ;)$ and $E' = (S', \bar{P}', \mathsf{s}', \t', \mathsf{id}', ;')$ is given by
maps $t : S \to S'$ and $\bar{q} : (\Sigma s : S.\, \Sigma p : \bar{P}'.\, \ia{t\,
s = \mathsf{s}'\, p)} \to \bar{P}$ such that $\mathsf{s}\, (\bar{q}\, (s, p)) = s$ and
\[
\begin{array}{c}
t\, (\t\, (\bar{q}\, (s, p))) = \t'\, p \\
\mathsf{id}\, \ia{s} = \bar{q}\, (s, \mathsf{id}'\, \ia{t\, s}) \\
\bar{q}\, (s, p) \mathbin{;} \bar{q}\, (\t\, (\bar{q} (s, p)), p') = \bar{q}\, (s, p \mathbin{;'} p')
\end{array}
\]
where the 3rd displayed equation is welltyped because the 1st holds.
Pictorially,
\[
\xymatrix@R=1.5pc@C=3pc{
s \ar@{->}[rr]^-{\bar{q}\, (s, p)} \ar@{|->}[dd]^t \ar@{|->}@/_3pc/[r]
& & \circ \ar@{|->}[dd]^t\\
& & \\
t\, s \ar[rr]_{p}
& \ar@{|->}[uu]_\bar{q} & \circ
}
\]
Directed polynomials and directed polynomial morphisms form a
category $\mathbf{DPoly}$.\footnote{Linear directed polynomial morphisms are much
simpler than general directed polynomial morphisms: they are nothing but
fully-faithful functors between small categories.}
Directed container morphisms and directed polynomial morphisms are
interconvertible by $\bar{q}\, (s, p) =_{\mathrm{df}} q\, s\, p$ resp.\ $q\, s\, p
=_{\mathrm{df}} \bar{q}\, (s, p)$. This extends the bijection up to isomorphism
between the collections of directed containers and directed
polynomials into an equivalence of the categories $\mathbf{DCont}$ and
$\mathbf{DPoly}$.
We see that a directed polynomial morphism $(t, \bar{q})$ between directed
polynomials $E$ and $E'$ is very far from anything like a functor
between $E$ and $E'$ as small categories. Instead, it is a bit like
$\bar{q}$ being an opcleavage for $t$, but with two big reservations.
First, $t$ is not a functor, but only an object mapping, and second,
the requirements on $\bar{q}$ are somewhat weak.
We could reasonably say that $\bar{q}$ is a split pre-opcleavage for
$t^\dagger: E \to S'^\dagger$ relative to $! : E' \to S'^\dagger$
where $S'^\dagger$ is the cofree category on $S'$, i.e., the small
category with $S'$ as the set of objects and a single morphism between any
two objects. This is according to the following terminology that we
have invented for the occasion.
We say that a \emph{split pre-opcleavage} for a functor $F : \mathbb{C} \to
\mathbb{D}$ is an assignment, to any object $X$ of $\mathbb{C}$ and any morphism $f$ of
$\mathbb{D}$ with $F\, X$ as the source, of a morphism $f_*\, X$ of $\mathbb{C}$ that has
$X$ as the source and satisfies $F\, (f_*\, X) = f$, in such a way
that $\mathsf{id}\, \ia{X} = (\mathsf{id}\, \ia{F\, X})_*\, X$ and $f_*\, X ; g_*\, Y
= (f ; g)_*\, X$. This is weaker than an opcleavage in that $f_*\ X$
does not have to be opCartesian. But at the same time, this is also
stronger in that the equations of a split opcleavage are already
required. As a variation, a \emph{split pre-opcleavage} for a functor
$F: \mathbb{C} \to \mathbb{D}$ \emph{relative} to a functor $J : \mathbb{J} \to \mathbb{D}$ is an
assignment, to any object $X$ of $\mathbb{C}$ and any morphism $f$ of $\mathbb{J}$ whose
source $Z$ satisfies $F\, X = J\, Z$, of a morphism $f_*\, X$ of $\mathbb{C}$ that
has $X$ as the source and satisfies $F\, (f_*\, X) = J\, f$, in such a
way that $\mathsf{id}\, \ia{X} = (\mathsf{id}\, \ia{F\, X})_*\, X$ and $f_*\, X ;
g_*\, Y = (f ; g)_*\, X$. Here the meaning of `relative'
is the same as in relative adjuctions \cite{Ulm:prodra} and relative
monads \cite{ACU:monnnb}.
We are not sure at this stage that this is the optimal analysis of
directed polynomial morphisms in terms of standard or close to
standard concepts, but it is the best we currently
have.
Let us revisit our examples. The small category for the stream comonad
has $S =_{\mathrm{df}} 1$, $\bar{P} =_{\mathrm{df}} \mathsf{Nat}$, $\mathsf{s}\, p =_{\mathrm{df}} {\ast}$, $\t\, p =_{\mathrm{df}}
{\ast}$, $\mathsf{id} =_{\mathrm{df}} 0$, $p \mathbin{;} p' =_{\mathrm{df}} p + p'$. (Of course this
is nothing else than the monoid $(\mathsf{Nat}, 0, +)$ seen as one-object
category.)
The small category for the nonempty lists and suffixes comonad is
given by $S =_{\mathrm{df}} \mathsf{Nat}$, $\bar{P} =_{\mathrm{df}} \Sigma s : \mathsf{Nat}.\, [0..s]$, $\mathsf{s}\,
(s, p) =_{\mathrm{df}} s$, $\t\, (s, p) =_{\mathrm{df}} s - p$, $\mathsf{id}\, \ia{s} =_{\mathrm{df}} (s,
0)$, $(s, p) \mathbin{;} (s - p, p') =_{\mathrm{df}} (s, p + p')$.
The small category for the nonempty lists and cyclic shifts
comonad has $S =_{\mathrm{df}} \mathsf{Nat}$, $\bar{P} =_{\mathrm{df}} \Sigma s : \mathsf{Nat}.\, [0..s]$,
$\mathsf{s}\, (s, p) =_{\mathrm{df}} s$, $\t\, (s, p) =_{\mathrm{df}} s$, $\mathsf{id}\, \ia{s} =_{\mathrm{df}} (s,
0)$, $(s, p) \mathbin{;} (s, p') =_{\mathrm{df}} (s, (p + p')
\mathbin{\mathrm{mod}} (s + 1))$.
The small category for the reader comonad has as $S$ any given set,
$\bar{P} =_{\mathrm{df}} \Sigma s : S.\, 1 \cong S$, $\mathsf{s}\, s =_{\mathrm{df}} s$, $\t\, s =_{\mathrm{df}}
s$, $\mathsf{id}\, \ia{s} =_{\mathrm{df}} s$, $s \mathbin{;} s =_{\mathrm{df}} s$. This is the
discrete category on the set of objects $S$---the free category on
$S$. The small category for the array comonad has as $S$ any given
set, $\bar{P} =_{\mathrm{df}} \Sigma s : S.\, S \cong S \times S$, $\mathsf{s}\, (s, s')
=_{\mathrm{df}} s$, $\t\, (s, s') =_{\mathrm{df}} s'$, $\mathsf{id}\, \ia{s} =_{\mathrm{df}} (s, s)$, $(s,
s') \mathbin{;} (s', s'') =_{\mathrm{df}} (s, s'')$. This category has a unique
morphism between any two objects and is the cofree
category on $S$.
\section{The Coproduct and a Tensor of Directed Containers}
\label{sect:coproductandtensor}
We can now look at some basic constructions of directed containers as
constructions of categories.
\subsection{Coproduct}
Given two small categories $(S_0, \bar{P}_0, \mathsf{s}_0, \t_0, \mathsf{id}_0, {;_0})$
and $(S_1, \bar{P}_1, \mathsf{s}_1, \t_1, \mathsf{id}_1, {;_1})$, we can construct a small
category $(S, \bar{P}, \mathsf{s}, \t, \mathsf{id}, {;})$ by
\[
\begin{array}{c}
S =_{\mathrm{df}} S_0 + S_1
\\
P =_{\mathrm{df}} P_0 + P_1
\\
\mathsf{s}\, (\mathsf{inl}\, p) =_{\mathrm{df}} \mathsf{inl}\, (\mathsf{s}_0\, p)
\\
\mathsf{s}\, (\mathsf{inr}\, p) =_{\mathrm{df}} \mathsf{inr}\, (\mathsf{s}_1\, p)
\\
\t\, (\mathsf{inl}\, p) =_{\mathrm{df}} \mathsf{inl}\, (\t_0\, p)
\\
\t\, (\mathsf{inr}\, p) =_{\mathrm{df}} \mathsf{inr}\, (\t_1\, p)
\\
\mathsf{id}\, \ia{\mathsf{inl}\, s} =_{\mathrm{df}} \mathsf{inl}\, (\mathsf{id}_0\, \ia{s})
\\
\mathsf{id}\, \ia{\mathsf{inr}\, s} =_{\mathrm{df}} \mathsf{inr}\, (\mathsf{id}_1\, \ia{s})
\\
\mathsf{inl}\, p \mathbin{;} \mathsf{inl}\, p' =_{\mathrm{df}} \mathsf{inl}\, (p \mathbin{;_0} p')
\\
\mathsf{inr}\, p \mathbin{;} \mathsf{inr}\, p' =_{\mathrm{df}} \mathsf{inr}\, (p \mathbin{;_1} p')
\end{array}
\]
This small category $(S, \bar{P}, \mathsf{s}, \t, \mathsf{id}, {;})$ is a coproduct of
$(S_0, \bar{P}_0, \mathsf{s}_0, \t_0, \mathsf{id}_0, {;_0})$
and $(S_1, \bar{P}_1, \mathsf{s}_1, \t_1, \mathsf{id}_1, {;_1})$ in the
category of small categories and functors, but it is likewise their
coproduct in the category of small categories and pre-opcleavages.
Via the isomorphism of the categories of directed polynomials and
directed containers, we have cheaply got a construction for the
coproduct of two directed containers. Given two directed containers
$(S_0, P_0, {\downarrow_0}, \o_0, {\oplus_0})$ and $(S_1, P_1, {\downarrow_1}, \o_1,
{\oplus_1})$, their coproduct is $(S, P, {\downarrow}, \o, {\oplus})$ where
\[
\begin{array}{c}
S =_{\mathrm{df}} S_0 + S_1
\\
P\, (\mathsf{inl}\, s) =_{\mathrm{df}} P_0\, s
\\
P\, (\mathsf{inr}\, s) =_{\mathrm{df}} P_1\, s
\\
\mathsf{inl}\, s \downarrow p =_{\mathrm{df}} \mathsf{inl}\, (s \mathbin{\downarrow_0} p)
\\
\mathsf{inr}\, s \downarrow p =_{\mathrm{df}} \mathsf{inr}\, (s \mathbin{\downarrow_1} p)
\\
\o\, \ia{\mathsf{inl}\, s} =_{\mathrm{df}} \o_0\, s
\\
\o\, \ia{\mathsf{inr}\, s} =_{\mathrm{df}} \o_1\, s
\\
p \oplus\, \ia{\mathsf{inl}\, s} p' =_{\mathrm{df}} p \oplus_0 \ia{s}\, p'
\\
p \oplus\, \ia{\mathsf{inr}\, s} p' =_{\mathrm{df}} p \oplus_1 \ia{s}\, p'
\end{array}
\]
The interpretation $\dcsem -$ takes the coproduct of two directed containers into the
coproduct of the corresponding comonads, i.e., it preserves
coproducts. The category of set comonads inherits its coproducts from
the category of set functors.
\subsection{A Tensor}
Given two small categories $(S_0, \bar{P}_0, \mathsf{s}_0, \t_0, \mathsf{id}_0, {;_0})$
and $(S_1, \bar{P}_1, \mathsf{s}_1, \t_1, \mathsf{id}_1, {;_1})$, we can also build a small category
$(S, \bar{P}, \mathsf{s}, \t, \mathsf{id}, {;})$ by
\[
\begin{array}{c}
S =_{\mathrm{df}} S_0 \times S_1
\\
P =_{\mathrm{df}} P_0 \times P_1
\\
\mathsf{s}\, (p_0, p_1) =_{\mathrm{df}} (\mathsf{s}_0\, p_0, \mathsf{s}_1\, p_1)
\\
\t\, (p_0, p_1) =_{\mathrm{df}} (\t_0\, p_0, \t_1\, p_1)
\\
\mathsf{id}\, \ia{s_0, s_1} =_{\mathrm{df}} (\mathsf{id}\, \ia{s_0}, \mathsf{id}\, \ia{s_1})
\\
(p_0, p_1) \mathbin{;} (p'_0, p'_1) =_{\mathrm{df}} (p_0 \mathbin{;_0} p'_0, p_1
\mathbin{;_1} p'_1)
\end{array}
\]
In the category of small categories and functors, $(S, \bar{P}, \mathsf{s}, \t, \mathsf{id}, {;})$
is the Cartesian product of \linebreak $(S_0, \bar{P}_0, \mathsf{s}_0, \t_0, \mathsf{id}_0, {;_0})$ and
$(S_1, \bar{P}_1, \mathsf{s}_1, \t_1, \mathsf{id}_1, {;_1})$. If we replace functors with
relative split pre-opcleavages, this ceases to be the case; the problem is that
we cannot define pairing. So we only get a binary operation on small
categories that is associative and functorial in both arguments (a
semimonoidal structure).
The corresponding construction on directed containers is the
following. Given two directed containers $(S_0, P_0, {\downarrow_0}, \o_0,
{\oplus_0})$ and $(S_1, P_1, {\downarrow_1}, \o_1, {\oplus_1})$, we build a new
directed container $(S, P, {\downarrow}, \o, {\oplus})$ by
\[
\begin{array}{c}
S =_{\mathrm{df}} S_0 \times S_1
\\
P\, (s_0, s_1) =_{\mathrm{df}} P\, s_0 \times P\, s_1
\\
(s_0, s_1) \downarrow (p_0, p_1) =_{\mathrm{df}} (s_0 \mathbin{\downarrow_0} p_0, s_1 \mathbin{\downarrow_1} p_1)
\\
\o\, \ia{s_0, s_1} =_{\mathrm{df}} (\o_0\, \ia{s_0}, \o_1\, \ia{s_1})
\\
(p_0, p_1) \oplus (p'_0, p'_1) =_{\mathrm{df}} (p_0 \mathbin{\oplus_0} p'_0, p_1
\mathbin{\oplus_1} p'_1)
\end{array}
\]
In Glasgow, this construction on the underlying
containers has been named Hancock's tensor.
The sum and tensor of containers provide a semiring category
structure on the category of containers. The category of small
categories and split pre-opcleavages (or directed containers)
inherits this structure.
\section{The Opposite Directed Container}
\label{sect:oppositedcontainer}
Given a small category $(S, \bar{P}, \mathsf{s}, \t, \mathsf{id}, {;})$, an obvious
related small category to look at is the \emph{opposite} category
$(S^\mathrm{op}, \bar{P}^\mathrm{op}, \mathsf{s}^\mathrm{op}, \t^\mathrm{op}, \mathsf{id}^\mathrm{op}, {;^\mathrm{op}})$ where
\[
\begin{array}{c}
S^\mathrm{op} =_{\mathrm{df}} S
\\
\bar{P}^\mathrm{op} =_{\mathrm{df}} \bar{P}
\\
\mathsf{s}^\mathrm{op}\, p=_{\mathrm{df}} \t\, p
\\
\t^\mathrm{op}\, p =_{\mathrm{df}} \mathsf{s}\, p
\\
\mathsf{id}^\mathrm{op}\, \ia{s} =_{\mathrm{df}} \mathsf{id}\, \ia{s}
\\
f \mathbin{;^\mathrm{op}} g =_{\mathrm{df}} g \mathbin{;} f
\end{array}
\]
Translated to directed containers, we get the following
construction. Given a directed container $(S, P, {\downarrow}, \o, {\oplus})$,
the ``opposite'' directed container is $(S^\mathrm{op}, P^\mathrm{op}, {\downarrow^\mathrm{op}},
\o^\mathrm{op}, {\oplus^\mathrm{op}})$ where
\[
\begin{array}{c}
S^\mathrm{op} =_{\mathrm{df}} S
\\
P^\mathrm{op}\, s =_{\mathrm{df}} \Sigma s' : S.\, \Sigma p : P\, s'.\, \ia{s = s' \downarrow p}
\\
s \downarrow^\mathrm{op} (s', p) =_{\mathrm{df}} s'
\\
\o^\mathrm{op}\, \ia{s} =_{\mathrm{df}} (s, \o\, \ia{s})
\\
(s', p) \oplus^\mathrm{op} \ia{s}\, (s'',
p') =_{\mathrm{df}} (s'', p' \oplus \ia{s''}\, p)
\end{array}
\]
For a datatype of node-labelled trees of some branching type, this
construction delivers the datatype of context-labelled trees of the
same branching type.
Let us work out what happens to the directed container for the
non-empty list and suffixes comonad.
The opposite category is given by
\[
\begin{array}{c}
S^\mathrm{op} =_{\mathrm{df}} \mathsf{Nat}
\\
\bar{P}^\mathrm{op} =_{\mathrm{df}}
\Sigma s : \mathsf{Nat}.\, [0..s]
\\
\mathsf{s}^\mathrm{op}\, (s, p) =_{\mathrm{df}} s - p
\\
\t^\mathrm{op}\,
(s, p) =_{\mathrm{df}} \mathsf{s}
\\
\mathsf{id}^\mathrm{op}\, \ia{s} =_{\mathrm{df}} (s, 0)
\\
(s - p, p')
\mathbin{;^\mathrm{op}} (s, p) =_{\mathrm{df}} (s, p + p')
\end{array}
\]
Accordingly, the opposite directed container is given by
\[
\begin{array}{c}
S^\mathrm{op} =_{\mathrm{df}}
\mathsf{Nat}
\\
P^\mathrm{op}\, s =_{\mathrm{df}} \Sigma s' : \mathsf{Nat}.\, \Sigma p : [0..s'].\, \ia{s =
s' - p}
\\
s \downarrow^\mathrm{op} (s', p) =_{\mathrm{df}} s'
\\
\o^\mathrm{op}\, \ia{s} =_{\mathrm{df}} (s, 0)
\\
(s', p) \oplus^\mathrm{op} \ia{s}\, (s'', p') =_{\mathrm{df}} (s'', p' + p)
\end{array}
\]
It is easy
to see that the second component of a position determines the first:
$s'$ must be $s + p$, so we can leave $s'$ out, removing the bound on
$p$ and letting it range over all of $\mathsf{Nat}$. Hence we can simplify:
\[
\begin{array}{c}
S^\mathrm{op} =_{\mathrm{df}} \mathsf{Nat}
\\
P^\mathrm{op}\, s =_{\mathrm{df}} \mathsf{Nat}
\\
s \downarrow^\mathrm{op} p =_{\mathrm{df}} s + p
\\
\o^\mathrm{op}\, =_{\mathrm{df}} 0
\\
p \oplus^\mathrm{op} p' =_{\mathrm{df}} p' + p
\end{array}
\]
We get that the underlying functor of the comonad is defined by
$D^\mathrm{op}\, X =_{\mathrm{df}} \Sigma s : \mathsf{Nat}.\, \mathsf{Nat} \to X \cong \mathsf{Nat} \times
\mathsf{Str}\, X$. This is exactly the datatype of context-labelled trees of
our chosen branching type; i.e., a datatype whose every element is a
tree together with a label for every possible one-hole context it can
fill. In our example, a tree is a nonempty list over $1$, identified
with a natural number. Its contexts are longer nonempty lists. The
counit extracts the label of the empty context in a context-labelled
tree. The comultiplication replaces the label of every context with
the corresponding context-labelled tree. Formally, $\varepsilon\, (s, xs)
=_{\mathrm{df}} \mathsf{hd}\, xs$, $\delta\, (s, xs) =_{\mathrm{df}} (s, \delta_0\, (s, xs))$
where $\delta_0\, (s, xs) =_{\mathrm{df}} (s, xs) :\!: \delta_0 (s+1, \mathsf{tl}\, xs)$.
\section{Bidirected Containers as Groupoids}
\label{sect:bdcontainers}
A groupoid is a category where every morphism is iso. In algebraicized
form, a \emph{groupoid} is a category $(S, \bar{P}, \mathsf{s}, \t, \mathsf{id}, {;})$
together with a map ${(-)}^{-1} : \bar{P} \to \bar{P}$ such that $\mathsf{s}\, (p^{-1})
= \t\, p$ and
\[
\begin{array}{c}
\t\, (p^{-1}) = \mathsf{s}\, p \\
p \mathbin{;} (p^{-1}) = \mathsf{id}\, \ia{\mathsf{s}\, p} \\
(p^{-1}) \mathbin{;} p = \mathsf{id}\, \ia{\t\, p}
\end{array}
\]
Here the 3rd displayed equation is welltyped because the 1st
holds. The 1st equation is in fact redundant, since it follows from
the 2nd equation together with the 1st and 2nd equations of a
category.
Translating this axiomatization to directed containers, we get what we call bidirected
containers.
A \emph{bidirected container} is a directed container $(S, P, {\downarrow},
\o, {\oplus})$ together with a map ${\ominus} : \Pi \ia{s : S}.\, \Pi p :
P\, s.\, P\, (s \downarrow p)$ such that
\[
\begin{array}{c}
(s \downarrow p) \downarrow (\ominus\, \ia{s}\, p) = s \\
p \oplus \ia{s}\, (\ominus\, \ia{s}\, p) = \o\, \ia{s} \\
(\ominus\, \ia{s} p) \oplus \ia{s \downarrow p}\, p = \o\, \ia{s \downarrow p}
\end{array}
\]
Again the 3rd displayed equation is welltyped because the 1st holds,
and again the 1st equation is redundant as derivable from the
2nd equation together with the 1st and 2nd equations of a directed
container.
The conversions between the two are given by $\ominus\, \ia{s}\, p =_{\mathrm{df}}
p^{-1}$ and $(s, p)^{-1} =_{\mathrm{df}} (s \downarrow p, \ominus\, \ia{s}\, p)$.
Intuitively, in a bidirected container, not only can positions of a
shape's subshape be translated to it, but also the other way
around. Indeed, $\ominus\, \ia{s}\, p$ should be seen as the translation of
the root position of the shape $s$ into the subshape determined by the
position $p$.
We recall that, if a category is a groupoid, then it is isomorphic to
its dual. But the converse is not generally true. For example, the small
category for the streams comonad is isomorphic to its own
dual (as is any category with one object), but it is not a groupoid.
The small category for the nonempty lists and cyclic shifts comonad is
a groupoid. In particular, we have $(s, p)^{-1} =_{\mathrm{df}} (s, - p
\mathbin{\mathrm{mod}} (s + 1))$. In the corresponding bidirected
container, we have $\ominus\, \ia{s}\, p =_{\mathrm{df}} - p
\mathbin{\mathrm{mod}} (s + 1)$.
The small category for the reader comonad is also a groupoid (as a discrete
category), via $s^{-1} =_{\mathrm{df}} s$. In the corresponding bidirected
container, we have $\ominus\, \ia{s}\, s =_{\mathrm{df}} s$. The small category
for the array comonad is a groupoid via $(s, s')^{-1} =_{\mathrm{df}} (s',
s)$. The corresponding bidirected container has $\ominus\, \ia{s}\, s'
=_{\mathrm{df}} s$.
\section{Conclusion}
We have witnessed that the polynomial view of containers reveals a
symmetry between shapes/subshapes of positions in the concept of a
directed container---the symmetry between sources/targets of morphisms
in the concept of a category. This makes specific constructions and
specializations available for those comonads whose underlying functors
are containers.
The concept of a directed container morphism however breaks this
symmetry; it is also quite intricate.
This situation seems to be quite special for containers that interpret
into comonads. For instance, containers that interpret into monads
do not admit a comparably simple explicit description.
As a continuation of this work, we would like to analyze our previous
results on compatible compositions and distributive laws of directed
containers \cite{AU:disldc} from the polynomial viewpoint. We expect
that this will lead to a generalization of the concepts of a Zappa-Sz\'ep
product and a matching pair of actions from monoids to small
categories.
We would also like to see if some analogs of the construction of
the opposite direct container and the concept of a bidirected
container are available for comonads directly.
\paragraph{Acknowledgements}
Ahman was funded by the Kristjan Jaak scholarship programme of the
Archi\-medes Foundation and the Estonian Ministry of Education and
Research. Uustalu was supported by the Estonian Ministry of Education
and Research institutional research grant no.~IUT33-13 and the
Estonian Science Foundation grant no.~9475.
\bibliographystyle{eptcs}
\newcommand{\doi}[1]{\href{http://dx.doi.org/#1}{doi: #1}}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 6,009
|
#include "FileServer.hpp"
static std::string path;
static ssize_t file_reader(void *cls, uint64_t pos, char *buf, size_t max)
{
FILE *file = (FILE*)cls;
(void)fseek(file, pos, SEEK_SET);
return fread(buf, 1, max, file);
}
static void free_callback(void *cls)
{
FILE *file = (FILE*)cls;
fclose(file);
}
int file_request(
void *cls,
struct MHD_Connection *connection,
const char *url,
const char *method,
const char *version,
const char *upload_data,
size_t *upload_data_size,
void **con_cls)
{
static int aptr;
struct MHD_Response *response;
int ret;
FILE *file;
struct stat buf;
if (0 != strcmp(method, MHD_HTTP_METHOD_GET)) {
return MHD_NO; /* unexpected method */
}
if (&aptr != *con_cls) {
/* do never respond on first call */
*con_cls = &aptr;
return MHD_YES;
}
*con_cls = NULL; /* reset when done */
std::string surl(&url[1]);
const char* filepath = (path + surl).c_str();
if (0 == stat(filepath, &buf)) {
file = fopen(filepath, "rb");
} else {
file = NULL;
}
if (file == NULL) {
response = MHD_create_response_from_buffer(strlen(filepath),
(void *)filepath,
MHD_RESPMEM_PERSISTENT);
ret = MHD_queue_response(connection, MHD_HTTP_NOT_FOUND, response);
MHD_destroy_response(response);
} else {
/* 32k page size */
response = MHD_create_response_from_callback(
buf.st_size,
32 * 1024,
&file_reader,
file,
&free_callback);
if (response == NULL) {
fclose(file);
return MHD_NO;
}
ret = MHD_queue_response(connection, MHD_HTTP_OK, response);
MHD_destroy_response(response);
}
return ret;
}
int fileServer(const int port, const std::string & _path )
{
path = _path;
MHD_Daemon* daemon = MHD_start_daemon(
MHD_USE_THREAD_PER_CONNECTION, port, NULL, NULL,
&file_request, NULL, MHD_OPTION_END);
if (!daemon) {
return 1;
}
while (1){usleep(3*1000000);};
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,088
|
IDF seals West Bank bookstore suspected of housing bomb workshop
Nablus shop believed used to make explosives by Hamas terror cell busted in December; army raids Jerusalem stabber's Sebastia home
By Judah Ari Gross 2 April 2017, 9:08 am 0 Edit
Judah Ari Gross is The Times of Israel's military correspondent.
The Israel Defense Forces welded shut a bookstore in the northern West Bank on Sunday that was suspected of being used to manufacture explosives for a Hamas cell broken up late last year, the army said.
In the early hours of Sunday morning, the troops arrived in the Palestinian city of Nablus to carry out an "additional element" of its cell-busting operation in December 2016, closing a shop used by the group of terrorists.
According to the military, the 20-man cell used the bookshop to make explosives for planned terror attacks in Jerusalem and Haifa, as well as printing "inciting" material.
In December, the IDF and Shin Bet security service arrested the cell members, who were in a state of "high readiness to carry out deadly suicide attacks," the Shin Bet said at the time.
Alleged members of a Hamas terror cell operating in the area of the West Bank city of Nablus, nabbed by the Shin Bet, December 22, 2016. (Shin Bet)
The suspects told investigators that between May and August 2016 they set up a lab in Nablus and produced nearly 15 pounds of TATP explosives intended for suicide bombings in Jerusalem, Haifa and bus stations across the country.
They also obtained M-16 rifles for attacks on Israeli civilians, and enlisted four suicide bombers. The terror cell was supported by a broad network of supporters who assisted in acquiring and storing weapons, transferring funds and hiding wanted persons, the Shin Bet said.
One of the victims of a stabbing in Jerusalem's Old City on April 1, 2017, is seen moments after the attack as Border Police swarm the scene (Twitter)
Also overnight Saturday-Sunday, the army raided the northern West Bank home of a terrorist who stabbed three people in Jerusalem on Saturday afternoon.
Ahmad Jazal, 17, from Sebastia, stabbed two Jewish Israeli youths in the Old City before fleeing, with police forces giving chase. He then stabbed one of the policemen before he was shot dead.
The victims — two civilians aged 18 and 20, and a border policeman in his early 20s — received treatment at the scene and were taken to Jerusalem hospitals. They were said to suffer light-to-moderate wounds. The two civilians were released from the hospital late Saturday night.
Pipe bombs seized from the home of a Palestinian prisoner in Jenin on March 31, 2017. (IDF Spokesperson's Unit)
On Friday night, Israeli soldiers in Jenin uncovered a cache of pipe bombs in the home of a Palestinian man who was arrested last month while throwing one of the explosives at the nearby al-Jalma crossing, the army said.
Elsewhere in the West Bank, Israeli troops arrested five Palestinians early Sunday morning who are suspected of throwing rocks or taking part in violent protests.
Three were arrested in Bayt Umar, north of Hebron; one was picked up in Beit Fajjar, northeast of Hebron ; and the fifth was arrested in Bayt Sahour, outside Bethlehem.
Ilan Ben Zion contributed to this report.
Nablus
Bayt Umar
Beit Fajjar
pipe bombs
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
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Jolyon Attwooll
Research provides hope for 'Holy Grail' coronavirus vaccine
The antibody response to COVID-19 vaccination among SARS survivors shows there is potential for a powerful new variant-proof vaccine.
A future vaccine has the potential to protect people against evolving variants of SARS-CoV-2, as well as other coronaviruses that might cause a future pandemic.
A Singapore-based study has fuelled hopes that a vaccine might one day offer protection against a range of different coronaviruses – and not just the SARS-CoV-2 virus that dominates now.
The research, published last week in the New England Journal of Medicine, tracked the post COVID-vaccine antibody responses of people who had previously been exposed to the 2002–04 severe acute respiratory syndrome (SARS) outbreak.
While the small-scale study only measured the reactions of eight Singaporean SARS survivors, the findings were striking. Participants showed a 'potent' and far broader immune response to related coronaviruses than was recorded in other control groups, including those already exposed to COVID-19.
Professor Bruce Thompson, the Dean of the School of Health Sciences at Swinburne University, described the findings as 'pretty exciting'.
'What these guys have done is smart,' he told newsGP. 'It's a very interesting idea. When I read it, I thought "this is like Barry Marshall".
'What they've done is thought "let's just go back to our lab book and have a look at SARS-CoV-1 and see what we can find here".
'It's very early days, but it did land itself into the New England Journal of Medicine for good reason. Nature has picked up the story and had a good look at it. The science is good.'
According to the study, participants who had successfully fought off SARS had very high levels of neutralising antibodies against SARS-CoV-2 even after just one dose of the Pfizer vaccine.
Their blood samples showed strong resistance against current variants of concern, including Alpha, Beta and Delta, as well as five bat and pangolin sarbecoviruses – a sub-genus of coronaviruses that includes SARS-CoV-1 and SARS-CoV-2.
'No such potent and wide-ranging antibody response was observed in blood samples taken from fully vaccinated individuals, even those who had also had COVID-19,' Nature reports.
'The researchers suggest that such broad protection could arise because the vaccine jogs the immune system's "memory" of regions of the SARS virus that are also present in SARS-CoV-2, and possibly many other sarbecoviruses.'
As a result of the findings, the authors believe a future vaccine could be developed that would protect recipients against any evolving variants of SARS-CoV-2, as well as other coronaviruses that might cause a future pandemic.
Dr David Martinez, a viral immunologist at the University of North Carolina at Chapel Hill who is also trying to develop a 'universal coronavirus vaccine', told Nature that the study is a 'proof of concept that a pan-coronavirus vaccine in humans is possible'.
However, the study authors say further investigation is needed, including on the responses in a wider cohort of SARS survivors, as well as to see if a similar antibody reaction is produced if the process is reversed. This is described in the study as 'priming from the SARS-CoV-2 clade followed by boosting from the SARS-CoV-1 clade'.
'If successful, this will lay a strong foundation for the development of a third-generation COVID-19 vaccine for controlling current and emerging variants of concern, as well as for preventing future sarbecovirus pandemics,' the scientists wrote.
Despite calls for a pan-coronavirus vaccine, the authors say a 'more urgent and realistic goal' would be the development of a more focused 'pan-sarbecovirus' vaccine, given the high potential transmissibility of viruses contained in this subgenus.
For Professor Thompson, the implications of the study are a cause for optimism and a sign that vaccination may be even more effective in the future.
'We got spoilt by the smallpox vaccine where you have your one injection and you're done. In reality most vaccines are not overly effective,' he said.
'The influenza [vaccine] doesn't work that way. It only lasts for about six months and it's not overly effective.
'The current COVID-19 vaccines are so fast-tracked. All the studies are done appropriately and it's been highly effective. But ordinarily you wouldn't get the side effects, ordinarily you wouldn't need two doses, ordinarily you wouldn't need to do the cold chain storage.
'This is the Holy Grail, isn't it? If we could actually have a vaccine that covers all the variants, that would be fantastic.'
AstraZeneca COVID-19 Pfizer SARS-CoV-2 vaccination vaccination rollout
COVID-19 booster clinics are inevitable. But how will they run?
Current COVID vaccines could be ineffective by next year: epidemiologists
How are COVID vaccines faring against Delta?
COVID-19 vaccine efficacy fades over time: Study
New US study shows profound impact of COVID-19 vaccination
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Il santuario di Montebruno si trova nel comune di Garzigliana, provincia di Torino, lungo le rive del fiume Pellice. Accanto al santuario si trovano i resti di quello che fu il castello di Montebruno (o di Mombrone).
Geologia
Analogamente alla vicina - e molto più imponente - Rocca di Cavour, a livello geologico la zona dove sorgono il santuario e il castello è caratterizzata dalla presenza di un inselberg, e cioè un rilievo roccioso isolato circondato da depositi sedimentari più recenti. Il rilievo si eleva di una decina di metri rispetto alla pianura circostante.
Storia
Il primo edificio risale al X secolo e costituiva il luogo di culto del paese di Garzigliana. Nel 1591 l'edificio fu abbandonato a causa di eventi bellici e ad una piena del vicino Pellice. Anche un borgo situato poco lontano dalla chiesa venne distrutto dalle piene del Pellice e i suoi abitanti furono costretti a trasferirsi a Garzigliana.
Ai primi del '900 il santuario fu ricostruito seguendo le linee architettoniche precedenti.
Note
Altri progetti
Collegamenti esterni
Montebruno
Chiese dell'arcidiocesi di Torino
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{"url":"https:\/\/www.physicsforums.com\/threads\/velocity-string-pulley-constraints.745633\/","text":"# Velocity - String(Pulley) constraints\n\n1. Mar 27, 2014\n\n### phoenixXL\n\n1. The problem statement, all variables and given\/known data\nA bead C can move freely on a horizontal rod. The bead is connected by blocks B and D by a string as shown in the figure. If the velocity of B is v. Find the velocity of block D.\n\n2. Relevant equations\nAs the string is inextensible the velocity of the string along the length is const.\n\n3. The attempt at a solution\nThe doubt I have is that, the following should be true\n$$v_c\\ =\\ v_b.cos53\u00b0\\ \\ \\ \\ ...(1)$$\n\nBut in the solution from the book I get that\n$$v_b\\ =\\ v_c.cos53\u00b0\\ \\ \\ \\ ...(2)$$\n\nI used relation 1 and got wrong results, I'm just confused how do we get relation 2.\nKindly help me out.\nThanks for your time\n\n2. Mar 27, 2014\n\n### Tanya Sharma\n\nHow is the tip of the string connected to bead C moving ? What is its velocity ?\n\n3. Mar 28, 2014\n\n### phoenixXL\n\nIts velocity is $v_b$,along the length of the string, the same as that of block B.\n\n4. Mar 28, 2014\n\n### Tanya Sharma\n\nThat means the tip of the string and bead C have different velocities . Is that so ?\n\n5. Mar 28, 2014\n\n### phoenixXL\n\nI think that so (may be my misconception). The bead is confined to the horizontal bar, and can only have velocity along the horizontal bar.\n\nFurthermore, is the velocity of TIP and the whole of the string, not the same.\n\n6. Mar 28, 2014\n\n### Tanya Sharma\n\nThe red spot in the picture depicts the tip of the string .Forget about all the pulleys and blocks for a moment.Just focus on the red spot .How does it move ?\n\n#### Attached Files:\n\n\u2022 ###### bead.PNG\nFile size:\n2.1 KB\nViews:\n119\n7. Mar 28, 2014\n\n### phoenixXL\n\nIt should have the velocity same as that of the bead $v_c$.\n\n8. Mar 28, 2014\n\n### haruspex\n\nIt hasn't been specified anywhere that I can see, but I presume the bead is tied to the string, so the string cannot slide through it.\n\nphoenixXL, if the bead moves to the right at velocity vb, what is the component of that towards the top-right pulley?\n\n9. Mar 28, 2014\n\n### phoenixXL\n\nharuspex,\nAs you are pointing, the following would be the diagram\n( assuming $v_b$ to be the velocity of the block( or string) and $v_c$ the velocity of the bead. )\n\nBut, I got confused and tried to solve the problem using the following diagram,\n\nSo, I will be grateful to know what misconception I do have, and how can I further prevent from getting errors.\n\n10. Mar 28, 2014\n\n### haruspex\n\nThe question of which vector equals a component of the other comes up in a few guises. In the present case, you just have to remember that it's the string length that's constant, so the rate at which the string passes over the pulley equals the rate at which the bead gets closer to that pulley.\nI find it can also help to imagine the process happening. If you pull down steadily on the string hanging from the pulley, do you expect the bead to get faster or slower?\n\n11. Mar 29, 2014\n\n### phoenixXL\n\nHow can we conclude this?\n\nFaster, of course.\n\n12. Mar 29, 2014\n\n### dauto\n\nYour misconception is the belief that the opposite ends of the string must have the same velocities. They don't. Only the component of the motion parallel to the string is constrained. The ends of the string are completely free to move in the direction perpendicular to the string.\n\n13. Mar 29, 2014\n\n### haruspex\n\nThe distance from bead to pulley is the length of string joining them. The rate at which the string passes over the pulley is the rate at which that length decreases.\n\n14. Mar 30, 2014\n\n### phoenixXL\n\nGot it.\n\nFor anyone with similar problem\n\nLet the distance of the bead from the pulley be r. Then $$-\\frac{dr}{dt}\\ =\\ v_b\\\\ \\implies\\ -\\frac{d\\sqrt{x^2\\ +\\ y^2}}{dt}\\ =\\ v_b\\\\ \\implies\\ -\\frac{1}{2\\sqrt{x^2\\ +\\ y^2}}.\\frac{dx^2}{dt}\\ =\\ v_b\\\\ \\implies\\ -\\frac{1}{2\\sqrt{x^2\\ +\\ y^2}}.2x.v_c\\ =\\ v_b\\\\ \\implies\\ -v_c.cos\u03b8\\ =\\ v_b\\\\$$\n\nThank you so much when I derive it myself, meager confidence builds up.\nThanks you so much\n\nKnow someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook\n\nHave something to add?\nDraft saved Draft deleted","date":"2017-08-20 17:40:29","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5315325856208801, \"perplexity\": 1078.7161034302455}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-34\/segments\/1502886106865.74\/warc\/CC-MAIN-20170820170023-20170820190023-00145.warc.gz\"}"}
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\section{Introduction}
In the early universe massive ($M\gtrsim100\,M_\odot$) black holes (BHs) are believed to
form from the collapse of massive stars \citep{Fryer01}, and these BHs may be the seeds of the
supermassive BHs at the nuclei of galaxies \citep{Madau01,Whalen12}.
These massive BHs have also been invoked to
explain ultraluminous X-ray sources (so termed because they emit at
10--100 times the Eddington rate for a $10\,M_\odot$ BH) in the
nearby universe \citep{colbert99,colbert04}. Until recently, both observations
of stellar clusters, e.g., \citet{Figer05} (although see also \cite{Massey03}),
and some theoretical arguments \citep{Mckee07} have suggested that stars above
$150\,M_\odot$ do not form at non-zero metallicities. Including the
effects of mass loss from winds, even at 1/10th solar metallicity,
this assumption produces masses of BH systems in the nearby
universe in the tens of solar masses \citep{2010ApJ...714.1217B}.
However, the discovery of several stars with current masses greater
than $150\,M_\odot$ and initial masses up to $\sim 300{\rm ~M}_{\odot}$ in the
R136 region of the Large Magellanic Cloud \citep{2010MNRAS.408..731C}
requires a rethinking of this argument. There are at least some
environments in which stellar
masses can apparently extend well beyond $150\,M_\odot$, and if these
stars do not have extremely large wind loss rates, then after their
cores collapse they may leave behind BHs with masses in
excess of $100\,M_\odot$.
It has been suggested that stars with initial masses between roughly
$150~M_\odot$ and $300~M_\odot$ at low to moderate metallicities explode due to an instability produced when
the core gets so hot that it produces electron/positron pairs, resulting in a
loss of energy which reduces the pressure and causes the core
to contract. As this happens the nuclear burning accelerates and
can disrupt the star entirely if the star is unable to stabilize
itself. If some fraction of superluminous supernovae are in fact
pair-instability supernovae \citep{woosley07,galyam09,cooke09,ofek14}
\citep[see, however,][]{Nicholl13}, then at least at metallicities
around $\sim 0.1Z_\odot$ (where $Z_\odot=0.014$) massive stars above $150~M_\odot$ exist.
Gravitational waves (GWs) can potentially provide additional evidence for
the formation and evolution of these massive stars. Massive stars are
usually found in binaries or multiple systems
\citep[e.g.,][]{Kobulnicky07,Kobulnicky12,2012Sci...337..444S,2013A&A...550A.107S}
with mass ratios that are flat \citep{2013MNRAS.432L..26S}. Indeed,
the most massive known binary has an estimated total mass of
$200$--$300\,M_\odot$ and a possible initial mass of $\sim
400\,M_\odot$ \citep{2013MNRAS.432L..26S}. Thus massive BHs formed
from the evolution of these massive stars are likely to be partnered
with comparably massive BHs. If very massive stars (VMS) with initial masses
above $150\,M_\odot$ also follow these trends, these stars may produce
massive BH binaries, some of which may merge. Keeping the binary's mass ratio fixed,
the total energy emitted in GWs is proportional to the binary's total mass, so coalescing
massive BH binaries can be detected much farther than stellar-mass BH binaries. Thus, they
could be very significant sources for advanced GW detectors.
In this paper, we explore in detail the evolution of binaries with initial (zero-age main sequence) component masses above $150 M_\odot$ and the formation of very massive BH-BH binaries; the fate of binaries with initial component masses up to $150 M_\odot$ was explored elsewhere \citep{2012ApJ...759...52D}. The
formation of merging, massive BH binaries depends sensitively
on a range of issues in stellar evolution --- for example the evolution of the core,
the expansion in the giant phase, and the details of the pair-instability supernovae.
We discuss how these uncertainties lead to a wide range of predictions for the merger
rates for these systems. Even an approximate measurement of the merger
rates will place insightful constraints on these stellar processes.
We discuss these uncertainties in detail, calculating the full range
of rate predictions for advanced LIGO/Virgo.
In Section~2 we discuss the physical processes and uncertainties
involved in the evolution of very massive binaries. In Section~3 we
provide a range of predictions for the rates of formation and merger of
massive binary stellar-mass BHs, based on different
assumptions with different codes. In Section~4 we consider dynamical
effects, particularly Kozai cycles and three-body interactions, and
find that even if most or all massive BH binaries are too
widely separated to merge on their own within a Hubble time, many will
be induced to merge by interactions with other objects. In Section~5
we map these coalescence rate predictions for massive binaries to
predictions for detection rates in future GW observatories. We
emphasize the importance of the merger and ringdown
phases of the gravitational waveform and cosmological effects,
due to the high masses of the BHs and the
significant redshift out to which they can be observed. Our discussion
and conclusions are in Section~6.
\section{BH-BH binary formation physics}
In this section we outline and discuss the basic evolutionary processes that
are involved in the formation of close (with coalescence times below the
Hubble time) BH-BH binaries from very massive stars.
Three major sources of uncertainty are involved:
\begin{enumerate}
\item {\it Common envelope evolution:} During this stage one of the stars in the binary expands
such that its envelope surrounds both stars. In order to ultimately
lead to a compact binary, the drag on the binary due to the envelope
must shrink the semimajor axis, but must eject the envelope before
the cores merge. There are many uncertainties about the efficiency
with which this happens, as well as about the conditions necessary for
common envelope evolution as opposed to stable mass transfer via Roche
lobe overflow.
\item {\it Stellar radius expansion:} In order for
the common envelope phase to be effective, it is necessary that the
stars in the binary expand significantly when they go off the main
sequence, because otherwise the stars would have had to be nearly in
contact and would thus have likely merged due to tidal effects. However,
current codes suggest the emergence of new effects for very massive
stars (such as convection that encompasses nearly the entire star) that
may suppress such expansion. These effects appear to have complex
dependencies on metallicity, rotation, and possibly even the code used
to do the analysis.
\item {\it Black-hole formation:} Massive stars
(with initial mass $\lesssim 150{\rm ~M}_{\odot}$) form an iron core and undergo core collapse at
the end of their evolution, thereby forming BHs. Very massive stars
($\lesssim 300{\rm ~M}_{\odot}$) are
potentially unstable to pair creation well before iron core formation. The
subsequent pair-instability supernova may disrupt the entire star and thus
prevent BH formation. For even more massive
stars pair creation cannot overcome the gravity of the collapsing star, and it is
expected that the entire star will end up forming a BH. The transition
from one regime to another depends on the internal temperature structure of a star
and is very sensitive to assumptions in the stellar evolutionary codes.
Additionally, there is significant uncertainty about the BH mass (whether
it forms from a supernova explosion with its associated mass ejection, or whether
the BH forms from the collapse of the entire star). Lastly,
it is possible that the resulting BH receives a significant natal kick,
disrupting the binary and eliminating massive BH-BH systems.
\end{enumerate}
We now discuss each of these issues in greater depth.
\subsection{Common envelope}
The formation of a close binary of two BHs from the initially wide
binary of two massive stars, which are large objects with Zero Age Main
Sequence (ZAMS) radii in excess of $10$--$30{\rm ~R}_{\odot}$ \citep[e.g.,][]{2000MNRAS.315..543H},
requires a process that leads to significant and fast orbital
decay. In isolated evolution, where there is no dynamical interaction
with other stars, a common envelope (CE) phase in which the expanding envelope of
a post-main-sequence star engulfs the entire binary system is the only available
process for sufficient orbital decay. For a recent comprehensive review of the physics of CEs and the many
remaining uncertainties see \citep{2013A&ARv..21...59I}.
To motivate this process in more detail, we recall that a star
undergoes a series of burning phases, where the core contracts and
heats up sufficiently such that the ashes of the previous phase are
ignited and burn. Concurrent with these phases the
envelope can also undergo phases of expansion. When the envelope
reaches the companion, the friction of the companion orbiting in the
envelope transfers orbital energy into the envelope. As a result, the
envelope may eventually become unbound, leaving a binary system
composed of the primary hot core and its mostly unaffected
companion. A large orbital contraction (factors of $\gtrsim 10$--$100$)
is expected for envelopes with mass $\gtrsim 10\%$ of the core mass
($\gtrsim 10$--$100{\rm ~M}_{\odot}$ for massive BHs). For binaries of two massive stars this process may
occur twice, as first the primary and then the secondary undergo
evolutionary expansion. This picture is generally accepted but, as we
now describe, the details of the CE phase are both highly uncertain and
extremely important for predicting the properties of any resulting
stellar-mass BH binaries.
First, when the more massive star comes into contact with its Roche lobe, the
binary is very likely eccentric and the individual stars are unlikely to have
spins that are synchronized with the orbital motion because the evolution of
massive stars is very rapid compared to the tidal timescale. Mass transfer
therefore occurs during periastron passage. Whether such intermittent mass transfer
continues, or whether it leads rapidly to circularization/synchronization is not
known. This translates into a highly uncertain initial separation at the onset of
the CE phase.
Second, it is not fully understood which binary configurations lead to a CE (i.e.,
mass transfer proceeding on a dynamical timescale) and which lead to stable Roche
lobe overflow (RLOF, i.e., mass transfer proceeding on the donor's nuclear or thermal
timescale). A standard argument begins by noting that the angular momentum of a
circular binary with a semimajor axis $a$, total mass $M$, and reduced mass $\mu$ is
$\mu\sqrt{GMa}$. In conservative mass transfer, $M={\rm const}$. Transfer from the
more to the less massive star increases $\mu$, whereas transfer from the less to the
more massive star decreases $\mu$. Angular momentum conservation thus implies that
mass transfer from the more to the less massive object shrinks the binary. This is
often used to argue that such transfer is unstable (compared to the stable mass
transfer from the less to the more massive star).
The real situation is more complicated, particularly for very massive binaries. Mass
and angular momentum can be lost from the system via winds, in some cases mass loss
can shrink stars faster than the orbital separation shrinks, and it is in particular
uncertain what happens for stars with radiative envelopes in large mass ratio
binaries. Typically it is estimated that for mass ratios $q \lesssim 1/3$--$1/2$ (where $q$
is the ratio of the mass of the companion to the mass of the donor) and for donors
with deep convective envelopes, RLOF will develop into CE. Both outcomes, CE and
stable RLOF, are adopted in the literature
\citep[e.g.,][]{Hjellming1987,Tauris1999,Wellstein2001,Ivanova2003,Dewi2003,2008ApJS..174..223B,
Mennekens2014}.
Third, there is no self-consistent physical model to calculate reliably the post-CE
orbital separation, which as we explained above is crucial to whether a system merges
into one object or leads to a compact object binary, and whether such a binary can
merge within the age of the universe. There are two existing approaches. One uses an
energy balance prescription which unfortunately does not conserve the angular
momentum of the system \citep{Webbink1984}. The other uses an angular momentum balance prescription
which unfortunately does not conserve energy \citep{Nelemans2005}. The two methods
may differ by as much as an order of magnitude in their predictions for post-CE orbital separation.
Each method has had success in reproducing the orbital periods of separate groups of post-CE white
dwarf binaries. It is not known which method (if either) is a reasonable approximation
for very massive binaries with BHs.
Fourth, the donor envelope binding energy directly affects the fate of the binary after
the CE phase, because as we describe above the envelope must be ejected to leave the
core. If the binding energy is too large, the components will merge. If the binary
survives, the final separation depends on the value of the binding energy.
There is, however, ambiguity in the definition of the envelope binding energy because
it is difficult to precisely define the core-envelope boundary. Different choices in the
literature \citep[e.g.,][]{Tauris2001,Podsiadlowski2003,Voss2003,Xu2010,Loveridge} include
a specific level of H-depletion, an entropy jump, or the position of the H-burning shell.
Given that most of the mass and binding energy of the envelope are from the part of the envelope
near the core, these choices may influence common envelope calculations. It has been suggested that
double compact object merger rates may be affected by as much as an order of magnitude (Tauris, private
communication 2012), while recently it was argued that the specific choice for the core-envelope
boundary does not play a significant role for massive stars (i.e., black hole progenitors with
$M_{\rm zams} \approx 70-100 {\rm ~M}_{\odot}$; \citealt{Wong2014}). If the internal
energy of the envelope is significant, this could make ejection easier. Similarly, if
there are nuclear burning shells in the envelope they could affect the ejection process,
although the sign of this effect is unclear. Finally, even for a given envelope binding energy the ejection
process will be affected by the fraction of the dissipated orbital energy which goes into the
ionization and dissociation of atoms and molecules in the envelope rather than into bulk
kinetic energy.
Fifth, for many massive stars the most significant radial expansion occurs right after
the main sequence, as the rapid core adjustment after the end of core hydrogen burning
causes the star to rapidly cross the Hertzsprung gap (HG). Hence it is expected that many
massive binaries will initiate the CE phase during the HG. However, it is not clear
whether at this point the stars already have a well developed core-envelope structure.
Some models indicate that the entropy profile is rather flat throughout the HG (i.e.,
it has similar structure to a main sequence star), which means that once the CE begins
it will always end in a merger of both components. Other models suggest that if the core
of the donor is exposed during this evolutionary phase (i.e., by the inspiraling companion),
it may remain at its compact size and thus there is the potential for CE survival.
\subsection{Stellar radius evolution}
For a common envelope to develop, the radius of at least one of the stars must increase
more rapidly than the Roche lobe radius. Because the Roche lobe radius is
$R_{\rm RL}\sim (m/M)^{1/3}a$, where $m$ is the mass of the donor, $M$ is the mass of the
binary, and $a$ is the binary separation, this requirement is approximately equivalent to
the requirement that the fractional expansion of the radius of one of the stars must exceed
the fractional increase in the binary separation. Very massive stars at non-zero metallicity
(e.g., Population I stars with heavy element fractions $Z=0.002$, such as those
in the Small
Magellanic Cloud) may lose half or more of their mass to stellar winds during the main
sequence (e.g., \citealt{2013MNRAS.433.1114Y}).
If mass is removed from a circular binary without changing the specific angular momentum
$\sqrt{GMa}$, the binary's separation would double when half of the mass is lost. Thus the
binary separation can increase by a factor of $\sim 2$ on the main sequence, and therefore
to initiate a CE phase one of the binary components needs to expand by more than a factor
of $2$.
However, as indicated above, if there is a CE phase during the main sequence then the
shallow entropy gradient leads to full inspiral and merger. Survival of the CE phase requires
that it be initiated beyond the main sequence, when the core-envelope structure is well-developed
and thus the envelope can be ejected while the core is unaffected. The radius evolution of a
very massive star is therefore critical to the fate of very massive binaries, but this evolution
is currently uncertain because it depends, rather sensitively, on the treatment of convection,
stellar winds, and rotational mixing in stellar models.
For example, models of $500~M_\odot$ stars done with the {\tt Geneva}
code \citep{2013MNRAS.433.1114Y} show no radial expansion beyond the main sequence for metallicities $Z=0.014$ (solar) and $Z=0.006$,
and only a mild expansion for $Z=0.002$ (from $\sim 50 {\rm ~R}_{\odot}$ at the middle of the main sequence to $\sim 110 {\rm ~R}_{\odot}$
after hydrogen core exhaustion).
Given that, as indicated above, the orbit can expand by up to
$\sim 30\%$ during this time, it is difficult for a binary to enter the CE phase and thus to
produce a close massive BH-BH binary.
This expected behavior is qualitatively distinct from that of stars below $\sim 100{\rm ~M}_{\odot}$, which
are believed to expand significantly after the main sequence. The difference for very massive
stars is that they are thought to have large convective cores (up to 90\% of the stellar mass at
the ZAMS for a star with an initial mass of $200{\rm ~M}_{\odot}$, and up to 95\% of the stellar mass for a
star with an initial mass of $500{\rm ~M}_{\odot}$; see \citealt{2013MNRAS.433.1114Y}). These cores stem
from the large radiation pressure at such high masses, and mean that fresh
hydrogen is constantly being
brought to the center and helium is mixed to the photosphere. In the models this leads to strong
Wolf-Rayet winds that can remove almost all of the hydrogen from the envelope,
resulting in highly helium-rich stars that experience little expansion.
The treatment of mixing induced by convection and rotation, along with the adopted wind mass loss
rates, are the crucial factors in modeling the radial expansion of very massive stars. However both
prescriptions are quite uncertain. Typical treatments are mostly based on theoretical estimates
that are only weakly constrained by observations (especially in the case of rare very massive stars).
Therefore, large uncertainties exist in the resulting radius evolution, leading
to outcomes anywhere between two extremes: (a)~no/small radial expansion, no/small envelope
mass after the main sequence \citep{2013MNRAS.433.1114Y}, (b)~significant radial expansion, large envelope mass after the main
sequence. Latter results were obtained using MESA calculations of very
massive stars, where a decisive effect in the radial extension of the
radiation-dominated regions of
very massive stars is envelope inflation \citep[see, e.g.,][]{Kato:1985,Ishii:1999,2006A&A...450..219P,2012A&A...538A..40G}.
In stellar evolution calculations crude approximations are made in order to deal with the
energy transport in these complex layers which largely affect the final radii of the stars \citep{2013ApJS..208....4P}.
For example, in the outer layers of the envelope the temperature decreases to few $\times 10^5$K
and iron recombines, leading to a large opacity \citep[see e.g.,][]{Cantiello:2009}.
As a result, in these layers the stellar luminosity
is much larger than the Eddington luminosity, which might seem to imply that convection will dominate
energy transport. However, due to the very low density in the envelope, convection is very inefficient
(superadiabatic) and cannot transport all of the energy, leaving some of it ``trapped" in the envelope.
A possible (but not unique) solution is that these layers expand, which changes the opacity profile
and allows the trapped energy to escape. This leads to an inflation of the stellar radius and the
formation of a density inversion (e.g., \citealt{2006A&A...450..219P,2012A&A...538A..40G}). We note
that in some codes this inflation does not occur because, for numerical reasons, convection is assumed
to be able to transport the entire energy flux \citep[see e.g.,][]{1987A&A...173..247M,2013ApJS..208....4P}.
This effect is shown in Fig.~\ref{fig:radius} where the photospheric radius evolution during the main sequence of a 500${\rm ~M}_{\odot}$ at $Z=0.002$ is calculated using two different assumptions
for the efficiency of convective energy transport. These models have been calculated using MESA with the usual mixing length theory (MLT) or assuming an
enhancement of the convective energy transport \citep[MLT++, see Sec.~7.2 in][]{2013ApJS..208....4P}.
These models are non-rotating and assume the mass loss recipe of \citet{Glebbeek:2009}.
The result shown by the solid line is in good agreement with a similar calculation using the {\tt GENEVA} code \citep{2013MNRAS.433.1114Y}.
It is estimated \citep{2006A&A...450..219P,2012A&A...538A..40G} that the mass contained in the shells that
would be affected by this inflation
is rather small: $10^{-9}{\rm ~M}_{\odot}$ for Wolf-Rayet stars and $10^{-2}{\rm ~M}_{\odot}$ for luminous blue variable stars.
However, the inflation can extend the radius of a star by a factor of a few. This in turn may lead to the
onset of a CE phase for very massive binaries on relatively close orbits. Once the CE phase is initiated
we require a significant envelope mass (in excess of $10{\rm ~M}_{\odot}$) to efficiently decrease the orbital
separation and form a close BH-BH system. For example, if we start with a massive binary ($400{\rm ~M}_{\odot}\,+\,200{\rm ~M}_{\odot}$)
in an orbit with $a=340{\rm ~R}_{\odot}$, the orbital separation will decrease to $290, 120,
14{\rm ~R}_{\odot}$ for envelope masses of
$1, 10, 100{\rm ~M}_{\odot}$, respectively. Here we have applied the most effective orbital contraction (by assuming energy balance)
with fully efficient transfer of orbital energy to the envelope ($\alpha_{\rm CE}=1.0$) and with large
envelope binding energy ($\lambda=0.1$).
Therefore it appears that very massive stars at low metallicity may or may not have massive H-rich envelopes
(due to the uncertainties in the treatment of internal mixing and wind mass loss rates) and that these envelopes
may or may not expand significantly after the main sequence (due to the uncertainties in the modeling of
radiation-dominated stellar envelopes). To assess the influence of these uncertainties on our predictions we
consider two extremes in Section~3. For the first we employ evolutionary models for very massive stars that show
both significant expansion and large envelope mass beyond the main sequence. For the second we assume that very
massive stars do not expand at all and therefore have no interactions in isolated (e.g., field stellar populations)
binary evolution.
\begin{figure}
\begin{center}
\includegraphics*[width=0.47\textwidth]{f1.ps}
\caption{Evolution of the photospheric radius as function of hydrogen core mass fraction
(X$_{\rm C}$) for MESA calculations of a $500{\rm ~M}_{\odot}$ model at $Z=0.002$. The dashed line shows a model
where the convective energy transport
is calculated according to the mixing length theory (MLT). The radial expansion is substantial and is
associated with a density inversion in the stellar envelope.
In this situation very short timesteps pose problems for the code and the model could not be evolved
past X$_{\rm C}\simeq 0.18$.
The solid line shows the same calculation assuming an enhancement in the efficiency of convective
energy transport (MLT++).
In this case no envelope inflation occurs and the code can evolve the star to the end of the main sequence.
}
\label{fig:radius}
\end{center}
\end{figure}
\subsection{Black-hole formation}
For stars above $100M_\odot$ the mass of the star at the point of core collapse generally determines the remnant
mass. If the Carbon/Oxygen (CO) core mass is above $\sim7.6\,M_\odot$ \citep[see, e.g., Section~2.3
of][]{2010ApJ...714.1217B}, it is likely that the core will collapse to a BH without producing a supernova
explosion, so the mass of the compact remnant is simply the mass of the star at collapse. However, if the core
has sufficient angular momentum, a disk can form around the newly formed BH with the potential to produce
a gamma-ray burst \citep{1993ApJ...405..273W,1999ApJ...524..262M}. In a series of $250\,M_\odot$ star simulations,
assuming efficient internal angular momentum transport from magnetic torques, \citet{2012ApJ...752...32W} found
that even without mass loss (and the resulting angular momentum loss), only the outer layers (containing $\sim16\,M_\odot$)
of these stars have sufficient angular momentum to produce a disk and drive an outflow. Any such outflow will have
a small effect ($<5$--$10$\%) on the final BH mass. Overall our uncertainty about the mass loss from stellar
winds dominates the uncertainties in mass estimates of the star at collapse and therefore of its compact remnant.
Very massive stars can produce massive helium cores (above $45{\rm ~M}_{\odot}$) that, after helium burning, can undergo an
instability where pair-production reduces the pressure in the core, allowing it to collapse. Compressional heating in
the collapse causes the CO and Si cores to reach much higher temperatures than occurs in normal core burning, and the
resulting burning phase can be so explosive that, in the most extreme cases, there is no remnant. These are the
hypothesized pair-instability supernova
\citep{1967PhRvL..18..379B,1984ApJ...280..825B,1984ApJ...277..445C,1985A&A...149..413G,2001ApJ...550..372F,2013ApJ...776..129C}.
For a sufficiently massive core, the center of the star is so hot that the photodisintegration instability is
encountered before explosive burning reverses the shock, accelerating the collapse \citep{1984ApJ...280..825B,2001ApJ...550..372F}.
These stars collapse to form large BHs and the mass at which this photodisintegration instability prevents
explosions marks the upper limit on the pair-instability progenitor mass. Whether or not the pair instability can
disrupt a star depends upon the conditions in the core, in particular the helium core mass, which as discussed
above depends on the details of stellar mixing. The lower and upper initial star mass limits for pair-instability
supernovae are typically thought to be roughly $150{\rm ~M}_{\odot}$ and $300{\rm ~M}_{\odot}$ \citep{2001ApJ...550..372F}, respectively,
but these limits are sensitive to the aforementioned uncertainties on the size of the helium core. To avoid
confusion with the initial mass range dependence on metallicity, the above limits are typically translated to final
CO core masses of $60, 130{\rm ~M}_{\odot}$ (e.g., \citealt{2013MNRAS.433.1114Y}) for the pair-instability mechanism
to operate.
Natal kicks during supernovae are another source of uncertainty in this modeling. It may happen that during core collapse a natal kick will modify the orbit in such a way as to increase the
eccentricity and/or decrease the orbital separation. Potentially, a close double BH binary may form.
However, it is very unlikely that such a favorable kick is encountered, so only a very small fraction of
binaries may be affected by this process. Nonetheless, such effects could lead to the formation of massive BH-BH
binaries in some cases. The tremendous reach of advanced ground-based instruments means that such coalescences need
only happen a few percent of the time to lead to many detections per year.
Supernova natal kicks may play an additional role in these massive stars. Without supernova explosions, kick
mechanisms relying on asymmetric mass ejecta (e.g., \citealt{1992ApJ...395..642H,2003PhRvL..90x1101B,2003ApJ...584..971B})
will not work. In the absence of kicks, we expect the spin axes to be aligned for the resulting binary BH systems.
This is because binary stars {\it (i)} may have been formed with rotation aligned with the orbital axis
(although see \citep{Albrecht2014} for examples of non-aligned binaries), {\it (ii)} may have been subject to
strong tidal interactions if on relatively close orbits (although see \citep{Claret2007} for a discussion of very inefficient radiative damping and tidal torquing for massive stars) and {\it (iii)} mass transfer and/or common envelope episodes may have aligned component rotation with the orbital angular momentum for close interacting
binaries (although see \citep{Sepinsky2010} for examples when mass transfer does not necessarily lead to effective tidal torquing and circularization/synchronization).
If this is the case, then the alignment of spin axes could be
used to distinguish a binary origin of massive BH-BH mergers from a dynamical origin. However, mechanisms invoking
asymmetries in the neutrino emission (e.g., \citealt{1996PhRvL..77.4872K,1997PhLB..396..197K,2005ApJ...632..531S,2006ApJS..163..335F})
are able to drive kicks as long as electron neutrinos are trapped in the collapsed core. These mechanisms require
large magnetic fields ($\gtrsim 10^{15}$G). For massive stars with zero-age main sequence masses above 1,000\,M$_\odot$, the electron
neutrino trapping region is small, but below this mass (which encompasses all the systems of interest in this paper),
the trapping region can be large \citep{2011AN....332..408F}. It is therefore possible that a neutrino driven kick
mechanism may work. Such kicks would alter our population studies and produce non-aligned spin axes and would reduce
close BH-BH formation rates. Without a better quantitative understanding of these kicks, however, it is difficult to
assess their effects.
\section{Estimates of BH-BH merger/formation rates}
In this section we give the results from two models that give a reasonable span
of possible rates. In Model~1 we assume that very massive stars expand
significantly and have massive H-rich envelopes beyond the main sequence. In
this approach we use population synthesis to estimate the merger rates of massive
close BH-BH binaries. In Model~2 we assume that very massive stars do not expand
significantly beyond the main sequence and we use simple order-of-magnitude
estimates to assess the formation rates of wide massive BH-BH binaries. In both
models we use an energy balance approach for the CE phase. We also limit the
range of pair-instability supernovae to stars that form final CO core masses of
$60$--$130{\rm ~M}_{\odot}$ and assume that in this range no BHs are formed. Outside this
range we assume that the entire star collapses to form a BH (minus the $10\%$ of
the mass that we assume leaves in the form of neutrino emission). Therefore, we
neglect any potential mass loss from collapsar outbursts. We also assume that these
massive stars do not impart natal kicks during the formation of their BHs.
In Section~4 we will explore dynamical processes to show that these may shorten the
merger time of these wide BH-BH binaries below a Hubble time and make them
potentially important for advanced GW detectors.
\subsection{Model 1: expanding VMS}
\subsubsection{Initial Conditions}
Recent evidence suggests that very massive stars exist above $1$--$10$\%
solar metallicity (where $Z_\odot=0.014$), but little is
known yet about their initial conditions in binaries, e.g., their initial mass function,
binary fractions, and orbital separations. We assume that the stellar initial mass
function for the primary mass $M_{\rm zams,a}$ has the form $dN/dM\propto M^{-\alpha}$
with $\alpha=1.3$ for the range $0.08\,M_\odot$--$0.5\,M_\odot$, $\alpha=2.35$ for
$0.5\,M_\odot$--$1\,M_\odot$, and $\alpha=2.7$ for $M>1\,M_\odot$
\citep{1993MNRAS.262..545K,2011MNRAS.412..979W}.
We only consider here very massive stars with $150<M_{\rm zams,a}<1000{\rm ~M}_{\odot}$.
We also assume a companion mass $M_{\rm zams,b}\leq M_{\rm zams,a}$ drawn from a
distribution uniform between $0$ and $1$ in the mass ratio $q\equiv M_{\rm zams,b}/M_{\rm zams,a}$
\citep[e.g.,][]{2012Sci...337..444S}, a uniform-in-the-log distribution of orbital separations
and a thermal-equilibrium distribution of eccentricities ($P(e)= 2e$ in range
$e=0-1$; \cite{1975MNRAS.173..729H}; \cite{Duquennoy1991}).
If very massive stars expanded as much as $M_{\rm zams} < 150 M_\odot$ stars, these distributions
would ensure that $\sim 50\%$ of binaries would experience Roche lobe overflow during their lifetime,
leading to a potential common envelope and subsequent orbital contraction \citep{2013A&A...550A.107S};
however, the lack of significant expansion of very massive stars may limit such interactions.
We only evolve binaries for which $M_{\rm zams,b}>150{\rm ~M}_{\odot}$ as in this study we are focused on very
massive star evolution and the formation of massive BH-BH binaries. We assume a binary
fraction of $50\%$ (i.e., $2/3$ of stars are in binaries). We also assume that
$50\%$ of the stars in the local universe (within the reach of advanced GW
instruments) have solar metallicity and $50\%$ of the local stars have $Z=0.002$
($\sim 10\% {\rm ~Z}_{\odot}$).
Some of these assumptions have linear effects on the predicted rate. For example,
changing the number of massive stars by a factor of two will change the number of
mergers by a factor of two, and changing the close binary fraction by a factor of
two changes the number of mergers by roughly a factor of two. In contrast, our
uncertainties about stellar evolution and binary interactions have non-linear
effects, and will dominate the errors in our rate estimates for the foreseeable
future.
\subsubsection{Population Synthesis Calculations}
Binary evolution calculations are treated as described in full detail by
\cite{2008ApJS..174..223B} with several recent updates on stellar wind mass
loss rates, compact object mass distribution and CE handling as outlined by
\cite{2012ApJ...759...52D}. In particular, we employ wind mass loss rates
from \cite{2001A&A...369..574V}. We use energy balance for CE evolution
that employs fully efficient transfer of orbital energy into the CE (i.e.,
$\alpha=1$) with physical calibration of donor binding energy \citep{Xu2010}.
A criterion for the development of CE is based on donor expansion/contraction
in response to mass loss and the related response of donor Roche lobe
due to mass transfer and orbital angular momentum losses. This approximately
translates into CE development for binaries with donors significantly (factor
of $\gtrsim 2$) more massive than their companions or with donors with deep
convective envelopes (e.g., red giants).
We apply the rapid supernova explosion model, which reproduces the mass gap
between neutron stars and BHs, to obtain compact remnant masses
\citep{2012ApJ...757...91B}.
The community currently lacks fully accepted models of very massive stars at high
metallicity. In lieu of such models, we extend the stellar evolutionary formulae of
\citet{2000MNRAS.315..543H} to calculate the evolution and fate of stars up to a ZAMS
mass of $M_{\rm zams}=1,000 {\rm ~M}_{\odot}$ using the population synthesis code \code{StarTrack }
\citep{2008ApJS..174..223B}. We apply a direct extrapolation with no high-mass
specific modifications to the original \citet{2000MNRAS.315..543H} models. We combine
these formulae with the wind mass loss rates compiled and calibrated by
\citet{2010ApJ...714.1217B}. This scheme was originally developed for stars with
$M_{\rm zams} \lesssim 100$--$150 {\rm ~M}_{\odot}$. These extrapolated VMS models expand
significantly and form massive H-rich envelopes beyond the main sequence, as expected
for stars with $M_{\rm zams} \lesssim 100$--$150 {\rm ~M}_{\odot}$.
In our solar metallicity models the CO core mass is approximately $12 {\rm ~M}_{\odot}$ for a
broad range of initial stellar masses, $M_{\rm zams}=100$--$500 {\rm ~M}_{\odot}$
(Fig.~\ref{fig:cocoremass}). At higher ZAMS masses the CO core mass rises sharply to
a maximum of $\sim 280 {\rm ~M}_{\odot}$ for $M_{\rm zams}=800{\rm ~M}_{\odot}$, then decreases for higher
initial star masses. At subsolar metallicity, the CO core mass is roughly $40 {\rm ~M}_{\odot}$
for $M_{\rm zams}=100$--$300{\rm ~M}_{\odot}$, above which the core mass rises monotonically to
a maximum of $300 {\rm ~M}_{\odot}$ for $M_{\rm zams}=1,000{\rm ~M}_{\odot}$. As we indicated in Section~2,
the BH mass approximately traces the CO core mass, and so depends on the initial
stellar mass in the same way that the CO core mass does, for both solar and subsolar
metallicity. However, whereas the maximum CO core mass is roughly the same for solar
and subsolar models, the maximum BH mass is much greater for subsolar metallicity stars.
This is because at subsolar metallicity the highest mass stars retain their H-rich
envelope, whereas at solar metallicity winds can efficiently remove the entire envelope.
Our calculation of CO core mass is based on the combination of extrapolated stellar
models presented by \citet{2000MNRAS.315..543H} and the wind mass loss rates collected
and calibrated by \citet{2010ApJ...714.1217B}. Within this framework the initial flatness
of the dependence of CO core mass on ZAMS mass is the result of increasing strength of
wind mass loss with ZAMS mass. Stars below $M_{\rm zams}=500{\rm ~M}_{\odot}$ and $M_{\rm zams}=300{\rm ~M}_{\odot}$
for solar and subsolar metallicity, respectively, are stripped of their H-rich envelopes and
they become WR stars. This further increases mass loss. Low metallicity stars above
$M_{\rm zams}=300{\rm ~M}_{\odot}$ have such massive H-rich envelopes that they never become WR stars,
and their pre-supernova mass (and therefore CO core mass) increases monotonically with ZAMS
mass. This happens also for solar metallicity stars above $M_{\rm zams}=500{\rm ~M}_{\odot}$. However,
at some point, high metallicity stars are subject to wind mass loss strong enough to remove
even very massive H-rich envelope and they become massive WR stars. Strong WR-type wind mass
loss leads to the efficient decrease of star mass. For stars above $M_{\rm zams}=800{\rm ~M}_{\odot}$
the final CO core mass decreases with initial ZAMS mass.
\begin{figure}
\begin{center}
\includegraphics*[width=0.7\textwidth]{f2.ps}
\caption{Final CO core mass (just prior to core collapse and BH formation) for our
evolutionary models of very massive stars. Here the stars are assumed to be either
single or non-interacting binary components, so this figure is only illustrative and is
not directly relevant for binary evolution leading to the formation of close BH-BH
systems.
}
\label{fig:cocoremass}
\end{center}
\end{figure}
These results may be compared to the detailed stellar evolutionary models of massive
stars published by \citet{2012IAUS..279..431Y}. They found that at solar metallicity
the final CO cores have masses $15$--$20 {\rm ~M}_{\odot}$ (assuming no rotation) or around
$25$--$35 {\rm ~M}_{\odot}$ (with significant rotation), for $M_{\rm zams}=100$--$500 {\rm ~M}_{\odot}$.
Our relation for the same regime is also flat but results in lower CO core masses
($12 {\rm ~M}_{\odot}$). Their lowest metallicity model, which has a metallicity of $\sim 10\%$
solar ($Z=0.002$; appropriate for the Small Magellanic Cloud), shows a monotonic
increase of final CO core mass from $90{\rm ~M}_{\odot}$ to $140{\rm ~M}_{\odot}$ in the mass range
$M_{\rm zams}=150$--$300 {\rm ~M}_{\odot}$. Our relation is flatter in that regime and results
in lower CO core masses ($40$--$50 {\rm ~M}_{\odot}$). In both solar and subsolar metallicity
evolution our evolutionary models result in lower CO core masses than are predicted
by \citet{2012IAUS..279..431Y}. Therefore, our estimate of BH mass is conservatively
low compared with the published detailed evolutionary models (see Fig.~\ref{fig:cocoremass}).
We also stress that for the relatively high metallicities, $Z>0.4~Z_\odot$, considered
by \citet{2012IAUS..279..431Y}, winds drive away the entire H-rich envelope for high-mass
stars. This is consistent with our findings, but may not be true for lower metallicity stars.
\begin{deluxetable}{lcccl}
\tablewidth{0pc}
\tablecolumns{5}
\tablecaption{Very Massive Star Model Properties\tablenotemark{a}}
\tablehead{%
\colhead{Phase} &
\colhead{Mass} &
\colhead{Radius} &
\colhead{ $M_{\rm CO}$} &
\colhead{ Comment} \\
\colhead{} &
\colhead{M$_\odot$} &
\colhead{R$_\odot$} &
\colhead{M$_\odot$} &
\colhead{}
}
\startdata
start MS & 500 & 50 & -- & $Z=0.014$ \\
end MS & 48 & 5 & -- & \\
end He-burning & 26 & 1 & 20 & BH formation \\
& & & & \\
start MS & 500 & 50 & -- & $Z=0.006$ \\
mid MS & & 100 & -- & \\
end MS & 102 & 7 & -- & \\
end He-burning & 75 & 2 & 65 & Pair inst. SN \\
& & & & \\
start MS & 500 & 30 & -- & $Z=0.002$ \\
mid MS & & 50 & -- & \\
end MS & & 10 & -- & \\
post MS & & 100 & -- & \\
end He-burning & & $<65$ & 150 & BH formation \\
\enddata
\label{sn}
\tablenotetext{a}{These results are taken (or extrapolated) from the rotating \citet{2013MNRAS.433.1114Y}
\vspace*{0.4cm}models.}
\label{vms}
\end{deluxetable}
We can also compare our results to the additional models in \citet{2013MNRAS.433.1114Y}.
Here we will focus on the highest mass models in these calculations, with an
initial mass of $M_{\rm zams}=500{\rm ~M}_{\odot}$; somewhat lower-mass stars (e.g.,
$M_{\rm zams}=300\,M_\odot$) evolve in qualitatively similar ways. We will use
only their rotating models, as these are more physical than non-rotating models.
Table~\ref{vms} shows the results from the calculations in \citet{2013MNRAS.433.1114Y}.
For the solar-metallicity $500{\rm ~M}_{\odot}$ star, the mass of the star is $26{\rm ~M}_{\odot}$ at the end
of core helium burning, dropping to $20{\rm ~M}_{\odot}$ when the CO core forms. Such a star will
most likely collapse to a BH with mass similar to the mass of its CO core mass. At about
$40\%$ solar metallicity ($Z=0.006$; typical of the Large Magellanic Cloud), the mass of
the star at the end of the main sequence is $102{\rm ~M}_{\odot}$ and at the end of core helium
burning is $75{\rm ~M}_{\odot}$. The star forms a $65{\rm ~M}_{\odot}$ CO core and at this mass it is likely to
undergo a pair instability supernova that completely disrupts the star and does not leave
behind a compact object remnant. For $10\%$ of solar metallicity, extrapolating the results
from \citet{2013MNRAS.433.1114Y} suggests that a $M_{\rm zams}=500{\rm ~M}_{\odot}$ star ultimately
produces a CO core mass of $150$--$170 {\rm ~M}_{\odot}$. The most likely fate of such a star is core
collapse and the formation of a BH with a mass of about $150{\rm ~M}_{\odot}$. For comparison, a
$300{\rm ~M}_{\odot}$ model at this metallicity finishes the main sequence as a $176{\rm ~M}_{\odot}$ star, and
ends core helium burning as a $150{\rm ~M}_{\odot}$ star that forms a CO core with a mass of $135{\rm ~M}_{\odot}$.
This CO core will likely form a BH of similar mass.
\subsubsection{Population Synthesis Results}
\label{sec:popsyn}
We find that only low metallicity environments/host galaxies could contribute significantly to
the formation of close BH-BH systems from very massive stars. This is qualitatively the same
result as obtained for lower mass stars \citep{Belczynski2010a}. Most of the close very
massive BH-BH systems ($75\%$) merge with short delay times ($t_{\rm delay} < 1$ Gyr).
For subsolar metallicity there are two separate populations of BH-BH systems. Most of the
systems ($93\%$) form with total mass $M_{\rm tot} = 50$--$100 {\rm ~M}_{\odot}$ and average mass ratio of
$q=0.9$, while there is a smaller population ($7\%$) of BH-BH systems with
$M_{\rm tot} = 100$--$300 {\rm ~M}_{\odot}$ and average mass ratio of $q=0.8$ for subsolar metallicity. The
less massive systems originate from stars with $M_{\rm zams} \approx 150$--$500 {\rm ~M}_{\odot}$, whereas
the more massive ones evolve from stars with $M_{\rm zams} \approx 500$--$1000{\rm ~M}_{\odot}$.
For solar metallicity, there are virtually no BH-BH systems with total mass
$M_{\rm tot} > 40 {\rm ~M}_{\odot}$.
We consider only close BH-BH binaries with total mass $M_{\rm tot} > 100 {\rm ~M}_{\odot}$, as these
binaries provide a clear signature of VMS existence and evolution. The lower mass systems
may have originated from regular stars (i.e., $M_{\rm zams} < 150 {\rm ~M}_{\odot}$). These massive
BH-BH systems would have aligned spins (as no supernova explosion and hence no natal kick
is expected for such massive stars; \citealt{2012ApJ...749...91F}). If core collapse for
such massive stars leads to a stalled shock rather than mass loss in a supernova, the BHs
that are formed will include the entire angular momentum of the pre-collapse progenitor.
This is likely to lead to rapidly spinning BHs.
Our major results discussed above are presented in Figure~\ref{fig:mtot},
~\ref{fig:q} and ~\ref{fig:tdel}.
\begin{figure}
\begin{center}
\includegraphics*[width=0.47\textwidth]{f3.ps}
\caption{Total mass of close (merging within a Hubble time) BH-BH binaries produced in
our Model $1$ with population synthesis calculations. Note that the low metallicity environment
dominates BH-BH formation. Also note two distinctive BH-BH subpopulations at low metallicity:
one with $M_{\rm tot}<100{\rm ~M}_{\odot}$ and one with $M_{\rm tot}>100{\rm ~M}_{\odot}$.}
\label{fig:mtot}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics*[width=0.47\textwidth]{f4.ps}
\caption{Close BH-BH binary mass ratio (less massive to more massive) for our Model $1$.
Note that mass ratios are rather high and are typically in range $q=0.7-1$ for the
dominant low metallicity BH-BH population.}
\label{fig:q}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics*[width=0.47\textwidth]{f5.ps}
\caption{Delay time distribution of close BH-BH binaries for our Model $1$.
Note that the distribution for the dominant low metallicity BH-BH population
falls off approximately as $t_{\rm delay}^{-1}$. The delay time is defined
as time elapsed from star formation (ZAMS) to the final BH-BH coalescence.}
\label{fig:tdel}
\end{center}
\end{figure}
With all of the previously discussed uncertainties, it is very difficult to produce reliable
quantitative results for BH binaries. However, within the framework of these
extrapolated normal stellar models we find that the common envelope phase is almost always
initiated by a star when it expands immediately after the main sequence, i.e., during
Hertzsprung gap evolution. If we assume the binary can survive this common envelope phase
and that pair instability supernovae do not occur for Population I stars ($Z>0.1 {\rm ~Z}_{\odot}$, which
encompasses all our models), we find that BH-BH merger rates are $0.5 \times 10^{-6}$
yr$^{-1}$ per Milky Way equivalent galaxy (MWEG) for BH-BH systems with total masses
larger than 100 $M_\odot$. This corresponds to a merger rate density of $5 \times 10^{-9}$
yr$^{-1}$ Mpc$^{-3}$. This is our most optimistic estimate. If we allow for pair
instability supernovae as discussed in Section~2 then the rates drop by two orders of
magnitude and we find that the BH-BH merger rate density is $5 \times 10^{-11}$ yr$^{-1}$
Mpc$^{-3}$. This is probably our most realistic model.
If we increase our CO core masses by a factor of two (consistent with \cite{2013MNRAS.433.1114Y},
who find CO cores $\sim 1.5-3$ times more massive than ours), the rate increases to
$3\times 10^{-9}{\rm yr}^{-1}~{\rm Mpc}^{-3}$. This is because our CO core masses for
close BH-BH systems with $M_{\rm tot}>100~M_\odot$ are $M_{\rm CO}=50-100~M_\odot$, which
is in the pair instability supernova range $M_{\rm CO,pair}=60-130~M_\odot$. Doubling our
CO core masses therefore moves most of them above the pair instability range and thus
allows many additional systems to evolve to BH-BH binaries.
Finally, if we do not allow for CE survival with Hertzsprung gap donors the merger rates
drop to zero.
We note that all of our findings in this section are a direct result of our {\it assumption}
that very massive stars of high metallicity behave qualitatively like normal massive stars.
If they do, then the large volume in which massive BH coalescence could be seen with
advanced LIGO/Virgo suggests that the observed rate could be many per year. The observation of
even one of these systems would refute the arguments against radial expansion of very massive
stars \citep{2013MNRAS.433.1114Y}, and would show that these binaries can survive the CE
phase with Hertzsprung gap donors. These constraints would provide insight into stellar
evolution models. If the rate is high, we could even place limits on the formation conditions
of these massive binaries (e.g., the binary mass ratio and initial mass function).
\subsection{Model 2: non-expanding VMS}
\label{sec:OoM}
In this model we assume that there is no significant expansion of VMSs. This means that both
binary components evolve as single stars, and in the end either form BHs or are disrupted by
pair-instability SNe. The initial orbital separation only expands due to the wind mass loss.
There is no CE phase that could decrease orbital separation as both binary components are within
their respective Roche lobes. Since we assume no natal kicks at the formation of the BHs, all
binaries with components that are not subject to pair-instability SNe should form wide BH-BH
binaries (i.e., with merger times much longer than the Hubble time). However, as we discuss in
Section~4, dynamical processes may be able to tighten such binaries so that they do merge
within a Hubble time. Here we present an
order-of-magnitude estimate of the formation rate of these wide BH-BH systems. We will limit
our estimate only to systems with BHs of $100{\rm ~M}_{\odot}$ or more\footnote{Note that in Model 1 we
have only considered BH-BH binaries with total mass above $100{\rm ~M}_{\odot}$, while the Model 1 total
mass distribution extended to about $300{\rm ~M}_{\odot}$.}.
We make the same assumptions about the initial mass function as before,
extending it to an upper limit of $10^3\,M_\odot$. The wind-driven mass loss rate for high-mass
stars is extremely uncertain, as is the dependence of this rate on metallicity. It is therefore
unclear what initial mass is required to leave behind a $100\,M_\odot$ BH, but for an
order-of-magnitude estimate we will assume that $M_{\rm zams}>500\,M_\odot$ is sufficient to form
a $100\,M_\odot$ BH. For comparison, our extrapolated evolutionary models produce a $100\,M_\odot$
BH for $M_{\rm zams}>600\,M_\odot$ and $M_{\rm zams}>400\,M_\odot$ for solar and $10\%$ solar
metallicity, respectively. For the initial mass function we have assumed, we find a fraction
$\approx 2\times 10^{-6}$ of stars will start with masses above $500\,M_\odot$. If, as we assumed
previously, the binary mass ratio distribution is roughly flat, then $\sim$half of the stars will
have companions at least half as massive as they are, and thus binary evolution will presumably
produce comparable-mass BHs.
Let us suppose that only some fraction of these binaries can avoid pair-instability supernova.
Following our earlier discussion we assume that stars with final CO core mass above $130{\rm ~M}_{\odot}$
avoid this fate and form massive BHs. Extrapolation of results presented by \citet{2012IAUS..279..431Y}
(see their Fig. 18) suggests that only stars at subsolar metallicity can avoid pair
instability SNe and form massive BHs above $100{\rm ~M}_{\odot}$. It appears that at $Z=0.002$ (SMC) all stars
with $M_{\rm zams}>500{\rm ~M}_{\odot}$ form these massive BHs, whereas only a small fraction (if any) of stars
with $M_{\rm zams}>500{\rm ~M}_{\odot}$ form massive BHs for $Z=0.006$ (such as for the Large Magellanic Cloud).
At higher metallicities (e.g., for the Milky Way) no massive BHs are expected. Given that the
metallicity distribution of stars is poorly constrained, we assume that only $10^{-1}$ can
avoid pair-instability SNe for $M_{\rm zams}>500{\rm ~M}_{\odot}$.
The Galaxy has $\sim 2\times 10^{11}$ stars, so our collection of assumptions implies that
$\sim 2\times 10^4$ wide very massive BH binaries per Milky Way Equivalent Galaxy (MWEG) will be
produced by a stellar binary population. The Galaxy is $\sim 10^{10}$~years old, and the comoving
number density of MWEGs is $\sim 10^{-2}~{\rm Mpc}^{-3}$ (e.g., \citealt{2008ApJ...675.1459K}).
Thus the formation rate density, averaged over cosmic history, is $\sim 10^{-8}~{\rm Mpc}^{-3}~{\rm yr}^{-1}$.
In Section~5 we discuss how these rates translate into advanced LIGO detection rates.
We can similarly estimate the formation rate of $\gtrsim
100\,M_\odot$ BHs with $\sim 10\,M_\odot$ BH companions. These
intermediate-mass-ratio binaries are of significant interest as
their inspirals may serve as precise probes of the spacetime around
BHs
\citep{2007CQGra..24R.113A,2007PhRvL..99t1102B,2011GReGr..43..485G,2012PhRvD..85f2002R}. If
we continue to assume that the mass ratio distribution is flat, then
we would expect $\sim 10\,M_\odot$ BHs to be companions to
$>100\,M_\odot$ BHs in $\sim 10$\% of systems, leading to a formation rate of $\sim 10^{-9}\,{\rm Mpc}^{-3}\,{\rm yr}^{-1}$.
\section{Dynamical processes affecting massive binaries}
\label{sec:dynamics}
As we have discussed, current stellar evolutionary theory suggests that although massive main
sequence binaries have a good chance of evolving into massive BH binaries, those binaries
seem unlikely to be close enough that, on their own, they will coalesce within a Hubble time.
However, many or most massive stars are born in stellar associations with initial number densities
of hundreds of stars or more per cubic parsec. Hence after the formation of a double BH
system there are additional interactions that can harden the binary. In addition, there is evidence
that massive stars are, in a few to $>10$\% of cases, in triple or higher-order systems (e.g.,
\citealt{2012ApJ...747...41K,2012ApJ...751....4K,2013arXiv1303.3028D}). Such systems can potentially
undergo Kozai resonance cycles \citep{1962AJ.....67..591K,1962P&SS....9..719L} that increase the
eccentricity of the massive binary sufficiently so that orbital energy and angular momentum loss through the
emission of GWs could cause rapid coalescence. In this section we examine these effects
and show that a significant fraction of initially wide very massive binaries may merge within a Hubble
time, and possibly much sooner.
\subsection{Binary-single interactions}
Suppose that our massive binary is born into a cluster with a central mass density of
$\rho \equiv 10^3\rho_3\,M_\odot\,{\rm pc}^{-3}$; note that R136 has a central density of at least
$1.5\times 10^4\,M_\odot\,{\rm pc}^{-3}$ \citep{2013A&A...552A..94S}, and that other young clusters
such as the Arches cluster can be even denser \citep{2001ApJ...551L.143L}. If our massive binary
has a total mass $M$ and a semimajor axis $a$, and if we assume that the single objects that
encounter the binary have much lower mass and need to get to within a distance $\sim a$ of the
center of mass of the binary to affect the binary semimajor axis and eccentricity, then for a
relative speed $v_\infty$ at infinity the cross section for the interaction is
\begin{equation}
\Sigma=\pi a^2\left({2 GM\over{av_\infty^2}}+1\right)\; .
\end{equation}
Stellar associations typically have velocity dispersions of a few km~s$^{-1}$, so the first term in
the parentheses dominates as long as $a$ is less than $\sim 10^3$~AU. For the same reason,
interactions of interloping stars with the binary will tend to harden the binary and change its
eccentricity $e$, causing it to sample a ``thermal" distribution $P(e)de=2ede$ (see
\citealt{1975MNRAS.173..729H} for a pioneering study). Interaction with interlopers with a total
mass approximately $2\pi/22$ times the binary's mass will reduce the semimajor axis by a factor of
$\sim 3$ \citep{1996NewA....1...35Q}. The time needed to interact with this much mass is
\begin{equation}
T={M\over{\rho\Sigma v_\infty}}\approx 6\times 10^8\, {\rm yr}\
\rho_3^{-1}\left(\frac{a}{10~{\rm AU}}\right)^{-1}\left(\frac{v_\infty}{3~{\rm km~s}^{-1}}\right).
\end{equation}
Note that because $\Sigma\propto v_\infty^{-2}$, a smaller velocity dispersion implies a more rapid
hardening of the binary. Note also that $M$ does not appear, because the greater number of
interactions required is offset by the larger gravitationally-focused cross section. If the
interloping objects are sufficiently massive then significant kicks could be delivered to the binary
in the binary-single interactions, but if the binary is much more massive than typical stars (which
we assume to be the case) then the binary should be able to remain within the stellar cluster. We
also note that because massive objects tend to swap into binaries, initially solitary massive BHs
have a good chance to become members of binaries in a short time (again, see \citealt{1975MNRAS.173..729H}
for an early discussion of this process).
If the binary orbit were forced to remain circular then its GW inspiral time is
\citep{1964PhRv..136.1224P}
\begin{equation}
\begin{array}{rl}
T_{\rm GW}(e=0)&=5a^4c^5/(256G^3\eta M^3)\\
&\approx
1.6\times 10^{15}\,{\rm yr}\left(\eta\over{0.25}\right)^{-1}\left(M\over{200\,M_\odot}\right)^{-3}
\left(a\over{10\,{\rm AU}}\right)^4 \\
\end{array}
\end{equation}
where $\eta=m_1m_2/M^2$ is the symmetric mass ratio for objects of masses $m_1$ and $m_2$ and total mass
$M$; we have normalized $\eta$ to $0.25$, which is its maximum value and which occurs for equal masses.
For a binary of eccentricity $e$ that is reasonably near unity, this time becomes \citep{1964PhRv..136.1224P}
\begin{equation}\label{TGWe}
T_{\rm GW}(e\approx 1) \approx (768/425)(1-e^2)^{7/2}T_{\rm GW}(e=0)\; .
\end{equation}
Thus for a binary of two $100\,M_\odot$ BHs in a 1\,AU orbit, an eccentricity of
$\approx 0.895$ [$0.88$ if the full expression from \citep{1964PhRv..136.1224P} is used rather than the approximation (\ref{TGWe})] is enough to drop the merger time to 1\,Gyr. If the BH binary has $a=10$\,AU, the
needed eccentricity for a 1\,Gyr merger time is $\approx 0.992$.
Binary-single interactions will thus drive up the eccentricity until the the inspiral time becomes
short and the binary will
merge (see \citealt{2006ApJ...640..156G} and \citealt{Mandel:2008} for similar arguments in the case of massive
BH binaries and intermediate-mass-ratio inspirals, respectively,
in globular clusters). As discussed above, the eccentricity distribution ($P(e)=2e$) is sampled roughly
uniformly in each interaction in the limit of three objects of comparable
mass. In the limit of a
massive binary and very low-mass interlopers, \citet{1996NewA....1...35Q} showed that three-body interactions
increase the eccentricity of the binary steadily but slowly. For example, from Quinlan's formulae, a
$100{\rm ~M}_{\odot}$--$100{\rm ~M}_{\odot}$ binary with $a=10$\,AU in a cluster of velocity dispersion $\sigma=3$\,km\,s$^{-1}$ will
increase its eccentricity from 0.7 to 0.99 in the time needed to reduce $a$ by 2.4 e-foldings ($\sim 1$\,Gyr
for our parameters), and from 0.7 to 0.999 in the time needed to reduce $a$ by 3.4 e-foldings. Eccentricity
fluctuations due to finite-mass interlopers will likely decrease the time to a given eccentricity. The
details depend on the initial distribution of semimajor axes and eccentricities, and on the mass density of
the cluster and the cluster's longevity, but it is plausible that in a significant fraction of cases where
massive BH binaries form from stellar evolution, they are induced to merge by repeated dynamical
encounters. The tilting of orbits during the dynamical encounters means that the BH spins will
typically not be aligned with the orbit during merger.
\subsection{Triple systems and the Kozai mechanism}
Another way that initially widely separated massive BH binaries might coalesce involves triple
systems. Observed massive stars have a probability, possibly greater than 10\%, of being in triple or
higher-order systems (e.g., \citealt{2012ApJ...747...41K,2012ApJ...751....4K, 2013arXiv1303.3028D}). If
the relative inclination of the inner binary and the tertiary is in the appropriate range, then over many orbits
of both the binary and the tertiary the mutual inclination will oscillate between two limits in such a way
that the eccentricity also oscillates \citep{1962AJ.....67..591K,1962P&SS....9..719L,1976CeMec..13..471L}.
In the standard Kozai approximation, in which the tertiary has a fixed and effectively infinite angular
momentum, the maximum eccentricity reached during a cycle is $(1-(5/3)\cos^2 i)^{1/2}$, where $i$ is the
initial relative inclination. For example, if $i=70^\circ$, the maximum eccentricity is 0.9. If, as is
likely in our case, the binary has as much or more angular momentum as the tertiary, then the critical
mutual inclination deviates from $90^\circ$ (see, e.g., \citealt{1976CeMec..13..471L,2002ApJ...576..894M}),
so the probability of achieving a high eccentricity assuming random inclinations will be somewhat smaller
than it would be for a critical inclination of $90^\circ$.
The time for a single Kozai cycle (from minimum to maximum eccentricity and back) is of order
$\sim (M/m)(b/a)^3$ times the orbital time of the binary, where $M$ is the mass of the binary, $m$ is the
mass of the tertiary, $b$ is the semiminor axis of the tertiary, and $a$ is the semimajor axis of the
binary (e.g., \citealt{1976CeMec..13..471L}). For $a=10$\,AU, $b/a=10$, $M=200\,M_\odot$, and $M/m=100$
(reasonable fiducial values), this time is roughly $2\times 10^5$\,yr, which is much less than the time
between close interactions with interloping stars. Thus systems that are favorably inclined for the Kozai
resonance can complete many cycles without being harassed by interlopers.
General relativistic pericenter precession can limit the maximum eccentricity during a Kozai cycle. However,
from the expressions in \citet{2002ApJ...576..894M}, this is not a limiting factor in our case. From their
equation~(6), the maximum eccentricity that can be attained for a binary of two $100\,M_\odot$ BHs at
1\,AU orbited by a $10\,M_\odot$ object with a semiminor axis of 10\,AU is 0.99, far above the $e\approx 0.9$
needed for merger within 1\,Gyr. If the binary has a semimajor axis of 10\,AU and the tertiary has a semiminor
axis of 100\,AU, the maximum eccentricity is 0.9999, compared with the $e\approx 0.99$ for a 1\,Gyr merger.
Note that such an eccentricity can be achieved by $\sim 10$\% of systems\ for an isotropic distribution of
initial mutual inclinations.
Thus, depending on the fraction of triple systems and the distribution of the masses, inclinations, and
separations of the tertiaries, it is possible that a few percent of initially wide very massive star binaries
(tens of percent of the $\sim 10$\% of systems that are triples) are induced to merge by Kozai cycles.
Such mergers would not have spins aligned with their orbits, because orbital tilting is produced during
the cycles. The studies of \citet{2002ApJ...578..775B} suggest that merger will happen near the point
of minimum mutual inclination between the tertiary and binary, and if this is at a point where the more
massive BH in the binary is reasonably aligned with the orbital axis and the binary component mass
ratio is not more than $\sim 2:1$, additional effects during the inspiral could help to align the axes
further \citep{2004PhRvD..70l4020S}.
In summary: in addition to the possibility of merger through isolated binary
evolution (which remains viable because of uncertainties in massive binary
evolution),
there are at least two dynamical
scenarios that might produce mergers of a few percent or more of the massive BH binaries that are
too wide to merge in a Hubble time through radiation reaction alone. Coalescences through isolated binary
evolution are likely to yield binary BHs with nearly aligned spins whose magnitude is close to the
astrophysical maximum, if supernova kicks for these binaries are minimal. Coalescences involving dynamical
processes will probably produce unaligned mergers, but because the BHs will have formed before the
dynamical interactions the spins may still be close to maximal. Thus detections will probe a variety of
stellar evolutionary and dynamical processes. We now discuss how coalescences between such objects could be
detected.
\section{Detection of BH-BH coalescences}
\label{sec:bhbh_coalescence}
Advanced LIGO \citep{AdvLIGO}
and Virgo \citep{AdvVirgo} interferometric GW detectors are
coming online within a few years, and are expected to reach design sensitivity by the end of the decade
\citep{scenarios}. In addition to improving overall sensitivity by a factor of $\sim 10$ relative to
their initial versions \citep{LIGO, Virgo}, these detectors will also extend the sensitivity to lower frequencies,
down to $\sim 10$ Hz, which will allow GW signatures of massive BH
binary mergers to be detected \citep[see][for upper limits from searches with initial LIGO and Virgo
detectors]{IMBHB:S5}. Matched filtering against known templates describing expected signals is the optimal
technique for extracting weak GW signals from noisy data. Although a network of multiple
detectors is needed to rule out noise artifacts and separate signals from background, a good rule of thumb for
detectability, which we follow here, is to consider a single detector and impose a matched-filtering
signal-to-noise ratio (SNR) threshold of $8$ as a proxy for detectability by the network \citep{ratesdoc}.
The detection rate $R_d$ can be expressed in terms of the merger rate per unit comoving volume per unit time ${\cal R}$ as an integral over all possible merger redshifts
\begin{equation}\label{Rd}
R_d = \int_0^\infty {\cal R} (z) \frac{dV_c}{dz} \frac{dt_s}{dt_o} (z) f_d(z) dz\, .
\end{equation}
Here the comoving volume of a given redshift slice $dV_c/dz$ is computed (e.g., see \citealt{1999astro.ph..5116H})
by assuming WMAP9 parameters $\Omega_M = 0.282$, $\Omega_\Lambda=0.718$, $h=0.697$ \citep{2012arXiv1212.5226H}. The factor $dt_s / dt_o = 1/(1+z)$ is the ratio between the clock at the source redshift $z$, which measures the merger rate, and a clock at the Earth, which measures the detection rate.
The detection fraction $f_d(z)$ measures the fraction of sources of a given mass at a given redshift that will be detectable.
The expectation value of the optimal matched filtering SNR for an overhead, face-on source is given by
\begin{equation}
\textrm{SNR}_{\textrm{opt}}^2 = 4 \Re \int_0^\infty
\frac{|\tilde{h}(f)|^2}{S_n(f)} df\, ,
\end{equation}
where $S_n(f)$ is the noise power spectral density of the detector and $\tilde{h}(f)$ is the frequency-domain
representation of a GW signal. For the waveforms $h(t)$, we use spinning, non-precessing, inspiral-merger-ringdown
effective-one-body waveforms calibrated to numerical relativity waveforms~\citep{Taracchini:2012}, specifically
their {\it SEOBNRv1} implementation in the LIGO Scientific Collaboration Algorithm Library \citep{LAL}. The waveform is corrected
for the redshift $z$ and its amplitude is inversely proportional to the luminosity distance to the source,
which scales with $z$ according to the assumed standard cosmology \citep{1999astro.ph..5116H}.
Face-on, overhead equal-mass binaries with a total rest-frame mass of $200 M_\odot$ can be detected to a redshift
of $z\sim2$ (luminosity distance of $\sim 16$ Gpc) if the components are non-spinning, or $z\sim2.6$ (luminosity
distance of $\sim 21$ Gpc) if both components have aligned spins with a dimensionless magnitude of $0.6$.
The actual SNR
for a binary with a given sky location $\alpha, \delta$, inclination $\iota$, and polarization $\psi$ is given
by $\textrm{SNR}_{\textrm{opt}} \times \Theta(\alpha,\delta,\iota,\psi)/4$, where the projection function $\Theta$
is defined in \cite{Finn:1996}. We compute the fraction $f_d(z)$ by taking into account the (numerically computed)
cumulative distribution function (CDF) of $\Theta/4$, and setting the detectability threshold at an SNR of 8 as
follows \citep[e.g.,][]{CygnusX3:2012}:
\begin{equation}
f_d (z) = 1 - \textrm{CDF}_{\Theta/4} \left[\min\left(\frac{8}{\textrm{SNR}_{\textrm{opt}}(z)},1\right)\right] \, .
\end{equation}
Under the simplifying assumption that the merger rate $\cal R$ is constant in redshift, which we use here,
Eq.~(\ref{Rd}) for the detection rate can be written as
\begin{equation}\label{Rdsimple}
R_d = {\cal R} \overline{V}_c\, ,
\end{equation}
where we have defined the detection-weighted sensitive comoving volume $\overline{V}_c$ for a given rest-frame mass combination as
\begin{equation}
\label{DWSCV}
\overline{V}_c = \int_0^\infty \frac{dV_c}{dz} f_d(z) \frac{1}{1+z} dz\, .
\end{equation}
\begin{figure}
\begin{center}
\includegraphics*[width=0.5\textwidth]{f6.ps}
\caption{The detection-weighted sensitive comoving volume $\overline{V}_c$ within
which a coalescence could be detected for BH binaries with total source-frame mass $M$,
mass ratios $q = 1$ or $0.5$, either non-spinning or with dimensionless
spins magnitudes $0.6$.}
\label{Fig:Vc}
\end{center}
\end{figure}
In Fig.~\ref{Fig:Vc} we plot the detection-weighted comoving volume as a function of the total system mass
in the source frame for mass ratios $q=0.5$ and $q=1$, and spins that are either zero or both
aligned with the angular momentum, with dimensionless magnitude $0.6$. We use the noise spectral density of
the high-power, zero-detuning configuration \citep{PSD:AL}, which corresponds to nominal
sensitivity that is expected for advanced LIGO detectors by the end of the decade \citep{scenarios}.
As expected, we find that when the mass ratio is
equal and the aligned spins are high, signals contain more power and the sensitive volume is increased.
Equation~(\ref{Rdsimple}) and Fig.~\ref{Fig:Vc} allow us to convert a merger rate into a detection rate.
In Section~\ref{sec:popsyn} we obtained a most optimistic merger rate of $5 \times 10^{-9}\,{\rm Mpc}^{-3}\,{\rm yr}^{-1}$ for BH-BH mergers with total mass above $100{\rm ~M}_{\odot}$. The peak of the total mass distribution for this model appears at $200{\rm ~M}_{\odot}$ and the BHs are of comparable mass. The weighted detectable volume for $M_{\rm tot}=200{\rm ~M}_{\odot}$ is
$6$--$12 \times 10^{10}$ Mpc$^3$
depending on BH spins, which yields $300$--$600$
detections per year. Our more realistic estimate, which accounts for pair-instability SNe, produces
a merger rate estimate of very massive BH-BH binaries of $5 \times 10^{-11}\,{\rm Mpc}^{-3}\,{\rm yr}^{-1}$,
with a predicted detection rate of $3$--$6$ a year. If we account for potential uncertainties in CE evolution
the merger rate decreases to zero, and no detections are predicted for very massive BH-BH binaries in the isolated
evolutionary scenario (Model 1).
In Section~\ref{sec:OoM} we argued for a plausible order-of-magnitude
formation rate of $\sim 10^{-8}\,{\rm Mpc}^{-3}\,{\rm yr}^{-1}$ for
wide binaries with $100{\rm ~M}_{\odot}$ or more massive BHs. In
Section~\ref{sec:dynamics} we estimated that $\sim 10\%$ of these wide
binaries may merge within a Hubble time due to dynamical interactions
with other stars. This yields a merger rate of $\sim 10^{-9}\,{\rm
Mpc}^{-3}\,{\rm yr}^{-1}$ and a corresponding detection rate of
$\sim 100$ per year if dynamical interactions
are efficient in forming close very massive BH-BH binaries (Model
2).
We also considered intermediate-mass-ratio binaries of
$\gtrsim 100\,M_\odot$ BHs with $\sim 10\,M_\odot$ BH companions, and concluded that a formation rate of $\sim 10^{-9}\,{\rm Mpc}^{-3}\,{\rm yr}^{-1}$ was plausible from order-of-magnitude arguments. Assuming that such systems can be brought to merge within a Hubble time by efficient dynamical hardening of the binary \citep[e.g.,][]{Mandel:2008}, they can be detected to $z\sim 0.5$,
which decreases the sensitive volume by a factor of $\sim 20$
relative to the $100\,M_\odot$--$100\,M_\odot$ case discussed
above. Therefore, up to $\sim 5$ intermediate-mass-ratio systems formed from very massive stars with lower-mass companions could be detected per year with advanced GW
instruments.
It is also interesting to compare the population synthesis model predictions with existing upper
limits from initial LIGO and Virgo runs. Their sensitivity to massive BH binaries
was poor because of the high value of the low-frequency cutoff, so the more interesting
existing LIGO/Virgo constraint will come from BH binaries with total mass between $50$ and $100$ solar masses.
As reported in Section~\ref{sec:popsyn}, such binaries represent $93\%$ of our entire close BH-BH
population, and this corresponds to a merger rate of $7 \times 10^{-8}\,{\rm Mpc}^{-3}\,{\rm yr}^{-1}$
for our most optimistic prediction. These binaries have formed from stars with initial mass
$M_{\rm zams} \approx 150-500{\rm ~M}_{\odot}$.
The initial LIGO/Virgo upper limits are $1.7 \times 10^{-7}\,{\rm Mpc}^{-3}\,{\rm yr}^{-1}$ and
$0.9 \times 10^{-7}\,{\rm Mpc}^{-3}\,{\rm yr}^{-1}$ for equal mass BH binaries
in the mass bins
$M_{\rm tot}=54$--$73{\rm ~M}_{\odot}$ and $M_{\rm tot}=73$--$91{\rm ~M}_{\odot}$, respectively \citep{2013PhRvD..87b2002A}.
Thus even our most optimistic rates do not violate the current upper limits for BH-BH detection.
Given our predictions of preferentially aligned spins for isolated binaries and the possibility of spins
misaligned with the orbital angular momentum for systems in which dynamics played an important role, it
is interesting to ask how well such systems can be distinguished based on gravitational-wave observations.
Several studies that considered a few individual events suggest that at least the spin magnitude of the
more massive component and the angle between it and the orbital angular momentum could be measured,
especially if this component is rapidly spinning, although it may prove difficult to measure the spin of
the lower-mass secondary \citep[e.g.,][]{VanderSluys:2008b, Raymond:2010}. A larger study \citep{Vitale:2014}
supports this view, and highlights the improvements to spin measurement when the binary is nearly edge-on
rather than face-on, and when the angular momentum of the secondary is small, reducing spin-spin terms.
Furthermore, Bayesian model selection may allow us to determine whether there's significant support for
precession induced by spin-orbit misalignment even if individual parameters cannot be measured precisely
\citep[e.g.][]{S6PE}. Unfortunately, the large size of the parameter space makes difficult a fully
systematic study based on astrophysically-motivated source distributions.
We conclude this section by pointing out the importance of {\it (i)}
accurate analytical and numerical modeling of inspiral-merger-ringdown waveforms,
since for massive BH-BH binaries, the SNR accumulates mostly
during the last stages of the binary evolution (e.g.,
see \cite{2013CQGra..31b5012H}), and
{\it (ii)} low-frequency detector sensitivity in searches for massive BH
binaries, which contribute most of the SNR below $\sim 35$ Hz. The sensitive volume plotted in Fig.~\ref{Fig:Vc} assumes that the predicted high-power, zero-detuning sensitivity \citep{PSD:AL} will be achieved down to $10$ Hz, which will require significant commissioning effort. Meanwhile,
third-generation ground-based detectors such as the
Einstein Telescope \citep{ET}, with sensitivity down to a few Hz, will
be able to probe such massive BH-BH binaries to $z\sim 15$
\cite[e.g.,][]{2011GReGr..43..485G}.
\section{Discussion and conclusions}
Since GWs from massive BH binaries can be detected to
cosmological distances, we have explored the event rates for the mergers of
these systems.
We find that only low-metallicity environments ($Z\ltorder 0.1$--$0.4\,Z_\odot$) may be favorable for
the formation of very massive stellar-origin BHs with mass exceeding $100{\rm ~M}_{\odot}$.
The formation of such BHs is possible if
{\it (i)} the initial mass function (IMF) extends above $500{\rm ~M}_{\odot}$, {\it (ii)} pair-instability SNe do not disrupt all
stars above $500{\rm ~M}_{\odot}$, and {\it (iii)} stellar winds for such massive stars are not greatly
underestimated. The formation of close massive BH-BH binaries requires that after the main sequence {\it
(iv)} very massive stars above $500{\rm ~M}_{\odot}$
expand significantly (by more than a factor of $2$), {\it (v)} their H-rich envelopes have a mass
larger than $10$--$100{\rm ~M}_{\odot}$, {\it (vi)} the evolution of such a binary involves a common envelope
phase, and {\it (vii)} the binary can survive the common envelope phase while the donor star is
a very massive Hertzsprung gap star. If conditions {\it (iv)} through {\it (vii)} are not met, then
isolated binary evolution (i.e., field stellar populations) may produce only wide massive BH-BH
binaries. We point out that even if these requirements are not met, there are several dynamical
processes that could lead to efficient lowering of the coalescence time of wide massive BH-BH
binaries both in dense stellar environments (cluster binary-single interactions) and in low-density field populations (Kozai mechanism in triple systems).
The resulting BH-BH merger rates depend sensitively on the amount of star forming mass with
low metallicity at redshifts $z<2$ (the maximum distance at which a $100$--$100{\rm ~M}_{\odot}$ BH-BH
binary will be detectable with the advanced LIGO/Virgo network). The amount of low metallicity
star formation in the last Gyr may have been as high as $\sim 50\%$ of total star formation
\citep{2008MNRAS.391.1117P}, and may have been even higher at the redshifts $z>1$ that
dominate our overall rates. Population synthesis models predict that $75\%$ of the close massive BH-BH systems merge within 1 Gyr of formation.
Based on simple estimates we find that realistic advanced LIGO/Virgo detection
rates for these massive BH-BH systems are on the order of a few per year. However, the large
uncertainties that burden our predictions allow for rates as high as hundreds of detections
per year to as low as no detections at all.
BH-BH systems originating from isolated binaries of very massive stars would likely have rather large
mass ratios ($q \gtorder 0.8$) and aligned spins. For a core collapse of a massive star that was
spin-aligned with the orbit via tidal interactions with its companion, and that ejects no mass and
has no linear momentum kick resulting from the collapse, our strong expectation is that the compact
remnant would have a spin aligned with the orbit. Given our still-rudimentary understanding of core
collapses there are of course situations in which this might not be accurate (e.g., oppositely-directed
neutrino jets on opposite sides of the proto-neutron star could impart spin angular momentum without
imparting linear momentum), but at present such scenarios seem contrived. Regular ($M_{\rm zams} < 150 {\rm ~M}_{\odot}$)
stars could not produce binaries with total mass in the $M_{\rm tot} \gtrsim 100$--$200 {\rm ~M}_{\odot}$ range.
Therefore, detections of coalescences between massive, aligned, rapidly spinning BHs would uniquely
identify systems originating from isolated binaries of very massive stars. Such detections would
indicate that the stellar IMF extends well beyond previously considered limits, and probably
as high as $M_{\rm zams} > 500 {\rm ~M}_{\odot}$, and that massive progenitor binaries survive
common envelope events even if the donors initiating these events are still in early
evolutionary stages (i.e., on Hertzsprung gap). This would also argue against models of very
massive stars that predict minimal expansion during post main-sequence evolution.
If observations show evidence for significant misalignment of BH spins, then either these
systems received kicks via asymmetric neutrino emission or dynamical processes must have been
involved in the formation of the merging BH-BH system. Moreover, \citet{Kalogera:2000} argued
that significant spin--orbit misalignment is unlikely even with supernova kicks, unless dynamical
effects are involved. This latter scenario would support the first set of published models of
very massive stars that show no (or very small) radial expansion \citep{2013MNRAS.433.1114Y}.
Alternatively, mergers of intermediate-mass BHs could be a consequence of dynamical processes in
globular clusters or involving globular cluster mergers
\citep{Fregeau:2006,AmaroSeoaneSantamaria:2009,2011GReGr..43..485G}.
Regardless, the detection of such systems would yield valuable information
about dynamical encounters and/or the multiplicity of very massive stars.
If instead we do not detect any massive BH-BH binaries with advanced LIGO/Virgo, any or all
of the effects {\it (i)--(vii)} discussed above may have contributed.
When mass is transferred from the secondary to the primary after the primary
has evolved to become a BH, the binary may be visible as an
ultra-luminous X-ray source (ULX), as the mass loss rate from the massive secondary can
be very high. This stage is likely to be quite short, given that both companions are
assumed to be massive and will have quite similar lifetimes. If 10\% of all such binaries
have a ULX stage lasting 1 million years---or, equivalently, all binaries have a ULX
stage lasting 100,000 years---the space density of observable ULXs created through this
channel will be equal to the merger rate times $10^5$ years. Since this is only one of
several channels for creating ULXs, an observed ULX space density of a few
$\times 10^{-2}$ Mpc$^{-3}$ \citep{Swartz:2011} yields an upper limit on the massive
binary merger rate of a few $\times 10^{-7}$ Mpc$^{-3}$ yr$^{-1}$. This is a factor of
several hundred higher than our very rough estimate of $10^{-9}$ Mpc$^{-3}$ yr$^{-1}$, so
it would be easy to hide the population of interest among the observed ULXs.
One possible constraint on the population of massive stars comes from
rates of pair-instability supernovae. If an IMF slope of $\sim -2.5$
is extended to arbitrarily high masses, then $\sim1\%$ of all stars
having a ZAMS mass above $8 M_\odot$ will have a ZAMS mass above $200
M_\odot$. Hence, if a significant fraction of very massive stars end
their life in pair-instability supernovae, one might expect as many as
1\% of all core-collapse supernovae to be pair-instability
supernovae. Meanwhile, recent work by \cite{Nicholl13} finds that this
fraction is no more than $10^{-4}$, and may be $< 10^{-5}$,
if the so-called ``superluminous'' supernovae are inconsistent with
expectations of pair instability supernovae \citep{Nicholl13}. If
pair-instability supernovae only produce superluminous supernovae,
these observations constrain either the number of massive stars
exceeding $\sim 150\,M_\odot$ or the mass range of stars that produce
pair-instability supernovae. In such a scenario, if advanced LIGO/Virgo observes a
large fraction of massive binary BH mergers, it would place
constraints on the pair-instability mechanism and the mass range for
which it occurs. Unfortunately, pair-instability supernovae seem to
be able to produce a wide range of light
curves \citep{Kasen11,Whalen14} and until these light-curves can be
better understood, it will be difficult to make any firm conclusions
using superluminous supernova observations.
In conclusion, advanced LIGO/Virgo detectors are
sensitive to the merger of massive BH binaries out to extraordinary distances
($z\sim2$). We argue that the rate density of these mergers is
such that event rates of a few per year, and perhaps as many as hundreds per
year, are possible given current uncertainties in stellar evolutionary
physics. The upper limits or detections expected from the coming generation of
advanced ground-based GW instruments will provide unique insights into the
evolution of very massive stars.
\acknowledgements
The authors thank Mirek Giersz, Duncan Brown, and especially Vicky Kalogera for useful comments.
KB and MW acknowledge support from Polish Science Foundation "Master2013"
Subsidy, by Polish NCN grant SONATA BIS 2. KB also acknowledges
NASA Grant Number NNX09AV06A and NSF Grant Number HRD 1242090 awarded to the
Center for Gravitational Wave Astronomy, UTB. AB acknowledges
support from NSF Grant No. PHY-1208881 and NASA Grant NNX12AN10G.
DEH acknowledges support from NSF CAREER grant PHY-1151836.
IM was partly supported by STFC, including an ET R\&D grant funded within the ASPERA-2 framework.
MCM acknowledges NASA grant NNX12AG29G, and a grant from the Simons Foundation
(grant number 230349). MCM thanks the Department of Physics and Astronomy
at Johns Hopkins University for hosting him during his sabbatical.
The authors thank the Kavli Institute for Theoretical Physics
(supported by the NSF Grant No.~PHY11-25915) for hospitality
during the genesis of this project.
The authors acknowledge the Texas Advanced Computing Center (TACC) at The
University of Texas at Austin for providing computational resources used for
this study.
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We were formed in 1970 when the Heretaunga Old Boys and Upper Hutt Wanderer's clubs amalgamated, the Upper Hutt Hockey club has a long and proud history as one of the most friendly and sociable clubs in the Wellington area.
We would love to share more about our club history and are keen to hear from past members, so please Contact us.
On 3 May 2013 the Maidstone Park Sports Centre, in Park Street, was officially opened. This Centre included two turfs - one a purpose built, international sand based pitch which is now the home of Upper Hutt Hockey Club. The first hockey game was played on the turf in May 2012.
Funders of the project included: the National Hockey Stadium Trust, Lion Foundation and Wellington Community Trust. The Pelorus Trust also made a significant contribution to the project.
Check out our award winners from past seasons here.
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{"url":"https:\/\/s54899.gridserver.com\/thermal-allodynia-bwbnzr\/what-is-the-following-quotient-2-4-f440c5","text":"Step-by-step explanation: Division of Fractions. Thanks. Question: When 8x3-4x2-3 Is Divided By 2x-1, The Quotient Is 4x2 And The Remainder Is - 3. 12 1\/2 split into 4 4. the quotient of 3 1\/5 and 2 1\/3 5. the quantity six times 3 1\/2 over 2 please help me Solution Yes, you have to memorize it. What is the following quotient? From Estimating the Quotient to HOME PAGE. 1 Answers. The division with remainder or Euclidean division of two natural numbers provides a quotient, which is the number of times the second one is contained in the first one, and a remainder, which is the part of the first number that remains, when in the course of computing the quotient, no further full chunk of the size of the second number can be allocated. 5.NBT.6 R\u20142.4 10, 15 2.3 5.NBT.B.6 Use base-ten blocks to model division. What is the quotient: (6x^4 + 15x^3 + 10x^2 + 10x + 4) \u00f7 (3x^2 + 2)? The calculator will find the difference quotient for the given function, with steps shown. Asked By adminstaff @ 16\/08\/2019 09:21 AM. She adjusted the quotient. About This Quiz & Worksheet. The sum of two natural numbers is always a natural number. Which Of The Following Division Statements Represents These Results? If the calculator did not compute something or you have identified an error, please write it in write sin x (or even better sin(x)) instead of sinx. 2) 15. Let $$f(x) = \\frac{x^2-3x+1}{x}$$. You have to use long division no other way. Use this online difference quotient calculator to find f(x+h) - \u2026 A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. Similarly, tanxsec^3x will be parsed as tan(xsec^3(x)). 2x^4 - 3x^3 + 6x^2 - 5x - 4 is divided by 2x - 3 Please help, this is urgent. James has 64 apples and wants to share them with his 3 friends. D = 7 . 4 What\u2019s In When you were in Grade 7, you had learned that polynomial is an algebraic expression whose variables must have nonnegative-integer powers. Use the difference quotient to verify that the slope of the tangent at this point is zero. of a Number by a 3-Digit Number, \u00e2\u0097\u008f Division x3 \u2212 2x2 \u2212 3x + 6 What is the quotient (6x4 \u2212 15x3 + 10x2 \u2212 10x + 4) \u00f7 (3x2 + 2)? 4) 36. 32 \u00f7 2 = 16; the quotient is 16. of Two-Digit by a One-Digit Numbers, Division Select One: A. 2. Dividend, divisor, quotient and remainder. 74 \u00f7 35 2. Emma estimated the first digit in the quotient of 2,183 \u00f7 42 as 4. Translate each of the following problem. Now, for an example, perform the difference quotient on the function, f (x) = x 2 \u2013 3x \u2013 4: Notice that you find the expression for f (x + h) by putting x + h in for every x in the function \u2014 x + h is the input variable. 1.Find the product of 2\/3 and 3\/5 2.What is the quotient of 2\/3 and 4\/9 3.Angel bought 6 3\/4 meters of silk and 3 1\/2 meters of velvet. What is the following quotient 9+sqrt 2\/4-sqrt 7 See answer xjayde28x xjayde28x 9 + \u221a2 \/ 4 - \u221a7. 152 r2 4 qw610 ... 8 2.4 5.NBT.B.6 Use partial quotients. Change the division sign to multiplication sign. Write an algebraic expression for the following: the quotient of a number and 0.76, increased by 6.5 the product of a number cubed and the sum of 57.6 and 3.42 . 1) (x \u22121\/4) ; n is the number you divide by; it is called the divisor. math Use this Google Search to find what you need. comments below. Difference quotient is used to find the slope for a curved line provided between the two points in a graph of a function 'f'. a). where: a is the initial number you want to divide, called the dividend. Chen is checking a division problem by doing the following: 152 __ \u00d7 4 608 __ + 2 610 What problem is Chen checking? about Math Only Math. C = 4 . Recall that we use the quotient rule of exponents to simplify division of like bases raised to powers by subtracting the exponents: $\\frac{x^a}{x^b}={x}^{a-b}$. of Four-Digit by a One-Digit Numbers. 2. It will not only give you the quotient answer, but also explain and show work so you can learn. ... A triathlon event consists of 2.4 miles of swimming, 112 miles of biking, and 26.2 \u2026 a\/n = q + r\/n. Mathematics. Please enter your fraction below: \/ Below are some examples of what the Quotient of Fractions Calculator can calculate: What is the quotient of 1\/2? To get tan^2(x)sec^3(x), use parentheses: tan^2(x)sec^3(x). Algebra. Solve the following portion 21% of 1,800 is. write your answer in your notebook 1. the quotient of 9 3\/4 and 5\/8 2. Or want to know more information you need spacers. Problems Involving Addition and Subtraction, Multiplication you know you need to multiply the 1st term (3x^2) by whatever makes it to whatever your dividing,so we're trying to get 6x^4 out,2x^2 times 3x^2 is 6x^4.Subtract or switch signsto get rid of the terms usually For quotients, we have a similar rule for logarithms. What is the quotient of 2\/3 and 5\/6. Which of the following is a polynomial with roots: \u2212square root of 3, square root of 3, and 2? If you get an error, double-check your expression, add parentheses and multiplication signs where needed, and consult the table below. 627 \u00f7 23 3. What is the quotient of 4\/5? The quotient of two natural numbers is always a natural number. about. Didn't find what you were looking for? There are 4 types of drinks to choose from, 4 types of sandwic \u2026 hes, and 2 types of chips. a) f(x) = 0.5x^2 + 6x + 7.5; (-6, -10.5) Difference quotient is f(a + h) - Math. In this step, I\u2019m replacing the \u201cf(x+h)\u201d in the left hand part of the numerator with the actual given function, 3x + 2: Recall also the concepts about naming polynomials according to its number of terms and its degree. Identify the quotient in the following division problems. Solve the above example using: A = 2 . 2. 15 1\/3 divide by 23\/18 3. Or want to know more information \u00c2\u00a9 and \u00e2\u0084\u00a2 math-only-math.com. 5 = 20So, estimated quotient = 20, \u00e2\u0097\u008f Word 2010 - 2020. 74 \u00f7 35 is approximately the same as 70 \u00f7 40, i.e., 7 \u00f7 4 (74 \u2192 70 & 35 \u2192 40) 7 \u00f7 4 is approximately 2. Multiply the numerator and denominator by the conjugate. The following are possible interpretations of the given expression. Example. The quotient of a number and six increased by 2 is 4.what is the number? a Number by a 2-Digit Number, \u00e2\u0097\u008f Multiplication Verify that all three methods give the same result. When you perform division, you can typically write down this operation in the following way:. Exact form: (36 + 9\u221a 7 + 4\u221a2 + \u221a14) \/ 9. or. x^4 + 3x^3 + 5x^2 - 6x - 8 is divided by x + 2 b). Show Instructions In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. Example Problem #1: Differentiate the following function: y = 2 \/ (x + 1) Solution: Note: I\u2019m using D as shorthand for derivative here instead of writing g'(x) or f'(x):. For each function, the point given is the maximum or minimum. Multiply and simplify. Identify g(x) and h(x).The top function (2) is g(x) and the bottom function (x + 1) is f(x). about 7.69:))) lublana lublana multiply by the conjugate of denominator. StartFraction StartRoot 120 EndRoot Over StartRoot 30 EndRoot EndFraction 2 4 2 StartRoot 10 EndRoot 3 StartRoot 10 EndRoot The quotient of 4, and a number increased by 6: \" \"4\/(x+6) The quotient of 4 and a number, increased by 6: \" \"4\/x +6 This is a good example of how a lack of any punctuation make the meaning of the sentence ambiguous: \"Quotient\" is the answer to a division. So, estimated quotient is 2. 1) What is the quotient of (5x 2 1) 5x + 2 2) 5x \u2212 2 3) 2x + 5 4) 2x \u2212 5 2)What is the remainder when (x 3 2 1) 7 \u2212 22x + 8) \u00f7 (x \u2212 4)? The quotient of \u200c4\u20446\u200c and \u200c2\u20449\u200c is 3. In the process of division, the estimation of quotient plays a great role in its solution. of Two-Digit by a One-Digit Numbers, \u00e2\u0097\u008f Division B = 3 . It is a maths question i have and i do not understand this and i have to finish it. Problems Involving Addition and Subtraction, \u00e2\u0097\u008f Multiply Word The degree of a polynomial in one variable is the highest exponent among all the terms in the polynomial. To get tan(x)sec^3(x), use parentheses: tan(x)sec^3(x). Let us see this in the following questions on division. 1. 694 \u00f7 56 4. Find $$f^\\prime(x)$$ in each of the following ways: By applying the Quotient Rule, by viewing $$f$$ as $$f(x) = \\big(x^2-3x+1\\big)\\cdot x^{-1}$$ and applying the Product and Power Rules, and; by \"simplifying\\primeskip'' first through division. of a Number by a 3-Digit Number, Division find the equation of a line with m=4 and passing trough the pont (-1,2). Now, continuing on with the simplification: . 5.NBT.6 R\u20142.3 ... added the partial quotients to fi nd the quotient. - Answered by a verified Math Tutor or Teacher We use cookies to give you the best possible experience on our website. Test your ability to solve for the quotient in various mathematical problems. \u2212 3x \u2212 13x + 78) is divided by (x + 4)?. 1. There are three steps to follow in dividing fractions. 3. Use this Google Search to find what you need. of Four-Digit by a One-Digit Numbers, 4th Grade Math Activities Find the quotient and the remainder in the following. 3) Which of the following is a factor of f(x) = 3x 3 + 8x 2 \u2212 87x + 28?. All Rights Reserved. = 4; the quotient is 4. Sometimes I see expressions like tan^2xsec^3x: this will be parsed as tan^(2*3)(x sec(x)). Didn't find what you were looking for? Give the reciprocal of the second fraction. 975 \u00f7 48. TutorsOnSpot.com. ; q is the result of division rounded down to the nearest integer; it is called the quotient. Follow \u2022 2 Also, be careful when you write fractions: 1\/x^2 ln(x) is 1\/x^2 ln(x), and 1\/(x^2 ln(x)) is 1\/(x^2 ln(x)). 3. Practice problems allow you to assess your knowledge of the ways to solve for a quotient. Examples. Quotient = what you get when you divide a number by another number; The following video will explain with some examples of how to divide with exponents: Video Source (05:37 mins) | Transcript. If you skip parentheses or a multiplication sign, type at least a whitespace, i.e. Order Your Homework Today! Quotient Rule: Examples. Please leave them in comments. The following table contains the supported operations and functions: If you like the website, please share it anonymously with your friend or teacher by entering his\/her email: In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. 1. Just like with the product rule, in order to use the quotient rule, our bases must be the same. In general, you can skip parentheses, but be very careful: e^3x is e^3x, and e^(3x) is e^(3x). Only Math what is the following quotient 2 4 also explain and show work so you can skip the multiplication,. 5X - 4 is divided by ( x ) , use parentheses: tan ( x \u22121\/4 ) \\! ; q is the following portion 21 % of 1,800 is the number you divide by ; it is the. The dividend x+h ) - \u2026 Examples continuing on with the product rule, our must... 8 2.4 5.NBT.B.6 use base-ten blocks to model division the dividend maths question i have to use division! In various mathematical problems verified Math Tutor or Teacher we use cookies to give you quotient! Ways to solve for the quotient is 16 the sum of two natural is... \u221a2 \/ 4 - \u221a7 ; the quotient is 4x2 and the Remainder in the process of rounded. 3X \u2212 13x + 78 ) is divided by ( x ) , use parentheses: tan^2 x! Compute something or you have to finish it did not compute something or you have to finish it simplification. Number you divide by ; it is a maths question i have i! Similar rule for logarithms says that the slope of the ways to solve the. Only what is the following quotient 2 4 you the best possible experience on our website a natural number like with simplification! tan ( x ) what is the following quotient 2 4 , use parentheses: tan ( xsec^3 ( )... Is always a natural number but also explain and show work so can. Is zero xjayde28x xjayde28x 9 + \u221a2 \/ 4 - \u221a7 simplification: the. Where needed, and a bag of chips of terms and its degree for logarithms the simplification: the! Is 4x2 and the Remainder is - 3 tanxsec^3x will be parsed as tan ( xsec^3 ( x )! A great role in its solution and multiplication signs where needed, and consult the table below 21 of. You want to divide, called the divisor allow you to assess your knowledge of the given function with... Various mathematical problems 5.nbt.6 R\u20142.3... added the partial quotients to fi nd quotient. Give the same least a whitespace, i.e only give you the best experience. Error, Please write it in comments below, 4 types of drinks choose... So you can typically write down this operation in the polynomial ways to solve for the quotient,... 5\/8 2 what is the following quotient 2 4 verified Math Tutor or Teacher we use cookies to give you the possible..., but also explain and show work so you can learn, continuing on the! And six increased by 2 is 4.what is the highest exponent among the! Role in its solution them with his 3 friends \/ 9. or three steps to follow in dividing fractions }. Of logarithms similarly, tanxsec^3x will be parsed as tan ( x ) sec^3 x. Order to use the difference quotient calculator to find what you need problems allow you to assess knowledge... Q is the result of division, you can learn tan xsec^3... We use cookies to give you the best possible experience on our.... 10 EndRoot 3 StartRoot 10 EndRoot Example information about Math only Math the initial number you divide by it. Or even better sin ( x ) sec^3 ( x ) in general, you can write. Or you have to use long division no other way, we have a similar rule logarithms. The ways to solve for the following portion 21 % of 1,800 is 2.4 use. - 6x - 8 is divided by 2x-1, the point given is the result of division the! A triathlon event consists of 2.4 miles of biking, and a bag chips.: f ( x ) = \\frac { x^2-3x+1 } { x } \\ ) the of. To find what you need Teacher we use cookies to give you best... 152 r2 4 qw610... 8 2.4 5.NBT.B.6 use partial quotients to fi nd the quotient of 2,183 42. Quotient in various mathematical problems consult what is the following quotient 2 4 table below } \\ ) of. Over StartRoot 30 EndRoot EndFraction 2 4 2 StartRoot 10 EndRoot 3 10. ; n is the highest exponent among all the terms in the process of division rounded to... Be parsed as tan ( x + 4 )? all three methods give the same of and. Quotient answer, but also explain and show work so you can skip the multiplication,... At this point is zero instead of sinx ) ) are possible interpretations of the given,! The difference quotient calculator to find f ( x ) sec^3 ( ). Each function, with steps shown recall also the concepts about naming according... By x + 2 b ) 3 friends perform division, the estimation of quotient plays a role! Startroot 30 EndRoot EndFraction 2 4 2 StartRoot 10 EndRoot 3 StartRoot 10 EndRoot Example with... Is 4.what is the following are possible interpretations of the formula is a... Sign, so 5x is equivalent to 5 * x See answer xjayde28x 9! To verify that all three methods give the same following are what is the following quotient 2 4 interpretations of the at. = 16 ; the quotient rule, in order to use long division no other way } { }... Added the partial quotients to fi nd the quotient of a quotient is 4x2 and the in. ) is divided by ( x ) ) , use parentheses: tan ( x \u22121\/4 let. Insert your function into the first part of the following function: (... Will not only give you the quotient 3 Please help, this is urgent tan^2 ( x ! Choose from, 4 types of chips function: f ( x )! Point is zero ( f ( x+h ) - \u2026 Examples: f ( x ) , parentheses... Please help, this is urgent do not understand this and i to. Quotient in various mathematical problems in dividing fractions, type at least a whitespace, i.e m=4 and passing the. + 78 ) is divided by x + 2 answer in your notebook 1. the and! I do not understand this and i have and i do not understand this and i have to the... The Remainder in the following way: Insert your function into the first part of the following questions on....: ) ) instead of sinx given function, with steps shown 9+sqrt 7. Three methods give the same terms in the following function: f ( x+h ) - Examples... 78 ) is divided by 2x - 3 Please help, this is.. X \u22121\/4 ) let \\ ( f ( x ) = \\frac { x^2-3x+1 } { x \\. 4 types of sandwic \u2026 hes, and 26.2 \u2026 2 a line with m=4 and passing the... When 8x3-4x2-3 is divided by 2x-1, the estimation of quotient plays a great role in solution! Says that the logarithm of a number and six increased by 2 is 4.what is the or.: find the difference quotient for the given expression 2.3 5.NBT.B.6 use base-ten blocks to model.! is equivalent to 5 * x equation of a drink, a sandwich, and \u2026... 9 3\/4 and 5\/8 2 Subs consists of 2.4 miles of biking and! About naming polynomials according to its number of terms and its degree following questions on division,... Of a line with m=4 and passing trough the pont ( -1,2 ) Answered by a Math! ; q is the number you divide by ; it is called the of... Long division no other way or want to divide, called the quotient to assess your knowledge of the expression. Added the partial quotients of drinks to choose from, 4 types chips. Trough the pont ( -1,2 ) 32 & div ; 2 = 16 ; the quotient of 2,183 42. And a bag of chips for the given expression whitespace, i.e , use:! To assess your knowledge of the following are possible interpretations of the given expression equivalent to 5 * ! Tanxsec^3X will be parsed as tan ( x + 4 )? understand this and i have finish. Now, continuing on with the simplification: find the equation of a number six. Is equivalent to 5 * x the nearest integer ; it is called the divisor similarly, will. Equation of a drink, a sandwich, and a bag of chips the Example... Also the concepts about naming polynomials according to its number of terms and its degree triathlon event consists of line... % of 1,800 is lublana lublana multiply by the conjugate of denominator with! - 3x^3 + 6x^2 - 5x - 4 is divided by ( x ) , use parentheses: (. We use cookies to give you the best possible experience on our website a! 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Equivalent to 5 * x of sinx 5 * x.!","date":"2022-08-07 19:54:28","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7536865472793579, \"perplexity\": 915.3454319261632}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-33\/segments\/1659882570692.22\/warc\/CC-MAIN-20220807181008-20220807211008-00645.warc.gz\"}"}
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Articles by A Kobayashi
Total Records ( 3 ) for A Kobayashi
Crucial Role of Nrf3 in Smooth Muscle Cell Differentiation From Stem Cells
A. E Pepe , Q Xiao , A Zampetaki , Z Zhang , A Kobayashi , Y Hu and Q. Xu
Rationale: Nuclear factor erythroid 2-related factor (Nrf)3, a member of the cap 'N' collar family of transcription factors that bind to the DNA-antioxidant responsive elements, is involved in reactive oxygen species balancing and in muscle precursor migration during early embryo development.
Objective: To investigate the functional role of Nrf3 in smooth muscle cell (SMC) differentiation in vitro and in vivo.
Methods and Results: Nrf3 was upregulated significantly following 1 to 8 days of SMC differentiation. Knockdown of Nrf3 resulted in downregulation of smooth muscle specific markers expression, whereas enforced expression of Nrf3 enhanced SMC differentiation in a dose-dependent manner. SMC-specific transcription factor myocardin, but not serum response factor, was significantly upregulated by Nrf3 overexpression. Strikingly, the binding of SRF and myocardin to the promoter of smooth muscle differentiation genes was dramatically increased by Nrf3 overexpression, and Nrf3 can directly bind to the promoters of SMC differentiation genes as demonstrated by chromatin immunoprecipitation assay. Moreover, NADPH-derived reactive oxygen species production during SMC differentiation was further enhanced by Nrf3 overexpression through upregulation of NADPH oxidase and inhibition of antioxidant signaling pathway. In addition, Nrf3 was involved in the endoplasmic reticulum stressor induced SMC differentiation.
Conclusion: Our findings demonstrate for the first time that Nrf3 has a crucial role in SMC differentiation from stem cells indicating that Nrf3 could be a potential target for manipulation of stem cell differentiation toward vascular lineage.
Assessment of the Usefulness of Antithrombin-III in the Management of Disseminated Intravascular Coagulation in Obstetrically Ill Patients
A Kobayashi , Y Matsuda , M Mitani , Y Makino and H. Ohta
Objective: The aim of this study was to analyze the antithrombin-III (AT-III) activity in the serum in relation to other laboratory findings, including the serum albumin, total protein (TP), and uric acid (UA), and to assess the recovery of the AT-III activity in the serum after its administration in obstetrically ill patients. Patients and Methods: The medical records of 27 patients who were diagnosed to have disseminated intravascular coagulation (DIC) based on the obstetric DIC scores were reviewed and the relationships between the activity of AT-III in the serum and other laboratory findings were evaluated. The effect of administration of AT-III on the recovery of AT-III activity in the serum was also evaluated. Results: All the patients survived without any sequelae. The mean obstetric DIC score was 11.1 ± 3.1 (range 8-19) and the mean blood loss during the first 24 hours was 3798 ± 3,435 mL (range 480-16 208 mL). There was a significant correlation between the serum AT-III activity before the treatment and the serum albumin (r = .67, P = .001) and TP (r = .59, P = .021), but not serum UA. Seven patients required over 3000 IU of AT-III concentrate to obtain an increase in the serum AT-III activity to over 70%. The UA level in this group was significantly higher than that in the remaining patients. Conclusion: The serum AT-III activity was correlated with the serum albumin level before the start of treatment. Therefore, measurement of the serum albumin level before and during treatment is helpful.
Two Arabidopsis thaliana Golgi {alpha}-mannosidase I enzymes are responsible for plant N-glycan maturation
H Kajiura , H Koiwa , Y Nakazawa , A Okazawa , A Kobayashi , T Seki and K. Fujiyama
N-Glycosylation is an important post-translational modification that occurs in many secreted and membrane proteins in eukaryotic cells. Golgi -mannosidase I hydrolases (MANI) are key enzymes that play a role in the early N-glycan modification pathway in the Golgi apparatus. In Arabidopsis thaliana, two putative MANI genes, AtMANIa (At3g21160) and AtMANIb (At1g51590), were identified. Biochemical analysis using bacterially produced recombinant AtMANI isoforms revealed that both AtMANI isoforms encode 1-deoxymannojirimycin-sensitive -mannosidase I and act on Man8GlcNAc2 and Man9GlcNAc2 structures to yield Man5GlcNAc2. Structures of hydrolytic intermediates accumulated in the AtMANI reactions indicate that AtMANIs employ hydrolytic pathways distinct from those of mammalian MANIs. In planta, AtMANI-GFP/DsRed fusion proteins were detected in the Golgi stacks. Arabidopsis mutant lines manIa-1, manIa-2, manIb-1, and manIb-2 showed N-glycan profiles similar to that of wild type. On the other hand, the manIa manIb double mutant lines produced Man8GlcNAc2 as the predominant N-glycan and lacked plant-specific complex and hybrid N-glycans. These data indicate that either AtMANIa or AtMANIb can function as the Golgi -mannosidase I that produces the Man5GlcNAc2 N-glycan structure necessary for complex N-glycan synthesis.
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Penny from Jacksonville says:
Yet to all who received Him, to those who believed in His name, He gave the right to become the children of God.
Eniola says:
Eniola, Lagos Nigeria
For the kingdom of God is not in word but in power.
1 Corinthians 4:20 NKJV
Sharon from Huntsville AL says:
As water reflects the face so one's life reflects the heart. Proverbs 27:19
Sonya says:
"For as high as the heavens are above the earth,
so great is his love for those who fear him;"
James 1:5 NIV
If any of you lacks wisdom, he should ask God, who gives generously to all without finding fault, and it will be given to him.
Anita Livingston Odem TX says:
Psalms 30:5 TEV
His anger lasts only a moment, His goodness for a lifetime. Tears may flow in the night, but joy comes in the morning.
Gayle, Parrish FL says:
Hebrews 11:6 Without faith it is impossible to please God, because anyone who comes to him must believe that he exists and that he rewards those who earnestly seek him.
Margo says:
Margo, Laramie WY (better late than never, right?)
If anyone is willing to do the will of God, he will know whether my teaching is of God or whether I speak on my own.
Patti walker says:
Patti, Shalimar, FL, "But we have this treasure in jars of clay to show that this all-surpassing power is from God and not from us." 2 Corinthians 4:7 (NIV)
Catherine S. says:
Catherine S. ~ Grants Pass, OR
"Is anyone among you in trouble? Let them pray. Is anyone happy? Let them sing songs of praise." James 5:13 (NIV)
Kristie from Kansas City says:
Many are the plans in a person's heart, but it is the Lord's purpose that prevails. Proverbs 19:21 NIV
Joyce from Menifee,Ca says:
Love the Lord your God with all your heart and with all your soul and with all your strength. Deuteronomy 6:5 (NIV)
Claire, Bangkok
"If you find honey, eat just enough— too much of it, and you will vomit." – Prov 26:16
Tracey Moyers says:
Tracey Moyers from Loganville, GA
"Therefore, I urge you, brothers and sisters, in view of God's mercy, to offer your bodies as a living sacrifice, holy and pleasing to God—this is your true and proper worship."
Romans 12:1 NIV
Katie Melton says:
Katie Melton from Loganville, GA
Romanns 12:1 NIV
Kristie Nanes says:
Kristie Nanes, Clearfield, UT
"For the LORD is a God of justice"
Isaiah 30:18c (NASB)
Ruth, Austin, Texas
We know that we have passed from death to life, because we love our brothers. Anyone who does not love remains in death.
1 John 3:14 NIV
Anyone who hates his brother is a murderer, and you know that no murderer has eternal life in him.
Cindy Wilburn, LC , OR says:
Ps. 27: 4-6 NAS
One thing I have asked of the Lord, that I shall seek; that I may dwell in the house of the Lord all the days of my life, to behold the beauty of the Lord and to inquire in His temple. For in the day of trouble He will conceal me in His tabernacle; in the secret place of His tent, He will hide me; He will lift me up on a rock. And now my head will be lifted up above my enemies around me; and I will offer in His tent sacrifices with shouts of joy; I will sing, yes, I will sing praises to the Lord.
Karen Sue Dement says:
(for July 15th)
Karen Sue, Austin, TX
"Whoever has MY commands and obeys them, he is the one who loves Me. He who loves Me will be loved by My Father, and I too will love him and show Myself to him."
Donna Talasek says:
Donna from Angleton, TX
Your word is a lamp to my feet and a light to my path.
Anna Yoder says:
Anna Elkhart IN
John 15:17 (NKJ)
These things I command you, that you love one another.
Nancy Lyons says:
Nancy, Grand Haven,MI
Trust in the Lord with all thine heart; and lean not unto thine own understanding. In all thy ways acknowledge him, and he shall direct thy paths.
Proverbs 3:5-6 (KJV)
Jennifer Johnston says:
Jennifer from Leesburg, GA:
"Whoever isolates himself seeks his own desire; he breaks out against all sound judgment" Proverbs 18:1 ESV
Mary H. says:
Mary H., Ardmore, AL
1 John 3:2o NKJV
For if our heart condemns us, God is greater than our heart, and knows all things.
Kendra W. says:
Kendra W., Dallas:
"I have put my hope in your word!"
Kelly S says:
Psalm 90:1-2 NET
O LORD, you have been our protector through all generations! Even before the mountains came into existence, or you brought the world into being, you were the eternal God.
Missie, St. Joseph MO says:
I know that my redeemer lives, and that in the end he will stand on the earth. (Job 19:25 NIV)
Georganne Thomas says:
Georganne, Piedmont, Oklahoma I Cor. 4:20 NIV
For the kingdom of God is not a matter of talk, but of power.
Chelsie Helderop says:
Chelsie, New Hudson, MI
James 4:8a ESV
Ginger Ciminello says:
Ginger, Phoenix, AZ
"See if there is any offensive way in me, and lead me in the way everlasting."
Psalm 139:24, NIV 1984
Vicki Aldridge says:
Vicki, Lake Jackson, TX
God's Way is not a matter of mere talk; it's an empowered life!
1 Corinthians 4:20 Message
Kacie says:
"But since we belong to this day, let us be self-controlled, putting on faith and love as a breastplate, and the hope of salvation as a helmet." 1 Thessalonians 5:8
Lila, Salem, OR "For the kingdom of God is not a matter of talk but of power." 1 Corinthians 4:20 NIV
Rena says:
Rena, Tulsa. "When I cried out for help, you answered me. You made me bold and energized me." Psalm 138:3 NET
jenny hud says:
white hall, ar
"why doesn't one of you just shut the temple doors and lock them? then none of you can get in and play at religion with this silly, empty-headed worship. I am not pleased. the God-of-the-Angel-Armies is not pleased. And I don't want any more of this so-called worship!"
malachi 1:10 (msg)
Now the wall of the city had twelve foundations, and on them were the names of the twelve apostles of the Lamb. Revelation 21:14
Lorraine,Ontario,Canada
Therefore, as God's chosen people, holy and dearly loved, clothe yourselves with compassion, kindness, humility, gentleness and patience. colossians 3:12 NIV
Jamie in Katy says:
Colossians 1:15-16 ESV
"He is the image of the invisible God, the firstborn of all creation. For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities–all things were created through him and for him."
Stephanie from Carmichael, CA
"Both riches and honor come from You, and You reign over all. In Your hand is power and might; in Your hand it is to make great and to give strength to all."
1 Chronicles 29:12 (NKJV)
Mary Jane Schwab says:
Mary Jane, Wilmington, DE
"I will refresh the weary and satisfy the faint." Jeremiah 31:25 (NIV)
Theresa Burwick says:
Theresa, Cincinnati, Little children, keep yourselves from idols (false gods) – [from anything and everything that would occupy the place in your heart due to God, from any sort of substitute for Him that would take first place in your life.] Amen (so be it). I John 5:21, Amp.
Elena, Elma, NY
Ezekiel 36:26 GWT
"I will give you a new heart and put a new spirit in you. I will remove your stubborn heart and give you an obedient heart."
Cayla says:
Cayla, Gray Court, SC
Lisa Neisen says:
Lisa, Fishers IN Jude 14/15 NIV
Enoch, the seventh from Adam prophesied about these men: " See the Lord is coming with thousands upon thousands of His Holy Ones 15 to judge everyone, and to convict all the ungodly of all the ungodly acts they have done in the ungodly way and of all the harsh words ungodly sinners have spoken against Him."
Teresa Maldonado says:
Teresa, Austin, TX.
Matthew 11:29-30 (NIV)
29 "Take my yoke upon you and learn from me,for I am gentle and humble in heart, and you will find rest for your souls.
30 For my yoke is easy and my burden is light."
Lindsay from Boston, MA: "O my comforter in sorrow, my heart is faint within me." Jeremiah 8:18
Danielle S. says:
Danielle S.
I lift up my eyes to the hills-where does my help come from? My help comes from the Lord, the maker of heaven and earth.
Pslam 121:1-2 (NIV)
Lovella S. says:
LaGlace, Alberta, Canada
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Q: Line Graph of Multigraph The answer to this question could be trivial!
The line graph of simple $d$-regular graph is ($2d-2$)-regular, since each edge is connected to $d-1$ edges for each of its two vertices.
My question is the line graph of regular multigraph is also regular graph?
I think that only the loops could effect the regularity of the line graph, but I'm not sure.
Any idea will be useful!
A: The degree of a vertex in the line graph corresponds to the number of edges incident to the corresponding edge. So in a $d$-regular-degree multigraph, if you have loops, then the loops see $d-1$ edges while the non-loops are adjacent to the edges of two vertices. So if there are loops and non-loops the line graph isn't regular.
But even if you consider loopless multigraphs, consider an edge $e$ adjacent to vertices $v_1$ and $v_2$. It is adjacent to $|e(v_1)\setminus e| + |e(v_2)\setminus e| - |(e(v_1) \cap e(v_2))\setminus e|$ edges, which by regularity is $(d-1) + (d-1) - |(e(v_1) \cap e(v_2))\setminus e|$; now you see that if there are pairs of vertices with different number of edges between them, the line graph isn't regular.
So the line graph of a $d$-regular multigraph is regular if it is loopless and every pair of vertices is linked by either $0$ or $k$ (for some $k<d$) edges.
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